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Angels are around us, whether we believe they are or not.
They are spiritual beings, entities made of light and love, dwelling in realms higher than our mortal minds are able to comprehend.
However, they come down to us and guide our destinies. Many people are skeptical when it comes to spiritual beliefs.
Angels do not mind that and keep remaining guardians of our earthly universe. Angels do not have free will as we do, because they exist in complete balance with divine power, the power of God.
Beliefs about angel-like beings are to be found in many different spiritual, religious ad belief systems; the idea of their existence is not restricted to only one tradition. They are only imagined or portrayed in different ways.
Regardless of what we think about angels and their existence, they are here.
They are not to be seen by mortal men, although there are some rare, blessed individuals who claimed they have seen angels or heard their songs.
Angels rather choose other channels of communicating with people. When they think we need a little bit of divine help us to recover, move on or get more energy and motivation on our life path, they send us messages.
Angels’ messages come in symbolic forms. Angels use various signs to somehow remind us they are here watching on us. Angels are pure beings, whose main purpose is to care about us and our well-being.
These spirits of divine power often send us numbers, to interpret them and get some of the heavenly life force.
These are called angel numbers.
Number 45 – What Does It Mean?
Number 45 could be a message from guardian angels, if you constantly keep seeing it in your environment, think about it or see it in your dreams.
Angel use number as a simple symbols to get us back on our track, help us find the meaning in what we are doing or discover some greater aim. Angel numbers are signs of heavenly guidance.
Number 45 is a two-digit number, so it has a complex symbolism.
The meaning hidden behind a 45 number symbol consists of mixed interpretations of numbers 4, 5 and 9; the latter is seen as a sum of two previous.
It is also important to know that number 5 takes over after the person turns forty-five years of age. Before that, we could think about all three digits.
Number 4 is an angel number that represents organization, devotion, patience, determination and pragmatism.
It is an important number for career and family life. Number 5 is a number of individualism, sensuality, uniqueness, personal freedom and so on. Combined together, these numerical make a powerful mixture.
That said, number 45 is a number of an enormous charisma, usually seen by people who are independent and extraordinary, very creative, but also organized and dedicated to their work.
Angels send this number to them to encourage them to develop and nurture their individualism and uniqueness.
The Secret Meaning and Symbolism
Number 45 possess great spiritual energy. People with this angel number are often full of great ideas. This number also reflects their incredibly strong intuition.
One would say they are clairvoyant, because they do have the ability to predict things. On the smaller plan, for example, they know what the person will say, before they hear an answer.
Number 45 also represents adaptability and a mask of illusions, meaning people who bear this angels number are able to hide their true emotions very well, especially when it comes to worries, sadness or desperation.
They possess strong positive energy within their soul, so they try to use it to the maximum, Angels send them symbol of number 45 to remind them of that ability.
It is important to mention that the astrological ruler of angel number 45 is the planet Mars, associated with strength, power and aggression.
Mars is a planet of War, which means people with angel number 45 are true fighters.
They are unlikely to give up their goals, hopes or dreams.
Number 45 is a symbol of persistence, effort, determination and focus, although numerical 5 might sometimes prevail and make them impatient.
Love and Angel Number 45
Speaking about love, angel number 45 represents passion, seduction and romantic relationship.
However, the understanding of love life differs in female and male individuals who are given angel number 45 as their guiding angelic symbol and force. Angels are mighty, but human hearts and souls are tricky to direct.
While women with angel number 45 search for an ideal, fairytale-like relationship, men with this angel number are seducers and lover boys who find it hard to settle.
However, they are attracted and enchanted by numbers 16 or 1.
A combination of a man 45 and a lady 1 or 16 can easily turn to something serious.
For women with 45 angel number, it is advisable not to fall in love with a man with the same angel number. Such a combination fails in almost all of the cases.
However, that is only a friendly advice; you cannot command people’s hearts!
Angels will know that much better and help you in searching for an ideal partner, as well. One thing is the same for all 45 people; they are passionate and have a lot of love to give.
Numerology Facts About Number 45
There are not many interesting facts about this angel number.
It is featured in some popular culture works, but does not have any specific meaning.
It does possess some negativity, because of its connection to Mars, as a symbol of war and destruction.
Number 45 is the atomic number of the element rhodium.
A regular school class lasts for exactly 45 minutes in educational institutions around the world.
Some gramophone records have rotational speed of 45 rpm.
Seeing Angel Number 45
If you keep seeing number 45, angels definitely want you to keep on doing what you do. They encourage your uniqueness and creativity.
You surely have some great ideas about your future or you simply enjoy expressing yourself in creative ways, embracing the beauty of the moment. Both things are great.
Angels want to tell you not to get discouraged by others’ judgments over what you are doing.
Angel number 45 also appears to remind you to restrain your immense energy and not to be pushing or intrusive.
People with this number could act aggressively or appear so, even if it is not their intention. Do not try to decide things for others and do not tell them what they are thinking or not.
People might find such behavior offensive. By acting so, you could hurt someone you care for.
Angels send you this number to help you understand what inner powers you have. Nurture your creativity and uniqueness, but do not neglect relationships with people around you.
Angel number 45 occurs to remind you that you have friends and people who care about you, even if you are very self-reliant, independent and strong.
Let them reach your soul. | https://angelnumber.org/45-angel-number-meaning-and-symbolism/ |
A Dance with Dragons is the fifth of seven planned novels in the epic fantasy series, A Song of Ice and Fire by American author George R.R. Martin. The book was released July 12, 2011.
The 'Dance of Dragons' is the name given to a civil war in the prior history of Westeros.
A Dance of Dragons was originally the title of the second novel in the sequence, when Martin still envisaged the series as a trilogy. Some early US editions of A Game of Thrones list A Dance of Dragons as the forthcoming second volume in the series. The anthology Legends, which features the novella The Hedge Knight, lists it as the fourth installment of the series.
Plot summaryEdit
A Dance with Dragons picks up where A Storm of Swords left off and runs simultaneously with events in A Feast for Crows. The War of the Five Kings seems to be winding down. In the North, King Stannis Baratheon has installed himself at the Wall and vowed to win the support of the northmen to continue his struggle to claim the Iron Throne, although this is complicated by the fact that much of the west coast is under occupation by the ironborn. On the Wall itself Jon Snow has been elected the 998th Lord Commander of the Night's Watch, but has enemies both in the Watch and beyond the Wall to watch for. Tyrion Lannister has been taken by ship across the Narrow Sea to Pentos, but his eventual goals are unknown even to him. In the far east, Daenerys Targaryen has conquered the city of Meereen, but has decided to stay and rule the city, honing her skills of leadership which will be needed when she travels on to Westeros. But Daenerys' presence is now known to many in Westeros, and from the Iron Islands and Dorne, from Oldtown and the Free Cities, emissaries are on their way to find her and use her cause for their own ends.
Sample chapters are available on Amazon.co.uk and George R.R. Martin's website.
Viewpoint charactersEdit
The tale is told through the eyes of 16 point-of-view characters and, as with previous volumes, a one-off prologue point-of-view and an epilogue.
- Prologue: Varamyr Sixskins, a skinchanger and one of the surviving wildlings north of the Wall.
*13 chapters: Jon Snow, the 998th Lord Commander of the Night's Watch.
*12 chapters : Tyrion Lannister, a kinslayer on the run in the Free Cities.
*4 chapters: Davos Seaworth, King's Hand to Stannis Baratheon.
*10 chapters : Daenerys Targaryen, heir to House Targaryen and Queen of Meereen.
*3 chapters: Bran Stark, The son of Eddard Stark, presumed dead.
*2 chapters: Arya Stark, a student of the Faceless Men of Braavos.
*3 chapters: Asha Greyjoy, the niece of King Euron Greyjoy of the Iron Islands.
*4 chapters: Quentyn Martell, an emissary from his father, Prince Doran Martell of Dorne, on a mission to the east.
*7 chapters: Theon Greyjoy, heir to the Iron Islands, a captive at the Dreadfort.
*1 chapter: Melisandre, the red priestess and chief advisor to Stannis Baratheon.
*2 chapters: Cersei Lannister, Queen Regent, imprisoned by the High Septon for fornication.
*1 chapter: Jaime Lannister, member of the Kingsguard, traversing the riverlands for the Iron Throne.
*2 chapters: Jon Connington, former Knight of Griffon's Roost in Westeros.
*4 chapters: Ser Barristan Selmy, head of Daenerys Targaryen's Queensguard.
*2 chapters: Victarion Greyjoy, brother of King Euron Greyjoy, heading for Meereen.
*1 chapter: Areo Hotah, protector to the Prince of Dorne.
*Epilogue: Kevan Lannister, Regent of the Iron Throne.
Split in publicationEdit
When the fourth novel in the series, A Feast for Crows, was published it did not contain point-of-view sections from many of the main/key characters of the series. This was because the book had become far too large to publish as one volume. Rather than simply split it in half and publish it as 'Part 1' and 'Part 2', Martin decided to split the book by character and location. Thus, characters in the South of the Seven Kingdoms and in the new locations of the Iron Islands and Dorne appeared in A Feast for Crows. Characters in the North and across the sea were held back for A Dance with Dragons, although Arya Stark and Asha Greyjoy will appear in both volumes.
Approximately one-third of the published A Dance with Dragons will consist of material that had been written for the pre-split A Feast for Crows, although much of this has already been rewritten by Martin. Martin has also promised to try to include some 'catch-up' chapters at the end of the novel to reveal what happened to some of that novel's characters after the cliffhanger endings of A Feast for Crows, such as Brienne of Tarth, Jaime and Cersei Lannister, but only if he has enough room at the end of the book. Martin has confirmed that, contrary to earlier statements, Sansa will not appear in the novel. Sansa chapters initially slated for Dance have instead been pushed back to The Winds of Winter, the planned sixth book in the series .
Delays in publicationEdit
Despite original predictions of possible completion in late 2006, the book was not finished by the end of 2008. Martin´s blog has featured updates on his progress, and in January 2008, he posted an update on his website affirming his vigilant commitment to finishing the book. In early 2008, publisher Spectra (a division of Random House) announced that A Dance with Dragons would be released on September 30, 2008, but Martin stated this would only be possible if he finished writing by the end of June, before a trip to Spain and Portugal, and he did not meet this goal.
On February 19, 2009, Martin posted on his website, "I am trying to finish the book by June. I think I can do that. If I do, A Dance with Dragons will likely be published in September or October." During Martin's visit to Finland and Estonia in July 2009, he confirmed that finishing the book had required an extension of the writing time to September or October, and he hopes that the book could be published as early as February 2010 in the UK.
EditionsEdit
Proposed cover art for both the UK and US editions was unveiled in 2008. The UK cover art is by Larry Rostant and consistent with the newer cover styles introduced in 2003. The US cover is consistent with newer cover styles introduced in the USA in 2005. However, a variant US cover (which shows the same dragon image on a black background with a spiral of green colour) has also been seen in some publicity material. It is unclear if this cover is meant to replace the earlier one.
Subterranean Press has confirmed that Marc Fishman has already started work on the illustrated edition of A Dance with Dragons for release after the Bantam and Voyager editions. | https://iceandfire.fandom.com/wiki/A_Dance_with_Dragons |
---
abstract: 'Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable ‘matrix’ quantum mechanics, which is recently proposed by Odake and the author. The ($q$-)Askey-scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of $q^x$ ($x$ being the population) corresponding to the $q$-Racah polynomial.'
---
Yukawa Institute Kyoto\
YITP-09-21\
March 2009
**Exactly Solvable Birth and Death Processes\
\
**
**Ryu Sasaki**
Yukawa Institute for Theoretical Physics,\
Kyoto University, Kyoto 606-8502, Japan
Introduction {#intro}
============
The Brownian motion, a typical stationary Markov process with a continuous state space, is known to be described well by the Fokker-Planck equation [@risken; @feller]. A [*birth and death process*]{}, on the other hand, being a typical stationary Markov chain with a set of non-negative integers as a state space [@schoutens], can be naturally considered as a discretisation of a one-dimensional Fokker-Planck equation. Although birth and death processes have a wide range of applications [@feller; @schoutens], demography, queueing theory, inventory models and chemical dynamics, we will focus on their mathematical aspect, [*i.e.,*]{} the exact solvability. In this paper we present 18 [*exactly solvable*]{} birth and death processes based on the ($q$-)Askey scheme of hypergeometric orthogonal polynomials having discrete orthogonality measures. They are also called orthogonal polynomials of a discrete variable [@askey; @ismail; @nikiforov]. For example, they are the ($q$-)Racah, the ($q$-)(dual)Hahn, the ($q$-)Krawtchouk, the ($q$-)Charlier and the ($q$-)Meixner polynomials [@askey; @ismail; @koeswart]. Various expressions of the transition probability are given explicitly together with the totality of the eigenvalues and the measures of the Karlin-McGregor type representation [@KarMcG].
It is well-known that the one-dimensional Fokker-Planck equation is related by a similarity transformation to a corresponding one-dimensional time-independent Schrödinger equation [@risken] or the eigenvalue problem for a suitable Hamiltonian. In other words, solutions of an exactly solvable Schrödinger equation give the solutions of the corresponding Fokker-Planck equation, which is now exactly solvable. The exact solvability means that the totality of the eigenvalues (in these cases, all are discrete) and the corresponding eigenfunctions are obtained exactly. Here the Hamiltonian in quantum mechanics is an hermitian (self-adjoint) linear operator in a certain Hilbert space. A natural [*discretisation*]{} of the Hamiltonians of 1-d quantum mechanics is hermitian matrices of a finite or infinite dimensions. Recently exactly solvable ‘matrix’ quantum mechanics was proposed by Odake and the present author [@os12] by adopting special types of [*tri-diagonal*]{} Jacobi matrices of finite or infinite dimensions as Hamiltonians. The eigenfunctions are spanned by the above mentioned orthogonal polynomials of a discrete variable. The corresponding discretisation of the Fokker-Planck equation is, as expected, the birth and death process with a [*reflecting wall*]{}(s). Among the 18 exactly solvable birth and death processes to be explored in this paper, some are quite well-known having the linear [@feller; @schoutens; @KarMcGLin; @KarMcGEhr] and quadratic [@vanaspralen] birth and death rates, corresponding to the Meixner §\[\[KS1.9\]\], Charlier §\[\[KS1.12\]\], Krawtchouk §\[\[KS1.10\]\] and Hahn §\[\[KS1.5\]\] polynomials. The others have rational functions (of the population $x$) of the birth and death rates corresponding to the dual Hahn §\[\[KS1.6\]\] and Racah §\[\[KS1.2\]\] polynomials and some others have $q^{\pm x}$- linear, quadratic and rational birth and death rates. The most generic one is the $q$-Racah polynomial §\[\[KS3.2\]\] having $q^x$ rational birth and death rates .
This paper is organised as follows. In section two, the general properties of the Hamiltonians in 1-d quantum mechanics (and/or the hermitian matrices) are reviewed in §\[hamproperty\]. The relationship between the Schrödinger equation and the corresponding Fokker-Planck equation is recapitulated in §\[FPequationsect\] and the solutions of the initial value problem of the Fokker-Planck equations and the transition probabilities are expressed in terms of the orthogonal polynomials constituting the eigenfunctions of the corresponding Scrödinger equation. In section three the birth and death operator is derived from the generic form of the Hamiltonian of the exactly solvable ‘matrix’ quantum mechanics of [@os12]. The solutions of the initial value problem of the birth and death equations and the transition probabilities are expressed in terms of the orthogonal polynomials constituting the eigenfunctions of the corresponding Scrödinger equation of the ‘matrix’ quantum mechanics. Various equivalent expressions of the transition probabilities are derived in terms of the dual polynomials. Section four provides various data, the birth and death rates, the energy spectra and the sinusoidal coordinates, the stationary probability, the normalisation constants, and the eigenpolynomials, of the exactly solvable 18 models, which are sufficient to evaluate the transition probability explicitly. These 18 models are named after the eigenpolynomials, such as the ($q$-)Racah, etc. The final section is for a brief summary and comments. Appendix A provides the collection of the definitions of basic symbols and functions for self-containedness. Throughout this paper we use the parameter $q$ in the range $0<q<1$.
Fokker-Planck Operator from Hamiltonian {#FPH}
=======================================
Here we recapitulate the well-known connection between the Fokker-Planck equation and the Schrödinger equation [@risken] in order to introduce appropriate notation and settings for the main purpose of the paper; connecting the birth and death process to the ‘matrix’ quantum mechanics to be explored in the next section.
Properties of Hamiltonians {#hamproperty}
--------------------------
Throughout this paper we discuss one degree of freedom systems only. The Hamiltonians to be discussed in this paper are [*time independent*]{} and share the properties listed below. Most properties are common to the the Hamiltonians having the continuous dynamical variable $x$ (to be used for the Fokker-Planck equation) and the discrete dynamical variable $x$ (to be applied to the birth and death processes). They are expressed by the same symbols. When they need different symbols, like the $L^2$ and $\ell^2$ norms, two different expressions are shown in a curly bracket as in and . The upper (lower) one is for the continuous (discrete) dynamical variable case. The former (the continuous variable) case corresponds to the ordinary quantum mechanics and the ‘discrete’ quantum mechanics with the pure imaginary shifts [@os13], which gives rise to the ‘deformed’ Fokker-Planck equations [@hs1].
(1)
: [*Factorisability*]{}, $$\mathcal{H}=\mathcal{A}^\dagger\mathcal{A},
\label{factor1}$$ in which ${}^\dagger$ denotes the hermitian conjugation with respect to the standard $L^2$ ($\ell^2$) inner product, see . This also means that the Hamiltonian $\mathcal{H}$ is [*positive semi-definite*]{}.
(2)
: [*Completeness of its eigenfunctions*]{} $\phi_n(x)$ [*belonging to discrete eigenvalues*]{} (all distinct), $$\mathcal{H}\phi_n(x)=\mathcal{E}(n)\phi_n(x),\quad
\mathcal{E}(0)<\mathcal{E}(1)<\cdots ,
\label{ham1}$$ and all the eigenvectors are square normalisable and orthogonal with each other $$(\phi_n,\phi_m){\stackrel{\text{def}}{=}}\left\{
\begin{array}{c}
\int \phi_n(x)^*\phi_m(x)dx\\[6pt]
\sum_{x} \phi_n(x)^*\phi_m(x)
\end{array}
\right\}\
=\frac{1}{d_n^2}\delta_{n\,m},\quad
0<d_n<\infty.
\label{innerpro}$$
The range of the integration (summation) depends on the specific Hamiltonian. Any element in the Hilbert space $\bf H$ is expanded by $\{\phi_n\}$: $$\forall f\in{\bf H}\Rightarrow f=\sum_{n}f_n\hat{\phi}_n,\quad
\hat{\phi}_n{\stackrel{\text{def}}{=}}d_n\phi_n,\quad f_n{\stackrel{\text{def}}{=}}(\hat{\phi}_n,f).$$ Here and hereafter $\hat{f}$ denotes a normalised vector $\hat{f}{\stackrel{\text{def}}{=}}f/\sqrt{(f,f)}$. We choose all the eigenfunctions $\{\phi_n\}$ to be [*real*]{}, which is always possible in one-dimensional quantum mechanics.
(3)
: [*The groundstate wavefunction*]{} $\phi_0$ [*is annihilated by*]{} $\mathcal{A}$ and is [*positive everywhere*]{}, $$\mathcal{A}\phi_0(x)=0 \quad \Rightarrow
\mathcal{H}\phi_0(x)=0,\quad
\mathcal{E}(0)=0,\quad \phi_0(x)>0.
\label{Aphi0}$$
(4)
: [*The eigenfunction*]{} $\phi_n(x)$ is $\phi_0(x)$ [*times a polynomial*]{}, $$\phi_n(x)=\phi_0(x)P_n(\eta(x)),\quad n=0,1,2,\ldots,
\quad P_0\equiv 1,
\label{eigenpoly}$$ in which a real function $\eta(x)$ is called a [*sinusoidal coordinate*]{} [@os7; @os12; @os13]. In other words $P_n(\eta)$ is an orthogonal polynomial with the orthogonality measure $\phi_0(x)^2$ $$\left\{
\begin{array}{c}
\int\phi_0(x)^2P_n(\eta(x))P_m(\eta(x))dx\\[6pt]
\sum_{x}\phi_0(x)^2P_n(\eta(x))P_m(\eta(x))
\end{array}
\right\}\
=\frac{1}{d_n^2}\delta_{n\,m}.
\label{inner2}$$
(5)
: [*The similarity transformed Hamiltonian*]{} $\mathcal{H}$ with respect to $\phi_0(x)$ $$\widetilde{\mathcal{H}}{\stackrel{\text{def}}{=}}\phi_0^{-1}\circ \mathcal{H}\circ \phi_0
\label{tildeham}$$
[*provides a differential*]{} ([*difference*]{}) [*equation governing the polynomial*]{} $P_n(\eta(x))$.
Fokker-Planck Equation {#FPequationsect}
----------------------
The Fokker-Planck equation in one dimension reads $$\frac{\partial}{\partial t}\mathcal{P}(x;t)=L_{FP}\mathcal{P}(x;t),
\quad \mathcal{P}(x;t)\ge0,\quad \int \mathcal{P}(x;t)dx=1,
\label{FPeq}$$ in which $\mathcal{P}(x;t)$ is the probability distribution over certain continuous range of the parameter $x$; for example $(-\infty,\infty)$, $(0,\infty)$ or $(0,\pi)$. The Fokker-Planck operator $L_{FP}$ corresponding to the Hamiltonian $\mathcal{H}$ is defined by [@risken; @hs1] $$L_{FP}{\stackrel{\text{def}}{=}}-\phi_0\circ\mathcal{H}\circ\phi_0^{-1},
\label{LFPdef}$$ in which $\phi_0$ is defined in .[^1] This guarantees that the eigenvalues of $L_{FP}$ are [*negative semi-definite*]{}. The square normalised groundstate eigenfunction $\phi_0(x)$ provides the [*stationary distribution*]{} $\hat{\phi}_0(x)^2$ of the corresponding Fokker-Planck operator: $$\frac{\partial}{\partial t}\hat{\phi}_0(x)^2=L_{FP}\hat{\phi}_0(x)^2=0,\quad
\int\hat{\phi}_0(x)^2dx=1.$$ It is obvious that $\phi_0(x)\phi_n(x)$ is the eigenvector of the Fokker-Planck operator $L_{FP}$: $$L_{FP}\phi_0(x)\phi_n(x)=-\mathcal{E}(n)\phi_0(x)\phi_n(x),\quad
n=0,1,\ldots.$$ Corresponding to an arbitrary initial probability distribution $\mathcal{P}(x;0)$, (with $\int \mathcal{P}(x;0)dx=1$), which can be expressed as a linear combination of $\{\hat{\phi}_0(x)\hat{\phi}_n(x)\}$, $n=0,1,\ldots$, $$\mathcal{P}(x;0)=\hat{\phi}_0(x)\sum_{n=0}^{\infty}c_n\hat{\phi}_n(x),\quad
c_0=1,\quad
c_n{\stackrel{\text{def}}{=}}(\hat{\phi}_n,\hat{\phi}_0(x)^{-1}\mathcal{P}(x;0)),\quad n=1,2,\ldots,$$ we obtain the solution of the Fokker-Planck equation $$\mathcal{P}(x;t)=\hat{\phi}_0(x)\sum_{n=0}^{\infty}c_n\,e^{-\mathcal{E}(n)t}\hat{\phi}_n(x),
\quad
t>0.$$ This is a consequence of the [*completeness of the eigenfunctions*]{} $\{\phi_n(x)\}$ (the polynomials) of the Hamiltonian $\mathcal{H}$. The positivity of the spectrum $\mathcal{E}(n)>0$, $n\ge1$ guarantees that the stationary distribution $\hat{\phi}_0^2(x)$ is achieved at future infinity: $$\lim_{t\to\infty}\mathcal{P}(x;t)=\hat{\phi}_0^2(x).$$
The [*transition probability*]{} from $y$ at $t=0$ (i.e., $\mathcal{P}(x;0)=\delta(x-y)$) to $x$ at $t$ is given by $$\mathcal{P}(y,x;t)=\hat{\phi}_0(x)\hat{\phi}_0(y)^{-1}
\sum_{n=0}^{\infty}e^{-\mathcal{E}(n)t}\hat{\phi}_n(x)\hat{\phi}_n(y),
\quad
t>0.
\label{tranprobcont1}$$ In terms of the polynomial $P_n(\eta(x))$, , it is expressed as $$\mathcal{P}(y,x;t)=\phi_0(x)^2
\sum_{n=0}^{\infty}d_n^2\,e^{-\mathcal{E}(n)t}P_n(\eta(x))P_n(\eta(y)),
\quad
t>0,
\label{tranprobcont2}$$ in which $d_n$ is the normalisation constant , .
As shown in [@hs1] in some detail, various examples of exactly solvable quantum mechanics [@infhul; @susyqm] and the ‘discrete’ quantum mechanics with the pure imaginary shifts [@os13; @os4; @os7] provide many explicit cases in which the transition probability - can be obtained exactly. The corresponding orthogonal polynomials are the Hermite, Laguerre and Jacobi polynomials in the ordinary quantum mechanics [@infhul; @susyqm] and the Meixner-Pollaczek, continuous (dual) Hahn, Wilson and Askey-Wilson polynomials [@hs1; @os13] and their degenerate polynomials, like the continuous $q$-Hermite polynomials.
Birth and Death process from ‘Matrix’ Quantum Mechanics {#BDgeneral}
=======================================================
The birth and death equation is a discretisation of the Fokker-Planck equation in one dimension . It reads $$\frac{\partial}{\partial t}\mathcal{P}(x;t)=(L_{BD}\mathcal{P})(x;t),
\quad \mathcal{P}(x;t)\ge0,\quad \sum_x \mathcal{P}(x;t)=1,
\label{bdeqformal}$$ in which $\mathcal{P}(x;t)$ is the probability distribution over a certain discrete set of the parameter $x$. Here we simply take a set of consecutive non-negative integers, either finite or infinite: $$x\in\mathbb{Z},\quad x\in[0,N]\text{ or }
[0,\infty).$$ The [*exactly solvable birth and death operator*]{} or a matrix $L_{BD}$ is derived from the generic form of an exactly solvable Hamiltonian $\mathcal{H}$ of a ‘discrete’ quantum mechanics with real shifts $$\mathcal{H}{\stackrel{\text{def}}{=}}-\sqrt{B(x)}\,e^{\partial}\sqrt{D(x)}
-\sqrt{D(x)}\,e^{-\partial}\sqrt{B(x)}
+B(x)+D(x),
\label{genham}$$ in which the two functions $B(x)$ and $D(x)$ are real and [*positive*]{} but vanish at the boundary: $$\begin{aligned}
B(x)>0,\quad D(x)>0,\quad D(0)=0\, ;\quad
B(N)=0\ \ \text{for the finite case}.
\label{BDcondition}\end{aligned}$$ The explicit forms of the functions $B(x)$ and $D(x)$ are given in each subsection of section four, which are named after the orthogonal polynomials appearing as the main part of the eigenfunctions. In the Hamiltonian $e^{\pm\partial}$ are formal shift operators acting on a function $f$ of $x$ as $$(e^{\pm\partial}f)(x)=f(x\pm1).$$ Thus the Schrödinger equation $\mathcal{H}\psi(x)=\mathcal{E}\psi(x)$ is a difference equation with real shifts: $$\begin{aligned}
\bigl(B(x)+D(x)\bigr)\psi(x)-\sqrt{B(x)D(x+1)}\,\psi(x+1)
&-\sqrt{B(x-1)D(x)}\,\psi(x-1)
=\mathcal{E}\psi(x),{\nonumber \\}&x=0,1,\ldots,(N),\ldots.
\label{diffeq}\end{aligned}$$ The boundary condition $D(0)=0$ is necessary for the term $\psi(-1)$ not to appear, and $B(N)=0$ is necessary for the term $\psi(N+1)$ not to appear in the finite dimensional matrix case.
Although the Hamiltonian $\mathcal{H}$ is presented in a difference operator form, it is in fact a real symmetric [*tri-diagonal*]{} (Jacobi) matrix: $$\begin{aligned}
\mathcal{H}&=(\mathcal{H}_{x,y}),\qquad
\mathcal{H}_{x,y}=\mathcal{H}_{y,x},\\
\mathcal{H}_{x,y}&=
-\sqrt{B(x)D(x+1)}\,\delta_{x+1,y}-\sqrt{B(x-1)D(x)}\,\delta_{x-1,y}
+\bigl(B(x)+D(x)\bigr)\delta_{x,y}.
\label{Jacobiform}\end{aligned}$$ As mentioned above, the Hamiltonian is factorisable , $\mathcal{H}=\mathcal{A}^\dagger\mathcal{A}$: $$\mathcal{A}^{\dagger}=\sqrt{B(x)}-\sqrt{D(x)}\,e^{-\partial},
\qquad
\mathcal{A}=\sqrt{B(x)}-e^{\partial}\sqrt{D(x)}.
\label{A}$$ In the matrix form $\mathcal{A}^{\dagger}$ has the diagonal and sub-diagonal elements only and $\mathcal{A}$ has the diagonal and super-diagonal elements only $$(\mathcal{A}^{\dagger})_{x,y}=
\sqrt{B(x)}\,\delta_{x,y}-\sqrt{D(x)}\,\delta_{x-1,y},\qquad
\mathcal{A}_{x,y}=
\sqrt{B(x)}\,\delta_{x,y}-\sqrt{D(x+1)}\,\delta_{x+1,y}.$$ The equation determining the groundstate wavefunction $\phi_0$ is easy to solve, since $\mathcal{A}\phi_0=0$ is a two term recurrence relation: $$\frac{\phi_0(x+1)}{\phi_0(x)}=\sqrt{\frac{B(x)}{D(x+1)}}
\label{phi0/phi0=B/D}.$$ It can be solved elementarily with the boundary (initial) condition $\phi_0(0)=1$, $$\phi_0(x)=\sqrt{\prod_{y=0}^{x-1}\frac{B(y)}{D(y+1)}},\quad
x=1,2,\ldots.
\label{phi0=prodB/D}$$ With the standard convention $\prod_{k=n}^{n-1}*=1$, the expression is valid for $x=0$, too. For the infinite matrix case, the requirement of the finite $\ell^2$ norm of the eigenvectors $$\sum_{x=0}^{\infty}\phi_0(x)^2=\sum_{x=0}^{\infty}
\,\prod_{y=0}^{x-1}\frac{B(y)}{D(y+1)}<\infty
\label{phizero2}$$ imposes constraints on the asymptotic behaviours of $B(x)$ and $D(x)$.
With the above explicit form of the groundstate wavefunction $\phi_0(x)$, the similarity transformed Hamiltonian is easily obtained $$\widetilde{\mathcal{H}}{\stackrel{\text{def}}{=}}\phi_0^{-1}\circ \mathcal{H}\circ\phi_0
=B(x)(1-e^{\partial})+D(x)(1-e^{-\partial}).
\label{tildeham1}$$ As mentioned above, $ \widetilde{\mathcal{H}}$ provides the difference equation for the polynomial eigenfunctions, $$(\widetilde{\mathcal{H}}P_n)(\eta(x))=\mathcal{E}(n)P_n(\eta(x)),$$ that is, $$B(x)\left(P_n(\eta(x))-P_n(\eta(x+1))\right)+
D(x)\left(P_n(\eta(x))-P_n(\eta(x-1))\right)=\mathcal{E}(n)P_n(\eta(x)).$$ The eigenpolynomials $\{P_n\}$ are the orthogonal polynomials of a discrete variable. See §5 of [@os12] for various forms of $B(x)$ and $D(x)$ and the corresponding orthogonal polynomails. It is also recapitulated in section 4 of this paper. For example, they are the ($q$-)Racah, the ($q$-)(dual)Hahn, the ($q$-)Krawtchouk, the ($q$-)Charlier and the ($q$-)Meixner polynomials [@askey; @ismail; @koeswart]. As a matrix, $\widetilde{\mathcal{H}}$ is another tri-diagonal matrix $$\widetilde{\mathcal{H}}=(\widetilde{\mathcal{H}}_{x,y}),\quad
\widetilde{\mathcal{H}}_{x,y}=B(x)(\delta_{x,y}-\delta_{x+1,y})+
D(x)(\delta_{x,y}-\delta_{x-1,y}).$$
Corresponding to , the [*inverse similarity transformation*]{} of the Hamiltonian $\mathcal{H}$ supplies the [*birth and death operator*]{} $L_{BD}$: $$L_{BD}{\stackrel{\text{def}}{=}}-\phi_0\circ\mathcal{H}\circ\phi_0^{-1}
=(e^{-\partial}-1)B(x)+(e^{\partial}-1)D(x).
\label{LBDdef}$$ Obviously the stationary probability is given by $\hat{\phi}_0(x)^2=d_0^2\phi_0(x)^2$. In the matrix form, $L_{BD}$ is again tri-diagonal: $$L_{BD}=({L_{BD}}_{x,y}),\quad
{L_{BD}}_{x,y}=B(x-1)\delta_{x-1,y}-B(x)\delta_{x,y}+
D(x+1)\delta_{x+1,y}-D(x)\delta_{x,y}.
\label{LBDdefmat}$$ In fact, $-L_{BD}$ is the transposed matrix of $\widetilde{\mathcal{H}}$: $$-L_{BD}=(\widetilde{\mathcal{H}})^t,\quad -{L_{BD}}_{x,y}=\widetilde{\mathcal{H}}_{y,x}.$$
With the explicit form of the birth and death operator $L_{BD}$, the [*birth and death equation*]{} in our notation reads $$\begin{aligned}
\frac{\partial}{\partial t}\mathcal{P}(x;t)&=\sum_y{L_{BD}}_{x,y}\mathcal{P}(y;t){\nonumber \\}&=-(B(x)+D(x))\mathcal{P}(x;t)+B(x-1)\mathcal{P}(x-1;t)+D(x+1)\mathcal{P}(x+1;t).
\label{BDeq}\end{aligned}$$ The standard interpretation is that $x$ is the population of a group, $\mathcal{P}(x;t)$ is the probability for the group to have the population $x$ at the time $t$, and $B(x)$ is the [*birth rate*]{}, $D(x)$ is the [*death rate*]{}, respectively, when the population is $x$. It is quite easy to remember. This is to be compared with the standard notation, for example, [@KarMcG], XVII.5 of [@feller], §5.2 of [@ismail]: $$\frac{\partial}{\partial t}p_n(t)=-(\lambda_n+\mu_n)p_n(t)+\lambda_{n-1}p_{n-1}(t)
+\mu_{n+1}p_{n+1}(t),$$ in which $\lambda_n$ is the [*birth rate*]{} and $\mu_n$ is the [*death rate*]{}. The following translation table of the notation will be helpful.
--------------------- ------------------------------ -----------------------------
standard [@feller; @ismail] this paper
\[4pt\] population $n=0,1,\ldots, (N), \ldots$ $x=0,1,\ldots, (N), \ldots$
\[4pt\] probability $p_n(t)$ $\mathcal{P}(x;t)$
\[4pt\] Birth rate $\lambda_n$ ($\lambda_N=0$) $B(x)$ ($B(N)=0$)
\[4pt\] Death rate $\mu_n$ ($\mu_0=0$) $D(x)$ ($D(0)=0$)
\[4pt\]
--------------------- ------------------------------ -----------------------------
\
Table I: Translation Table.
The boundary condition for the finite case, $\lambda_N=0$ ($B(N)=0$) is said that the system has a reflecting wall at the population $N$.
The [*transition probability*]{} from $y$ at $t=0$ (i.e., $\mathcal{P}(x;0)=\delta_{x,y}$) to $x$ at $t$ has exactly the same expression as that in the Fokker-Planck equation $$\mathcal{P}(y,x;t)=\hat{\phi}_0(x)\hat{\phi}_0(y)^{-1}
\sum_{n=0}e^{-\mathcal{E}(n)t}\hat{\phi}_n(x)\hat{\phi}_n(y),
\quad
t>0.
\label{tranprobdisc1}$$ In terms of the polynomial $P_n(\eta(x))$, , it is expressed as $$\mathcal{P}(y,x;t)=\phi_0(x)^2
\sum_{n=0}d_n^2\,e^{-\mathcal{E}(n)t}P_n(\eta(x))P_n(\eta(y)),
\quad
t>0.
\label{tranprobdisc2}$$ It should be emphasised that in these formulas - everything is known including the measure in contradistinction to the general formula by Karlin-McGregor [@KarMcG].
Let us mention several equivalent expressions of the transition probability in terms of the [*dual polynomials*]{} [@leonard; @bannaiito; @terw; @os12]. It is well-known that with proper normalisation $$\eta(0)=0=\mathcal{E}(0),\quad P_0\equiv1\equiv Q_0,\quad P_n(0)=Q_x(0)=1,$$ the two polynomials, $\{P_n(\eta)\}$ and its [*dual*]{} polynomial $\{Q_x(\mathcal{E})\}$, coincide at the integer lattice points [@os12]: $$P_n(\eta(x))=Q_x(\mathcal{E}(n)),\quad n=0,1,\ldots,(N),\ldots,
\quad x=0,1,\ldots,(N),\ldots.
\label{Duality}$$ The dual polynomial $\{Q_x(\mathcal{E}(n))\}$, $x=0,1,\ldots$, is a [*right eigenvector*]{} of the similarity transformed Hamiltonian $\widetilde{\mathcal{H}}$ matrix with the eigenvalue $\mathcal{E}(n)$: $$\sum_{y}\widetilde{\mathcal{H}}_{x,y}Q_y(\mathcal{E}(n))=\mathcal{E}(n)Q_x(\mathcal{E}(n)).$$ The above equation is the [*three term recurrence relation*]{} for the dual polynomials $\{Q_x(\mathcal{E})\}$: $$\begin{aligned}
&\left(B(x)+D(x)\right)Q_x(\mathcal{E}(n))-B(x)Q_{x+1}(\mathcal{E}(n))
-D(x)Q_{x-1}(\mathcal{E}(n))=\mathcal{E}(n)Q_{x}(\mathcal{E}(n)),\\
&Q_0=1,\ Q_1(\mathcal{E})\!=\!(B(0)-\mathcal{E})/B(0),\
Q_2(\mathcal{E}\!)=\!(B(0)-\mathcal{E})(B(1)+D(1)-\mathcal{E})/(B(0)B(1)),\ldots.\end{aligned}$$ For historical reasons, this polynomial $Q_x(\mathcal{E})$ is called the birth and death polynomial or the Karlin-McGregor polynomial [@KarMcG].
In terms of the dual polynomials or the Karlin-McGregor polynomial, the transition probability is $$\mathcal{P}(y,x;t)=\phi_0(x)^2
\sum_{n=0}d_n^2\,e^{-\mathcal{E}(n)t}Q_x(\mathcal{E}(n))Q_y(\mathcal{E}(n)),
\quad
t>0.
\label{tranprobdisc3}$$ Following [@ismail], let us introduce $$F_x(\mathcal{E}(n)){\stackrel{\text{def}}{=}}\phi_0(x)^2Q_x(\mathcal{E}(n)).$$ Since $L_{BD}$ and $\widetilde{\mathcal{H}}$ is related by $$L_{BD}=-\phi_0^2\circ \widetilde{\mathcal{H}}\circ \phi_0^{-2},$$ it is easy to see that $F_x(\mathcal{E}(n))$ is a left eigenvector of $\widetilde{\mathcal{H}}$ and thus a right eigenvector of the birth and death operator $L_{BD}$: $$\begin{aligned}
\sum_{y}{L_{BD}}_{x,y}F_y(\mathcal{E}(n))&=-\phi_0(x)^2\sum_{y}
\widetilde{\mathcal{H}}_{x,y}Q_y(\mathcal{E}(n)){\nonumber \\}&=-\mathcal{E}(n)\phi_0(x)^2Q_x(\mathcal{E}(n))
=-\mathcal{E}(n)F_x(\mathcal{E}(n)).\end{aligned}$$ In terms of the right eigenvectors of $L_{BD}$, we obtain another expression of the transition probability [@ismail] $$\mathcal{P}(y,x;t)=\frac{1}{\phi_0(y)^2}
\sum_{n=0}d_n^2\,e^{-\mathcal{E}(n)t}F_x(\mathcal{E}(n))F_y(\mathcal{E}(n)),
\quad
t>0.
\label{tranprobdisc4}$$
The explicit forms of the transition probability , , and can be evaluated straightforwardly if the Hamiltonian $\mathcal{H}$ of an exactly solvable discrete quantum mechanics is given. Thus we may call the functions $B(x)$ and $D(x)$ in the Hamiltonian $\mathcal{H}$ of an exactly solvable discrete quantum mechanics , the birth and death rates of an [*exactly solvable birth and death process*]{}. As mentioned above, the association of the birth and death rates and the orthogonal polynomial in this paper and in the literature [@KarMcG; @ismail; @vanaspralen] are dual to each other. Therefore the names of the polynomials in the next section are the dual of the corresponding Karlin-McGregor polynomial except for the self-dual cases of the Krawtchouk §\[\[KS1.10\]\], Meixner §\[\[KS1.9\]\] and Charlier §\[\[KS1.12\]\].
In the subsequent section we will present 18 examples of exactly solvable birth and death processes.
18 Examples
===========
Now let us proceed to give the 18 explicit examples of exactly solvable birth and death processes. The input is simply the function forms of the birth and death rates $B(x)$ and $D(x)$. The rest is calculable. But here we also provide other data, taken from [@os12], such as the energy eigenvalue $\mathcal{E}(n)$, the sinusoidal coordinate $\eta(x)$, the unnormalised stationary probability $\phi_0(x)^2$, the normalisation constants $d_n^2$ and the polynomials $P_n(\eta)$. Following the order of our previous work on the exactly solvable discrete quantum mechanics [@os12], we handle the most generic one first, and then followed by the simpler ones. There is a logical reason for this order. The simpler ones are usually obtained by specialising or restricting the parameters of the generic ones. Each example is called by the name of the corresponding orthogonal polynomial $P_n(\eta)$ with the number [*e.g.*]{} \[KS3.2\] attached to it indicating the subsection in the standard review of Koekoek and Swarttouw [@koeswart]. The finite ($N$) cases are discussed first and then the infinite ones. In each group the Askey-scheme of hypergeometric orthogonal polynomials (non-$q$ polynomials) will be discussed first and followed by the $q$-scheme polynomials.
Please note that the set of parameters is slightly different from the conventional ones [@askey; @ismail; @koeswart] for some polynomials, the reason explained in [@os12]. For some polynomials, for example, the ($q$-) Racah, (dual, $q$-) Hahn, etc, there are many non-equivalent parametrisations of $B(x)$ and $D(x)$, which could lead to non-equivalent birth and death processes. Here we give only one of them as a representative, since the purpose of the paper is to show exactly solvable structure, not to provide an exhaustive list of all solvable models. See [@os12] for more general parametrisations and the allowed ranges of the parameters. In the same spirit we did not include some of the polynomials listed in [@os12].
[**Finite Dimensional Cases**]{}
Racah \[KS1.2\] {#[KS1.2]}
---------------
The Racah polynomial is the most generic hypergeometric orthogonal polynomial of a discrete variable. All the other (non-$q$) polynomials are obtained by restriction or limiting procedure. The function $B(x)$ and $D(x)$ depend on four real parameters $a$, $b$, $c$ and $d$, with one of them, say $c$, being related to $N$, $c\equiv -N$: $$B(x)
=-\frac{(x+a)(x+b)(x+c)(x+d)}{(2x+d)(2x+1+d)},\quad
D(x)
=-\frac{(x+d-a)(x+d-b)(x+d-c)x}{(2x-1+d)(2x+d)}.
\label{racahbd}$$ The other data are: $$\begin{aligned}
\mathcal{E}(n)&= n(n+\tilde{d}),\quad
\eta(x)=x(x+d),\quad
\tilde{d}{\stackrel{\text{def}}{=}}a+b+c-d-1,\\
&\qquad\qquad\qquad\quad\ a\ge b,\ d>0,\ a>N+d,\ 0<b<1+d,
\end{aligned}$$ $$\begin{gathered}
\phi_0(x)^2=\frac{(a,b,c,d)_x}{(1+d-a,1+d-b,1+d-c,1)_x}\,
\frac{2x+d}{d},\\[4pt]
d_n^2=\frac{(a,b,c,\tilde{d})_n}
{(1+\tilde{d}-a,1+\tilde{d}-b,1+\tilde{d}-c,1)_n}\,
\frac{2n+\tilde{d}}{\tilde{d}}\times
\frac{(-1)^N(1+d-a,1+d-b,1+d-c)_N}{(\tilde{d}+1)_N(d+1)_{2N}}.\end{gathered}$$ Here $(a)_n$ is the Pochhammer symbol . Throughout this section, the format for $d_n^2$ consists of two parts separated by a $\times$ symbol: $d_n^2=(d_n^2/d_0^2)\times d_0^2$. The second part $d_0^2$ satisfies the relation $\sum_x\phi_0(x)^2=1/d_0^2$. The polynomial is $$\begin{aligned}
&P_n(\eta(x))
={}_4F_3\Bigl(
\genfrac{}{}{0pt}{}{-n,\,n+\tilde{d},\,-x,\,x+d}
{a,\,b,\,c}\Bigm|1\Bigr),\
\end{aligned}$$ in which ${}_4F_3$ is the standard hypergeometric series . The dual polynomial is again the Racah polynomial with the parameter correspondence $(a,b,c,d)\leftrightarrow (a,b,c,\tilde{d})$. The rational (a quartic polynomial divided by a quadratic polynomial) birth and death rates have not yet been discussed but the Racah polynomial appears in [@vanaspralen].
Hahn \[KS1.5\] {#[KS1.5]}
---------------
This is a well-known example of quadratic (in $x$) birth and death rates with two real positive parameters $a$ and $b$: $$B(x)=(x+a)(N-x),\quad
D(x)= x(b+N-x).$$ It has a quadratic energy spectrum $$\begin{aligned}
\mathcal{E}(n)&= n(n+a+b-1),\quad
\eta(x)=x,\quad
\phi_0(x)^2
=\frac{N!}{x!\,(N-x)!}\,\frac{(a)_x\,(b)_{N-x}}{(b)_N},\\
d_n^2
&=\frac{N!}{n!\,(N-n)!}\,
\frac{(a)_n\,(2n+a+b-1)(a+b)_N}{(b)_n\,(n+a+b-1)_{N+1}}
\times\frac{(b)_N}{(a+b)_N},\\[4pt]
P_n(\eta(x))
&={}_3F_2\Bigl(
\genfrac{}{}{0pt}{}{-n,\,n+a+b-1,\,-x}
{a,\,-N}\Bigm|1\Bigr).
\end{aligned}$$ The dual polynomial is the dual Hahn polynomial of the next subsection \[\[KS1.6\]\]. The quadratic birth and death rates are discussed in [@vanaspralen] associated with the dual Hahn polynomial.
dual Hahn \[KS1.6\] {#[KS1.6]}
-------------------
The set of parameters is the same as the Hahn polynomial case. The birth and death rates are rational functions of $x$, $$B(x)=\frac{(x+a)(x+a+b-1)(N-x)}
{(2x-1+a+b)(2x+a+b)},
\quad
D(x)=\frac{x(x+b-1)(x+a+b+N-1)}
{(2x-2+a+b)(2x-1+a+b)},
\label{dualhahnBD2}$$ giving rise to a linear energy spectrum $$\begin{aligned}
&\mathcal{E}(n)=n,\quad
\eta(x)= x(x+a+b-1),\quad
\phi_0(x)^2
=\frac{N!}{x!\,(N-x)!}
\frac{(a)_x\,(2x+a+b-1)(a+b)_N}{(b)_x\,(x+a+b-1)_{N+1}},
\label{dualhahneeta}\\
&\qquad\qquad d_n^2
=\frac{N!}{n!\,(N-n)!}\,\frac{(a)_n\,(b)_{N-n}}{(b)_N}
\times\frac{(b)_{N}}{(a+b)_N},\\[4pt]
&P_n(\eta(x))
={}_3F_2\Bigl(
\genfrac{}{}{0pt}{}{-n,\,x+a+b-1,\,-x}
{a,\,-N}\Bigm|1\Bigr). \end{aligned}$$
Krawtchouk \[KS1.10\] (self-dual) {#[KS1.10]}
---------------------------------
The case of linear birth and death rates are a very well-known example (the Ehrenfest model) [@KarMcGEhr] of an exactly solvable birth and death processes [@feller; @schoutens]: $$\begin{aligned}
B(x)&=p(N-x),\quad
D(x)=(1-p)x,\quad 0<p<1,\\
\mathcal{E}(n)&=n,\qquad
\eta(x)=x,\\
\phi_0(x)^2&=
\frac{N!}{x!\,(N-x)!}\Bigl(\frac{p}{1-p}\Bigr)^x,\quad
d_n^2
=\frac{N!}{n!\,(N-n)!}\Bigl(\frac{p}{1-p}\Bigr)^n\times(1-p)^N,\\[4pt]
P_n(\eta(x))
&={}_2F_1\Bigl(
\genfrac{}{}{0pt}{}{-n,\,-x}{-N}\Bigm|p^{-1}\Bigr). $$ This is a simplest example of self-dual polynomials. The stationary probability $\phi_0(x)^2d_0^2$ is the binomial distribution.
$q$-Racah \[KS3.2\] {#[KS3.2]}
--------------------
This is the first example of the $q$-scheme of the orthogonal polynomials. Among them the $q$-Racah polynomial is the most generic. The set of parameters is four real numbers $(a,b,c,d)$, which is different from the standard one in the same manner as for the Racah polynomial. We restrict them $$c=q^{-N},\ \ a\leq b,\ \ 0<d<1,\ \ 0<a<q^Nd,\ \ qd<b<1,\ \
\tilde{d}<q^{-1},\ \ \tilde{d}{\stackrel{\text{def}}{=}}abcd^{-1}q^{-1}.$$ The functions $B(x)$ and $D(x)$ are $$\begin{aligned}
B(x)
&=-\frac{(1-aq^x)(1-bq^x)(1-cq^x)(1-dq^x)}
{(1-dq^{2x})(1-dq^{2x+1})}\,,\\[4pt]
D(x)
& =- \tilde{d}\,
\frac{(1-a^{-1}dq^x)(1-b^{-1}dq^x)(1-c^{-1}dq^x)(1-q^x)}
{(1-dq^{2x-1})(1-dq^{2x})}.
\label{qracahbd}\end{aligned}$$ The other data are $$\begin{aligned}
&\mathcal{E}(n)=(q^{-n}-1)(1-\tilde{d}q^n),\qquad
\eta(x)=(q^{-x}-1)(1-dq^x),\\
& \phi_0(x)^2=\frac{(a,b,c,d\,;q)_x}
{(a^{-1}dq,b^{-1}dq,c^{-1}dq,q\,;q)_x\,\tilde{d}^x}\,
\frac{1-dq^{2x}}{1-d},\\[4pt]
&d_n^2
=\frac{(a,b,c,\tilde{d}\,;q)_n}
{(a^{-1}\tilde{d}q,b^{-1}\tilde{d}q,c^{-1}\tilde{d}q,q\,;q)_n\,d^n}\,
\frac{1-\tilde{d}q^{2n}}{1-\tilde{d}} \times
\frac{(-1)^N(a^{-1}dq,b^{-1}dq,c^{-1}dq\,;q)_N\,\tilde{d}^Nq^{\frac12N(N+1)}}
{(\tilde{d}q\,;q)_N(dq\,;q)_{2N}},\\
&P_n(\eta(x))
={}_4\phi_3\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,\tilde{d}q^n,\,q^{-x},\,dq^x}
{a,\,b,\,c}\Bigm|q\,;q\Bigr), $$ in which ${}_4\phi_3$ is the basic hypergeometric series and $(a;q)_n$ is the $q$-Pochhammer symbol . The dual $q$-Racah polynomial is again the $q$-Racah polynomial with the parameter correspondence $(a,b,c,d)\leftrightarrow (a,b,c,\tilde{d})$.
$q$-Hahn \[KS3.6\] {#[KS3.6]}
------------------
The $q$-Hahn polynomial has two positive parameters $a$ and $b$ and the birth and death rates are quadratic polynomials in $q^x$: $$B(x)=(1-aq^x)(q^{x-N}-1),\quad
D(x)= aq^{-1}(1-q^x)(q^{x-N}-b),\quad 0<a,b<1.$$ The other data are $$\begin{aligned}
\mathcal{E}(n)
&=(q^{-n}-1)(1-abq^{n-1}),\qquad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2
&=\frac{(q\,;q)_N}{(q\,;q)_x\,(q\,;q)_{N-x}}\,
\frac{(a;q)_x\,(b\,;q)_{N-x}}{(b\,;q)_N\,a^x}\,,\\[4pt]
d_n^2
&=\frac{(q\,;q)_N}{(q\,;q)_n\,(q\,;q)_{N-n}}\,
\frac{(a,abq^{-1};q)_n}{(abq^N,b\,;q)_n\,a^n}\,
\frac{1-abq^{2n-1}}{1-abq^{-1}}
\times\frac{(b\,;q)_N\,a^N}{(ab\,;q)_N},\\[4pt]
P_n(\eta(x))
&={}_3\phi_2\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,abq^{n-1},\,q^{-x}}
{a,\,q^{-N}}\Bigm|q\,;q\Bigr).
$$ Obviously the $q$-Hahn and dual $q$-Hahn are dual to each other.
dual $q$-Hahn \[KS3.7\] {#[KS3.7]}
-----------------------
For obvious reasons, we adopt the same parameters $(a,b)$ for the $q$-Hahn and dual $q$-Hahn polynomials. The birth and death rates are rational functions of $q^x$:
$$\begin{aligned}
B(x)&=
\frac{(q^{x-N}-1)(1-aq^x)(1-abq^{x-1})}
{(1-abq^{2x-1})(1-abq^{2x})},\qquad 0<a,b<1,\\[4pt]
D(x)&=aq^{x-N-1}
\frac{(1-q^x)(1-abq^{x+N-1})(1-bq^{x-1})}
{(1-abq^{2x-2})(1-abq^{2x-1})},\\[4pt]
\mathcal{E}(n)&=q^{-n}-1,\qquad
\eta(x)=(q^{-x}-1)(1-abq^{x-1}),\\[4pt]
\phi_0(x)^2
&=\frac{(q\,;q)_N}{(q\,;q)_x\,(q\,;q)_{N-x}}\,
\frac{(a,abq^{-1}\,;q)_x}{(abq^N,b\,;q)_x\,a^x}\,
\frac{1-abq^{2x-1}}{1-abq^{-1}}\,,\\[4pt]
d_n^2
&=\frac{(q\,;q)_N}{(q\,;q)_n\,(q\,;q)_{N-n}}\,
\frac{(a\,;q)_n(b\,;q)_{N-n}}{(b;q)_N\,a^n}
\times\frac{(b\,;q)_N\,a^N}{(ab;q)_N}\,,\\[4pt]
P_n(\eta(x))
&={}_3\phi_2\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,abq^{x-1},\,q^{-x}}
{a,\,q^{-N}}\Bigm|q\,;q\Bigr).
\end{aligned}$$
quantum $q$-Krawtchouk \[KS3.14\] {#[KS3.14]}
---------------------------------
This has one positive parameter $p>q^{-N}$. The birth and death rates are quadratic polynomials in $q^x$: $$\begin{aligned}
B(x)&=p^{-1}q^x(q^{x-N}-1),\qquad
D(x)=(1-q^x)(1-p^{-1}q^{x-N-1}),\\
\mathcal{E}(n)&=1-q^n,\qquad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2
&=\frac{(q\,;q)_N}{(q\,;q)_x(q\,;q)_{N-x}}\,
\frac{p^{-x}q^{x(x-1-N)}}{(p^{-1}q^{-N}\,;q)_x}\,,\\[4pt]
d_n^2
&=\frac{(q\,;q)_N}{(q\,;q)_n(q\,;q)_{N-n}}\,
\frac{p^{-n}q^{-Nn}}{(p^{-1}q^{-n}\,;q)_n}\,
\times(p^{-1}q^{-N}\,;q)_N,\\[4pt]
P_n(\eta(x))
&={}_2\phi_1\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x}}{q^{-N}}\Bigm|q\,;pq^{n+1}\Bigr).\end{aligned}$$
$q$-Krawtchouk \[KS3.15\] {#[KS3.15]}
-------------------------
This has one positive parameter $p>0$ and the birth and death rates are linear in $q^x$: $$\begin{aligned}
B(x)&=q^{x-N}-1,\qquad
D(x)=p(1-q^x),\\
\mathcal{E}(n)&=(q^{-n}-1)(1+pq^n),\qquad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2&=\frac{(q\,;q)_N}{(q\,;q)_x(q\,;q)_{N-x}}\,
p^{-x}q^{\frac12x(x-1)-xN},\\
d_n^2
&=\frac{(q\,;q)_N}{(q;q)_n(q;q)_{N-n}}\,
\frac{(-p\,;q)_n}{(-pq^{N+1}\,;q)_n\,p^nq^{\frac12n(n+1)}}\,
\frac{1+pq^{2n}}{1+p}
\times\frac{p^{N}q^{\frac12N(N+1)}}{(-pq\,;q)_N},\\[4pt]
P_n(\eta(x))
&={}_3\phi_2\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x},\,-pq^n}{q^{-N},\,0}\Bigm|q\,;q\Bigr).\end{aligned}$$
affine $q$-Krawtchouk \[KS3.16\] (self-dual) {#[KS3.16]}
--------------------------------------------
This has one positive parameter $p$ and the birth and death rates are quadratic polynomials in $q^x$: $$\begin{aligned}
B(x)&=(q^{x-N}-1)(1-pq^{x+1}),\quad
D(x)=pq^{x-N}(1-q^x),\quad 0<p<q^{-1}, \\
\mathcal{E}(n)&=q^{-n}-1,\qquad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2&=\frac{(q\,;q)_N}{(q\,;q)_x(q\,;q)_{N-x}}\,
\frac{(pq\,;q)_x}{(pq)^x}\,,\quad
d_n^2
=\frac{(q\,;q)_N}{(q\,;q)_n(q\,;q)_{N-n}}\,
\frac{(pq\,;q)_n}{(pq)^n}\times(pq)^N,\\[4pt]
P_n(\eta(x))
&={}_3\phi_2\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x},\,0}{pq,\,q^{-N}}\Bigm|q\,;q\Bigr).\end{aligned}$$
[**Infinite Dimensional Cases**]{}
In contrast to the finite dimensional case, the structure of the polynomials is severely constrained by the asymptotic forms of the functions $B(x)$ and $D(x)$ .
Meixner \[KS1.9\] (self-dual) {#[KS1.9]}
-----------------------------
This is the best known example of exactly solvable birth and death processes [@KarMcGLin] and the birth and death rates are both linear in $x$ with simple linear energy spectra $\mathcal{E}(n)=n$ and $\eta(x)=x$. It has two positive parameters $\beta$ and $c$: $$\begin{aligned}
B(x)&=\frac{c}{1-c}(x+\beta),\quad
D(x)=\frac{1}{1-c}\,x,\quad \beta>0,\quad 0<c<1,
\label{MeixnerBD}\\
\mathcal{E}(n)&=n,\qquad
\eta(x)=x,
\label{MeixnerEeta}\\
\phi_0(x)^2&=\frac{(\beta)_x\,c^x}{x!}\,,\quad
d_n^2
=\frac{(\beta)_n\,c^n}{n!}\times(1-c)^{\beta},
\label{Meixnerphi0d}\\
P_n(\eta(x))
&={}_2F_1\Bigl(
\genfrac{}{}{0pt}{}{-n,\,-x}{\beta}\Bigm|1-c^{-1}\Bigr).
\label{MeixnerP}\end{aligned}$$
Charlier \[KS1.12\] (self-dual) {#[KS1.12]}
-------------------------------
This is another best known example of exactly solvable birth and death processes with a constant birth rates $a>0$ and a linear death rates: $$\begin{aligned}
B(x)&=a,\qquad
D(x)=x,
\label{charlBD}\\
\mathcal{E}(n)&=n,\qquad
\eta(x)=x,
\label{charlEeta}\\
\phi_0(x)^2&=\frac{a^x}{x!}\,,\qquad
d_n^2
=\frac{a^{n}}{n!}\times e^{-a},
\label{charlphi0d}\\
P_n(\eta(x)
&={}_2F_0\Bigl(
\genfrac{}{}{0pt}{}{-n,\,-x}{-}\Bigm|-a^{-1}\Bigr).
\label{charlP}\end{aligned}$$ The stationary probability $\phi_0(x)^2d_0^2$ is the Poisson distribution.
little $q$-Jacobi \[KS3.12\] {#[KS3.12]}
----------------------------
This has two parameters $a$ and $b$. The birth and death rates grow exponentially as $x$ tends to infinity: $$\begin{aligned}
B(x)&=a(q^{-x}-bq),\quad
D(x)=q^{-x}-1,\quad 0<a<q^{-1},\quad b<q^{-1},\\
\mathcal{E}(n)&=(q^{-n}-1)(1-abq^{n+1}),\qquad
\eta(x)=1-q^x,\\
\phi_0(x)^2&=\frac{(bq\,;q)_x}{(q\,;q)_x}(aq)^x,
\label{littleqjacobiphi0}\\
d_n^2
&=\frac{(bq,abq\,;q)_n\,a^nq^{n^2}}{(q,aq\,;q)_n}\,
\frac{1-abq^{2n+1}}{1-abq}
\times\frac{(aq\,;q)_{\infty}}{(abq^2\,;q)_{\infty}}\,,
\label{littleqjacobidn}\\[4pt]
P_n(\eta(x))
&=(-a)^{-n}q^{-\frac12n(n+1)}\frac{(aq\,;q)_n}{(bq\,;q)_n}\,
{}_2\phi_1\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,abq^{n+1}}{aq}\Bigm|q\,;q^{x+1}\Bigr).
\label{littleqjacobinorm}\end{aligned}$$ The normalisation of the polynomial is different from the conventional one.
$q$-Meixner \[KS3.13\] {#[KS3.13]}
----------------------
This has two positive parameters $b$ and $c$. The birth and death rates are quadratic in $q^x$ and as $x$ goes to infinity, the birth rates tend to zero and the death rates tend to unity: $$\begin{aligned}
B(x)&=cq^x(1-bq^{x+1}),\quad
D(x)=(1-q^x)(1+bcq^x),\quad 0<b<q^{-1},\quad c>0,\\
\mathcal{E}(n)&=1-q^n,\qquad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2&=
\frac{(bq\,;q)_x}{(q,-bcq\,;q)_x}\,c^xq^{\frac12x(x-1)},\quad
d_n^2
=\frac{(bq\,;q)_n}{(q,-c^{-1}q\,;q)_n}
\times\frac{(-bcq\,;q)_{\infty}}{(-c\,;q)_{\infty}}\,,\\[4pt]
P_n(\eta(x))
&={}_2\phi_1\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x}}{bq}\Bigm|q\,;-c^{-1}q^{n+1}\Bigr).\end{aligned}$$
little $q$-Laguerre/Wall \[KS3.20\] {#[KS3.20]}
------------------------------------
This has one positive parameter $a$ and both the birth and death rates grow exponentially as $x$ tends to infinity: $$\begin{aligned}
B(x)&=aq^{-x},\qquad\quad
D(x)=q^{-x}-1,\qquad 0<a<q^{-1},\\
\mathcal{E}(n)&=q^{-n}-1,\qquad
\eta(x)=1-q^x,\\
\phi_0(x)^2&=\frac{(aq)^x}{(q\,;q)_x}\,,\qquad
d_n^2
=\frac{a^nq^{n^2}}{(q,aq\,;q)_n}\times(aq\,;q)_{\infty}\,,\\[4pt]
P_n(\eta(x))
&={}_2\phi_0\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x}}{-}\Bigm|q\,;a^{-1}q^x\Bigr).
\label{littleqlaguerrenorm}\end{aligned}$$ The normalisation of the polynomial is different from the conventional one.
Al-Salam-Carlitz II \[KS3.25\] {#[KS3.25]}
-------------------------------
This has one positive parameter $a$ and the birth and death rates are quadratic in $q^x$. As $x$ goes to infinity the birth rates tend to zero and death rates tend to unity: $$\begin{aligned}
B(x)&=aq^{2x+1},\qquad\quad
D(x)=(1-q^x)(1-aq^x),\quad 0<a<q^{-1},\\
\mathcal{E}(n)&=1-q^n,\qquad\quad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2&=\frac{a^xq^{x^2}}{(q,aq\,;q)_x}\,,\quad
d_n^2
=\frac{(aq)^n}{(q\,;q)_n}\times(aq\,;q)_{\infty}\,,\\[4pt]
P_n(\eta(x))
&={}_2\phi_0\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x}}{-}\Bigm|q\,;a^{-1}q^n\Bigr).
\label{alsalamIInorm}\end{aligned}$$ The normalisation of the polynomial is different from the conventional one.
alternative $q$-Charlier \[KS3.22\] {#[KS3.22]}
-----------------------------------
This has one positive parameter $a$. The birth rates are constant $a$ whereas the death rates grow exponentially as $x$ goes to infinity: $$\begin{aligned}
B(x)&=a,\quad
D(x)=q^{-x}-1,\quad a>0,\\
\mathcal{E}(n)&=(q^{-n}-1)(1+aq^n),\quad
\eta(x)=1-q^x,\\
\phi_0(x)^2&=\frac{a^xq^{\frac12x(x+1)}}{(q\,;q)_x}\,,
\ \,
d_n^2
=\frac{a^nq^{\frac12n(3n-1)}}{(q\,;q)_n}\,
\frac{(-a\,;q)_{\infty}}{(-aq^n\,;q)_{\infty}}\,
\frac{1+aq^{2n}}{1+a}
\times\frac{1}{(-aq\,;q)_{\infty}}\,,\\[4pt]
P_n(\eta(x))
& =q^{nx}\,{}_2\phi_1\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x}}{0}\Bigm|q\,;-a^{-1}q^{-n+1}\Bigr).
\label{alcharliernorm}
$$ The normalisation of the polynomial is different from the conventional one.
$q$-Charlier \[KS3.23\] {#[KS3.23]}
-----------------------
This has one positive parameter $a$ and as $x$ goes to infinity the birth rates tend to zero and the death rates tend to unity: $$\begin{aligned}
B(x)&=aq^x,\qquad\qquad
D(x)=1-q^x,\quad a>0,\\
\mathcal{E}(n)&=1-q^n,\qquad\quad
\eta(x)=q^{-x}-1,\\
\phi_0(x)^2&=\frac{a^xq^{\frac12x(x-1)}}{(q\,;q)_x}\,,\quad
d_n^2
=\frac{q^n}{(-a^{-1}q,q\,;q)_n}\times\frac{1}{(-a\,;q)_{\infty}}\,,\\[4pt]
P_n(\eta(x))
&={}_2\phi_1\Bigl(
\genfrac{}{}{0pt}{}{q^{-n},\,q^{-x}}{0}\Bigm|q\,;-a^{-1}q^{n+1}\Bigr).\end{aligned}$$
Summary and Comments {#summary}
====================
Following the simple line of arguments summarised in the following diagram, we presented 18 models of exactly solvable birth and death processes and their solutions, the transition probabilities. In the diagram ‘ES’ stands for Exactly Solvable. $$\begin{aligned}
\framebox{\shortstack{$\,$ES 1d Quantum $\,$ \\ \\Mechanical systems}}
&{\smash{\mathop{\hbox to 45mm{\rightarrowfill}}\limits^{\mbox{give solutions}}}}&
\framebox{\shortstack{ES 1d Fokker-Planck\\ \\
equations}}\\
{\Bigg\downarrow\rlap{$\vcenter{\hbox{$\scriptstyle\mbox{discretisation}$}}$}}\hspace{20mm}&&
\hspace{15mm}{\Bigg\downarrow\rlap{$\vcenter{\hbox{$\scriptstyle\makebox{
\shortstack{discretisation}}$}}$}}\\
\hspace*{-5mm}
\framebox{\shortstack{ES `Matrix' Quantum \\ \\ Mechanical systems}}
&{\smash{\mathop{\hbox to 45mm{\rightarrowfill}}\limits^{\mbox{give solutions}}}}&
\framebox{\shortstack{ES Birth and Death \\ \\
processes}}\end{aligned}$$ The exactly solvable ‘matrix’ quantum mechanics, or the 1-d ‘discrete’ quantum mechanics with real shifts was explored in detail in [@os12] to cover most of the hypergeometric orthogonal polynomials of a discrete variable in the ($q$-) Askey scheme [@askey; @ismail; @koeswart]. For the ‘explanation’ of the exact solvability, see a recent work [@os14]. By comparing the present simple results with those in the literature [@KarMcG; @schoutens; @ismail; @vanaspralen] one would realise the essential role played by the energy spectrum $\mathcal{E}(n)$ and the sinusoidal coordinate $\eta(x)$. They are the eigenvalues of the two operators, called the Leonard pair, which characterise the orthogonal polynomials completely [@leonard; @bannaiito; @terw].
In this paper we did not discuss the generalisation of the birth and death processes which has $\mu_0>0$ ($D(0)>0$), the [*non-vanishing death rate at zero population*]{}, although this has led to a new type of orthogonal polynomials in the cases when the birth and death rates $B(x)$ and $D(x)$ are linear and quadratic in $x$, [@new1; @new2]. It would be interesting to try further generalisation in this direction for which $B(x)$ and $D(x)$ are rational, [*e.g.*]{} the Racah case §\[\[KS1.2\]\] or $q$-linear, [*e.g.*]{} the $q$-Krawtchouk §\[\[KS3.15\]\], or $q$-quadratic, [*e.g.*]{} the the affine $q$-Krawtchouk §\[\[KS3.16\]\], or even the $q$-rational, [*e.g.*]{} the $q$-Racah §\[\[KS3.2\]\] cases.
It is a big challenge to try and find a closed form expression for $$\sum_{n=0}d_n^2\,e^{-\mathcal{E}(n)t}P_n(\eta(x))P_n(\eta(y)),$$ appearing as a part of the transition probability , for various examples in section four. To the best of our knowledge, such expressions are known only for the linear energy spectrum $\mathcal{E}(n)\propto n$. For example, for the Fokker-Planck equation corresponding to the harmonic oscillator Hamiltonian, or the Ornshtein-Uhlenbeck process [@risken; @hs1], we have: $$\begin{aligned}
\mathcal{H}&{\stackrel{\text{def}}{=}}-\frac{d^2}{dx^2}+x^2-1,\quad
\quad
L_{FP}=\frac{d^2}{dx^2}+2\frac{d}{dx} x,\quad \mathcal{E}(n)=2n,\quad \eta(x)=x,\\[4pt]
\mathcal{P}(y,x;t)&=\frac{e^{-x^2}}{\sqrt{\pi}}
\sum_{n=0}^\infty\frac{H_n(x)H_n(y)}{2^nn!}\,e^{-2nt}
=\frac{1}{\sqrt{\pi}\sqrt{1-e^{-4t}}}
\exp\left[-\frac{(x-y\,e^{-2t})^2}{1-e^{-4t}}\right].\end{aligned}$$ The last equality was derived based on (6.1.13) of [@askey]. Another example is $$\begin{aligned}
\mathcal{H}&{\stackrel{\text{def}}{=}}-\frac{d^2}{dx^2}+x^2+\frac{g(g-1)}{x^2}-(1+2g),\quad
L_{FP}=\frac{d^2}{dx^2}+2\frac{d}{dx}(x-\frac{g}{x}),\\
& \qquad\qquad \mathcal{E}_n=4n,\quad \eta(x)=x^2, \quad \beta{\stackrel{\text{def}}{=}}g-1/2,\\
\mathcal{P}(y,x;t)&=2e^{-x^2}x^{2g}
\sum_{n=0}^\infty\frac{n!\,L_n^{(\beta)}(x^2)L_n^{(\beta)}(y^2)}{\Gamma(n+\beta+1)}\,e^{-4nt}\\
&=\frac{2x^{2g}}{(1-e^{-4t})}
\exp\left[-\frac{(x^2+y^2\,e^{-4t})}{(1-e^{-4t})}\right](xye^{-2t})^{-\beta}I_{\beta}\left(\frac{2xye^{-2t}}{1-e^{-4t}}\right),\end{aligned}$$ in which $I_\beta$ is the modified Bessel function of order $\beta$. The last equality was derived based on (6.2.25) of [@askey]. We would like to ask experts in special functions and orthogonal polynomials to derive such bilinear generating functions for various energy spectra: $$\begin{aligned}
\mathcal{E}(n)= n(n+d), \ q^{-n}-1,\ 1-q^n,\ (q^{-n}-1)(1-{d}q^n).\end{aligned}$$
Acknowledgements {#acknowledgements .unnumbered}
================
We thank Mourad Ismail and Choon-Lin Ho who induced us to the present research. This work is supported in part by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, No.18340061 and No.19540179.
Appendix A: Some definitions related to the hypergeometric and $q$-hypergeometric functions {#appendA .unnumbered}
===========================================================================================
For self-containedness we collect several definitions related to the ($q$-)hypergeometric functions [@koeswart].
$\circ$ Pochhammer symbol $(a)_n$ : $$(a)_n{\stackrel{\text{def}}{=}}\prod_{k=1}^n(a+k-1)=a(a+1)\cdots(a+n-1)
=\frac{\Gamma(a+n)}{\Gamma(a)}.
\label{defPoch}$$ $\circ$ $q$-Pochhammer symbol $(a\,;q)_n$ : $$(a\,;q)_n{\stackrel{\text{def}}{=}}\prod_{k=1}^n(1-aq^{k-1})=(1-a)(1-aq)\cdots(1-aq^{n-1}).
\label{defqPoch}$$ $\circ$ hypergeometric series ${}_rF_s$ : $${}_rF_s\Bigl(\genfrac{}{}{0pt}{}{a_1,\,\cdots,a_r}{b_1,\,\cdots,b_s}
\Bigm|z\Bigr)
{\stackrel{\text{def}}{=}}\sum_{n=0}^{\infty}
\frac{(a_1,\,\cdots,a_r)_n}{(b_1,\,\cdots,b_s)_n}\frac{z^n}{n!}\,,
\label{defhypergeom}$$ where $(a_1,\,\cdots,a_r)_n{\stackrel{\text{def}}{=}}\prod_{j=1}^r(a_j)_n
=(a_1)_n\cdots(a_r)_n$.\
$\circ$ $q$-hypergeometric series (the basic hypergeometric series) ${}_r\phi_s$ : $${}_r\phi_s\Bigl(
\genfrac{}{}{0pt}{}{a_1,\,\cdots,a_r}{b_1,\,\cdots,b_s}
\Bigm|q\,;z\Bigr)
{\stackrel{\text{def}}{=}}\sum_{n=0}^{\infty}
\frac{(a_1,\,\cdots,a_r\,;q)_n}{(b_1,\,\cdots,b_s\,;q)_n}
(-1)^{(1+s-r)n}q^{(1+s-r)n(n-1)/2}\frac{z^n}{(q\,;q)_n}\,,
\label{defqhypergeom}$$ where $(a_1,\,\cdots,a_r\,;q)_n{\stackrel{\text{def}}{=}}\prod_{j=1}^r(a_j\,;q)_n
=(a_1\,;q)_n\cdots(a_r\,;q)_n$.
[99]{}
H. Risken, [*The Fokker-Planck Equation*]{} (2nd. ed.), Springer-Verlag, Berlin, (1996).
W. Feller, [*An Introduction to Probability Theory and its Applications, I*]{}, (2nd ed.), Wiley, New York, (1966).
W.Schoutens, [*Stochastic processes and orthogonal polynomials*]{}, Lecture Notes in Statistics [**146**]{} Springer, New York, (2000).
G.E.Andrews, R.Askey and R.Roy, [*Special Functions*]{}, Encyclopedia of mathematics and its applications, Cambridge, (1999).
M.E.H.Ismail, [*Classical and quantum orthogonal polynomials in one variable*]{}, Encyclopedia of mathematics and its applications, Cambridge, (2005).
A.F.Nikiforov, S.K.Suslov, and V.B.Uvarov, [*Classical Orthogonal Polynomials of a Discrete Variable*]{}, Springer-Verlag, Berlin, (1991).
R.Koekoek and R.F.Swarttouw, “The Askey-scheme of hypergeometric orthogonal polynomials and its $q$-analogue,” [arXiv:math.CA/9602214]{}.
S.Karlin and J.L.McGregor, “The differential equations of birth-and-death processes," Trans. Amer. Math. Soc. [**85**]{} (1957) 489-546.
S.Odake and R.Sasaki, “Orthogonal Polynomials from Hermitian Matrices," J. Math. Phys. [**49**]{} (2008) 053503 (43 pages), [arXiv:0712.4106\[math.CA\]]{}.
S.Karlin and J.L.McGregor, “Linear growth, birth-and-death processes," J. Math. Mech. [**7**]{} (1958) 643–662.
S.Karlin and J.L.McGregor, “Ehrenfest urn models," J. Appl. Prob. [**19**]{} (1965) 477–487.
W. van Assche, P.R. Parathasarathy and R.B. Lenin, “Spectral representation of certain finite birth and death processes," Math. Sci. [**24**]{} (1999) 105–112.
S.Odake and R.Sasaki, “Exactly solvable ‘discrete’ quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states," Prog. Theor. Phys. [**119**]{} (2008) 663-700, [arXiv:0802.1075\[quant-ph\]]{}.
C.-L.Ho and R.Sasaki, “Deformed Fokker-Planck equations," Prog. Theor. Phys. [**118**]{} (2007) 667-674; “Deformed multi-variable Fokker-Planck equations," J. Math. Phys. [**48**]{} (2007) 073302.
S.Odake and R.Sasaki, “Unified Theory of Annihilation-Creation Operators for Solvable (‘Discrete’) Quantum Mechanics,” J. Math. Phys. [**47**]{} (2006) 102102 (33 pages), [arXiv:quant-ph/0605215]{}; “Exact solution in the Heisenberg picture and annihilation-creation operators," Phys. Lett. [**B641**]{} (2006) 112-117, [arXiv:quant-ph/0605221]{}.
L.Infeld and T.E.Hull, “The factorization method,” Rev. Mod. Phys. [**23**]{} (1951) 21-68.
See, for example, a review: F.Cooper, A.Khare and U.Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. [**251**]{} (1995) 267-385.
S.Odake and R.Sasaki, “Shape Invariant Potentials in “Discrete Quantum Mechanics,” J. Nonlinear Math. Phys. [**12**]{} Suppl. 1 (2005) 507-521, [arXiv:hep-th/0410102]{}.
D.Leonard, “Orthogonal polynomials, duality, and association schemes," SIAM J. Math. Anal. [**13**]{} (1982) 656–663.
E. Bannai and T. Ito, “Algebraic Combinatorics I: Association Schemes," Benjamin/Cummings (1984).
P.Terwilliger, “Leonard pairs and the $q$-Racah polynomials," Linear Algebra Appl. [**387**]{} (2004) 235–276, [arXiv:math.QA/0306301]{}; “Two linear transformations each tri-diagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials," [arXiv:math.QA/0408390]{}.
S.Odake and R.Sasaki, “Unified theory of exactly and quasi-exactly solvable ‘discrete’ quantum mechanics: I. Formalism," Preprint DPSU-09-2, YITP-09-14, [arXiv:0903.2604\[math-ph\]]{}.
R.Askey and J. Wimp, “Associated Laguerre and Hermite polynomials," Proc. Roy. Soc. Edinburgh, Sec. A, [**96**]{} (1984) 15-37.
M.E.H.Ismail, J. Lettessier and G. Valent, “Linear birth and death models and associated Laguerre and Meixner polynomials," J. Approx. Theory, [**55**]{} (1988) 337-348; “Quadratic birth and death processes and associated continuous dual Hahn polynomials," SIAM J. Math. Anal. [**20**]{} (1989) 727-737.
[^1]: It should be emphasised that the [*inverse similarity transformation*]{} in terms of $\phi_0$ is used here: $
L_{FP}=-\phi_0^2\circ\widetilde{\mathcal{H}}\circ\phi_0^{-2}.
$
| |
3 edition of Geographic information/GIS institutionalization in the 50 states found in the catalog.
Geographic information/GIS institutionalization in the 50 states
Lisa Warnecke
Published
1995 by National Center for Geographic Information and Analysis in [Santa Barbara, CA] .
Written in English
Edition Notes
|Statement||by Lisa Warnecke.|
|Series||Technical report ;, 95-11, Technical report (National Center for Geographic Information & Analysis (U.S.)) ;, 95-11.|
|Contributions||National Center for Geographic Information & Analysis (U.S.)|
|Classifications|
|LC Classifications||G70.212 .W37 1995|
|The Physical Object|
|Pagination||1 v. (various pagings) :|
|ID Numbers|
|Open Library||OL3995713M|
|LC Control Number||2001337247|
|OCLC/WorldCa||35992458|
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Making appropriations for the Department of the Interior and related agencies for the fiscal year ending September 30, 2002, and for other purposes
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life of Krishna in Indian art
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Using a hands-on approach grounded in relevant GIS and disaster management theory and practice, this textbook continues the tradition of the benchmark first edition, providing coverage of GIS. The book "Ground Truth: The Social Implications of Geographic Information Systems," edited by Pickles () aimed to locate discussion of these questions in a variety of these possible interpretative frameworks, and thereby to provide illustrations that might lead others to deepen the analysis of the intellectual and practical commitments and.
1 Esri Open Data Hub. Inthe Esri Open Data Hub is a hidden gold mine of free GIS data. For example, it now houses over ,+ open data sets from 5,+ organizations worldwide.
For this reason, we have it at the top of our list of free GIS data. In some cases, you’ll have to sift through piles of data because they’re not conveniently merged into one. Praise for the Second Edition: A tour de force. Anyone seeking a combined primer and state-of-the-art summary on almost any facet of current geographical information systems (GIS) will find it here.
--International Journal of Geographical Information Science Stands as a definitive reference to GIS a thorough and up-to-date overview of the subject. --Australian Geographical Studies. Geographic Information Systems are an essential tool for analyzing and representing quantitative spatial data.
Qualitative GIS explains the recent integration of qualitative research with Geographical Information Systems.
With a detailed contextualising introduction, the text is organised in three sections: Representation: examines how researchers are using GIS to create new types of. USGS is a primary source of Geographic Information Systems (GIS) Data.
Our data and information is presented both spatially and geographically including The National Map, Earth Explorer, GloVIS, LandsatLook, and much more. Start exploring by topic below. The following open-source desktop GIS projects are reviewed in Steiniger and Bocher (/9): GRASS GIS – Geospatial data management, vector and raster manipulation - developed by the U.S.
Army Corps of Engineers; gvSIG – Mapping and geoprocessing with a 3D rendering plugin; ILWIS (Integrated Land and Water Information System) – Integrates image, vector and thematic data. A geographic information system (GIS) is a conceptualized framework that provides the ability to capture and analyze spatial and geographic data.
GIS applications (or GIS apps) are computer-based tools that allow the user to create interactive queries (user-created searches), store and edit spatial and non-spatial data, analyze spatial information output, and visually share the results of. Links to learning pathways and blogs relate the practical use of GIS in each of the case studies.
GIS for Science: Applying Mapping and Spatial Analytics, Volume 2, is available in print (ISBN:pages, US$) and as an e-book (ISBN:US$). Both editions can be obtained from most online retailers worldwide.
In Submarine Optical Cable Engineering, Types of Geographic Information System. The geographic information system (GIS) is a decision support system that has the various characteristics of information systems (Liu and Lin, ).The main difference between GIS and other information systems is that the information stored and processed is geographic coded, and the geographic.
GIS Customer Service GIS Online Services. Gisella is a mobile GIS application that allows you to create and manage all geographic objects directly on your mobile device. Examples, instructions, and support are available at The Geographic Information System offers you everything from map object management to layers to entire map projects.
Our GIS application supports common data formats as KML, GeoJSON and ESRI. This article has been paraphrased from Roger Tomlinson and M. Toomey, "GIS and LIS in Canada," chapter 15 in Mapping a Northern Land: The Survey of CanadaGerald McGrath and Louis Sebert, eds.
(McGill-Queen's University Press, ). At the heart of the innovations that led to the Canada Geographic Information System was the fundamental idea of using computers to ask. The GIS Essential Skills, updated for ArcGIS® Desktoppresents step-by-step instructions, illustrations, and practical tips on how to perform the top 20 sills needed to successfully use a geographic information system (GIS).
These skills include finding and editing data, querying GIS maps, creating reports, and sharing and publishing. Pima County Geographic Information Systems Parcel Information Search.
Parcel information is derived from Pima County Assessor records and other sources. See the Pima County Assessor Parcel Search for official Assessor information. Taxpayer Name Search. Enter last name (a. Finding books in the WSU Search It catalog. Try keyword searches. gis or "geographic information system*" (Note that 'gis' as a keyword will include GI's as in General Infantry.
Click on an item's Details tab to see the highlighted keyword.). United States About Blog GIS Lounge is where you can learn about geographic information systems (GIS), geospatial technologies, cartography, and maps. Also featured are GIS jobs, conferences, and GIS industry news. Frequency 1 post / day Blog Facebook fans K ⋅ Twitter followers K ⋅ Social Engagement ⓘ ⋅ Domain Authority 56 ⓘ ⋅ Alexa Rank.
Getting to Know Web GIS, Fourth Edition, is available in print (ISBN:pages, US$) and as an e‑book (ISBN:US$). The Protected Areas Database of the United States (PAD-US) is the official inventory of protected open space in the United States.
With over million acres in thousands of holdings, the spatial data in PAD-US include public lands held in trust by national, State, and some local governments, and by some nonprofit conservation organizations.
In May of that year, Tomlinson boarded an airplane flying from Ottawa to Toronto, Canada. He was on a business trip as a year-old geographer .Below is a partial listing of careers that students within the GIS and Spatial Analysis specialization are well-suited and where previous graduates have found employment.
Planner: transportation, urban, health services, land use, etc. Example: I would like to find articles about streams or stream hydrology and the use of GIS in the modeling.
Search Strategy: (GIS or geographic information systems) AND (stream* and hydrology) Examples: I would like to find articles about use of GIS technology in researching crime reporting and analysis. | https://piqyzahogi.naba-hairstreak.com/geographic-informationgis-institutionalization-in-the-50-states-book-1592sa.php |
Maria Montessori worked in the fields of psychiatry, education and anthropology. She believed that each child is born with a unique potential to be revealed, rather than as a “blank state” waiting to be written upon.
Dr. Montessori developed an educational theory, which combined ideas of scholar Froebel, anthropologist Giuseooe Sergi, French physicians Jean Itard and Edouard Sequin, with methods that she had found in medicine, education and anthropology.
Montessori had a revelation. “I felt that mental deficiency presented chiefly a pedagogical, rather than mainly a medical problem”. The children she was working with could not be treated in the hospitals, they needed to be trained in schools. Given her new insight, she began to transfer her time towards perfecting education. She wanted to use nature in the school in order to meet the real needs of children (Montessori Method, the 1912).
In her medical practice, her clinical observations led her to analyze how children learn, and she concluded that they build themselves from what they find in their environment; shifting her focus from the body to the mind.
Dr. Montessori's methods have continued to spread throughout the world. Her message to those who emulated her was always to turn one's attention to the child, to "follow the child".
Dr. Montessori believed that by giving children some freedom in a specially prepared environment that was rich in activities, children learned to read on their own, chose to work rather than play most of the time, loved order and silence, and developed a real social life in which they worked together instead of competing against one another (Standing, 1952).
The teacher must pay attention to the child, rather than the child paying attention to the teacher.
The child proceeds at his own pace in an environment controlled to provide means of learning.
Each of them is self-correcting, thus enabling the child to proceed at his own pace and see his own mistakes.
If you were to look inside a Montessori classroom, you would get the impression of “controlled chaos” because each child would be quietly working at his private encounter with whatever learning task he or she chose (Montessori in Perspective 1966).
The Montessori Method is based on the premise that the child wants to learn, and independence and order are key. The child, given primary respect, makes spontaneous choices within a prepared environment, and is “free to create himself.” She believed that children learned through exposure to cultural activities. The teacher’s role was not to teach, but to prepare and arrange a series of learning opportunities which each child can move through instinctively. Maria Montessori concluded that children build themselves from what they find in their environment.
Children learn best by interacting with concrete materials and by being respected as individuals. The teacher's role is primarily in organizing materials and establishing a general classroom culture. Most activities are individual, though the children interact in groups in some activities.
The Montessori method is based on the premise that the child wants to learn, and independence and order are key.
……..educational revolution that changed the way we think about children more than anyone before or since?
THEN THE EDUCATION OF THE INTELLECT. | http://montessorischoolhouse.ca/aboutmontessori.html |
Following its “New Silk Roads” policies to improve connectivity with neighbouring countries in Asia, China proposed earlier this year to establish a “Trans-Himalaya Economic Region” to be led by India and itself. Details of the proposal are not clear but they should focus on building four trans-Himalayan economic corridors to connect South Asia with Central and East Asia.
Commentary
CHINA’S EMERGENCE as the “Factory of the World” based on its focus on exporting labour-intensive manufactures is well-known. Less well-known is the role that infrastructure played in this strategy. In the short run, infrastructure development boosts investment and economic growth. In the longer run, quality infrastructure boosts productivity of a county and enhances the competitiveness of its exports.
A recent issue of The Economist magazine cites a McKinsey Global Institute report which finds that from 1992 to 2007 China spent 8.5% of its GDP on infrastructure, well over the developing country norm of 2-4%. During the period 1992 to 2007 it built 35,000 km of highways at a cost of $120 billion.
China’s infrastructure spree
China’s push for infrastructure development within its borders picked up pace with the Western Development or the Go West policy implemented in 2000. Prior to this policy China’s development was confined to the eastern coastal region of the country. China’s success in attracting investment into the coastal special economic zones made the country the fastest growing economy in the world. But it also led to widening economic disparity between the coastal region and the rest of the country specially the inner western part of the country. The Go West Policy sought to address this disparity by building basic infrastructure towards the country’s hinterland and by attracting investment in the western region.
Last year, China came up with the “New Silk Roads” policies to enhance connectivity with its neighbouring countries. These policies have two components. First, Xi Jinping, the President of China, made a call for a “Silk Road Economic Belt” with Central Asia. Second, a “21st Century Maritime Silk Road” is also to be developed to connect China with ASEAN initially and ultimately with South Asia as well.
China’s actions have led to the revival of the Northern Silk Road. Cities in inner provinces, such as Kunming, Chongqing, Chengdu, Xi’an, and Xining have emerged as major metropolitan cities with urban infrastructure projects paralleling those in the coastal areas. China has built an east-west railway line to connect far-flung cities like Urumqi and Kashgar to Xi’an and the coastal cities. This railway line has been extended to Moscow, using Central Asia as an economic corridor, and then on to Duisburg (in Germany) to become the China-Europe railway line. Cross-country East-west pipelines such as the Kazakhstan-China and Central Asia-China pipelines have also been built.
Together with India which is actively implementing its Look East policies, China is building the BCIM Economic Corridor to connect the Yunnan province of China with Myanmar, Bangladesh, and India. This is an important segment of the less well-known Southern Silk Road of old.
Himalayas not a barrier to connectivity
In June this year, the Chinese Ambassador in New Delhi, Wei Wei, proposed to establish a “China and India double-engine powered Trans-Himalaya Economic Growth Region (THEGR)” so that the two countries could interconnect and prosper. Like many such proposals from China, details are not known as yet. Nonetheless, the proposal is welcome as it addresses an important missing link in attempts to promote the Silk Roads of the bygone era.
It is expected that establishing new economic corridors between India and China through Nepal would be one component of the recent Chinese proposal. Another would be establishing India-China connectivity through the Nathu La pass in Sikkim. Recently the Global Times published by the ruling Communist Party’s official People’s Daily said that the extension of the Beijing-Lhasa railway to Shigaste, a Chinese city close to the Nepal border, would open next month. It also mentioned that the railway line would be extended by 2020 to two separate points, one on the border of Nepal (Kerung) and the other on the border with India and Bhutan.
Trans-Himalayan economic corridors
In a recent study prepared for the Asian Development Bank (ADB), a colleague and I have conceptualized four multimodal Trans-Himalayan Economic Corridors (THECs) beginning in New Delhi and Kolkata, passing through Kathmandu and Tibet, with two turning east to Southeast Asia and another two turning west to Pakistan, Afghanistan and Central Asia. We have also proposed that the BCIM project be expanded to cover all of the SASEC (South Asia Sub-regional Economic Cooperation) countries including Nepal and Bhutan.
China’s “THEGR” proposal should focus on the four THECs. This is because complemented by the three economic corridors in the Greater Mekong Sub-region and the six in Central Asia, the THECs would lead to a seamless Asia extending all the way from Central Asia to South Asia and East Asia and create a “win win” situation for all countries.
Just as it did in the Greater Mekong sub-region and in Central Asia, the ADB should carry forward the idea of the four THECs as a “facilitator, financier, honest broker, and technical advisor.” The THECs will have to be put together like pieces of the jigsaw puzzle, that is one at a time, and for which new sources of financing, in addition to the old ones, are the newly-established BRICS bank and the soon to be established Asian Infrastructure Investment Fund. | http://www.newbusinessage.com/MagazineArticles/view/929 |
1. What is the postmortem interval (PMI), which is also sometimes referred to as the postmortem index? How can you use forensic entomology assist in determining the PMI?
2. Other than PMI, what are three other uses for insects in death investigations and how can this help a death investigation?
3. List the six basic stages for the collection of insect evidence for entomology examination.
Byrd, J. H. (2013, July 9). Forensic entomology. Retrieved from
https://emedicine.medscape.com/article/1780557-overview#showall
Joseph, I., Mathew, D. G., Sathyan, P., & Vargheese, G. (2011, July-December). The use of insects in forensic investigations: An overview on the scope of forensic entomology.
Journal of Forensic Dental Science, 3(2), 89-91. Retrieved from the U.S. National Library of Medicine, National Institutes of Health website:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3296382/
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe. | https://collewriters.com/2022/11/28/apa-7answer-each-question-thoroughlymin-2-referencesmin-700-words-total-not-including-referen/ |
One of the ways to not have to crowed your kids rooms with shelves and cupboard is by having l shaped white kinds bookshelves and toy shelves. L shaped book and toys shelves integrated with their bed will definitely save spaces. The design of the bed is it can be in high structured bed where underneath the bed, there are some shelves to put their toys. They shelves are spacious or many depends on your preference. While next to the shelves on the other wing of the bed, there attached a bookshelves and little desk for your kids to study and put their books. Kids Room. | http://www.footcap.com/tag/bunk-beds-kids/ |
This year’s Christmas Revels production will take audience members to a holiday celebration in a small Quebec village, complete with French-Canadian folk music and dancing styles from the 19th century.
The 35th annual Christmas show — which opens Saturday — centers around the travels of five voyagers leaving their Quebec town, their adventures on a magic flying canoe and their hopes of making it back to the village in time to celebrate the holidays. As the story unfolds, the audience will learn about French settlers in Canada during the time period, along with the traditions created in the New World when mixed with those of their British counterparts.
“You get this window on a culture, and that’s very meaningful to the audience,” said Greg Lewis, the Washington Revels’ executive director and a performer in the show at George Washington University’s Lisner Auditorium.
The show’s music includes songs in French and in English, giving audience members the chance to sing along with the traditional tunes and dance to the music of brass instruments, flutes, a violin and an accordion. Cast members dance through the aisles as well as on the stage, clapping and tapping their feet as they go.
Lewis said he made audience participation a priority when organizing the show. Featuring a conductor who faces the crowd, the show will include call-and-response music, which allows audience members to repeat lines being sung by cast members. They can also follow along with the lyrics printed in the program.
He added that part of the “magic” of the show is the educational aspect, which allows both the cast and audience to immerse themselves in the French culture and language. Even the roughly 20 children in the cast are taught to pronounce the lyrics and dialogue in French, Lewis said.
“We spend a tremendous amount of time on authenticity, whether it be on costumes, pronunciation, and a huge amount of time on learning languages, not to speak but to pronounce,” Lewis said.
The show is historically accurate in part because of Steve Winick, an eminent expert on Quebec culture and a lead actor and singer in the production. Winick works in the Library of Congress’ American Folklife Center, and performed in 2008, the last time the Christmas Revels offered a version of the Quebec-themed show.
Winick was introduced to the Washington Revels when the show’s organizers visited the Library of Congress for research into the authentic songs from the period, he said. He landed the leading role after he sang one of the folk tunes he didn’t have a recording for — impressing the Revels organizers both with his musical abilities and his knowledge on the topic.
The show’s main characters represent a historically significant element of Quebec culture, Winick said, as voyagers who traveled to sell furs to Native Americans comprised an important occupation during the time period.
The show will include singing from adult, teen and children’s choirs, bringing together more than 100 singers, dancers and actors in the cast, ranging in age from 8 to 80 years old.
Helen Fields, a chorus member in the show, will mark her 10th performance as a cast member for the Christmas Revels this year. She said she went to the show many times as a child, starting when she was in eighth grade, and has made attending the Christmas Revels’ annual show part of her family’s holiday celebration.
“It didn’t feel like Christmas until we saw the Christmas Revels,” she said of her family’s tradition. “That is what really started the season for my family.”
She said one main aspect that has drawn people annually to the Christmas Revels is the sense of community created by the audience participation. She calls the cast her personal “village,” which includes cast members who have been performing in the show since it began in D.C. in 1983.
Fields added that organizers assign cast members stage “families” — she has a stage husband and two children — that strengthens the sense of community among the cast members. The families stand together in group scenes, making it easier for the directors to instruct the cast.
Fields said her favorite scene is called “Chasse Gallerie,” which features the voyagers coming home on a magical canoe and the villagers swirling onto the stage holding food plates and stage houses.
“It’s fun to tell this story and create this experience for the audience,” Fields said. “It feels like inviting an audience to be part of the village.”
The Quebec government and local French cultural organizations have enthusiastically promoted this year’s show using their social media pages and other methods, said Jo Rasi, the marketing and programs director for the Washington Revels.
But Rasi also expects a good number of annual attendees alongside any first-timers among the nearly 1,500 people expected during each performance of the show.
“We have families that make this their holiday tradition every year,” she said. “Nobody seems to get tired of the Revels celebration.”
The show will be running from Dec. 9 through 17 for a total of eight performances at Lisner Auditorium, 730 21st St. NW. Tickets range from $12 to $50. For details, visit revelsdc.org. | https://currentnewspapers.com/holidays-in-washington-annual-revels-show-evokes-historic-quebec-village/ |
The security researcher Axelle Apvrille revealed that infect Fitbit trackers with a malware is too easy.
Axelle Apvrille has managed to infect FitBit Flex fitness tracker and uses them as infection vector to spread the malicious agent to any computers the devices are connected to.
The expert exploited a vulnerability in the Bluetooth that she discovered in March, despite the flaw was reported to the manufacturer it has yet to be patched.
Axelle Apvrille discovered that the popular FitBit Flex fitness trackers have the Bluetooth port open, this security issue could allow a nearby attacker to deliver an infected packet that is able to compromise the wearable object … in less than 10 seconds.
According to Apvrille, the rest of the attack occurs by itself, and the attacker doesn’t have to be near for that.
concerning that scenario of infecting a fitness tracker, it’s important to read the slide on limitations 1/ it’s a PoC, no malicious code
— Axelle Ap. (@cryptax) 21 Ottobre 2015
“[When] the victim wishes to synchronize his or her fitness data with FitBit servers to update their profile … the fitness tracker responds to the query, but in addition to the standard message, the response is tainted with the infected code,” Axelle Apvrille explained to The Register.
“From there, it can deliver a specific malicious payload on the laptop, that is, start a backdoor, or have the machine crash [and] can propagate the infection to other trackers (Fitbits).”
The wearable devices use proprietary technology, Axelle Apvrille searched for security issues by reverse-engineering the messages the device exchange the USB Bluetooth dongle.
The expert conducted a series of tests that allowed her to discover other security issues related to the on the Fitbit trackers, including the way to manipulate the information received by the devices, mimicking motion even when the Fitbit trackers are stopped.
Apvrille presented the findings of her research on the Fitbit trackers at the Hack.lu conference in Luxembourg .
(Security Affairs – Fitbit trackers, IoT)
UPDATE October 23, 2015
I was contacted by a person on behalf of the Fitbit company that emailed me the following statement that provides further info on the scenario described by the Apvrille.
“On Wednesday October 21, 2015, reports began circulating in the media based on claims from security vendor, Fortinet, that Fitbit devices could be used to distribute malware. These reports are false. In fact, the Fortinet researcher, Axelle Apvrille who originally made these claims has confirmed to Fitbit that this was only a theoretical scenario and is not possible. Fitbit trackers cannot be used to infect users’ devices with malware. We want to reassure our users that it remains safe to use their Fitbit devices and no action is required.
As background, Fortinet first contacted us in March to report a low-severity issue unrelated to malicious software. Since that time we’ve maintained an open channel of communication with Fortinet. We have not seen any data to indicate that it is possible to use a tracker to distribute malware. | https://securityaffairs.co/wordpress/41313/hacking/fitbit-trackers-hacking.html |
I have a question on interpreting coefficients in a regression model. To be specific, the regression model is as given below:
$$y=a+b_1x_1+b_2x_2+b_3Z+b_4Zx_1+b_5Zx_2$$
where
y= continuous dependent variable x1= independent variable all values are positive (min=0) x2= independent variable all values are negative (max=0) Z = Normalized variable with values between (0,1)
Given this set up, how would we interpret
a) positive and significant coefficient b1 b) negative and significant coefficient b4 c) What can we say about a joint test of b1+b4=0
x1 and x2 represent the same variable X (continous) and the goal is to allow for different slopes when X is positive and negative. Any help is much appreciated.
The question is motivated from the regression output in the following paper
Greve, Henrich R. "A behavioral theory of R&D expenditures and innovations: Evidence from shipbuilding." Academy of management journal 46.6 (2003): 685-702. | https://stats.stackexchange.com/questions/273203/interpreting-regression-model-output |
On the same day Ontario courts announced a two-month shutdown of all non-urgent family trials and criminal trials, the province expanded its efforts to confront the impending chaos in the corrections system.
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The government extended temporary absences to intermittent inmates, meaning those offenders will not have to report to a correctional facility every weekend to “avoid cycling individuals back and forth” between the community and a correctional facility.
tap here to see other videos from our team.
'A looming and predictable disaster': Defence lawyers sound alarm over jails amidst Ontario court chaos Back to video
The response to the novel coronavirus crisis was outlined Friday in a joint statement from Deputy Premier and Minister of Health Christine Elliott and Solicitor General Sylvia Jones, in an effort to “protect our frontline workers and our health care system from the burden an outbreak in our correctional system could cause.”
Senior corrections officials will now be allowed to expand the use of temporary absences, the ministry announced, and the Ontario Parole Board will be able implement alternatives to in-person hearings by “electronic or written means, rather than solely in-person.”
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Longer-term temporary absences, according to the ministry, will allow for early release of inmates who are near the end of their sentence.
“To ensure public safety, inmates would be carefully assessed to ensure they are a low risk to reoffend,” the solicitor general stated. “Those inmates who have been convicted of serious crimes, such as violent crimes or crimes involving guns, would not be considered for early release.”
With security guards posted outside the Ottawa courthouse this week allowing only the most essential parties in, defence lawyers, Crown attorneys, judges, clerks and staff on the inside have been working furiously to process as many urgent cases as possible.
To limit the number of folks in courtrooms, hearings on Friday were held remotely using cellphones and video conferencing platforms like Zoom. Courtrooms that were brimming with 40 people earlier this week were reduced to one or two by Friday, including the presiding judge.
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For urgent in-custody matters, accused people appeared by video, and guilty pleas and bail hearings were done remotely. One issue that arose over the verification of sureties was resolved Friday as lawyers had sureties take selfies with identification and email or text it in — believed to be a first in Canadian legal history.
Over the last two days, according to Karin Stein, president of the Defence Counsel Association of Ottawa, the Ontario Court of Justice has been functioning “almost completely remotely.”
“Everybody came together to make it work — the bench, the clerks, the police and counsel. Extra phones have been brought in to facilitate contact between the accused in custody and (their lawyers).
“Crown and defence were for the most part participating via teleconference with the courts and in many cases the accused did not have to be brought in from either the police station or the detention centre and were also able to participate remotely,” Stein said. “There was a significant reduction in the number of people required to be at the courthouse.”
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The DCAO also stepped in when Legal Aid Ontario removed its lawyers earlier this week to cover the cases normally represented by duty counsel.
On Friday, criminal defence lawyer Solomon Friedman participated in bail hearings remotely, teleconferencing from his dining room while his kids did homework.
“Today demonstrated what defence lawyers have long known and said to anyone willing to listen — there is tremendous room for creativity, innovation and adaptation in our criminal justice system. I am enormously proud of the fact that, when the going got tough — or even appeared impossible — court staff, defence counsel, prosecutors and the court didn’t take no for an answer. We got it done,” Friedman said.
But while the pandemic crisis has spurred some technological innovation and seen some positive proactive measures at court, according to defence lawyer Michael Spratt, “it remains to be seen if the jails are doing enough to avert a looming and predictable disaster behind bars.”
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“No solution is going to be perfect but doing nothing is going to lead to courthouses and jails becoming petri dishes of infection that risk spreading the virus and ultimately resulting in deaths, given the vulnerable populations involved.
Courts have encouraged social distancing by mandating the use of modern technology to file documents or to replace routine, non-essential court appearances, Spratt said. “Things that, ironically, the defence bar has been asking for for years and has been told were too difficult or cumbersome to bring into practice.”
While the justice system remains “in flux” during the crisis, Spratt said they have held remote hearings, bail hearings where sureties don’t need to attend court and instead send in pictures of their driver’s licences, and bail discussions over the phone and email in place of an in-court appearance.
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“But it’s not enough for each lawyer to seek bail for their client, the system simply doesn’t have the capacity for individual defence lawyers to schedule all these bail hearings and conduct them. We’re trying to move water that would normally go through a firehose through a sprinkler,” Spratt said.
But while courts have shown they can “accommodate and survive” the disruption, Spratt has been outspoken in calling on the province to act just as swiftly to depopulate the jails to avoid a potential “firestorm.”
“The solution is very simple,” Spratt said. “Everyone serving a sentence or on remand (awaiting trial) for a non-violent offence should be released. Either released on conditions of bail and monitored in the community, or released on a temporary absence permit if they’re serving a sentence.
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“There is no reason for a young man serving the last two months of a fraud sentence to be in jail,” Spratt said. “And there’s no reason for someone who is awaiting a trial for shoplifting from a liquor store or other property offences to be in custody waiting for bail right now… We’re not talking about releasing murderers or violent offenders, and when we’re looking at court delays these are not cases that are going to be thrown out of court due to delays. This is clearly a very exceptional circumstance…
“The sad reality is that our jails at the best of times are filthy, germ-ridden and overcrowded. And now with COVID-19 one case in the jail will cause a firestorm that will not only cause infection and death and risk community safety, but will compound the delays and the scheduling chaos that we’re going to see in court when court starts back up again.”
As part of Friday’s announcement the Ontario government said it “continues to evaluate all options to limit the possible spread of COVID-19 within our correctional system” beyond the regulatory amendments already implemented.
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Is it safe to eat takeout food during a pandemic? | https://ottawacitizen.com/news/a-looming-and-predictable-disaster-defence-lawyers-sound-alarm-over-jails-amidst-ontario-court-chaos/ |
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Origin and Habitat: Garden origin
Synonyms:
Obregonia denegrii f. aurata hort.
Accepted name in llifle Database:
Obregonia denegrii Frič
Život v Přír. 29(2), 14 [Kakt. a Succ. 3] fig. (1925); cf. Gray Herb. CardCat., Issue 114.
Synonymy: 3
- Obregonia denegrii Frič
- Ariocarpus denegrii (Frič) W.T.Marshall
- Strombocactus denegrii (Frič) G.D.Rowley
Obregonia denegrii f. cristata hort.
Accepted name in llifle Database:
Obregonia denegrii f. monstruosa hort.
Description: Obregonia denegrii f. surata (schizochromic form), only deviate from the standard species for the stem which is uniformly yellow due to the absence (or very reduced production) of chlorophyll pigments. This form with yellow stems is very attractive and highly prized. This schizochromic form is always seen grafted on stronger columnar species, and cannot can be grown on its own roots. The typical Obregonia denegrii (commonly known as the "artichoke cactus") is among the most famous of all cacti for is unique shaped stem. It grows almost always as a solitary plant levelled with the ground, with the sunk and woolly apex. It is considered an intermediate form between Ariocarpus and Lophophora.
Variegation, albinism & schizochromism.
Variegation: A variegated plant has sectors, patches or stripes with two or more different colours, even distinct shades of green. Plants with variegated stems or leaves are often attractive and highly prized. In most species the stems or leaves are normally green, and variegated epidermis is an uncommon mutation, termed a chimera. A chimeral variegation is due to losing the ability to produce chlorophyll in some of the plant’s tissue, so that this tissue is no longer green. Tissues lacking chlorophyll are usually white or pale yellow coloured (due to carotenoid pigments) or red (due to betalain or anthocyanin pigments) contrasting with the normal green tissue. There are several forms of variegation, depending on the tissues that have been affected. The variegation in some forms is unstable. The extent and nature of the variegation can vary, and sometimes the plant will return to the green form. In others it is stable and does not change under normal conditions. Because the variegation is due to the presence of two kinds of plant tissue, propagating the plant must be by a vegetative method of propagation that preserves both types of tissue in relation to each other.
Albinism: Every once in a while a plant exhibits albinism (completely lacking chlorophyll pigment). This means that its tissue is unable to carry out photosynthesis. The result is a completely cream-white plant. This plant will be weaker than a green plant, and albinism is generally a fatal trait (it can't produce its own food and it's not getting it from anything else). Without chlorophyll, the albino plant has no way to manufacture the food needed for survival and growth to maturity. This implies that these plants cannot survive on their own roots and necessitate being grafted on a normal green plant that provides food. Some of these albino plants are indeed very popular, and sought after by collectors.
Schizochromism: The yellow or red appearance of some plants is more precisely caused by another aberration called "schizochromism". Here, though, the specific green pigment (chlorophyll) is missing: every other pigment is present at normal levels. The dominant green colouration is lost, but the plant will still more than likely have normal other pigments that give the yellow overall appearance of stems and the red colouration of spines.
Subspecies, varieties, forms and cultivars of plants belonging to the Obregonia denegrii group
- Obregonia denegrii Frič: has an unique artichoke shaped stem that grows levelled with the ground, with a sunk and woolly apex. Distribution: Mexico (Tamaulipas: Ciudad Victoria)
- Obregonia denegrii f. aurata hort.: schizochromic form with uniformly yellow stems due to the absence (or very reduced production) of chlorophyll pigments.
- Obregonia denegrii f. cristata hort.: crested form. The stem which is fan shaped up to 30 cm (or more) long with age.
- Obregonia denegrii f. monstruosa hort.: monstrous form. Has a free branching habit (Obregonia denegrii is always solitary) with stocky, rounded tubercles with woolly white areoles, the spines are also shorter.
Cultivation and Propagation: Variegated and albinos cacti are regarded as choice and difficult in cultivation, but despite that many of them are relatively easy to grow. But be aware that they cannot tolerate prolonged exposure to direct sun light (especially during the hottest summer days), so grow them in half-shade or under filtered sun. They are sometime seen as grafted plants, but many grow well on their own roots, too.
On the contrary, the albinos can survive only if grafted on a strong green base.
Use mineral well-permeable substratum with little organic matter (peat, humus). Water sparingly from March till October and keep perfectly dry in winter at temperatures from 5 to 15 degrees centigrade. (In general these plants are more tender and cannot endure freezing temperatures ) In the rest period no high atmospheric humidity!!
Propagation: Plants are usually grafted onto a more vigorous and easier columnar stock. | https://llifle.com/Encyclopedia/CACTI/Family/Cactaceae/29903/Obregonia_denegrii_f._aurata |
What color is 919EB9?
The RGB color code for color number #919EB9 is RGB(145, 158, 185). In the RGB color model, #919EB9 has a red value of 145, a green value of 158, and a blue value of 185. The CMYK color model (also known as process color, used in color printing) comprises 21.6% cyan, 14.6% magenta, 0.0% yellow, and 27.5% key (black). The HSL color scale has a hue of 220.5° (degrees), 22.2 % saturation, and 64.7 % lightness. In the HSB/HSV color space, #919EB9 has a hue of 220.5° (degrees), 21.6 % saturation and 72.5 % brightness/value.
Color Codes - Color Space Conversions
HEX #919EB9 color codes / color number / color space conversions - RGBA, HSL, HSV/HSB, HYZ, CMY
|
|
RGBA - RGB(145, 158, 185)
|Red||145 (56.9%)|
|Green||158 (62.0%)|
|Blue||185 (72.5%)|
|Alpha||1 (100.0%)|
|
|
HSL
|Hue||220.5°|
|Saturation||22.22 %.|
|Lightness||64.71 %.|
|LRV||~ 34 %|
|Munsell Color System||3.2PB 6.3/3.2|
|XYZ||X : 32.66
|
Y : 33.98
Z : 50.74
|YXY||Y1 : 33.98
|
X : 0.28
Y2 : 0.29
|CMY||C : 43.14%
|
M : 38.04%
Y : 27.45%
|
|
CMYK
|Cyan||21.62 %.|
|Magenta||14.59 %.|
|Yellow||0.00 %.|
|Key||27.45 %.|
|
|
HSV/HSB
|Hue||220.5°|
|Saturation||21.62 %.|
|Brightness / Value||72.55 %.|
|CIE-Lab||L : 64.94
|
A : 1.32
B : -15.5
|CIE-Lch||L : 64.94
|
C : 15.55
H : 274.86
|CIE-Luv||L : 64.94
|
U : -8.22
V : -23.68
|Hunter-Lab||L : 58.29
|
A : -1.99
B : -10.8
Color Names and Paint
Color Name of HEX #919EB9
Paint color for Hex #919EB9
Benjamin Moore
Behr
Sherwin Williams
PPG Paints
Color Combinations
#919EB9 Color Palettes and Scheme Combination
Monochromatic Color Palette
Monochromatic colors belong to the same hue angle but different tints and shades. Monochromatic color palette can be generated by keeping the exact hue of the base color and then changing the saturation and lightness.
Analogous Color Palette
Analogous colors are a group of colors adjacent to each other on a color wheel. Group of these adjacent colors forms Analogous color scheme Palette. Analogous Palette can be generated by increasing or decreasing the hue value by 30 points.
Here is the Triadic and Tetradic Color Scheme of ~ Cool Gray. The triadic color palette has three colors separated by 120° in the RGB color wheel and tetradic colour scheme composed of two sets of complementary colors in a rectangular shape on the color wheel.
Hexadic Color Palette
Hexadic color scheme palette is derived from drawing a hexagon on a color wheel. The palette contains three pairs of complementary colors, each colors are separated by a 120-degree hue angle.
Complementary Color Palette
Complementary or Dyadic color combination is composed using two colors opposite each other on the color wheel. Then the color Palette is be generated by changing the lightness/brightness of these two colors.
Split-Complementary Color Palette
Split-Complementary color combination contains three colors, a base color and secondary colors of complementary color. | https://www.colorxs.com/color/hex-919eb9 |
Purpose: Reliable correlation between internal tumor and external marker motion is important for effective radiation treatment based on external signal, such as external gating and the CyberKnife Synchrony System. This study is to analyze the internal/external correlation stabilities by calculating the missed tumor volume. Methods and Materials: Internal tumor and external marker motion of eight patients with multiple fractions were acquired simultaneous at 30Hz. Internal signal is the 3D tumor motion and external signal is the 1D motion of abdominal surface. The internal/external correlation was constructed using the first 3 breathing cycles. The correlated tumor position was calculated based on this correlation model with external signal. The missed tumor volume was calculated based on the distance between the internal and the correlated positions at each acquired data point. The inter‐patient, inter‐fractional, and intra‐fractional variations of the missed volume percentage were analyzed. Results: The results of a solid sphere tumor with different sizes were performed based on the true patient motion data. For a sphere tumor with 20mm diameter, the average missed volume percentage averaged over all treatment fractions of one patient was between 5.14% and 15.3%. The percentages changed from one fraction to another. The daily percentages varied from 3% to 6.5% for the patient with the smallest average patient‐wide missed percentage. The intra‐fraction motion changed from one breathing cycle to another. In one fraction of a patient, the average cycle percentages changed from 6% to 26%. Even within the same breathing cycle, the missed percentages changed greatly from one breathing state to another, with larger values (∼30%) at the inhale and exhale states and smaller value (∼3%) at the end‐of‐exhale state. Conclusions: Strong correlations between internal and external motion exist but change overtime. Verification and updating the correlation in real‐time delivery is required for effective treatment. | https://indiana.pure.elsevier.com/en/publications/suffj115-evaluation-of-internalexternal-correlation-with-missed-v |
From 1723 he was employed as Thomaskantor (cantor at St. Thomas) in Leipzig. He composed music for the principal Lutheran churches of the city, and for its college's pupil ensemble Collegium Musicum. From 1726 he printed a few of his keyboard and organ music.
He acquired the title of 'Royal Court Composer' from Augustus III in 1736. Bach's health and imaginative and prescient declined in 1749, and he died on 28 July 1750. Bach enriched established German kinds by way of his mastery of counterpoint, harmonic and motivic organisation, and his adaptation of rhythms, varieties, and textures from abroad, significantly from Italy and France. Bach's compositions embody hundreds of cantatas, both sacred and secular.
He composed Latin church music, Passions, oratorios, and motets. He typically adopted Lutheran hymns, not solely in his bigger vocal works, however for instance additionally in his 4-part chorales and his sacred songs. He wrote extensively for organ and for other keyboard instruments. He composed concertos, as an example for violin and for harpsichord, and suites, as chamber music as well as for orchestra.
In the final many years of his life he reworked and prolonged many of his earlier compositions. He died of issues after eye surgery in 1750 on the age of 65. List of compositionsSignatureJohann Sebastian Bach (31 March [O.S. 21 March] 1685 – 28 July 1750) was a German composer and musician of the Baroque interval.
The Bach household already counted a number of composers when Johann Sebastian was born as the last youngster of a metropolis musician in Eisenach. After being orphaned at age 10, he lived for 5 years together with his eldest brother Johann Christoph, after which he continued his musical formation in Lüneburg.
In August 1703, he grew to become the organist on the New Church, with light duties, a relatively generous salary, and a brand new organ tuned in a temperament that allowed music written in a wider range of keys to be played. Bach was born in 1685 in Eisenach, in the duchy of Saxe-Eisenach, into an in depth musical family. His father, Johann Ambrosius Bach, was the director of the city musicians, and all of his uncles were professional musicians. His father in all probability taught him to play the violin and harpsichord, and his brother Johann Christoph Bach taught him the clavichord and uncovered him to a lot of the modern music. Apparently on his own initiative, Bach attended St. Michael's School in Lüneburg for two years.
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Six point eight million: that’s the number of children who are already students in school systems with trans-inclusive policies in place, allowing transgender students to play on teams with their correct gender. Throughout these systems, few to no issues have arisen. These school systems use their policies to create an all-inclusive environment for both cisgender and transgender youths in their athletic programs, all while maintaining a level playing field.
Recently, several states have passed or proposed bills banning transgender students from playing in-school sports on teams with their correct gender, instead forcing them to play as the gender they were assigned at birth.
Shannon Clawson, the Outreach Manager at Georgia Equality, calls these bills “solutions in search of a problem,” comparing them to the slew of bathroom ban bills that were proposed several years ago, such as the HB2 bill in North Carolina.
Clawson also emphasized that allowing transgender children to participate in school sports as their correct gender not only helps to affirm their gender identity and make them feel safe and welcomed in a supporting environment, but also has the same benefits that school sports have for any other student. They create tight-knit friend groups which can foster a safe space for students as well as teaching leadership, teamwork, and decision-making skills which have real world benefits throughout life. Allowing transgender children to participate on the correct teams can also help benefit their mental health, which is key for transgender children. According to the CDC, “35% of trans students have already attempted suicide by the time they reach high school.” According to Clawson, “the last thing we need are policies that further isolate and stigmatize these children.”
Many politicians have claimed that these bills are here to increase fairness and are being drafted in order to “protect” cisgender female athletes, but Clawson points out that the best way to help female athletes would be to provide better funding for their programs, increase Title IX reporting, and support female coaches. Many of these bills require that students “confirm their gender.” While the bills are not particularly clear about the processes that would be used to confirm a child’s gender, Clawson points out that these bills state nothing about intersex children or cisgender children who do not conform to traditional gender stereotypes. Any child going through puberty is prone to body image issues and insecurities regardless of their gender identity, and being forced to go through invasive examinations or submit personal medical records could be a traumatizing experience that could stay with a child as they develop.
Many of the bills recently passed or proposed have also targeted the medical treatment of transgender children. According to a BBC World News report, a recent ban passed by the Republican-controlled House and Senate in Arkansas (despite being vetoed by the Republican governor for being what he deemed a “vast government overreach”) “in effect bans doctors from providing puberty blockers, or from referring them to other providers for the treatment.”
When commenting on these medical bans, Clawson says that these types of bans are the “hardest on transgender children and parents.” Treatment that can help put off the effects of puberty for transgender children is lifesaving, and criminalizing the doctors who provide this essential care to these children helps no one. Clawson says that encouraging doctors to practice in the rural areas of states like Arkansas or Georgia is already difficult enough. Stacking additional legislation against medical professionals does no favors for any politician or constituent seeking a sound medical system in their area.
These bans may seem to be about fairness on the surface, but they are simply working to alienate a small, already vulnerable portion of the population. Treating transgender students as their correct gender from 8am to 3pm, only to treat them as their incorrect gender from 3pm to 5pm, creates a confusing, nonaffirming, and potentially hostile environment. It sends the message to all students that transgender students are not to be treated with respect.
These bans seem to be Republican representatives using buzz words and hot topics to gain support from their followers by perpetuating their fight against trans inclusion in public spaces. Now that the bathroom ban bills have fizzled out, they’re moving on to infringing upon the rights of minors. These bills are harmful not only to transgender children, but to communities, athletic programs, and medical systems as a whole, and they need to stop now. | https://thegavoice.com/news/transgender-sports-bans-are-a-solution-looking-for-a-problem/ |
LEIBAR, Urtzi et al. Grapevine nutritional status and K concentration of must under future expected climatic conditions texturally different soils. J. Soil Sci. Plant Nutr. [online]. 2017, vol.17, n.2, pp.385-397. ISSN 0718-9516. http://dx.doi.org/10.4067/S0718-95162017005000028.
Nutrition is a relevant issue for winegrowers because it influences grapevine growth, berry composition, as well as must and wine quality. In this research, the following impacts on the nutritional status of cv. Tempranillo grapevines were evaluated: simulated 2100 expected CO2, temperature (T) and relative humidity (RH) conditions (FCC; 700 µmol CO2/mol air, 28/18°C day/night and 33/53% RH, day/night) vs. current CO2, T and RH conditions (Curr; 390 µmol CO2/mol air, 24/14°C and 45/65% RH); well-watered (WW) vs. future expected water deficit (WD); and three texturally different soils with different clay contents (41, 19 and 8%). FCC resulted in reduced concentrations in leaf blades of N and Ca at veraison and N and Zn at full maturity. WD resulted in higher leaf blade Na and Mn concentrations at veraison and maturity, respectively compared to WW. However, K concentrations in the leaves and must were higher for WW than WD. Higher concentrations of Ca and Mn were found in leaf blades of grapevines sampled at full maturity from more clayey soils. Even when nutrient inputs exceeded plant extractions, high soil clay content increased the K concentration in must and consequently, could affect wine quality in terms of acidity loss. However, future expected water stress will have the opposite effect, reducing the berry K uptake under high soil clay (41%) conditions.
Palabras clave : Climate change; leaf analysis; potassium; clay content; water deficit. | https://scielo.conicyt.cl/scielo.php?script=sci_abstract&pid=S0718-95162017000200009&lng=es&nrm=iso&tlng=en |
The Center for Creative Cognition, one of the few centers in our country, is dedicated towards education and research in the field of Cognitive Science. Cognitive Science is the study of the mind and helps us to understand the processes involved in representing and retrieving knowledge and its implications. This interdisciplinary field combines ideas and methods from psychology, computer science, linguistics, philosophy, education and neuroscience. Research in cognitive science has a broad scope and application in the field of technology creation, development and implementation, education, health, and social behavior.
The center aims at promoting the understanding of cognition and designing and developing human centered innovations. The center boasts of stimulating teaching-learning environment to cater to the needs of engineering students by being interdisciplinary in nature. The center aspires to be an incubator for promoting and exploring new researches in cognitive science. The center also takes pride in providing the facility of assessment of psychological attributes for counselling and guidance of the students to promote inclusive and harmonious mental wellbeing.
The center is committed to fulfil the following vision and mission since its inception in 2015:
Vision
To be a leader empowering engineering achievement through applied cognitive research
Mission
Empower learners to appreciate and apply cognition in their personal and professionallife
Create critical and creative thinkers who will formulate innovations based on a human-centric engineering approach.
Guide learners in discovering their cognitive strengths and weaknesses and reaching theirfull potential
Conduct multidisciplinary research and consultancy services.
Impact the regional educational ecosystem by empowering educators with cognition.
The primary thrust areas of the center are –
Cognitive Assessment: The center is facilitating the assessment of the cognitive skills and personality of students. Discovering who they are, their purpose, strengths, weaknesses, and motivators can empower students to realize their full potential.
Teacher Training: The center is leading an educational revolution in K-12 area in the state of Telangana by conducting teacher training. The training aims at enabling teachers to understand students, connect with them and empower them using cognitive science.
Cognitive Process in Design Thinking: The center is researching the natural thought processes employed by designers in creative problem solving, identifying issues faced by them, and developing intervention strategies or tools to improve their innovativeness
Human Machine Interfaces: The center is researching the cognitive processes involved in the use of the human-machine interfaces. The insights from this work can lead to the development of user-friendly products.
Dr. Raja Shekar P V
Associate Professor & Head
Dept.of H&Sc
Interests: Design Fixation, Creative Problem Solving, Idea Generation, Learning Strategies, Personality Traits in Design & Entrepreneurship
Email: [email protected]
Mr. Jyoti Tripathi
Assistant Professor
Dept.of H&Sc
Interests: Organizational Psychology, Counseling, Psychometric Testing
Email: [email protected]
Ms. G. Madhuri
Assistant Professor,
Dept.of ECE
Interests: Idea Generation, Problem Solving
Email: [email protected]
Mr. P. Pramod Kumar
Senior Assistant Professor,
Dept.of CSE
Email: [email protected]
Dr. Syed Mushtak Ahmed
Professor
Dept.of ECE
Interests: Cognitive Capabilities, Neuropsychological Disorders
Email: [email protected]
Dr. R. Archana Reddy
Professor
Dept.of H&Sc.
Interests: Social Psychology, Advertisements & Attitude Change
Email: [email protected]
Dr. P V Ramana Rao
Associate Professor
Dept.of H&Sc.
Interests: Memory, Attention, Perception, Human Behavior
Email: [email protected]
Dr. Sridhar Condoor
Professor, Department of Aerospace & Mechanical Engineering,
Saint Louis University, USA
Dr. Bapi Raju Surampudi
Professor, School of Computer and Information Sciences,
University of Hyderabad, Hyderabad
Dr. Narayanan Srinivasan
Professor & Head,
Center of Behavioral and Cognitive Sciences,
University of Allahabad, Allahabad
Dr. Prabir Mukhopadhyay
Associate Professor & Head, Design Discipline,
IIIT D&M, Jabalpur
Dr. Priyanka Srivastava
Senior Research Scientist, Cognitive Science Lab,
IIIT Hyderabad
Dr. Jaison A Manjaly
Associate Professor & Head,
Department of Philosophy & Cognitive Science,
IIT, Gandhinagar
Dr. Ark Verma
Assistant Professor, Department of Humanities and Social Sciences
IIT Kanpur
Mr. Vishnukant Tripathi
Interests: Social Cognitive Neuroscience, Design Fixation & Mitigation, Organizational Psychology, Psychometrics
Email: [email protected]
Ms. Shuchita Gupta
Interests: Visuo-Spatial Perception, Visual Working Memory, Social Psychology, Advertisements & Attitude Change
Email: [email protected]
Ms. Preneeja Peelukhana
Interests: Criminal Psychology, Autobiographical Memory, Affective Memory, Problem Solving, Decision Making, Creative Thinking
Email: [email protected]
Mr. Arukonda Siddartha
Interests: Industrial Engineering, Production Management, Design Fixation
Email: [email protected]
Ms. Sushma
Interests: Data Science, Algorithmic Thinking
Email: [email protected]
Ms. Soumya
Interests: Data Science, Algorithmic Thinking
Email: [email protected]
The center offers the following courses under Cognitive Science Track as an open elective to undergraduate students:
Foundations to Cognitive Science
Design Cognition
Cognitive Management
Psychology
These courses foster the following outcomes:
Apply cognitive science concepts and theories to individual, social, cultural, engineering and management issues
Apply critical and creative thinking to understand human behavior, conceive innovative concepts, evaluate different scenarios, interpret results, and make informed decisions
Identify the customer's/user's needs, abilities, expectations etc. in product design
Evaluate the usability and experience of existing artifacts and systems from a cognitive perspective and identify areas of improvement
Understand the impact of design decisions for its users in terms of perception, acceptance, ease of use, and emotional attachment
Learn the importance of various domains of Psychology to understand human behavior, values and attitudes in organizational setting and enabling them to handle psychological issues of daily life.
The center is advancing applied research in the field of cognitive science. To this, the center continually conducts research in the thrust areas. To accelerate the growth, it applies for grants from the Department of Science & Technology (DST), All India Council for Technical Education (AICTE) and University Grants Commission (UGC). The center actively engages in scholarly publications and innovations by involving faculty and students.
Completed :
Understanding design fixation in Indian engineering students – (2012-15)
Ongoing :
The effect of repeat advertisements and advertisement variations on attitude change of Indians towards social messages
Mitigating design fixation in Indian engineering students
The role of human memory in deceit and fairness
Cognitive driving capabilities in aging adults in India
Design Fixation: A comparison between Native and Foreign Domains, Journal of Engineering Education Transformations, 29, 35-39 (2015).
An Experimental Investigation of Divergent Thinking Abilities in Engineering Design Activity, Elk Asia Pacific Journal of Mechanical Engineering Research, 01, 11-16 (2015).
Analysis of Divergent Thinking in Indian Engineering Students, Journal of Engineering Education Transformations, 29, 98-102 (2015).
Measuring Levels of Design Fixation in Indian Engineers, Proceedings of 11th IRF International Conference, 01, 4-7 (2015).
Measuring the Impact of Design Fixation on Indian Engineering Students, Proceedings of the International Conference on Transformations in Engineering Education, 02, 307-314 (2014).
Behavioral aspects of an Entrepreneur – A Cognitive Approach, Proceedings of International Conference on Next Generation Education for Entrepreneurial Engineers (ICNGE3) 01, 34-37 (2014).
The center conducts educational outreach programs for the students at SREC and the local community. Currently, the center engages in five main outreach activities on a regular basis.
Workshops :To enhance the understanding of the students about how cognitive science helps in innovation, creativity and effective problem solving.
Discussion Forum :Interdisciplinary discussion forums to understand the academic needs of students and provide cognitively effective solutions to those needs are periodically conducted. It also conducts discussion forums with experts to decide upcoming work scope of the center.
CogSci Showcase :The showcase is a pack of 5 different hands-on experiences (activities) themed around the notion of ‘neuroplasticity’ - one of the most fundamental biological properties of the brain.
Awareness Program : Awareness programs are organized, time to time, inside the campus and nearby community to make individuals aware of the field and its application in daily life.
News Letter : A quarterly newsletter informing the activities and advances in the field of cognitive science as well as departmental activities is being published.
The center is involved in imparting training and internships to enhance the teaching skills and research aptitude among trainees and interns
Teacher Training Program :Teacher Empowerment through Cognition, is a teacher training program where our team of faculty visit various nearby schools in Warangal to mentor teachers to strengthen their current pedagogical practices and tools, particularly related to educational technology, using theories of learning and cognition.
Guest Lectures : Interdisciplinary experts in the field visit the campus and share their knowledge in the form of lectures to broaden the knowledge of students and faculty.
Lecture Series :Weekly lecture series on various interdisciplinary topics are delivered by core faculty of the center.
Awareness Program : Undergraduate engineering students are exposed to LEGO programmable blocks. Students prepare 3D-models to explore and assess their visuo-spatial abilities
Internship Program : The internship program attracts exceptional students across the departments to spend a summer at the center. The intern program aids in integrating the theory and practice. The participants benefit by participating in the professional development programs conducted in the center and they are equipped with skills of developing a scholarly work - research paper, patent or product - requiring innovation and technical skills.
Center organizes various competitions to promote innovative and creative thinking among student community. The center conducts following competitions:
Idea Fest: Every semester, students identify a local problem and submit their ideas, through a rigorous collaborative screening process, on how best to solve that problem. The students pitch their ideas and the best ones are rewarded and mentored. He/She also gets an opportunity to be incubated, to achieve the entrepreneurial potential of his/her idea.
Logo Design Competition: Students are encouraged and mentored to participate in logo design challenges conducted by Creative Corner of mygov.in.
400 sq. ft. Creative Cognition Laboratory houses the state-of-the-art infrastructure to conduct research in cognitive science. The resources include:
LEGO MINDSTORMS Education (LME) EV3 Robotics
Tobii Pro X2-60 Eyetracker
Psychometric Tests
Theory of Inventive Problem Solving-Triz (Innovation Workbench, Problem Formulator, Ideation Brainstorming)
Computing Facilities (Desktops & Laptops)
Video Conferencing Facilities
Video and Audio Recorders
The center has in-house Psychological Counselling Cell that is equipped to assess the following psychological attributes:
Personality
Intelligence
Attitudes
Values
Learning & Thinking Styles
Leadership
The cell also provides counselling to the students who suffer from a variety of problems such as stress, anxiety, relationship difficulties, concentration issues and academic problems. Proper and timed counselling helps individuals to perform to their fullest potential.
Graduates and professionals can find openings in academic sectors (teaching, doctoral and post-doctoral work), developing innovative (technology) solutions (with emphasis on user experience design) and new product innovations that lead to startups.
We are looking for people in various positions from the following domains to work with us:
Cognitive Science
Cognitive Neuroscience
Human-computer Interaction
Interaction Design
Product Design
Informatics
People with expertise in other disciplines interested in applied aspects of cognitive science are also welcome to contact.
Dr. Raja Shekar P V
Associate Professor & Head,
Centre for Creative Cognition,
SR Engineering College,
Hasanparthy, Warangal – 506 371, T.S. | http://srecwarangal.ac.in/cognitive-science-center.php |
This course is designed to enhance the professional development of young scholars and other young professionals who are interested or actively engaged in research and teaching about international relations and the future of global governance and human security in the context of dynamic and often unpredictable forces and consequences of globalization. It will offer participants an in-depth analysis of the forces that affect and the challenges that confront governance at all levels in the twenty-first century as well as various steps that might be taken to enhance the effectiveness of international institutions and other mechanisms of global governance in responding to those challenges.
Course Level and Target Audience
The course is designed specifically for young scholars from transitional and developing societies who have a university degree, hold a teaching job at a college or university in their home country or work as an administrator or a professional, and possess a basic knowledge about international relations and multilateral affairs. Graduate students with teaching experience may also apply. We encourage applications from a wide variety of disciplines, intellectual traditions, professional orientations.
Course Content
In the foreword to the book, Governance in a Globalizing World, Robert Keohane and Joseph Nye distinguish between "globalism," a static condition of interrelations and interdependence, and "globalization" or the process by which globalism in enhanced or increased. They present a systemic view of globalization that includes economic, political and socio-cultural areas of interaction. Yet despite global and cosmopolitan values, which may be present and increasing, the principles of territoriality, nationality and sovereignty remain. That is, every person exists and is governed within a territory, and most persons and groups of persons base their activities on this premise. These issues are especially relevant to the question of governance for two reasons. First, the rise of globalization affects the abilities of "domestic" governments to govern, and "domestic" governance tries to influence the path of globalization. Second, there are areas of international interaction wherein there is no government. Also, globalization is not a neutral phenomenon and effects different people(s) in drastically different ways, empowering and enriching some and impoverishing many others.
In this context, the course will explore the dynamic processes of globalization and the needs, opportunities, and dilemmas posed for governance. There is concern, for example, about increased vulnerability to unpredictable economic shocks and crises, which bring with them social dislocation and economic instability. There is concern over loss of sovereignty and control over domestic resources and policies. There is anxiety about maintaining the integrity of cultural heritage and traditional societal values and norms. On the other hand, there is hope of higher living standards, new economic opportunities, and diffusion of much needed technology and skills. In this context, governance and security can no longer be conceived in solely national or domestic terms. Things that once were meaningfully viewed as "domestic" now make sense only when conceived in international terms–the global and the local, the macro and the micro have become blurred. In the twenty-first century, security can only be meaningfully conceived in human terms.
The course will systematically address the questions, "What is governance?" and, in international situations, "How do you get governance without government?" The same questions of governance that apply to globalism/globalization apply to governance at more localized levels. That is, who possesses the capacity and/or legitimacy to act authoritatively in the international (or national or local) sphere? Who has legitimacy and/or authority, and from where does such authority they derive? We will explore the relationship between global governance and the creation and maintenance of democratic open societies at the local and national levels.
Governance and human security are inextricably linked, and the notion of human security focuses attention directly on individuals and their circumstances, and thereby constitutes a not so subtle challenge to state sovereignty. To make people psychologically secure may, under some circumstances, be the antithesis of making the governments of states and their territorial boundaries physically secure. The course will critically analyze the evolving meanings of security with a particular focus on the concept of human security.
Participants are challenged to reconceptualize international relations and governance in non-state-centered terms and to move beyond state/nonstate conceptualizations, such as "domestic/foreign," "inside/outside," or "we/they." Class activities will explore the concept of civil society and will discuss the ways in which diverse agents and forces of society can be brought more effectively into our models and theories of international relations. Special emphasis will be placed on identifying actual and potential partnerships between international institutions and those diverse, often contradictory, and sometimes conflictual social forces and entities that lie beyond state control.
Traditional approaches to multilateralism and global governance have been predominantly hierarchical, concentrating on great power relationships. Such a top-down approach, however, obscures important aspects of dominant-subdominant relationships at the international level and reifies and promotes certain ideas and constitutive principles held by the most powerful participants. In recent years, however, an increasing body of literature has emerged, which challenges such a traditional orientation. These new approaches to multilateralism and global governance will be analyzed with particular emphasis placed on identifying implications for enhancing the effectiveness of international institutions for promoting human security.
Larger Context of the Course
This special course is a component of a much larger transnational research and professional development program for young scholars in the social sciences and humanities—a project titled "Creating Effective Partnerships for Sustainable Human Security." This United Nations University project, coordinated by course co-director Roger Coate, is being undertaken in partnership with the CEU, the Office of the UN Secretary-General, the Academic Council on the United Nations System, the International Studies Association, and numerous other academic institutions and professional associations. The core mission of the course proposed here and the associated SUN 2002 course, titled "The United Nations, Civil Society, and the Private Sector: Creating Effective Partnerships for Sustainable Human Security," as well as that of the larger project, is the professional development of young scholars and professionals from emerging democracies worldwide.
Emphasis is placed on establishing self- sustaining interdisciplinary research and teaching networks among scholars and professionals from different nationalities, cultures, professions, and disciplines. An important goal of the course (and project) is to enhance young scholars’ substantive knowledge and theoretical understanding of processes of global governance, especially as related to building and sustaining effective partnerships between international institutions and civil society for promoting human security. Other important goals include: facilitating young scholars’ access to and engagement with global and regional academic and professional communities, UN agencies and staff, and transnational internet-based research networks; facilitating access for young scholars in remote locations to information, resources, and institutional arenas related to their research needs and interests; facilitating exchange and cross fertilization among scholars and practitioners of multilateralism from around the world; enhancing the training of young scholars from regions with emergent or re-emergent civil societies in the design and conduct of research through an ongoing series of workshops and seminars; and establishing mentorship relations, linking young scholars with their more senior colleagues around the world. The larger project also seeks to provide opportunities for young scholars to gain "hands-on" experience in the work of UN agencies through a program of fellowships as well as through direct involvement in ongoing research activities in UN agencies.
In the context of the larger project, this summer university course serves primarily as the regional "workshop" for young scholars in Central and Eastern Europe, the former Soviet Union and Mongolia. However, the course is open without discrimination to participants from developing and transitional societies throughout the world. "Regional" courses, such as this one, will be followed by a series of global workshops and seminars in which selected participants from the various regions will be given the opportunity to participate together. Those global workshops and seminars will be held in conjunction with the annual meetings of ACUNS and/or ISA, held respectively during June and March of each year. Participation in those global sessions will give participants the opportunity to become engaged in larger scholarly communities and will provide the follow through necessary for promoting effective professional development. Priority is placed on creating transnational research networks among the participants so as to ensure that the learning process transcends the course and workshop settings and is sustained on an ongoing and ever-evolving basis.
Course Format
The course will be conducted in a mixed in-residence/distance learning format, consisting of three interrelated modules.
Module One – The first part of the course entails a two-week distance-learning module to be held July 1 – 14, 2002. This time will be spent interacting with the course directors over the Internet, using email and web-based communications, to introduce the course and prepare participants for the in-residence part of the course.
Module Two – The second part of the course will be held in residence at CEU in Budapest from July 15 – August 2, 2002. This face-to-face part of the course will be conducted in a mixed format, including daily lecture/discussion sessions, seminar sessions, Internet-based research and grant-seeking workshops, interactive teaching workshops, production of a research design paper, individual and group panel presentations, and periodic informal "forum" sessions during which small groups of participants discuss intellectual and other issues of common concern. Each participant is expected to produce a written research design and to present it orally on a panel at a mock professional conference. There is no formal grading in the course, but participants whose performance is especially exemplary may be invited to participate on a continuing basis in the larger research program of which the course is a part. Each participant will be assigned one or more faculty mentors, with whom to work during the term.
Module Three – Optional distance education format, August 19 – November 29, 2002. This time will be spent interacting over the Internet, using email and web-based communications, with mentors and research groups to complete and revise research papers, grant proposals, workshop proposals, and/or research reports. | http://summeruniversity.ceu.edu/node/1461 |
Click to learn more about author Paolo Tamagnini.
The Guided Labeling series of blog posts began by looking at
when labeling is needed — i.e., in the field of machine learning when most
algorithms and models require huge amounts of data with quite a few specific
requirements. These large masses of data need to be labeled to make them
usable. Data that is structured and labeled properly can then be used to train
and deploy models.
In the first episode of our Guided Labeling series, An Introduction to Active Learning, we looked at the human-in-the-loop cycle of active learning. In that cycle, the system starts by picking examples it deems most valuable for learning, and the human labels them. Based on these initially labeled pieces of data, a first model is trained. With this trained model, we score all the rows for which we still have missing labels and then start active learning sampling. This is about selecting or re-ranking what the human-in-the-loop should be labeling next to best improve the model.
There are different active learning sampling strategies, and in
today’s blog post, we want to look at the label density technique.
Label Density
When labeling data points, the user might wonder about any of
these questions:
- “Is
this row of my dataset representative of the distribution?”
- “How
many other still unlabeled data points are similar to this one that I’ve already
labeled?”
- “Is
this row unique in the dataset — is it an outlier?”
The above are all fair questions. For example, if you only label
outliers, then your labeled training set won’t be as representative as if you
had labeled the most common cases. On the other hand, if you label only common
cases of your dataset, then your model would perform badly whenever it sees
something just a bit exceptional to what you have labeled.
The idea behind the Label
Density strategy is that when labeling a dataset, you want to
label where the feature space has a dense cluster of data points. What is the
feature space?
Feature Space
The feature space represents all the possible combinations of column values (features) you have in the dataset. For example, if you had a dataset with only people’s weight and height, you would have a 2-dimensional Cartesian plane. Most of your data points here will probably be around 170 cm and 70 kg. So, around these values, there will be a high density in the 2-dimensional distribution. To visualize this example, we can use a 2D density plot.
In Figure 1, density is not simply concentrical to the
center of the plot. There is more than one dense area in this feature space.
For example, in the picture, there is one dense area featuring a high number of
people around 62 kg and 163 cm and another area with people who are around 80
kg and 172 cm. How do we make sure we label in both dense areas, and how would
this work if we had dozens of columns and not just two?
The idea would be to explore and move in the dataset
n-dimensional feature space from dense area to dense area until we have
prioritized all the most common feature combinations in the data. To measure
the density of the feature space, we compute a distance measure between a given
data point and all the others surrounding it using a certain radius.
Euclidean Distance Measure
In this example, we use the Euclidean distance measure on top of the weighted mean subtractive clustering approach (Formula 1 below), but other distance measures can be used too. By means of this average distance measure to data points in the proximity, we can rank each data point by density. If we take the example in Figure 1 again, we can now locate which data point is in a dark blue area of the plot simply by using Formula 1. This is powerful because it will also work no matter how many columns you have.
This ranking, however, has to be changed each time we add more labels. We want to avoid always labeling in the same dense areas and continue exploring for new ones. Once a data point is labeled, we don’t want the other data points in its dense neighborhood to be labeled as well, in future iterations. To enforce this, we reduce the rank for data points within the radius of the labeled one (Formula 2 below).
Once the density rank is updated, we can retrain the model and move to the next iteration of the active learning loop. In the next iteration, we explore new dense areas of the feature space thanks to the updated rank, and we show new samples to the human-in-the-loop in exchange of labels (Figure 2 below).
Wrapping Up
In this episode, we’ve looked at:
- Label density
as an active sampling strategy
- Labeling
in all dense areas of feature space
- Measuring
the density of features space with the Euclidean distance measure and
the weighted
mean subtractive clustering approach
In the next blog article in this series, we’ll be looking at
model uncertainty. This is an active sampling technique based on the prediction
probabilities of the model on still unlabeled rows. Coming soon! | https://itcareersholland.nl/guided-labeling-episode-2-label-density/ |
How to Define a Theme in Literature
In literature, the theme is a central subject within a narrative work. This central subject can be separated into two different categories: thematic concept and thematic statement. The former refers to what readers perceive the work to be about, and the latter refers to what the work says about that subject. Both are important in creating an effective story.
Symbols
When defining a theme, it’s important to consider symbols. Most symbols in literature are universal, and writers use them intuitively. However, certain generic symbols can represent conflicting ideas in different works. For example, light and dark are commonly used as symbols, but in different works, light can symbolize one idea and darkness another. However, interpreting these symbols is not difficult, especially if you read classics.
Motifs
A motif in a story is a distinctive feature or idea that appears repeatedly. It often helps develop other aspects of the story.
Motifs in a story
The use of motifs in a story helps to enhance its theme. They are patterns of images, situations, or language that make readers feel the same way. When combined with other elements in the story, they create a richer experience for the reader.
Major themes
A major theme is a central idea that underlies a story or narrative. A story must have a major theme and a minor theme. The themes are the ideas people mull over and use as the deeper reason for creating the story.
Minor themes
A minor theme is a theme that appears briefly in a story before giving way to a more prominent theme later in the work. It can be a part of a scene or a chapter, but it’s usually less noticeable than a major theme. In “Pride and Prejudice,” for example, the major theme is matrimony, but there are several minor themes that play important roles in the story.
Examples
Having a clear concept of the theme in your story can help you flesh out the details. You can develop the theme through the setting, characters, plot, and other details. For example, if you want to explore the theme of loss, you might write about the character’s grief and the actions she takes to express her feelings. | https://phpsite.com/how-to-define-a-theme-in-literature/ |
Infotech Lead India: InfotechLead.com is presenting recommendations of Joint Working Group on Cyber Security in the country.
These recommendations were presented by Shivshankar Menon, national security advisor, to India government.
1. One of the primary challenges facing both government as well as industry is to ensure the security of their computer networks and systems. Cyber security cannot be achieved in isolation by either government or industry alone. It requires joint efforts and collaboration. Following discussion with representatives of the private sector on their role in enhancing cyber security, it was decided to set up a Joint Working Group (JWG), under the chairpersonship of the Deputy National Security Advisor, to work out the details of the Roadmap for cyber security cooperation that needed to be evolved. This JWG included representatives of both government and private sector.
2. The JWG had constituted five Sub-Groups to flesh out the details of such engagement. These five Sub-Groups submitted their reports to the JWG on 16 August, 2012, which thereafter finalized its recommendations.
3. Guiding Principles
The JWG has identified the following guiding principles and objectives that would underpin the public-private partnership (PPP) in cyber security:
a) Given the diverse stakeholders in cyber security, institutional mechanisms should be set up to promote convergence of efforts both in public and private domains;
b) Use existing institutions and organizations to the extent possible in both private sector and government and create new institutions where required to enhance cyber security;
c) Set up a permanent mechanism for private public partnership;
d) Identify bodies that can play a wider role in funding and implementation in the public and private sector;
e) Identify areas where both private and public sector can build capacities for cyber security;
f) Put in place appropriate policy and legal frameworks to ensure compliance with cyber security efforts;
2 Recommendations of Joint Working Group on Engagement with Private Sector on Cyber Security
g) Promote active PPP cooperation in international forums and in formulating India’s position on global cyber security policies;
h) Establish India as a global hub of development of cyber security products, services and manpower; and
i) Promote indigenization and work on joint R&D projects to meet the cyber security needs of the country.
4. “Roadmap” for PPP on Cyber Security Issues
(1) Institutional Framework
On the basis of these guiding principles, the following coordination and oversight structure is proposed:
(a) There should be a permanent Joint Working Group (JWG) under the aegis of the National Security Council Secretariat (NSCS) with representatives from Government as well as Private Sector.
(b) This JWG will act as an advisory body and coordinate Public-Private Partnership (PPP) on cyber security.
(c) A Joint Committee on International Cooperation and Advocacy (JCICA) will be set up as a permanent advisory committee of the JWG in promoting India’s national interests at various international fora on cyber security issues.
(d) The composition of both JWG and JCICA will be finalized in consultation with industry associations.
(e) The private sector will set up Information Sharing & Analysis Centres (ISACs) in various sectors and cooperate with the sectoral CERTs at the operational level.
(2) Capacity Building
(a) Critical shortage of cyber security professionals need to be tackled in mission mode with innovative recruitment and placement procedures along with specialized training of existing manpower. Thisprogramme may be implemented in PPP mode.
(b) There has to be a concerted effort to increase the number of cyber security professionals and equip them to efficiently meet the challenges of Cyber Security.
(c) Ministry of Communication and Information Technology (MCIT) and Ministry of Human Resource Development (MHRD) and the private sector may jointly establish a cyber security capacity building framework.
(d) Establishing a competency framework to assess skills required, identify gaps, Recommendations of Joint Working Group on Engagement with Private Sector on Cyber Security 3 and devise strategies and programmes for capacity-building. This may include designing security certification schemes for IT professionals and advising cyber security related curriculum for formal sector (B.Tech, M.Tech.,MBA etc).
(e) Work towards establishing a multi-disciplinary Centre of Excellence (COEs) in Cyber security areas including best practices, forensics, cyber crime investigation, studies, research and international frameworks/ institutions.
(f) MCIT and private sector should jointly run cyber security awareness campaigns for the general public, teenagers, children, etc.
(g) Ministry of Home Affairs (MHA) and MCIT may setup training facilities for training of Law Enforcement Agencies (LEAs) in cyber crime investigations and cyber forensics. Private sector may be associated with establishment of training facilities and provide basic and advanced level trainings to the LEAs.
(h) Government and private sector may fund research & development for development of indigenous cyber security products and solutions that meet international standards and address the global market.
(3) Security Standards and Audits
Given the role of security standards and audit in enhancing the level of preparedness and assurance in cyber security, the private sector would be an active partner in undertaking the following activities:
(a) Define baseline security standards and practices/guidelines for the critical sector organizations both in the public and private sectors. The standards may be developed by a MCIT led body with active involvement of the industry and academia.
(b) Define enhanced standards and guidelines for organizations that fall in the high risk category i.e. the critical information infrastructure organisations.
(c) Laying down of security standards and guidelines for acquisition of IT products and services.
(d) Develop protection profiles, capturing users’ cyber security concerns, to aid the procurement of IT products as well as compliance verification of IT products prior to deployment.
(e) Work jointly towards the establishment of Institute of Cyber Security Professionals of India (similar to ICAI for CAs). This could be an autonomous institution under the patronage of MCIT.
(f) Make cyber security audit mandatory by appropriate amendment in the listing requirements under the Companies Act.
(4) Testing & Certification
The following measures may be taken for enhancing testing & certifying facilities to address the growing concerns relating to supply-chain vulnerability:
(a) Establishment of National Testing and Certification Schemes, under the supervision and oversight of appropriate empowered entities under the MCIT.
(b) While action is underway for establishment of Telecom Testing and Certification Centre in telecom sector, there is a need for establishment of an independent government certification body for IT products under the MCIT. The certification body should be separate from the testing facilities. In the interim, Standardisation
(c) Development of skills and competence of evaluators, validators and certification body personnel for successfully running the National Testing and Certification Scheme.
(d) Establishment of private owned testing labs, duly accredited by the certification body; Government may provide the necessary incentives for the private sector for opening testing labs.
(e) Encourage active participation in the communities of interest for defining protection profiles for addressing the security requirements of specific sector.
(f) Take necessary steps to transition from a ‘Common Criteria Certificate Consuming Nation’ to a ‘Common Criteria Certificate Authorizing Nation’.
5. Pilot projects
As the first step towards the implementation of the above recommendations, four pilot projects have been identified for early implementation:
(a) Setting up of a pilot testing lab,
(b) Conducting a test audit,
(c) Study vulnerabilities in a sample Critical Information Infrastructure, and
(d) Establishment of a multi-disciplinary Centre of Excellence (COE).
6. The permanent JWG (to be constituted) will work out the Action-Plan for implementation of the recommendations. | https://infotechlead.com/security/recommendations-of-joint-working-group-on-cyber-security-3336 |
---
author:
- |
Roman Romanov[^1]\
Mihail Tihomirov
title: 'On Selfadjoint Subspace of One-Speed Boltzmann Operator'
---
Introduction
============
It is well-known [@Na; @N] that a nonself-adjoint operator in a Hilbert space can be represented as an orthogonal sum of a self-adjoint one, and an operator having no reducing subspaces on which it induces a self-adjoint operator. A natural question about operators arising in applications is whether the first (selfadjoint) component in this sum is trivial, that is, whether the operator is completely nonself-adjoint. For differential Schrödinger operators this question was studied earlier [@Pav1] and is related to the unique continuation property for solutions. In this note we study complete nonself-adjointness for one-speed Boltzmann operator [@JLh] arising in the theory of neutron transport in a medium with multiplication.
The main result of the paper – theorem 2 – is that the selfadjoint subspace is non-trivial for any Boltzmann operator with polynomial collision integral if the multiplication coefficient has a lattice of gaps in the support of arbitrarily small width, that is, if the coefficient vanishes on an $ \varepsilon $-neighborhood of the set $ a \mathbb{Z} $ for some $ a , \varepsilon > 0 $. On the other hand, the operator of the isotropic problem turns out to be completely nonself-adjoint if the multiplication coefficient is non-zero on a semi-axis (proposition \[halfax\]). For anisotropic problem we give an example (corollary \[half\]) showing that under an appropriate choice of the collision integral the operator may turn out to be completely nonself-adjoint for any non-vanishing multiplication coefficient. Finally, for the three-dimensional Boltzmann operator we establish non-triviality of the selfadjoint subspace for any non-zero multiplication coefficient (theorem \[3dim\]).
Let us describe the structure of the paper. Proposition 1 gives a version of the abstract theorem on decomposition of an operator in the sum of selfadjoint and completely nonself-adjoint ones convenient for our purposes. A close assertion in terms of the resolvent is contained in [@N]. Theorem 2 is proved by a direct construction of a non-zero function lying in the self-adjoint subspace. It occupies sections 3 and 4. The same problem for the three-dimensional Boltzmann operator is studied in section 5.
The authors are indebted to P. Kargaev for a useful discussion.
The following notation is used throughout:
- If $\big\{S_i\big\}_{i\in I}$ is a family of subsets of a Hilbert space, then $\bigvee\limits_{i\in I} S_i$ is the closure of the linear span of the set $\bigcup\limits_{i\in I} S_i$.
- If $f\in L^2({\mathbb{R}^{}})$, then $\Hat{f}\in L^2({\mathbb{R}^{}})$ is the Fourier transform of $f$: $$\Hat{f}(p) \overset{\mathrm{def}}{=}
\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty}e^{-ipx}f(x)\,{\mathrm{d}}x .$$
- $H^2_\pm $ — the Hardy classes of analytic functions in the upper and lower half planes, respectively.
- The abbreviation a. e. refers to the Lebesgue measure on $\mathbb{R} $. For a measurable function $f$ on ${\mathbb{R}^{}}$ the notation $\mathrm{supp}f $ stands for the set $\left\{x\in\ \mathbb{R}:\; f(x)\ne 0\right\}$ defined up to a set of zero measure.
Definitions and Preliminaries
=============================
The Boltzmann operator acts in the space $L^2({\mathbb{R}^{}}\times[-1,1])$ of functions $ u = u ( x,\mu)$ ($ x \in {\mathbb{R}^{}} $, $\mu \in [ -1 , 1 ] $) endowed with the standard Lebesgue measure, by the formula:
$$( Lu ) ( x , \mu ) = i\mu \left( {\partial}_x u \right) ( x , \mu ) + i
\sum_{\ell=1}^{n}c_{\ell}(x)\varphi_{\ell}(\mu) \int_{-1}^{1} u (
x , \mu^\prime ) \overline {\varphi_\ell (\mu')}\,{\mathrm{d}}\mu'.
\label{Bo}$$
Here the functions $c_{\ell}\in L^{\infty}({\mathbb{R}^{}})$, $\varphi_{\ell}\in L^\infty
[-1,1]$, $\ell = 1,...,n$ are known parameters of the problem. The functions $c_{\ell}$ are assumed to be real-valued. The case $ n = 1 $, $ \varphi_1 \equiv 1 $ (isotropic scattering) is of special interest. In this situation the function $ c_1 $ is called the local multiplication coefficient, and the index $ 1 $ is omitted. Without loss of generality, one assumes throughout that the functions $\left\{\varphi_{\ell}\right\}_{\ell=1}^{n}$ are linearly independent.
Under the conditions imposed the operator $ L $ is the sum of the operator $ L_0 = i\mu{\partial}_x $, selfadjoint on its natural domain, and a bounded one (see [@JLh; @Shikhov] for details). According to the non-stationary Boltzmann equation, if $ u^t $ is the particle density at time $ t $, then $ u^t = e^{ itL } u^0 $. Notice that the literature on the Boltzmann operator uses for it an expression different from (\[Bo\]) by the factor $ i $, because of a different definition of the exponential function. The evolution operator $ u^0 \mapsto u^t $ in our notation coincides with the standard one.
Let $ D $ be an operator in a Hilbert space $H$ of the form $ D
= A + i K $, where $ A $ is selfadjoint, and $ K $ is selfadjoint and bounded.
The subspace $H_0 \subset H $ is the selfadjoint subspace of the operator $D$, if
1. $H_0$ reduces[^2] $D$, and the restriction $\left. D\right|_{H_0}$ is a selfadjoint operator in $H_0$;
2. any reducing subspace $H^\prime $ of the operator $D$ such that $\left. D\right|_{H^\prime}$ is a selfadjoint operator in $H^\prime $ is contained in $ H_0$.
An operator $ D $ is called completely nonself-adjoint if its selfadjoint subspace is trivial.
\[th1\] The orthogonal complement of the selfadjoint subspace of the operator $D$ coincides with the subspace $$H_1\overset{\mathrm{def}}{=}\bigvee_{t\in{\mathbb{R}^{}}}e^{iAt}\mathrm{Ran}\,K.$$
Let $H_0$ be the selfadjoint subspace of the operator $D$. By definition, the subspace $H_1$, and hence $ H_1^\perp $, reduces the operator $ A $. Since, obviously, $H_1^\perp
\subset\mathrm{Ker}\, K $ we obtain from this that $H_1$ and $ H_1^\perp
$ are reducing subspaces of the operator $ D $ such that the restriction of $ D $ to $ H_1^\perp $ is a selfadjoint operator. Thus, $H_1^\perp \subset H_0 $. Let us show that $ H_1 \subset
H_0^\perp $. Indeed, the subspace $ H_0 $ reduces $ D $, and therefore the operator $ A = \left( D + D^*
\right)/2 $ as well. This means, in particular, that $
e^{iAt}\mathrm{Ran}\, K \subset H_0^\perp $ for all real $ t $, since $ H_0\subset\mathrm{Ker}\, K $.
In what follows we are going to use the fact that the selfadjoint subspace $ H_0 $ is reducing for the operator $ A $ as well, and the selfadjoint part of $ L $ coincides with the restriction of $ A $ to $ H_0 $.
For the Boltzmann operator (\[Bo\]) $ A = L_0 = i\mu{\partial}_x $, and a straightforward calculation gives $$\label{exp1d}
\big(e^{itA}f\big)(x,\mu)=f(x - \mu t,\mu).$$
For a function $ \xi \in L^{\infty}({\mathbb{R}^{}}) $ let us denote by $ \mathcal{D}_\xi $ the set of compactly supported functions $ h \in L^2 ( \mathbb{R} ) $ vanishing outside $\mathrm{supp}\, \xi $.
\[l1\] A function $ f\in L^2({\mathbb{R}^{}}\times[-1,1]) $ belongs to the selfadjoint subspace of the operator (\[Bo\]) if and only if $$\label{cond}
\int_{[-1,1]\times \mathbb{R}} f(x-\mu
t,\mu){\overline{\varphi_{\ell}(\mu)}} h ( x ) \,{\mathrm{d}}\mu {\mathrm{d}}x = 0$$ for all $\ell = 1,...,n$, $t\in{\mathbb{R}^{}}$, and $ h \in
\mathcal{D}_{c_{\ell}}$.
Thus, we have to find out if there exists a non-zero function $ f $ satisfying the condition (\[cond\]). Let us first explain on the formal level the method we use. For simplicity, let the function $ c $ be the indicator of an interval $ I $, and $ \varphi \equiv 1 $. Then the condition of the lemma means that $$\int_{-1}^1 f(x-\mu t,\mu)\,{\mathrm{d}}\mu = 0$$ for all $ t\in{\mathbb{R}^{}} $ and $ x \in I $. We will search for the function $ f $ in the form $$f ( x , \mu ) = \int_{\mathbb{R}} e^{i\tfrac{xq}\mu} u
( q,\mu )\,\mathrm{d}q .$$ Substituting and interchanging the order of integrations, we obtain: $$0 = \int_{\mathbb{R}}{\mathrm{d}}q\, e^{-iqt}
\int_{-1}^1 e^{i\tfrac{xq}\mu} u(q,\mu)\,\mathrm{d}\mu .$$ Since this equality is an identity in $ t $, the inner integral must be zero for all $ q $. After the change of variable $ p
= 1/\mu $ in this integral we arrive at the following uniqueness problem for the Fourier transform: is there a nonzero function $ v ( q , p ) $ such that its Fourier transform in the second variable $ \mathcal{F} v $ vanishes at all points of the form $ ( q , -xq )$, $ q \in \mathbb{R} ,\, x \in I $. A rigorous argument requires analysis of certain integral transforms of the Fourier type, definitions and elementary properties of which are given in the next section.
Integral Transforms
===================
Let $ \omega \subset \mathbb{R} $ be a compact interval. We set the notation for certain classes of functions of variables $q\in \mathbb{R}$ and $\mu\in[-1,1]$ and transforms between them:
- $H = L^2({\mathbb{R}^{}}\times[-1,1]) $.
- $\overset{\circ}{C}_\omega $ — the linear set of functions $u\in C_0^{\infty}({\mathbb{R}^{}}\times
[-1,1])$ vanishing for $ q \notin \omega $.
- $ H_\omega $ — the subspace in $ L^2\big(\mathbb{R}
\times [-1,1],|\mu|\,{\mathrm{d}}q \, {\mathrm{d}}\mu\big) $ of functions vanishing for $ q \notin \omega $.
- $ \Phi $ and $ \Phi^\ast $ — unitary mutually inverse operators $$\Phi : H \rightarrow
L^2({\mathbb{R}^{}}\times[-1,1],|\mu|\mathrm{d}q \, \mathrm{d}\mu) ,$$ $$\Phi^\ast :
L^2({\mathbb{R}^{}}\times[-1,1],|\mu|\mathrm{d}q \, \mathrm{d}\mu) \rightarrow H,$$ defined on finite smooth functions by formulae $$\big(\Phi f\big)(q,\mu) = \frac{1}{\sqrt{2\pi}}\int_{\mathbb{R}}
e^{-i xq\mu}f(x,\mu)\,\mathrm{d}x,$$ $$\big(\Phi^{\ast} u\big)(x,\mu) = \frac{1}{\sqrt{2\pi}}\int_{{\mathbb{R}^{}}}
e^{i\tfrac{xq}{\mu}}u(q,\mu)\,\mathrm{d}q .$$
\[eqvi\] It is obvious that $\Phi\big(-i\mu{\partial}_x\big)\Phi^{\ast}$ is the operator of multiplication by the independent variable $q$ in $L^2({\mathbb{R}^{}}\times[-1,1],|\mu|\mathrm{d}q \, \mathrm{d}\mu)$.
Let us denote by $ {\mathcal{F}}$ the unitary operator $ {\mathcal{F}}\colon
L^2({\mathbb{R}^{2}}) \to L^2({\mathbb{R}^{2}}) $ of the Fourier transform in the second variable: $$\big({\mathcal{F}}u\big)(q,p)= \frac 1{\sqrt{2\pi}}\int_{\mathbb{R}}
e^{-isp}u(q,s)\,\mathrm{d}s .$$
We are going to use the change of variables $$( J v ) ( q , s ) :
=
\begin{cases} s^{-2} v \left( q , s^{ -1} \right), & |s| > 1 \cr 0, &
|s| < 1 , \cr \end{cases}$$ which defines an isometry $$J \colon
L^2({\mathbb{R}^{}}\times[-1,1],|\mu|\mathrm{d}q \, \mathrm{d}\mu) \to
L^2({\mathbb{R}^{2}},| p|\mathrm{d}q \, \mathrm{d}p) .$$
For any smooth finite function $v $ defined in the strip $ {\mathbb{R}^{}}\times
[-1,1] $ let $$\label{psi} \big(\Psi v\big)(q,x) = \frac{1}{\sqrt{2\pi}}\int_{|p|
> 1 } e^{ixqp} p^{ -2 } v\left( q,\frac 1p \right)\,\mathrm{d}p .$$
For any closed interval $ \omega $ not containing $ 0 $, the transform defined by the formula (\[psi\]) on $
\overset{\circ}{C}_\omega $ is extended to a bounded operator $\Psi$ from $H_\omega $ to $L^2({\mathbb{R}^{2}})$ acting by the following formula: $$\label{PsH} \big(\Psi v\big)(q,x) = ( {\mathcal{F}}J v) ( q , -xq ) , \; \; v \in H_\omega .$$
By definition (\[psi\]), the equality (\[PsH\]) is satisfied for all $ v \in \overset{\circ}{C}_\omega
$, and the Fourier transform $ {\mathcal{F}}$ in it can be understood classically. Then, for any $ g \in L^2({\mathbb{R}^{2}}) $ vanishing when $ |q| < a \colon = \mbox{dist} ( 0 ,
\omega ) $, we have: $$\int_{{\mathbb{R}^{2}}} \left| ( {\mathcal{F}}g ) ( q , -xq ) \right|^2 \mathrm{d}q \,
\mathrm{d}x = \int_{\mathbb{R}} \mathrm{d}q \frac 1{|q|}
\int_{\mathbb{R}} \left| ( {\mathcal{F}}g ) ( q , x ) \right|^2
\mathrm{d}x \le \frac{1}{a}\int_{{\mathbb{R}^{2}}} \left| g ( q , x )
\right|^2 \mathrm{d}x \, \mathrm{d}q .$$ Thus, the map $ \Psi $ is a composition of the bounded operator $ J \colon H_\omega \to L^2({\mathbb{R}^{2}}) $ and the map $ g
\mapsto (\mathcal{F}g)( q , -xq ) $, which is a bounded operator from the subspace $ J H_\omega \subset L^2({\mathbb{R}^{2}}) $ to $
L^2({\mathbb{R}^{2}}) $. Since the linear set $\overset{\circ}{C}_\omega $ is dense in $H_\omega $, it follows that the map $ \Psi $ defines a bounded operator. Simultaneously, we have proved (\[PsH\]).
\[qwerty\] Let $ \omega $ be a closed interval not containing $ 0 $, and let $ \varphi \in L^\infty ( -1 , 1) $. Then for any compactly supported function $ h \in L^2 (\mathbb{R}) $ and any $u \in H_\omega $ the following equality is satisfied for all $ t \in \mathbb{R}$: $$\label{ggg} \int\limits_{[-1,1]\times \mathbb{R}} {\mathrm{d}}\mu\, {\mathrm{d}}x \,
\overline{h ( x )} \varphi(\mu)\big(\Phi^{\ast} u\big)(x-\mu
t,\mu) = \int_{-\infty}^{\infty}{\mathrm{d}}q\, e^{-iqt}\left\langle \Psi
(u \varphi )( q,\cdot ), h \right\rangle_{ L^2 ( \mathbb{R} ) } .$$
Since $\overset{\circ}{C}_\omega $ is dense in $ H_\omega $, it is enough to prove (\[ggg\]) for arbitrary function $u\in\overset{\circ}{C}_\omega $. We have: $$\begin{aligned}
\lefteqn{\int_{-1}^{1} \varphi(\mu) \big(\Phi^{\ast}u\big)(x-\mu
t,\mu){\mathrm{d}}\mu
= \frac{1}{\sqrt{2\pi}} \int_{-1}^{1}{\mathrm{d}}\mu \, \varphi(\mu)\int_{-\infty}^{\infty}
e^{i\tfrac{(x-\mu t)q}{\mu}}u(q,\mu)\,\mathrm{d}q =}\\
& = & \int_{-\infty}^{\infty}{\mathrm{d}}q\,
e^{-iqt}\frac{1}{\sqrt{2\pi}}\int_{-1}^1
e^{i\tfrac{xq}{\mu}}u(q,\mu) \varphi(\mu)\,\mathrm{d}\mu=
\int_{-\infty}^{\infty}{\mathrm{d}}q\, e^{-iqt}\big(\Psi (u \varphi )\big)(q,x).\end{aligned}$$ Multiplying this equality by $ \overline h $ and integrating in $ x $, we obtain (\[ggg\]). The interchange of integrations in $ x $ and $
q $ in the right hand side is possible because of the function $ h $ having a compact support.
Conditions of Complete Nonself-Adjointness
==========================================
In what follows, the functions $\varphi_{\ell}\in L^\infty [-1,1] $ from the definition of the Boltzmann operator are supposed to be extended by zero to the whole of the real line.
\[th2\] Let the function $ F(q,p) \in L^2({\mathbb{R}^{2}},|p|{\mathrm{d}}q{\mathrm{d}}p)$ satisfy the following conditions: $$\begin{aligned}
& \label{Lmu} F ( q , p ) = 0 \; \text{for} \; |p| < 1 ; &
\\
\label{criterium} & \int_{\mathbb{R}} e^{ipxq}
F(q,p)\overline{\varphi_{\ell}(\tfrac{1}{p})}\,{\mathrm{d}}p = 0 &\end{aligned}$$ for all $\ell = 1,...,n,$ and a. e. $q\in{\mathbb{R}^{}}$, $x\in\mathrm{supp}\,c_{\ell} $. Then the vector $$\begin{aligned}
\label{expli}
& f = \Phi^\ast u , & \\ \nonumber
& u ( x , \mu ) \colon = \mu^{-2} F\left( q, \mu^{ -1 } \right),
\; \; | \mu | < 1, &\end{aligned}$$ belongs to the selfadjoint subspace $ H_0 $ of the operator (\[Bo\]). The mapping $ F \mapsto f $ defines an isomorphism of the subspace $ X \subset L^2({\mathbb{R}^{2}},|p|{\mathrm{d}}q{\mathrm{d}}p)$ singled out by conditions (\[Lmu\]) and (\[criterium\]), and the space $ H_0 $. In particular, the space $ H_0 $ is non-zero if, and only if, there exists a non-zero function $ F $ satisfying conditions (\[Lmu\]) and (\[criterium\]).
The equality (\[criterium\]) is understood as a condition of vanishing of the Fourier transform in the second variable of the function $
F(q,p)\overline{\varphi_{\ell}( p^{-1})}$ lying in the space $L^2({\mathbb{R}^{2}})$, on the set $ M_\ell \equiv \{ ( q ,
-xq ): \; q \in \mathbb{R} , \, x \in \mathrm{supp}\,c_\ell \} $ of positive planar Lebesgue measure.
Substituting $ p = \mu^{ -1 } $, we immediately verify that the map $ F \mapsto f $, defined in the theorem, is an isometry from $ X $ to $ H $. Let us show that $ f \in H_0
$ for any $ F $ from the dense in $ X$ linear set of functions $ F \in X $ such that $ F(q,p) = 0 $ when $ q \notin \omega $ for some closed interval $ \omega = \omega ( F ) $ not containing $ 0 $. For such $ F $’s the function $ v
=u\overline{\varphi}_\ell $ obeys the equality (\[PsH\]): $$\label{Psf} \Psi \left[
u\overline{\varphi}_\ell \right] ( q , x ) = \mathcal{F} \left[
F\left( q, p \right) \overline{\varphi_\ell \left( p^{ -1 }
\right) } \right] ( q , -xq ).$$ By assumption (\[criterium\]), the right hand side vanishes on the set $ \{ ( q , x ): \; q \in \mathbb{R} , \, x \in \mathrm{supp}\,c_{\ell} \} $, and thus $ \Psi \left[ u\overline{\varphi}_\ell \right] ( q
, x ) h ( x ) $ is identically zero for any function $ h \in L^2
( \mathbb{R} ) $ supported on $ \mathrm{supp}\,c_{\ell} $. Applying the identity (\[ggg\]), we conclude from this that $$\int\limits_{[-1,1]\times \mathbb{R}} {\mathrm{d}}\mu{\mathrm{d}}x \,
\overline{h ( x ) \varphi_\ell (\mu)}\big(\Phi^{\ast} u\big)(x-\mu
t,\mu) = 0$$ for all $ t\in{\mathbb{R}^{}}$ and $ h \in \mathcal{D}_{c_{\ell}}$, that is, $f$ satisfies the condition of corollary \[l1\].
It remains to check that the range of the map $ F \mapsto f $ is the whole of $ H_0 $. Let $ f_0 \in H $ be a vector of the form $ f_0 =
P_\omega g $, where $ g \in H_0 $, $ \omega $ is a closed interval not containing point $ 0 $, and $ P_\omega $ is the spectral projection of $
L_0 $ corresponding to the interval $ \omega $. Then, $ f_0 \in H_0 $ since the subspace $H_0$ reduces the operator $ L_0 $, and hence any of his spectral projections. We shall show that $ f_0 $ lies in the range of the constructed isometry from $ X $ to $ H $.
Let $ u = \Phi f_0 $, and let $ F(q,p) = p^{ -2 } u(q,p^{ -1
})$ for $ q \in \omega $ and $|p| > 1$, $ F(q,p) = 0 $ for any other $(q,p)\in{\mathbb{R}^{2}}$. By construction, the function $ F $ belongs to $ L^2({\mathbb{R}^{2}},|p|{\mathrm{d}}q\, {\mathrm{d}}p)$ and satisfies (\[Lmu\]) and (\[expli\]) with $ f = f_0 $. Notice that the function $ u $ vanishes when $ q \notin \omega $ since, according to remark \[eqvi\], $\Phi L_0\Phi^{\ast} $ is the operator of multiplication by the $q$ variable. Thus, the function $u
\in H_\omega $, lemma \[qwerty\] applies to it because $ 0 \notin \omega $, and the equality (\[Psf\]) holds true. As the function $f_0$ belongs to $ H_0 $, and hence obeys condition (\[exp1d\]), the left hand side in (\[ggg\]) vanishes for the $ u $ under consideration for all $ t\in{\mathbb{R}^{}}$ and $ h \in
\mathcal{D}_{c_{\ell}}$, $ \ell = 1, \dots ,n $. By uniqueness of the Fourier transform it follows that $$\left\langle \Psi
\left[ u\overline {\varphi_\ell} \right]( q,\cdot ), h
\right\rangle_{ L^2 ( \mathbb{R} ) } = 0$$ for a. e. $ q \in
\mathbb{R} $ and all $ h \in \mathcal{D}_{c_{\ell}}$. The arbitrariness of $ h $ implies that the function $ \Psi \left[
u\overline{\varphi}_\ell \right] ( q , x ) $ vanishes on $ \mathbb{R} \times \mathrm{supp}\, c_{\ell}$. Then the right hand side in (\[Psf\]) also vanishes on $
\mathbb{R} \times \mathrm{supp}\, c_{\ell}$, that is, condition (\[criterium\]) is satisfied. It remains to notice that the set of vectors $ f_0 $ of the form under consideration is dense in $ H_0 $ since the operator $ L_0 $ is absolutely continuous.
Let the function $c(x)$ be bounded, and let there be $ a,\varepsilon
> 0 $ such that $ c ( x ) = 0 $ for $ | x - x_0 - aj | <
\varepsilon $, $ j \in \mathbb{Z} $, with some $ x_0 \in
\mathbb{R} $, and let all the functions $ \varphi_\ell ( \mu ) $, $ 1
\le \ell \le n $, be polynomials. Then the selfadjoint subspace $ H_0 $ of the Boltzmann operator $$\label{Both2} L = i\mu {\partial}_x + i c(x)
\sum_{\ell=1}^{n}\varphi_{\ell}(\mu) \int_{-1}^{1} \cdot \;
\overline {\varphi_\ell (\mu')}\,{\mathrm{d}}\mu'$$ is non-trivial, and, moreover, the restriction of the selfadjoint part of the operator $ L $ to its spectral subspace corresponding to the interval $ [ - \pi / a , \pi / a ] $ has Lebesgue spectrum of infinite multiplicity[^3].
Without loss of generality one can assume that $ x_0 = 0 $ and $ n = 1 + \max_\ell \deg \varphi_\ell $. Let us search for a function $ F $, satisfying the conditions of theorem \[th2\], in the form $ F ( q , p ) =
\chi ( q ) f ( p q ) $, where $ \chi $ is an arbitrary bounded function on the real axis such that $ \mathrm{supp}\, \chi = [ - b , b ] $ for some positive $ b < \pi / a $, and $ \chi ( q ) / q
\in L^2 $. The conditions of Theorem 1 will be met if the function $ f \in
L^2 ( \mathbb{R} , |p| {\mathrm{d}}p ) $ obeys the following requirements:
() $ f ( p ) = 0 $ for $ | p | \le b $;
() $ \mathrm{supp}\, \widehat{f p^{ -j }} $ is contained in the $ \varepsilon $-vicinity of the set $ a \mathbb{Z} $ for all $
j $, $ 0 \le j \le n - 1 $.
We are going to use the following observation: let $ h \in L^2_{ loc } (
\mathbb{R} ) $ be an arbitrary $ 2 \pi $-periodic function, and $ \omega $ be a smooth function on the real line supported on an interval $ ( - \delta , \delta ) $, $ \delta > 0 $. Then the function $ \xi = h \hat{\omega} $, obviously, belongs to $ L^2 (
\mathbb{R} , | p | {\mathrm{d}}p ) $, and its Fourier transform vanishes outside the $ \delta $-vicinity of $ \mathbb{Z} $. This observation follows from elementary properties of convolution since $ h = \hat{ \rho } $ where $ {\mathrm{d}}\rho = \sum_j \rho_j
\delta ( x - j ) $ is the discrete measure with masses being the Fourier coefficients $ \rho_j $ of the restriction of the function $ h $ to a period.
Fix an arbitrary nonzero function $ h $, satisfying the conditions above and such that $ h ( p) = 0 $ for $ | p | \le \pi
- \nu $, $ \nu > 0 $. Let $ \delta = \varepsilon/a $, choose an arbitrary nonzero function $ \omega_0 \in C_0^\infty
( \mathbb{R} ) $ supported on $ ( - \delta , \delta )
$ and define the corresponding function $ \xi $ setting $ \omega =
\omega_0^{ (n) } $. Define $ f ( p ) = \xi ( a p ) $. By construction, conditions () and () hold true for the function $ f $ for all $ \nu
> 0 $ small enough. Fix such a $ \nu $ and let: $$u (q,\mu) = \mu^{ -2 } F \left(q, \frac{1}{\mu} \right) .$$ By theorem 1 the nonzero function $ g \overset{\mathrm{def}}{=} \Phi^{\ast} u
$ belongs to $ H_0 $, and the non-triviality of the subspace $ H_0 $ is proved.
To establish the assertion about the multiplicity of the spectrum notice that, as follows from remark \[eqvi\], the restriction of $ L_0 $ to its reducing subspace generated by the function $ g $ is unitarily equivalent to the operator of multiplication by the independent variable in the space $ L^2 $ over the support of $ \chi $, that is, in $ L^2 ( - b ,
b ) $. Each choice of the function $ h $ in the construction above then corresponds to a reducing subspace, and if continuous functions $ h_j $, $ j = 1, \dots , N $, $ N < \infty $, are mutually linearly independent, then so are the corresponding reducing subspaces $ Y_j \subset H_0 $. Indeed, the last assertion means that for any finite $
M $, any $ h_j $ satisfying the conditions above, and any $
\chi_j \in L^2 ( - b , b ) $, $ j \le N $, the following implication is true: $$\sum_1^M h_j ( p q ) \hat{\omega} ( pq ) \chi_j ( q ) \equiv 0
\Rightarrow \chi_j ( q ) \equiv 0 \, \forall j \le N ,$$ which is easily verified by induction. It is then enough to choose an arbitrary $ c \ne 0 $ such that $ \hat{ \omega } ( c ) \ne 0 $, and $ h_j ( c ) \ne 0 $ for at least one $ j $, and let $ p = c/ q $.
Thus, we have proved that for any $ b < \pi / a $ there is a reducing subspace in $ H_0 $ such that the restriction of the operator to it has Lebesgue spectrum of infinite multiplicity on $ [ -b , b ] $, hence the same is true of $ b = \pi / a $. Since the operator $ L_0 $ is absolutely continuous, it follows that the restriction of $ L $ to $ H_0 $ possesses the same property.
The proof of theorem 2 is constructive – nonzero vectors from $ H_0
$ were found explicitly.
Sometimes it is possible to say more about the spectrum of the selfadjoint part.
\[compact\] Let the function $ c ( x ) $ be compactly supported, and let all the functions $ \varphi_\ell ( \mu ) $, $ 1 \le \ell \le n $, be polynomials. Then the selfadjoint part of the operator $ L $ of the form (\[Both2\]) is unitarily equivalent to an orthogonal sum of infinitely many copies of the operator of multiplication by the independent variable[^4] in $ L^2 ( \mathbb{R} ) $.
Let us first consider the case $ n = 1 $, $ \varphi_1 \equiv 1 $. Let $ I $ be an arbitrary closed interval, $ \chi ( q ) $ its indicator function. We shall search for the function $ F ( q , p ) $ in the form of the product $ \chi ( q ) f ( p ) $ where $ f \in L^2 ( \mathbb{R}
, |p| {\mathrm{d}}p ) $ is a function vanishing on $ [ - 1 , 1 ] $ and such that $ \hat{f} $ vanishes on an interval $ [ -M, M ] $. It is clear that for $ M $ large enough such a function $ F $ obeys all the conditions of theorem \[th2\]. A supply of functions $ f $ with the desired properties is provided by the following lemma.
\[example\] Let $\alpha > 0$, and let $ \rho ( z ) $ be an arbitrary nonzero function analytic in the plane cut along a compact interval $ J \subset (-\infty, -1] $ and such that $
\rho ( z) = O \left( \left| z \right|^{-2 } \right) $ when $ |z|
\to \infty $ uniformly in $ \mathrm{arg}\, z $, and the restrictions of $ \rho
( z ) $ to $ \mathbb{C}_\pm $ belong to $ H^2_\pm $, respectively. Define the function $$\label{Falp}
\phi_\alpha (z) = \exp\left[2i\alpha\left(-\frac{z}{2} +
\frac{1}{ 1-\sqrt{\frac{z-1}{z+1}} }\right)\right] \rho ( z ) ,$$ where the branch of the square root is chosen so that $ \phi_\alpha
( z ) $ be analytic in the plane cut along the rays $ (-\infty,
-1]\cup [ 1, +\infty) $, and $\mathrm{Im}\sqrt{\frac{z-1}{z+1}}
> 0 $. Let $ f_\alpha^\pm $ be the boundary values of the function $ \phi_\alpha $ on the real axis in the sense of the Hardy classes.
Then the (obviously, nonzero) function $$f_\alpha (x) \overset{\mathrm{def} }{=}
f_\alpha^+ (x) - f_\alpha^- (x)$$ obeys:
1. $f_\alpha \in L^2({\mathbb{R}^{}},|p|{\mathrm{d}}p) $;
2. $f_\alpha (x) = 0$ for $|x|<1$;
3. $\Hat{f}_{\alpha}(p) = 0$ for $ |p| \le\alpha $.
Property 2 is obvious. Since the boundary values of the exponent in (\[Falp\]) on the real axis have the modulus $ \le 1 $ for the given choice of the square root brunch, the inclusion $f^{\pm}_\alpha \in L^2({\mathbb{R}^{}}, |p| {\mathrm{d}}p) $ is immediate from the assumptions about the function $ \rho ( z ) $. It remains to check the property 3.
The following asymptotics hold for $\lvert z\rvert\to\infty$ in each of the halfplanes $
\mathbb{C}_\pm $ uniformly in $ \mathrm{arg}
\, z $: $$\begin{aligned}
\frac{1}{ 1-\sqrt{\frac{z-1}{z+1}} } =\frac{1}{
1-\left(1-\frac{1}z+ O\left(\frac{1}{z^2}\right)\right) }= z +
O(1),\; \; \text{for} \; \mathrm{Im}\, z
> 0; \\ \frac{1}{ 1-\sqrt{\frac{z-1}{z+1}} }=\frac 1{
1+\left(1-\frac{1}z+ O\left(\frac{1}{z^2}\right)\right) }= O(1),
\;\; \text{for}\; \mathrm{Im}\, z < 0 . &\end{aligned}$$ Therefore for $ \lvert z\rvert\to\infty $ we have: $$\exp\left[2i\alpha\left(-\frac{z}{2} +
\frac{1}{ 1-\sqrt{\frac{z-1}{z+1}} }\right)\right]=
\exp\big(i\alpha z\,\mathrm{sign}(\mathrm{Im}\,z)+O(1)\big).$$ Thus, the restrictions of the functions $ e^{\mp i\alpha z}\phi_\alpha $ to the halfplanes $ \mathbb{C}_{\pm} $ are in $ H^2_\pm $, respectively. By the Paley-Wiener theorem this implies that $\widehat{f^\pm_\alpha}(p)=0$ when $ \pm p\le\alpha $, hence $
\Hat{f}_\alpha (p ) = 0 $ for $ |p| \le \alpha $.
For the function $ \rho $ in this lemma one can take, for instance, the branch of the function $ \ln^n\left(\dfrac{z+a}{z+b}\right) $, $ 1 < b < a
$, $ n \ge 2 $, analytic in the plane cut along the interval $ [-a, -b] $, fixed by the condition ${\left.\mathrm{Im}\ln{\frac{z+a}{z+b}}\right|}_{z=0}=0$.
[*End of proof of proposition \[compact\].*]{} Let $ \alpha $ be a number such that $ | q x | < \alpha $ for all $ q \in I $, $ x \in \mathrm{supp} \, c $, $f_\alpha \in L^2 ( \mathbb{R} , |p| {\mathrm{d}}p ) $ an arbitrary function vanishing on $ [ - 1 , 1 ] $ and such that $
\hat{f_\alpha} $ vanishes on the interval $ [ - \alpha , \alpha ] $. Let $ F ( q , p ) = \chi ( q ) f_\alpha ( p ) $. Define a vector $ g \in H_0 $ via the function $ F $ in the same way as in the proof of theorem 2. The restriction of the operator $ L $ to its reducing subspace $
Y = Y( f_\alpha ) $, generated by the vector $ g $, is unitarily equivalent to the operator of multiplication by the independent variable in the space $ L^2 ( I ) $, and if functions $ f_{\alpha , j }
$, $ j = 1 , \dots , n < \infty $, are mutually linear independent, then so are the corresponding subspaces $ \left\{ Y( f_{\alpha , j } )
\right\} $. The assertion of the proposition now follows from this and the fact that the linear space of functions $ f_\alpha $ constructed in lemma \[example\] is infinite-dimensional.
The general case ($ n \ne 1 $) is considered in a similar way, we only require additionally the function $ \rho $ in lemma \[example\] to have a zero of order $ n - 1 $ at the point $ 0 $. If this requirement is satisfied, the Fourier transforms of $ f p^{ -j }
$ vanish on $ [ - \alpha , \alpha ] $ for all $ j \le
n - 1 $, and the proof proceeds as above.
[*Commentary to the proof of theorem 2.*]{} The question if there exists a nonzero function $ f \in L^2 (\mathbb{R}) $ such that the restrictions $ \left. f \right|_S = 0 $ and $ \left. \hat{f}
\right|_\Sigma = 0 $ for a given interval $ S $ and a set $
\Sigma \subset \mathbb{R} $ is known as the Beurling problem and has been studied for a long time [@HJ]. For instance, the Amrein-Berthier theorem [@HJ] establishes the existence of such functions if the set $ \Sigma $ has finite measure, the Kargaev theorem [@kargaev] – in a situation generalizing theorem 2 to the case of gaps narrowing at infinity. These results are, however, not immediately applicable to the problem under consideration, when the function $ f $ is subject to an additional condition of square summability with the growing weight $ |p| $. To use them, one would have to smoothen up the functions constructed which would lead to assertions close to theorem 2 and proposition \[compact\], obtained here by elementary methods.
The selfadjoint subspace found in theorem 2 is quite large, and it is natural to ask if there is much else. On this is the following
Results in paper [@KNR] show that in the isotropic problem the essential spectrum of the restriction of the operator $ L $ to $ H_0^\perp $ coincides with the real line if the function $ c $ is compactly supported, and $ c ( x ) \ge 0 $ a. e.
In the direction opposite to theorem 2 the following simple assertion holds.
\[halfax\] Let the function $c \in L^\infty (\mathbb{R})$ be such that $ c ( x ) \ne 0 $ a. e. on a semi-axis. Then the Boltzmann operator $$L= i\mu{\partial}_x + i c(x) \int_{-1}^1 \cdot\,{\mathrm{d}}\mu'$$ is completely nonself-adjoint.
Without loss of generality one can assume that $ c ( x ) \ne 0 $ for a. e. $ x > 0 $. Suppose that the selfadjoint subspace $ H_0
\ne \{ 0 \} $. Then by theorem \[th2\] (see (\[criterium\])) there exists a nonzero function $ F ( q , p ) \in L^2({\mathbb{R}^{2}})$ such that for a. e. $ q > 0 $ we have: $ ( \mathcal{F}^* F) ( q , x
) = 0 $ for a. e. $ x > 0 $. By the Paley-Wiener theorem this implies that $F(q,\cdot)\in H^2_+ $ for a. e. $ q > 0 $, and, since $
F(q,p)=0 $ for $ |p| < 1 $, by properties of the Hardy classes it follows that the function $ F(q,\cdot) = 0 $ for a. e. $ q
> 0 $. Similarly, one considers the case $ q < 0 $. We thus obtain that $ F $ is the zero function, a contradiction.
The following proposition is aimed at clarifying the main result of theorem 2. The operator in a strip of half-width dealt in it has possibly no physical relevance.
Let $\varphi \in L^\infty ( 0 , 1 ) $, $ \mathrm{supp} \, \varphi = [ 0 , 1] $; $ c \in L^\infty (
\mathbb{R} ) $, and let $ L $ be an operator in the Hilbert space $ H = L^2({\mathbb{R}^{}}\times[0,1])$ defined by the formula $$( Lu ) ( x , \mu ) = i\mu \left( {\partial}_x u \right) ( x , \mu ) + i
c(x)\varphi (\mu) \int_0^1 u ( x , \mu^\prime ) \overline {\varphi
(\mu')}\,{\mathrm{d}}\mu' \label{Bohalf}$$ on a natural domain of its real part $ L_0
= i\mu {\partial}_x $. Then the operator $ L $ is completely nonself-adjoint if $
c \not \equiv 0 $.
Arguing as in the poof of theorem 1, it is easy to see that the operator defined by (\[Bohalf\]) is completely nonself-adjoint if any function $F( q , p ) \in L^2({\mathbb{R}^{2}},|p| {\mathrm{d}}q {\mathrm{d}}p)$, satisfying the condition (\[criterium\]) and such that $ F(q,p)=0 $ for $ p < 1 $, vanishes identically. The condition (\[criterium\]) means that for a. e. $ q \in \mathbb{R} $ the Fourier transform in the second variable of the function $ G ( q , p )
= F(q,p)\overline{\varphi \left( p^{ -1} \right)}$ vanishes on a set of positive measure. On the other hand, $ G ( q , p ) = 0 $ for $ p < 1 $. By properties of the Hardy classes this implies that the function $ G (q,\cdot) \equiv 0 $ for a. e. $ q \in \mathbb{R} $, and thus $ F \equiv 0 $.
A similar assertion holds for the strip $ {\mathbb{R}^{}}
\times[-1,0]$. Considering the orthogonal sum, we obtain the following
\[half\] Let the functions $ \varphi_{1,2} \in L^\infty ( -1 , 1 ) $ be such that $ \mathrm{supp}\,\varphi_1 = [ 0 , 1 ] $, $
\mathrm{supp}\,\varphi_2 = [ -1 , 0 ] $. Then the Boltzmann operator of the form $$L= i\mu{\partial}_x + i
c_1(x) \varphi_1 ( \mu ) \int_{-1}^1 \cdot\,\overline{\varphi_1
(\mu')}\,{\mathrm{d}}\mu' + i c_2 (x) \varphi_2 (\mu)\int_{-1}^1
\cdot\,\overline{\varphi_2 (\mu')}\,{\mathrm{d}}\mu'$$ is completely nonself-adjoint if neither of the functions $c_1 $, $ c_2 $ vanishes identically.
Thus, in the anisotropic case the Boltzmann operator may turn out to be completely nonself-adjoint for perturbations having arbitrarily small support.
Three Dimensional Boltzmann Operator
====================================
Let $ \mathbb{S}^2 = \{ s \in \mathbb{R}^3 :
\; |s| = 1 \} $. The 3D Boltzmann operator acts in the space $L^2({\mathbb{R}^{3}}\times \mathbb{S}^2)$ of functions $u =
u(x,\mu)$ ($x\in{\mathbb{R}^{3}}$, $\mu\in \mathbb{S}^2$) by the formula: $$( Lu ) ( x , \mu ) = i\mu \left( \nabla_x u \right) ( x , \mu ) +
i \sum_{\ell=1}^{n}c_{\ell}(x)\varphi_{\ell}(\mu)
\int_{\mathbb{S}^2} u ( x , \mu^\prime ) \overline {\varphi_\ell (\mu')}\,{\mathrm{d}}S(\mu').
\label{Bo3}$$
Here $c_{\ell} \in L^{\infty}({\mathbb{R}^{3}}) $ and $ \varphi_{\ell} \in L^2
( \mathbb{S}^2 ) $, $\ell = 1,...,n$, are known functions. The operator $ L $ is a bounded perturbation of the operator $ L_0 =
i\mu\nabla_x $ selfadjoint on is natural domain.
\[3dim\] The selfadjoint subspace of the Boltzmann operator (\[Bo3\]) is non-trivial.
Let $ U: H \to H $ be the Fourier transform in the $ x $ variable. Let $ \hat L = U L U^* $, $ \hat L_0 = U L_0
U^* $ etc. As in the 1D case, a vector $u$ belongs to the selfadjoint subspace of the operator (\[Bo3\]) if, and only if $$\int_{\mathbb{S}^2} v(x-\mu
t,\mu)\overline{\varphi_{\ell}(\mu)}\,{\mathrm{d}}S(\mu) = 0$$ for all $\ell = 1,...,n$, $t\in{\mathbb{R}^{}}$, and a. e. $x\in\mathrm{supp}\,c_{\ell}$. It is easy to see that this equality is satisfied if $\hat{v}:=Uv$ obeys $$\label{bobobo}
\int_{\mathbb{S}^2} \exp\big(it\langle p,\mu\rangle_{{\mathbb{R}^{3}}}\big)
\hat{v}(p,\mu)\overline{\varphi_{\ell}(\mu)}\,{\mathrm{d}}S(\mu) = 0$$ for a. e. $p\in{\mathbb{R}^{3}} $ and all $t\in{\mathbb{R}^{}}$, $\ell = 1,...,n$.
For each $p\in {\mathbb{R}^{3}}$ define the spherical coordinates $(\psi_{p}, \theta_{p})$ on the sphere $\mathbb{S}^2$ of the $ \mu $ variable choosing the polar axis aimed along the vector $ p $. Here $\theta_p $ and $\psi_p$ are the azimuthal and precession angles, respectively. Then, obviously, any smooth function $u\in L^2({\mathbb{R}^{3}}\times
\mathbb{S}^2)$ such that $$\int_{-\pi}^{\pi} u\big(p,\mu(\psi_{p}, \theta_{p})
\big)\overline{\varphi_{\ell}\big(\mu(\psi_{p},
\theta_{p})\big)}\,{\mathrm{d}}\psi_{p} = 0$$ for a. e. $p\in{\mathbb{R}^{3}}$, $\theta_{p}\in
[-\frac{\pi}{2},\frac{\pi}{2}]$, $\ell = 1,...,n$, satisfies (\[bobobo\]), and hence $U^\ast u$ belongs to the subspace $ H_0 $.
The reducing subspace of the selfadjoint part of the operator constructed in the course of the proof, is, in general, a proper subspace in $ H_0 $.
[99]{}
B. Szökefalvi-Nagy and C. Foias, [*Analyse Harmonique des Operateurs de l$^{\prime }$Espase de Hilbert*]{}, Masson et C$^{ie}$/ Academiai Kiado, 1967.
S.N. Naboko, “A functional model of perturbation theory and its applications to scattering theory”, [*Trudy MIAN*]{} [**147**]{} (1980), 86 - 114 ([*Russian*]{}); English transl. in: [*Proc. Steklov Inst. Math.*]{} (1981), No. 2, 85 - 116.
J. Lehner, “The spectrum of the neutron transport operator for the infinite slab”, [*J. Math. Mech.*]{}, [**11**]{} (1962), No. 2, 173–181.
B.S. Pavlov, “Selfadjoint dilation of the dissipative Schrödinger operator and its resolution in terms of eigenfunctions”, [*Mat. Sb.*]{}, [**102**]{}:4 (1977), 511–536 ([*Russian*]{}); English transl. in: [*Math. USSR Sbornik*]{}, [**31**]{} (1977), No. 4, 457 - 478.
S.B. Shikhov, [*Problems in the Mathematical Theory of Reactors. Linear Analysis*]{}, Atomizdat, Moscow, 1973 ([*Russian*]{}).
Yu. Kuperin, S. Naboko and R. Romanov, “Spectral analysis of the transport operator: a functional model approach”, [*Indiana Univ. Math. J.*]{} [**51**]{}(2002), No. 6, 1389 - 1425.
V. Havin and B. Jöriсke, [*The uncertainty principle in harmonic analysis*]{}, Springer-Verlag, Berlin, 1994.
P. Kargaev, “The Fourier transform of the characteristic function of a set, vanishing on an interval”, [*Mat. Sb.*]{}, [**117(159)**]{}:3 (1982), 397–411 ([*Russian*]{}); English transl. in: [*Math. USSR Sbornik*]{}, [**45**]{}:3 (1983), 397–410.
[^1]: The was partially suppported by INTAS Grant 05-1000008-7883 and RFBR Grant 06-01-00249.
[^2]: that is, the orthogonal projection on $ H_0 $ in $ H $ preserves the domain $\cal D $ of the operator $ D $, and $ D f \in H_0 $, $ D^* f \in H_0 $ for all $ f \in H_0
\cap {\cal D} $.
[^3]: This means that the restriction is unitarily equivalent to an orthogonal sum of infinitely many copies of the operator of multiplication by the independent variable in $ L^2
$ over this interval.
[^4]: Theorem 2 in the situation under consideration only ensures the existence of the spectrum in a vicinity of $ 0 $.
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"Pre-Trigonometry"
Section M-7 describes the basic problem of trigonometry (drawing on the left): finding the distance to some far-away point C, given the directions at which C appears from the two ends of a measured baseline AB.
This problem becomes somewhat simpler if:
The baseline is perpendicular to the line from its middle to the object, so that the triangle ABC is symmetric. We will denote its side by r:
AC = BC = r
The length c of the baseline AB is much less than r. That means that the angle α between AC and BC is small; that angle is known as the parallax of C, as viewed from AB.
We do not ask for great accuracy, but are satisfied with an approximate value of the distance--say, within 1%.
The method presented here was already used by the ancient Greeks more than 2000 years ago. They knew that the length of a circle of radius r was 2πr, where π (a modern notation, not one of the Greeks, even though π is part of their alphabet) stands for a number a little larger than 3, approximately
π = 3.14159...
(The Greek mathematician Archimedes derived π to about 4-figure accuracy, though he expressed it differently, since decimal fractions only appeared in Europe some 1000 years later.)
Draw a circle around the point C, with radius r, passing through A and B (drawing above). Since the angle α is so small, the length of the straight-line "baseline" b (drawing on the right; distance AB renamed) is not much different from the arc of the circle passing A and B. Let us assume the two are the same (that is the approximation made here). The length of a circular arc is proportional to the angle it covers, and since
b covers an angle
α2π r covers an angle 360°
we get
2π r = (360°/
α) b
and dividing by 2π
r = (360°/2 π α) b
Therefore, if we know b, we can deduce r. For instance, if we know that α = 5.73°, 2 π α = 36° and we get (approximately)
Stretch your arm forward and extend your thumb, so that your thumbnail faces your eyes. Close one eye (A') and move your thumb so that, looking with your open eye (B'), you see your thumbnail covering the landmark A.
Then open the eye you had closed (A') and close the one (B') with which you looked before, without moving your thumb. It will now appear that your thumbnail has moved: it is no longer in front of landmark A, but in front of some other point at the same distance, marked as B in the drawing.
Estimate the true distance AB, by comparing it to the estimated heights of trees, widths of buildings, distances between power-line poles, lengths of cars etc. The distance to the landmark is 10 times the distance AB.
Why does this work? Because even though people vary in size, the proportions of the average human body are fairly constant, and for most people, the angle between the lines from the eyes (A',B') to the outstretched thumb is about 6°, close enough to the value 5.73° for which the ratio 1:10 was found in an earlier part of this section.
That angle is the parallax of your thumb, viewed from your eyes. The triangle A'B'C has the same proportions as the much larger triangle ABC, and therefore, if the distance B'C to the thumb is 10 times the distance A'B' between the eyes, the distance AC to the far landmark is also 10 times the distance AB.
The biggest baseline available for measuring such distances is the diameter of the Earth's orbit, 300,000,000 kilometers. The Earth's motion around the Sun makes it move back and forth in space, so that on dates separated by half a year, its positions are 300,000,000 kilometers apart. In addition, the entire solar system also moves through space, but that motion is not periodic and therefore its effects can be separated.
And how much do the stars shift when viewed from two points 300,000,000 km apart? Actually, very, very little. For many years astronomers struggled in vain to observe the difference. Only in 1838 were definite parallaxes measured for some of the nearest stars--for Alpha Centauri by Henderson from South Africa, for Vega by Friedrich von Struve and for 61 Cygni by Friedrich Bessel.
Such observations demand enormous precision. Where a circle is divided into 360 degrees (360°), each degree is divided into 60 minutes (60')--also called "minutes of arc" to distinguish them from minutes of time--and each minute contains 60 seconds of arc (60"). All observed parallaxes are less than 1", at the limit of the resolving power of even large ground-based telescopes.
In measuring star distances, astronomers frequently use the parsec, the distance to a star whose yearly parallax is 1"--one second of arc. One parsec equals 3.26 light years, but as already noted, no star is that close to us. Alpha Centauri, the sun-like star nearest to our solar system, has a distance of 4.3 years and a parallax of 0.75".
Alpha Centauri is not a name, but a designation. Astronomers designate stars in each constellation by letters of the Greek alphabet--alpha, beta, gamma, delta and so forth, and "Alpha Centauri" means the brightest star in the constellation of Centaurus, located high in the southern skies. You need to be south of the equator to see it well.
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New security threats are re-shaping international borders. It wouldn’t be accurate, in the world of today, to imagine these borders as merely physical frontiers between neighbouring countries. These borders are rather a complex set of physical and virtual spaces, through which our personal data also travels. And sometimes we are not even aware of that.
What are biometric identifiers?
All of us have unique and measurable biological characteristics, which can be processed by biometric identity systems. In some cases, these characteristics are also relatively permanent. Fingerprints are the most widely used biometric identifier, but there are many others, such as facial images, voice patterns, irises, complete palm prints, and even our DNA structure.
Through the use of specialized devices, information systems are able to translate these characteristics into mathematical patterns that are easy to process. In an ideal scenario (that’s to say when biometric identifiers are correctly taken, processed and matched), the most biometric identifiers used, the easiest it is for an information system to accurately identify a specific individual.
Biometrics can help to prevent mistaken identity, and can reduce the risk of people being wrongfully apprehended and arrested. They could also potentially be used to optimise the tracking of people who are reported missing. In addition, the risk of discriminatory ethnic profiling at borders may be reduced by introducing a higher degree of automation in border control.
The processes controlling the use of biometrics, however, must be audited and reviewed regularly to guarantee the correct use of the information systems, to observe the respect of the principle of purpose limitation and hence, safeguarding the fundamental rights of the travellers.
What happens when we cross an international border?
Depending on the existing agreement between the country of origin of an individual, the country where that individual is coming from (which may not be the same), and the country to which that person is travelling (which may or may not be the country of origin), biometric identifiers might be taken at the time the person physically crosses the border. Sometimes these identifiers are even taken in advance, when applying for a visa. This means that our personal identifiers are being stored and managed by third parties, even if we finally decide not to travel.
This has a direct and immediate effect on our right to privacy, on the securitization of migrations, and on the forms of surveillance and state control practices. And it’s happening all over the world.
Implications
The use of biometrics may challenge our right to privacy if the systems used to obtain and process the information are not secure enough, have not been designed considering privacy aspects and are not audited regularly.
Furthermore, controls must be put in place to guarantee the biometric data is being used solely for the specific purpose of border control. If this is not the case, individuals must be informed and must be able to provide consent.
If there is an information breach, the implications for the security and privacy of the victims are enormous.
False positives and false negatives may occur, as the use of biometrics is not always completely accurate, not only due to technical factors but also because such accuracy relies on human factors, such as those related to a right association between a biometric identifier and the non-biometric data of an individual (names, surnames, etc.). This means that an individual may be mistaken for someone else – and this is a major security concern, but also something that potentially leads to someone’s rights being abused.
Mechanisms for conflict resolution (automated or not) must be put in place too, in order to solve potential flaws of the systems.
The use of biometrics may have undesired consequences for risk populations, immigrants, asylum seekers or refugees, which is why the rules of use of these systems must be clear, as should the regulatory framework. For some of these groups the process may be a traumatic experience. In order to avoid making bad decisions, there is a need to ensure that the data connected with the biometric identifier is correct and of high quality.
The use of biometrics is already a reality and is becoming a standard. When used correctly, this technology could be very helpful for different purposes. Nonetheless, its regulation is necessary, as its misuse may compromise security, privacy and fundamental rights. At Eticas Foundation we are interested in leading this discussion and providing valuable resources related to the topic. | https://eticasfoundation.org/migration_and_biometrics |
The topic of renewable energy is an evergreen subject, especially, in a world dominated by fossil fuels. Renewable energy is widely talked about in the contemporary world because it is unlimited, which means it’s sustainable and does not emit greenhouse gasses that are detrimental to the environment and human health.
A classic example of renewable energy is wave energy. Wave energy can be considered a large and mostly untapped reservoir. Harnessing the power of waves breaking on the shore, or that of the phenomenal mass displacement of the gulf stream could potentially bring a significant amount of renewable energy in mankind’s portfolio. In this article, we will discuss the wave energy diagram. Read this new blog in Linquip to find out more.
What is wave energy?
Wave power is the capture of energy of wind waves to do useful work; for example, electricity generation, water desalination, or pumping water. A machine that exploits wave power is a wave energy converter (WEC).
The wave energy formula is:
With P the wave energy flux per unit of wave-crest length, Hm0 the significant wave height, Te the wave energy period, ρ the water density, and g the acceleration by gravity. The above formula states that wave power is proportional to the wave energy period and to the square of the wave height. When the significant wave height is given in meters, and the wave period in seconds, the result is the wave power in kilowatts (kW) per meter of wavefront length.
How does wave energy work?
There are many types of technology used to convert wave energy into electricity. One of these methods is Oscillating bodies that use floating buoys or platforms rising and falling with the swell. They are fixed to the seafloor via a hydraulic pump. The buoy moves up and down along ocean swell crests and troughs, activating the hydraulic pump which pushes water or air through a turbine, which in turn rotates a generator to produce electricity.
Below is a diagram of how wave energy is used to generate electricity.
The diagram of wave energy devices
As mentioned above, many types of wave energy devices were designed and are currently being used to extract electrical energy from wave energy. In this part, we will explain the working principle of some of the main types with their diagrams.
-
Point Absorber
The pitching and heaving of the waves cause a relative motion between an absorber and reaction point. The left-hand wave energy device shown in the figure below uses a heavy ballast plate suspended below the floating buoy. The buoy is prevented from floating away by a mooring line attached to a sea-floor anchor. This mooring line allows the point absorber to operate offshore in deeper waters.
As the buoy bobs up-and-down in the waves, an oscillatory mutual force reaction is generated between the freely moving absorber and the heavy plate causing a hydraulic pump in between to rotate a generator producing electricity. The middle wave energy device operates in a similar manner to the previous floating buoy device. The difference this time is that the freely heaving buoy reacts against a fixed reaction point such as a fixed dead-weight on the ocean floor. As this type of point absorber is bottom-mounted, it is operated in shallower nearshore locations.
The third device is an example of a linear absorber (wave attenuator) that floats on the surface of the water. It is tethered to the ocean floor so that it can swing perpendicularly towards the incoming waves. As the waves pass along the length of this snake-like wave energy device, they cause the long cylindrical body to sag downwards into the troughs of the waves and arch upwards when the crest of the wave is passing.
Below is shown the diagram of the point absorber.
-
Oscillation water column
As the incident waves outside enter and exit the chamber, changes in wave movement on the opening cause the water level within the enclosure to oscillate up and down acting like a giant piston on the air above the surface of the water, pushing it back and forth. This air is compressed and decompressed by this movement every cycle. The air is channeled through a wind turbine generator to produce electricity as shown.
The type of wind turbine generator used in an oscillating water column design is the critical element to its conversion efficiency. The air inside the chamber is continually reversing direction with every up-and-down movement of the seawater producing a sucking and blowing effect through the turbine. If a conventional turbine were used to drive the attached generator, this too would continuously be changing direction in unison with the airflow. To overcome this problem the type of wind turbine used in oscillating water column schemes is called a Wells Turbine.
The Wells turbine has the remarkable property of rotating in the same direction regardless of the direction of airflow in the column. The kinetic energy is extracted from the reversing airflow by the Wells turbine and is used to drive an electrical induction generator. The speed of the airflow through the wells turbine can be enhanced by making the cross-sectional area of the wave turbine duct much less than that of the sea column.
The wave energy diagram of the Oscillation water column is illustrated in the figure below.
-
Overtopping device
The basic impoundment structure can be either fixed or a floating structure tethered to the sea bed. The wave overtopping device uses a ramp design on the device to elevate part of the incoming waves above their natural height.
As the waves hit the structure they flow up a ramp and over the top (hence the name “overtopping”), into a raised water impoundment reservoir on the device in order to fill it. Once captured, the potential energy of the trapped water in the reservoir is extracted using gravity as the water returns to the sea via a low-head Kaplan turbine generator located at the bottom of the wave capture device.
Other such wave capture devices are located at the shoreline where the waves are channeled along a horizontal man-made channel. This channel is funnel-shaped which is wide towards the sea where the waves enter and gradually narrows towards an impoundment reservoir at the other end. As the waves propagate along the narrowing channel, the wave height is lifted due to the funneling effect to a level exceeding the horizontal upper edge of the channel wall, excess water from the wave is allowed to spill into a confined basin above the normal sea level.
As the water is now at a height above the sea level, the potential energy of the water trapped in the basin is then extracted by draining the water back to the sea through a low-head Kaplan turbine as before.
The diagram of the overtopping device is shown below.
So, now you know everything you need to know about the wave energy diagram. If you enjoy this article in Linquip, let us know what you think by leaving a reply in the comment section. We will be more than glad to have your viewpoint on the article. Is there any question we can help you through? Feel free to sign up on our website where our experts are prepared to provide you with the most professional advice. | https://www.linquip.com/blog/the-ultimate-overview-of-wave-energy-diagram/ |
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United States District Court, E.D. Texas, Texarkana Division
November 4, 2019
TOMMY LEE YATESv.CATHY McPEAK, ET AL.
MEMORANDUM ADOPTING REPORT AND RECOMMENDATION OF THE
UNITED STATES MAGISTRATE JUDGE AND GRANTING IN PART
DEFENDANTS' MOTION FOR SUMMARY JUDGMENT ON THE ISSUE OF
ADMINISTRATIVE REMEDIES
RODNEY
GILSTAP, UNITED STATES DISTRICT JUDGE.
The
Plaintiff Tommy Lee Yates, proceeding pro se, filed this
civil rights lawsuit under 42 U.S.C. §1983 complaining
of alleged violations of his constitutional rights. This
Court ordered that the case be referred to the United States
Magistrate Judge pursuant to 28 U.S.C. §636(b)(1) and
(3) and the Amended Order for the Adoption of Local Rules for
the Assignment of Duties to United States Magistrate Judges.
As Defendants, Plaintiff named Telford Unit Practice Manager
Cathy McPeak, Nurse Steven Roberts, Nurse T. Fowler, Nurse
Practitioner J. Martin, and four unknown defendants
identified as policymakers. This Order concerns the motion
for summary judgment limited to the issue of exhaustion of
administrative remedies filed by the identified Defendants
and also addresses the unknown Defendants.
I.
Background
Plaintiff
asserts on December 24, 2015, he slipped in a puddle of water
and broke his right hand. He took a shower and discovered he
could not use his hand, so after he showered, he told Officer
Mathis he had fallen and needed to go to the medical
department. He complains of the treatment he received from
Nurse Roberts, Nurse Fowler, and Nurse Practitioner Martin
and states Practice Manager Cathy McPeak denied his
grievances.
II. The
Defendants' Motion for Summary Judgment on the Issue of
Exhaustion
The
Defendants filed a motion for summary judgment on the issue
of exhaustion stating that Plaintiff was injured on December
24, 2015, but did not file his Step One grievance on the
incident until April 17, 2016. Because the grievance was not
filed within 15 days of the incident, the Defendants argues
that it was untimely and thus did not serve to exhaust
Plaintiff's administrative remedies. Plaintiff did not
file a response to the motion for summary judgment.
III.
The Report of the Magistrate Judge
After
review of the pleadings, the Magistrate Judge issued a Report
recommending the motion for summary judgment be granted with
regard to Practice Manager McPeak, but denied as to the other
named Defendants. The Magistrate Judge also recommended
summary judgment be granted in favor of the unknown parties.
Although
the Defendants argued Plaintiff's grievance was untimely,
the Magistrate Judge observed the grievance was not rejected
as untimely, but was answered on the merits. Consequently,
the Defendants cannot now claim failure to exhaust based upon
untimeliness. Gates v. Cook, 376 F.3d 323, 331 and
n. 6 (5th Cir. 2004).
However,
the Magistrate Judge went on to state Plaintiff did not file
any Step One grievances complaining about Practice Manager
McPeak or about any unknown policymakers. While he did
mention Practice Manager McPeak in three of his Step Two
grievance appeals, complaining about her responses to his
Step One grievances, the Magistrate Judge concluded this did
not exhaust Plaintiff's administrative remedies against
Practice Manager McPeak or the unknown defendants because in
order to exhaust, the prisoner must pursue his claims through
both steps of the grievance procedure. Johnson v.
Johnson, 385 F.3d 503, 515 (5th Cir. 2004). Although the
unknown defendants did not join in the motion for summary
judgment, the Magistrate Judge determined they were entitled
to benefit from the motion. Lewis v. Lynn, 236 F.3d
766, 768 (5th Cir. 2001).
IV. The
Plaintiff's Objections
The
Defendants did not file objections to the Report;
accordingly, they are barred from appealing the factual
findings and legal conclusions of the Magistrate Judge which
are accepted and adopted by the district court except upon
grounds of plain error. Douglass v. United Services
Automobile Association, 79 F.3d 1415, 1430 (5th Cir.
1996) (en banc).
In his
objections, Plaintiff appears to contend he made his need for
medical care known to the medical staff in various ways,
including through the grievance he filed. He argues he should
have a trial on his deliberate indifference claims, but
overlooks the fact the Magistrate Judge did not recommend
dismissal of his deliberate indifference claims against the
nurses or the nurse practitioner. Plaintiff complains neither
the unit grievance officer nor Practice Manager McPeak
contacted him to ascertain and clarify his complaint or
perfect a true investigation.
Plaintiff
contends Practice Manager McPeak “fails in duty,
responsibility, and obligation while acting under color of
state law, ” but he does not address the fact he did
not file any Step One grievances complaining about the
actions of Practice ...
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Dried bonito dashi: taste qualities evaluated using conditioned taste aversion methods in wild-type and T1R1 knockout mice.
The primary taste of dried bonito dashi is thought to be umami, elicited by inosine 5'-monphosphate (IMP) and L-amino acids. The present study compared the taste qualities of 25% dashi with 5 basic tastes and amino acids using conditioned taste aversion methods. Although wild-type C57BL/6J mice with compromised olfactory systems generalized an aversion of dashi to all 5 basic tastes, generalization was greater to sucrose (sweet), citric acid (sour), and quinine (bitter) than to NaCl (salty) or monosodium L-glutamate (umami) with amiloride. At neutral pH (6.5-6.9), the aversion generalized to l-histidine, L-alanine, L-proline, glycine, L-aspartic acid, L-serine, and monosodium L-glutamate, all mixed with IMP. Lowering pH of the test solutions to 5.7-5.8 (matching dashi) with HCl decreased generalization to some amino acids. However, adding lactic acid to test solutions with the same pH increased generalization to 5'-inosine monophosphate, L-leucine, L-phenylalanine, L-valine, L-arginine, and taurine but eliminated generalization to L-histidine. T1R1 knockout mice readily learned the aversion to dashi and generalized the aversion to sucrose, citric acid, and quinine but not to NaCl, glutamate, or any amino acid. These results suggest that dashi elicits a complex taste in mice that is more than umami, and deleting T1R1 receptor altered but did not eliminate their ability to taste dashi. In addition, lactic acid may alter or modulate taste transduction or cell-to-cell signaling.
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The Kepler spacecraft of NASA, to date, has spotted more than thousand planets outside our solar system. One thing astronomers have found when examining those planets is that they have minimum resemblance with planets of our solar system.
The majority of those exoplanets are located very close to the star they are orbiting and when it comes to their size, they are larger than Earth and smaller than Neptune.
The planets in our solar system, on the contrary, are located far away from the Sun. A recent research conducted by astronomers Konstantin Batvgin and Gregory Laughlin has revealed that the two planets Saturn and Jupiter might be responsible for this.
In a research paper published recently in the widely read science journal Proceedings of the National Academy of Sciences, Laughlin and Batvgin wrote that during the early years of our solar system, Jupiter used to be much nearer to the Sun than what it’s now.
According to the astronomers the distance between Jupiter and the Sun used to be just 140 miles. The present orbit of the giant planet is located 483 miles away from the Sun. Scientists say that this has happened due to constant gravitational interactions between the Sun and Jupiter.
It is believed that the massive size of Jupiter and the strong gravity of the planet took its toll on all the super-Earths that used to exist during the early days of our Solar System. According to astronomers, Jupiter forced those super-Earths to shift their orbits and eventually get destroyed by the heat of the Sun.
The authors of the above mentioned paper wrote that this finding perfectly fits with recent developments regarding the causes behind the evolution of our solar system. What’s more, the findings by Laughlin and Batvgin have also helped in filling in several gaps.
However, Laughlin and Batvgin are not the first ones to suggest that Saturn and Jupiter, used to be much nearer to the Sun. In 2001, a research group partly established the theory; the study was revived again a decade later i.e. in 2011.
I suspect Jupiter was indeed much closer to Sol than now. I have proposed that Sol filled the space now occupied by the rocky inner planets. Sol’s controlled implosion under a massive magnetic field reduced him to his current size, and produced the rocky inner planets.
There may not be sufficient information to theorize the 2 body novas scientists prefer, and I suggest that magnetic fields are the responsible party. Since the systems Kepler has found are not our type, one may theorize that Sol’s system is newly created, aka the implosion and creation of the secondary inner planetary system, and that with time, Jupiter will indeed move into the inner planets and destroy them, producing the system Kepler now sees almost exclusively.
Then the question is why are we the last man standing? The other choice is that we are the leading man in this play and everyone else has yet to follow suit. That does not seem to be the case.
May I suggest, as I have done in my papers on Google Drive, that our result stems from an overloaded magnetic field that blew apart the black hole of the Magellenic galaxy, and resulted in a rift in space and time allowing the solar system known as Sol’s to be rifted to our current place in the Orion Arm of the Milky Way.
What caused the overload? Perhaps the compression of matter that scientists now see instead of continual and faster expansion. | https://www.thehoopsnews.com/study-suggests-that-jupiter-destroyed-early-planets-4071 |
IT Services is committed to making IT resources at Warwick accessible to all. Access to equipment and other adjustments to meet users' needs is handled through our Human Resources Department for staff, and through the Disability Co-ordinator for students. Both these offices are equipped to carry out assessments and to make recommendations, so in order to make sure that you receive the best possible support for your needs, please contact one of them in the first instance. The disability information web site also contains information relating to physical access, dyslexia, disabled students' allowances and more.
The Library provides support for students on assistive technology and accessibility.
We are happy to make adjustments to our facilities where possible; please contact us to discuss any changes that would help you.
A text only display of web pages can be accessed from the top of any page by clicking on the link entitled 'Text only'. We welcome feedback on the effectiveness of our web pages for visually impaired users. | https://warwick.ac.uk/services/its/about/policies/accessibility |
In Washington, D.C. medical malpractice cases, the plaintiff must prove several elements in order to prove their case. One of the elements that a plaintiff must establish is that the care rendered by the defendant medical provider fell “below that which would have been taken by a reasonably prudent physician.”
The idea behind this requirement is that the law does not require doctors to be perfect and always obtain the best results. However, when the care the doctor provides falls below the generally accepted standard of care, the doctor can be held legally responsible for any harm suffered by the patient.
In order to establish the applicable standard of care, and to show that the defendant’s care fell below that level, a Washington, D.C. plaintiff must present an expert witness. An expert witness is usually a doctor who specializes in the same field as the defendant doctor, or who possesses some specialized knowledge in that area of medicine. A plaintiff’s failure to present an expert witness may result in a case’s premature dismissal. A recent case illustrates how one plaintiff’s case was dismissed based on a failure to include an expert’s affidavit supporting his claim.
The Facts of the Case
The plaintiff was an inmate at a correctional facility. The defendant doctor had contracted to be on call 24 hours a day. However, the facility was staffed with nurses most of the time, and the doctor would only occasionally visit when it was necessary. The doctor left the nurses with a rubber signature stamp so that they could submit lab requests and “sign” other paperwork, including the form documenting an inmate’s refusal of medication.
One day, the plaintiff complained of nausea and severe abdominal pain. The defendant nurse was on duty and prescribed medication. The plaintiff, believing that the medication would not help, refused it. The form documenting his refusal was stamped with the doctor’s signature by the nurse. This occurred for three days in a row, at which point the plaintiff was found lying on the floor of his cell. He was subsequently hospitalized and treated. The doctor was not made aware of the plaintiff’s condition until the plaintiff was hospitalized.
The plaintiff filed a medical malpractice lawsuit against the nurse and the doctor, claiming the rubber-stamp system created a situation in which his legitimate medical issues were not adequately being addressed. However, the only expert witness he presented did not authoritatively state that the care provided by the defendants fell below the generally accepted level of care. Thus, the court dismissed the plaintiff’s claim due to the lack of expert testimony.
Have You Been a Victim of Medical Malpractice?
If you or a loved one has recently been a victim of what you believe to have been negligent medical care, you may be entitled to monetary compensation through a Washington, D.C. medical malpractice lawsuit. These cases, however, can be extremely complex and will require at least one expert medical witness. The dedicated Washington, D.C. personal injury attorneys at the law firm of Lebowitz & Mzhen Personal Injury Lawyers have extensive experience handling all types of medical malpractice claims, and we focus on the unique aspects of each case and each client to ensure that we craft our representation accordingly. Call 410-654-3600 to schedule a free consultation with an attorney today.
More Blog Posts: | https://www.washingtondcinjurylawyerblog.com/medical-malpractice-plaintiffs-case-dismissed-lack-expert-testimony/ |
The properties of metal ions are determined by their size and charge. The lanthanide elements are all typically trivalent and are almost identical in size, and their chemical properties are almost identical. The separation of one of the lanthanide from another is an exceedingly difficult task, almost as difficult as the separation of isotopes of one element. The classical methods of separation exploits slight differences in basic properties, stability or solubility. These are outlined below. However, in recent years, the only methods used in separating the lanthanide elements are ion exchange and valency change.
Precipitation
Precipitation is also used in separating the lanthanide elements. With a limited amount of precipitating agent, the substance with the lowest solubility is precipitated most rapidly and most completely. Suppose hydroxyl ions are adder to a solution containing mixture of Ln(NO3)3. The weakest base Lu(OH)3 is precipitated first, and the strongest base La(OH)3 is precipitated last. The precipitate contains more of the elements at the right of the series. Thus the solution contains more of the elements at the left of the series. The precipitate can be filtered off. Only partial separation is effected, but the precipitate can be redissolved in HNO3 and the process repeated to obtain greater purity.
Thermal Reaction
If a mixture of Ln(NO3)3 is fused, a temperature will be reached when the least basic nitrate changes to the oxide. The mixture is leached with water. The nitrates dissolve and can be filtered off, leaving the insoluble oxides. The oxides are dissolved in HNO3 and the process repeated.
Fraction Crystallization
This can be used to separate lanthanide salts. The solubility decreases from La to Lu. Thus, salts at the end of the series will crystallize out first. Nitrates, sulphates, bromates, perchlorates and oxalates have all been used as and also have double salts such as Ln(NO3)2 . 3Mg(NO3)2 . 24H2O because they crystallize well. The process needs repeating many times to obtain good seperations. Non-aqueous solvents such as diethyl ether have been used to separate Nd(NO3)3 and Pr(NO3)3.
Complex Formation
A mixture of lanthanide ions is treated with a complexing agent such as EDTA (ethylenediaminetetraacetic acid). All the ions form complexes. Those ions at the right hand side of the lanthanide series Lu3+ form the strongest complexes as they have the smaller ions. Oxalates of the lanthanide are insoluble. However, addition of oxalate ions to this solution does not give a precipitate since the Ln3+ ions are all complexed with EDTA.
If some acid is added to the solution, the least stable EDTA complexes are dissociated. This releases ions at the left hand side of the series Ce3+, Pr3+, Nd3+ which are immediately precipitated as the oxalates. These are filtered off. Separation is not complete, so the oxalates are redissolved and the process repeated many times.
Solvent Reaction
The heavier Ln3+ ions are more soluble tri-n-butylphosphate than are the lighter Ln3+ ions. Their solubilities in water and ionic solvents, however, are reversed. The ratios of the partition coefficients of La(NO3)3 and Gd(NO3)3 between a solution of the metal ions in strong HNO3 and tri-n-butylphosphate is 1 : 106. This difference is quite small, but by using a continuous counter-current apparatus a very large number of partitions can be performed automatically. This is much less tedious than performing 10,000 or 20,000 crystallizations. Kilogram quantities of 95% pure Gd has been obtained by this method. The technique was originally developed in the early days of atomic energy to separate and identify the lanthanide elements produced by fission of uranium.
Valency Change
The Valency change is a property used in separating the lanthanide elements. A few lanthanides have oxidation states of (+IV) or (+II). The properties of Ln4+ or Ln2+ are so different from those of Ln3+ that separation is fairly easy.
Cerium can be separated from lanthanide mixtures quite easily as it is the only lanthanide which has Ln4+ ions stable in aqueous solution. Oxidizing a solution containing a mixture of Ln3+ ions with NaOCl under alkaline conditions produces Ce4+. Because of the higher charge, Ce4+ is much smaller and less basic than Ce4+ or any other Ln3+. The Ce4+ is separated by carefully controlled precipitation of CeO2 or Ce(IO3)4, leaving the trivalent ions in solution.
Alternatively, Ce4+ cvan readily be extracted from other Ln3+ lanthanides by solvent extraction in HNO3 solution using tributyl phosphate. Ninety-nine per cent pure Ce can be obtained in one stage from a mixture containing 40% Ce.
Valency change is still a useful method of purifying Ce and Eu despite the advent in recent years for exchange.In a similar way, the properties of Eu2+, are very different from those of Ln3+. European sulphate Eu2+SO resembles the Group 2 sulphates and is insoluble in water. Ln3+ sulphates are soluble. If a solution of Ln3+ ions is reduced electrolytically using a mercury cathode, or by using zinc amalgam, then Eu2+ will be produced. If H2SO4 is present EuSc4 will be precipitated. This can be filtered off. (Sm2+ and Yb2+ may also produced in the same way, but these are oxidized slowly by water).
Ion Exchange
This is the most important, the most rapid and most effective general method for the separating the lanthanide elements and their purification
. A solution of lanthanide ions is run down a column of synthetic ion-exchange resin such as Dowex-50. This is a sulphonated polystyrene and contains the functional group – SO3H. The Ln3+ ions are absorbed onto the resin and replace the hydrogen atom on – SO3H.
Ln3+(aq) + 3H(resin)(s) Ln(resin)3(s) + 3H+(aq)
The H+ ions produced are washed through the column. Then the metal ions are eluted, that is are washed off the column in a selective manner. The eluting agent is a complexing agent, for example a buffered solution of citric acid/ammonium citrate, or a dilute solution of (NH4)3(H.EDTA) at pH 8. Consider the citrate case. An equilibrium is set up;
Ln(resin)3 + 3H+ + (citrate)3 – 3H(resin) + Ln(citrate)
As the citrate solution flows down the column, Ln3+ ions are removed from the resin and form the citrate complex. A little lower down the column the Ln3+ ions go back onto the resin. As the citrate solution runs down the column, the metal ions form complexes alternately with the resin and the citrate solution many times. The metal ion gradually travels down the column, and eventually passes out of the bottom of the column as the citrate complex. The smaller lanthanide ions such as Lu3+ form stronger complexes with the citrate ions spend more time in solution, and less time on the column, and are thus eluted from the column first. The difference metal ions present separate into bands which pass down the column. The progress of the bands may be followed spectroscopically by atomic fluorescence. The solution leaving the column is collected by means of an automatic fraction collection in separated. The metals may be precipitated as insoluble oxalates, and then heated to give the oxides.
The chromatographic process is analogous to carrying out many separations or many crystallizations, but the separation is carried out on a single column. By using a long ion-exchange column, the elements may be obtained 99.9% pure with one pass. | https://gulpmatrix.com/methods-of-separating-the-lanthanide-elements/ |
ABOUT IF DDR
Today’s social conditions are characterized worldwide by intensified capitalist exploitation, ongoing neocolonial dependency, armed conflicts and growing signs of crisis. Unimaginable wealth stands in stark contrast to unimaginable impoverishment. The most elementary objectives, such as providing people with sufficient food and access to health, housing, education and culture, appear less and less attainable within the existing framework. On the contrary, economic dependencies, insecurity and competition are exacerbating social conditions both in the Global North and, in particular, in the countries of the Global South. The intensification of these contradictions is accompanied by growing resistance struggles that bring fundamental questions of social organization and coexistence to the fore.
Against this background, we, the International Research Centre DDR (IF DDR), are investigating the history of the German Democratic Republic (DDR) and the societal changes it achieved. In doing so we seek to enrich current debates with historical experience. The DDR’s 40-year commitment to progress, peace, anti-fascism, anti-colonialism, internationalism and socialism represents a wealth of knowledge for progressive movements seeking to tackle social challenges today.
We examine and evaluate the socialist conditions of the DDR, which stood in sharp contrast to capitalist West Germany. To this end, we analyze the functioning of key aspects of DDR society: the organisation of the economy, the health care system, the legal system, agriculture, education and so on. A critical appraisal of this history offers a deeper perspective on the fundamental possibilities and difficulties of alternative social, economic and political models.
The IF DDR focuses in particular on internationalism and how state and societal actors of the DDR built relationships with other countries and anti-colonial movements. The DDR’s solidarity and support for economic and political sovereignty are still remembered in many countries across Latin America, Africa and Asia. Indeed, the German abbreviation “DDR” often still represents a positive point of reference in these countries, and this is why we use it throughout our multilingual publications.
Our research is driven by the specific needs of the emergent anti-colonial, anti-capitalist and socialist movements that are searching for economic and social alternatives to today. We produce our material explicitly in their interest.
With a small team of young humanities scholars from East and West, the IF DDR examines available literature, together with first-hand experiences from eyewitness interviews, to develop accessible scholarly publications in a variety of media formats. We work closely with the globally organized research institute Tricontinental: Institute for Social Research, which is an important partner in connecting us with movements in the Global South.
Subscribe to our newsletter (in German): | https://ifddr.org/en/about/ |
What's Your Favorite Management Bias?
Is it Subverting Your Planning Process?
by Holly G. Green
As business leaders, we like to think of ourselves as thoughtful, rational creatures that carefully weigh all the evidence and then make logical, informed decisions.
If only it were that simple.
Far too often, our “rational” decision-making processes fall victim to our own preconceived notions about how the world should work, as well as a myriad of largely unconscious behavior patterns.
For years I’ve been talking about how our “thought bubbles” — the attitudes, beliefs and assumptions through which we view the world — negatively impact the planning process. But thought bubbles aren’t the only human trait to impact our leadership abilities. We also have a bundle of behavioral biases to deal with.
Earlier this year, the McKinsey Quarterly Journal (March 2010) published an article entitled “The Case for Behavioral Strategy.” In it, the authors identified five categories of behavioral biases that have the same negative effects on the planning process as our thought bubbles.
Action-oriented biases drive us to take action without considering all the potential ramifications of those actions. These biases cause us to overestimate the odds of positive outcomes while underestimating the chances of negative ones. We put too much faith in our ability to produce the desired outcomes, while taking too much credit for past successes. And we discount or ignore possible competitive responses during the planning process.
Interest biases stem from conflicting incentives, including non-monetary and emotional ones. They show up as misaligned incentives that reward individual effort at the expense of team, unit or organizational outcomes; inappropriate emotional attachments to certain elements of the business, such as “legacy” employees, products or brands; and disagreements (often unspoken) concerning the relative importance of key corporate objectives.
Pattern recognition biases lead us to recognize patterns where none exist. They include behaviors like putting too much stock in evidence that supports favored beliefs. Minimizing or ignoring evidence that contradicts them. Using comparisons with situations that are not directly comparable. And supporting plans based on the status of the person presenting them rather than on factual evidence.
Stability biases create a tendency toward inertia in the face of uncertainty. We lock on so hard to a treasured value that we refuse to make necessary adjustments. We allow the pain of unrecoverable historical costs to guide future courses of action. Or we fight to maintain the status quo in the absence of pressure to change it.
Social biases arise from the preference for harmony over conflict. They manifest themselves in things like the desire to quickly reach consensus rather than explore alternative courses of action, and the tendency for groups to align with the leader’s viewpoint.
Recognize any of these biases in your organization?
If not, make a list and distribute it to each member of your team prior to your next management meeting. Ask team members to put a red checkmark next to each bias that comes up during the meeting. Don’t be surprised if those lists come back with a lot of red on them!
To counter these biases, the article recommends strategies such as getting comfortable with uncertainty, and populating teams and meetings with diverse participants who bring different ways of thinking and perspectives to the table. It also recommends changing people’s “angle of vision” by learning to look at the data in new and different ways. And to deliberately shake up the status quo by challenging long-standing beliefs and assumptions, including the notion that the way we have always done things will continue to make us successful.
In the past, perhaps the most important leadership skill (from a planning standpoint) was the ability to gather information, analyze it, and then project what the future would look like three to five years out. But in today’s world, we can never have all the information. And for most companies, planning more than 12 to 18 months ahead is an exercise in futility.
The current business environment demands strategic agility — the ability to react swiftly to rapidly changing marketing conditions without losing focus. In order to develop that skill, today’s leaders must get very good at three things:
- Identifying and constantly challenging our underlying assumptions
- Identifying and eliminating our organization’s behavioral biases
- Constantly assessing and evaluating how we process information and make decisions
Our thought bubbles and behavioral biases are out to get us. As leaders, we can continue to buy into the illusion that all our decisions are rational and carefully thought out. Or we can learn to recognize our thought bubbles and biases when they occur, employ the appropriate strategies to counter their affects, and significantly improve our planning and decision-making processes.
I’m going with option B. How about you?
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Holly is the CEO of THE HUMAN FACTOR, Inc. (www.TheHumanFactor.biz) and is a highly sought after and acclaimed speaker, business consultant, and author. Her unique approach to creating strategic agility, helping others go slow to go fast, will change your thinking.
NEVER MISS ANOTHER NEWSLETTER! | https://www.disruptorleague.com/blog/2010/11/05/whats-your-favorite-management-bias/ |
- How and when did you become interested in photography?
My artistic skills developed quite early, since childhood I has been fascinated with photography and painting. I was 14 years old when I bought my first analog camera 35 mm and I start to take pictures. Graduated at the Art School with specialization in Photography e Graphic Design. I was very fascinated by reportage and landscapes. I loved always to experiment creativity printed in the darkroom preferring high contrast papers, my favorite film was Kodak Tmax. Over the years I have attended courses with international photographers who have helped me to better understand my vision and focus on my creative potential. I have traveled frequently in the States and London, I have also lived some years in Greece whose culture and philosophy have inspired many of my works.
- Is there any artist/photographer who inspired your art?
When I began photographing I was fascinated by the artist Mario Giacomelli, I always loved his whites and deep blacks, emotions and poetry that transpired from his photographs, in those highly contrasted images I have always found the essence of my emotions . Other photographers that I always loved was Tina Modotti, one of the pioneer women of photography, his images full of humanity and contrasts have always fascinated me and Julia Margaret Cameron with her beautiful works and portraits photography. Today my inspiration is purely personal, comes from the small everyday things, from my family and emotions, my fears, my unconscious. Also from my cultural background, from love for painting, poetry, books and travel.Often what influences me are my dreams, every photographic project was born from a need to tell a part of me to others in the form of images, an emotion, a story, a feeling are the key of my inspirations.
- Why do you work in black and white rather than colour?
The black and white conveys most of our emotions, give more feelings and drama. I love telling stories, and with black and white I can convey more meaning to the viewer It must focus on the content and simplification.
- How much preparation do you put into taking a photograph/series of photographs?
My digital cameras are Leica and Nikon. I prefer natural light that allow me to capture my emotions , the nature and the human figure weaving dreamlike stories with them. I really like to use multiple exposures to create fantastic stories with real things. With the advent of digital I began the use of post processing that provide to emphasize the tones in black and white, making them much more contrasted and dramatic. In the same way as when I worked in the darkroom and I liked superimpose two negatives with the sandwich technique, now also working in some series in digital overlaying texture to create surreal situations that are able to affect the emotions.
- UNDEREXPOSED MAG
- How does being a female photographer influence your work? Do you encounter any challenges in your practice related to that?
Being a woman has definitely influenced my work. Making pictures of female subjects creates a feeling that I carry with me. My work is dreamy and my feminine instinct pushes me to believe in emotions and dreams rather than to think about technicality and rationality. Being carried away by emotions to conceive an idea and to transform it through the lens of my camera, is the essence of my photographic work. All this gives me opportunities for professional and artistic growth.
Do you want to share something about your body of work? What are you working on right now?
I love surreal and conceptual photography with a touch of mystery. I have many projects to pursue. At the moment I’m focused on my creative series about nature and flow of seasons, isolated subjects contemplating of the environment. This series of photographs is dreamy and emotional. It reflects the feeling of decay in nature during winter time, and it is permeated by a sense of sweet melancholy. In this creative work I prefer the use of texture to accentuate the dramatic elements of the winter and the emotions that emerge.
5. How do you get inspiration? Who do you admire?
I take inspiration from the little things of everyday life. I try to open my eyes and look at things in a different perspective then others, offering myself in everything I do. I let myself be carried away by dreams and emotions and when I have an idea in my head I try to turn it into a project. Usually it takes time to work on it, and I have to wait for the right moment, the right place and the right light. Sometimes it all happens randomly. But when I’m on the right way the project takes shape and my emotions begin to turn ideas into reality. I also love painting and I admire Renaissance art and Surrealism. Often I am also inspired by music and poetry. | https://carmelitaiezzi.com/projects/interviews-awards-fine-art-print-publications-exhibitions/ |
Department of Electrical and Electronics Engineering
Program Educational Objectives (PEOs):
- PEO 1: Graduates will acquire technical competence to analyze, design and solve engineering problems in the field of Electrical and Electronics engineering and use modern engineering tools, techniques and software.
- PEO 2: Graduates will be able to acquire necessary skills and obtain employment and will be productive in the professional practice of Electrical and Electronics Engineering and related fields.
- PEO 3:Graduates will be sensitive to professional and social contexts, committed to ethical action and engaged in lifelong learning skills.
PROGRAM OUTCOMES (PO’S)
Engineering Graduates will be able to:
- Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering specialization to the solution of complex engineering problems.
- Problem analysis: Identify, formulate, review research literature, and analyze complex engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences.
- Design/development of solutions: Design solutions for complex engineering problems and design system components or processes that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations.
- Conduct investigations of complex problems: : Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions.
- Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations.
- The engineer and society:Apply reasoning informed by the contextual knowledge to assess societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the professional engineering practice.
- Environment and sustainability: Understand the impact of the professional engineering solutions in societal and environmental contexts, and demonstrate the knowledge of, and need for sustainable development.
- Ethics:Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering practice.
- Individual and team work: Function effectively as an individual, and as a member or leader in diverse teams, and in multidisciplinary settings.
- Communication: Communicate effectively on complex engineering activities with the engineering community and with society at large, such as, being able to comprehend and write effective reports and design documentation, make effective presentations, and give and receive clear instructions.
- Project management and finance: Demonstrate knowledge and understanding of the engineering and management principles and apply these to one’s own work, as a member and leader in a team, to manage projects and in multidisciplinary environments.
- Life-long learning: Recognize the need for, and have the preparation and ability to engage in independent and life-long learning in the broadest context of technological change.
PROGRAM SPECIFIC OUTCOMES (PSOs)
- EEE students will be able to design, analyze Power Systems & Electrical Machines to solve complex engineering problems.
- EEE students will be able to design and analyze Electrical and Power Electronic Circuits.
- EEE students will be able to use and apply modern software tools and techniques related to Electrical Engineering. | https://www.vce.ac.in/Departments/EEE/PEO_PSO_PO_EEE |
New health rules for competition horses announced
Modifications to the FEI’s Veterinary Regulations in relation to horse health requirements will come into force from January 1, 2022, as will the use of the FEI HorseApp.
The horse health requirements, derived from the EHV-1 By-Laws applied in Europe, aim to protect horses and the sport from the consequences of infectious diseases being transmitted before, during and after FEI Events, and to maintain and further improve the conditions for the international movement of sport horses.
From January 1, all horses competing at an FEI event must fulfill the Horse Health Requirements through the HorseApp.
The relevant requirements are controlled by FEI Veterinarians and FEI Officials at the Examination at Arrival and throughout FEI Events. FEI Veterinarians officiating at FEI Events will also need to perform the Examination at Arrival using the FEI HorseApp.
Sanctions for non-compliance are already in force for horses competing at FEI Events in mainland Europe, these will be introduced worldwide in due course.
Changes to the 127-page long Veterinary Regulations from January 1, 2022, are shown here.
Further information is outlined on the FEI’s Horse Health Hub.
The FEI also announced that its Veterinary Education System has been revised and will be implemented from January 1.
• The FEI’s Clean Sport for Humans information has been updated and expanded, providing a more comprehensive overview as well as an explanation of the key human anti-doping rationale and concepts.
“They are the starting point for anyone in the sport, especially athletes and athlete support personnel, to understand this essential aspect of their equestrian activity,” the FEI said.
Athletes and athlete support personnel are encouraged to take an online course in order to learn the skills necessary to comply with the human anti-doping rules and avoid unintentional doping violations. | https://www.horsetalk.co.nz/2021/12/13/health-rules-competition-horses/ |
Over the past decade, changes in meat consumption patterns have resulted in chicken becoming the most commonly consumed type of meat in Australia (Australian Bureau of Agricultural and Resource Economics and Sciences, 2017). At the same time, there has been an increase in the prevalence of vegetarianism and consumption of 'mostly meat-free' diets.
This research seeks to increase understanding of Australian chicken meat consumption trends and preferences. This is critical for the development of effective industry and policy strategies for reducing barriers and growing consumer demand for chicken meat in Australia’s changing meat consumption climate, and for creating opportunities for the domestic industry. Additionally, in line with the KPI for objective two (‘Deliver safe food and good animal welfare outcomes’) of the Chicken Meat Program Five-Year RD&E Plan 2014-2019, findings from this research will reveal whether consumers perceive chicken meat as a wholesome and safe product, amongst other views they may hold.
Project Objectives
- Provide a comprehensive understanding of current consumer usage of and attitudes towards chicken meat products; and compare current usage and attitudes data (collected in 2018 and 2019) with data from the previous RIRDC chicken usage and attitudes survey (conducted in 2008).
- Understand recent trends in and provide future demand projections of chicken consumption behaviour and drivers of chicken meat purchase preferences and purchasing behaviour of Australian consumers.
- Understand heterogeneity in chicken product preferences and potential viable market segments for different stakeholders, to recommend how stakeholders can meet consumer demands in the future.
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Provide industry and policy advice on strategies for reducing potential barriers to meeting and growing consumer demand for chicken meat.
Project materials, outputs and publications
- Agrifutures Report
- Agrifutures Australia media release
- Professor Wendy Umberger gave a radio interview on 11 March about the Agrifutures Australia Chicken meat project with Sophie Clarke from ‘Rural News’ on 2GB 87.3AM. | https://www.adelaide.edu.au/global-food/news/list/2019/08/30/future-market-insights-for-australias-chicken-meat-industry |
Training material for pilot coordinators
Are you part of a redistribution organisation or do you know one that could be interested in our solution? Here you can find two things:
a. A video on how to organise a SavingFood Gleaning/Farmers' market event to check all the quick and easy steps you need to follow to organise a general food rescue event via the Platform.
b. The ultimate guide to replicate our ICT solution and our overall behavioural change strategy.
If your organisation works on making your community more sustainable, building stronger relations between producers and consumers, and reducing food surplus, you might want to consider implementing the SavingFood platform.
The SavingFood platform aims to help three key groups – donors, recipient organisations, and volunteers – by means of an online platform in order to foster collaboration between food donors and recipient organisations based on knowledge sharing and make collection of surplus food and leftover crops efficient and scalable.
By implementing the SavingFood platform in a new country, city or community, you can:
The SavingFood platform was tested in Belgium, Greece, Hungary, and the UK.
This handbook contains the information necessary to use and localise the SavingFood approach: namely the SavingFood platform, as well as the behaviour change methodologies that come hand in hand to achieve a successful replication. | https://foodwin.savingfood.eu/intro_new/training-material.asp |
Vanessa R. Heim is an attorney with Tiffany & Bosco, P.A/. in Phoenix, Arizona. A top-rated and award-winning lawyer with more than nine years of total legal experience, Ms. Heim provides exceptional counsel and support to clients throughout the state who have legal needs involving any of the following:
- Trust and Estate planning
- Trust/Probate Administration and Litigation
- Guardianships, Conservatorships, Adoptions
As an attorney, Ms. Heim has gained a reputation for her compassion and integrity as well as her patience when dealing with her clients as she helps them make the best-informed decisions on the matters that will affect them and their families for years to come. She delivers a thorough analysis of her clients' needs and desired goals, and she works hard to help her clients achieve the favorable outcomes and positive results they seek as efficiently and cost-effectively as possible.
In honor of her outstanding professionalism and service, Ms. Heim has earned consistent top rankings and endorsements from her peers. She has also received designation as an Elite Service Provider by ARAG Legal Plans along with recognition from the American Institute of Legal Counsel. Moreover, she has received many testimonials and referrals from her satisfied clients, and she finds great reward in being able to guide her clients through very difficult and uncertain times in their lives. | https://profiles.superlawyers.com/arizona/phoenix/lawyer/vanessa-r-heim/c1a23826-db07-49ed-b34b-73c06e3b6b02.html |
The EU-funded FIGARO precision project has designed DDS, -Decision Supporting System to improve irrigation management. They have been invited to present the precision irrigation system at a special workshop on coping with climate change and water scarcity at the Expo Milano 2015.
Dr. Adriano Battilani, senior researcher at the Canale Emiliano Romagnolo (CER) research institute in Bologna, Italy and a FIGARO partner, will make a presentation on “How to Integrate Knowledge to Improve Water Productivity in Agriculture” at the Agri-Water Workshop to be held on June 17 at the EXPO 2015 – EU Pavilion. The workshop will deal with methods to cope with climate change and water scarcity in Africa and Europe by improving monitoring and water-use efficiency in agriculture.
“The workshop is a great opportunity for FIGARO to present the progress we have made so far and show how we can help fight water scarcity,” said Battilani. “By offering a crop-oriented management tool, FIGARO optimizes irrigation and fertilizer dosing, significantly reducing the use of fresh water.”
The FIGARO (Flexible and Precise Irrigation Platform to Improve Farm Scale Water Productivity) platform acts as an SAAS platform. It periodically runs leading and approved crop models to provide farmers with on-line recommendations regarding the best irrigation and fertilization schedules for their farms. Data is provided for specific crops and soils, water and climate conditions.
In order to make the recommendations precise, the FIGARO platform is connected to actual sensors, and collects environmental and crop-growth data from a wide variety of in-field and remote sensors and data sources including soil moisture, water meters, satellite images and weather stations. The data are fed automatically or manually into the DSS platform models and supply the crop module operating on real-time data.
Nine European countries have field tested the FIGARO system, all with promising results. | https://precision.agwired.com/2015/06/16/figaro-to-present-at-2015-agri-water-workshop/ |
Riot Games has found Korean team Azubu Frost guilty of unsportsmanlike conduct; the team will be fined 20 percent of its winnings; fine to be donated to a Riot Games charity in Korea.
Riot Games has come to a decision concerning cheating allegations on day three of the League of Legends World Playoffs, following an extensive investigation.
Riot Games has issued a fine after investigating cheating allegations.
Writing on the League of Legends forums, Riot vice president of eSports Dustin Beck outlined that Korean team Azubu Frost (AzF) has been found guilty of unsportsmanlike conduct, and will be fined $30,000, a figure representing 20 percent of the team's current tournament winnings.
The fine will be donated to Riot Games' charity in Korea.
Three other teams were issued warnings for unsportsmanlike conduct, and one other team was cleared of any misconduct.
During the investigation, Riot found that AzF Woong had violated the rules by looking at the stage screens displaying the opposing team's minimap during game 1 of quarterfinal number 3, and that his actions yielded benefits for his team in the game. According to Riot's investigation, other members of AzF modified their gameplay based upon the information obtained by AzF Woong.
Riot re-examined photos, videos, and renders of the stage layout to better understand sight lines between the players and the maps placed overhead before coming to a final decision.
"We evaluated these cases based on intent, severity and tangible impact to the course of the game," Beck said. "Based on our investigation, the Azubu Frost incident is the only one where we determined there to be tangible impact; we believe other members of AzF modified their gameplay based upon the information gained. We don’t believe, however, that these actions decided the winner of the game.
"We take this stuff seriously. Our rules on sportsmanlike conduct are clearly communicated to competitors, and our decisions here are based on those rules. More importantly, this sort of behavior shouldn't have been possible in the first place, and we recognise that and have taken steps to ensure it doesn't happen in the future." | https://www.gamespot.com/articles/riot-fines-league-of-legends-cheaters-30000/1100-6398055/ |
Advanced Intelligent Predictive Models for Urban Transportation
The tremendous growth in transport systems and the increase in the number of vehicles on the roads in recent decades have created a significant problem in urban areas, namely traffic congestion. Traffic congestion inroads have been the biggest problem in the largest cities around the globe, especially cities in developing countries, where roads are not well designed and traffic on the roads is poorly managed. Traffic congestion increases fuel consumption and causes air pollution. In recent years, minimizing road traffic congestion has been a significant challenge; many researchers have focused on discovering the causes of traffic congestion.
Some recent research works have merely identified the causes of traffic jams and suggest alternate routes to avoid traffic congestion. Besides, traffic forecasting requires accurate traffic models which can analyze the actual traffic condition statistically.
Intelligent transport systems (ITS) are being designed to develop the quality and sustainability of mobility by incorporating data as well as communication technologies with transport engineering. Other studies on ITS from the perspective of artificial intelligence (AI) have also been done. ITS depends on a capillary network of sensors which are installed on the roads to provide information on traffic variables like flow, speed, and density. These variables are monitored by administration centers to approximate traffic dynamics and apply control operations.
This book recommends a smart framework for the domain of transportation that performs traffic prediction with a fuel consumption model and analyzes traffic flow congestion using a genetic and regression model. It also proposes a traffic light controller and traffic deviation system based on a multi-agent system. First, this framework proposes a smart traffic prediction and congestion avoidance system based on the genetic model to reduce fuel consumption and pollution. The model uses Poisson distribution for the prediction of vehicle arrival based on recurring size. This model comprises traffic identification, prediction, and congestion avoidance phases. The system checks for the fitness function to determine traffic intensity and further uses predictive analytics to determine future traffic levels. It also integrates a fuel consumption model to save time and energy.
This framework then predicts short-term traffic flow using structure pattern and regression methods. Short-term traffic prediction is one of the required fields of study in the transportation domain. It is beneficial to develop a more advanced transportation system to control traffic signals and avoid congestion. The framework proposed will improve the traffic system and thereby also protect the environment, allowing rerouting, improving fuel consumption, and saving time. The traffic flow structure pattern can be constructed from freeway toll data. Based on the pattern, a prediction method was proposed, which is based on locally weighted learning (LWL) and regression. | https://azam.engineer-1.com/2022/03/Intellig-Predic.html |
[The placebo as a nonspecific treatment factor].
Nonspecific drug actions result from the social interaction between physician and patient and the medical environment. Positive (therapeutic) placebo effects are produced in approximately 30-35% of treated patients, especially in cases of vegetative and psychic disturbances. There appears to be no distinct group of individuals with specific personality features that can be classified as "placebo responders". Negative (toxic) placebo effects, which are usually minor, are reported in 4-50% of treated patients. The occurrence of side effects may cause the patient to assume treatment with an active agent, thus increasing the therapeutic efficiency of the treatment (placebo amplification by side effects). On the other hand, the lack of a certain side effect may diminish the therapeutic effect of an active drug. The notion that placebo-induced analgesia is endorphin-mediated is not established. Hence at present psychological mechanisms have to be assumed for the placebo effect. The conscious use of a placebo as a therapeutic agent is problematic for ethical reasons, whereas the placebo component of drugs with specific actions should be exploited to enhance their therapeutic efficiency.
| |
The LINEST funtion returns the slope and intercept values for a best fit straight line.
This function includes an option to include additional regression statistics (stats = true).
This function uses the "least squares" method to calculate a best fit line.
Straight lines satisfy the equation "y=mx+b" when you have one independent x-value.
b is the value where the line crosses the y-axis and corresponds to the "const" argument.
When "const" is left blank (or True) the slope and intercept is calculated and returned.
Enter the following data arranged in two columns. One column for the x-values and one for the y-values.
You must select two cells in the same row. Not two cells in the same column.
Enter the following formula as an Array Formula (using Ctrl + Shift + Enter) into the cells "B10:C10".
The slope of the best fit straight line has been added to cell "B10".
The intercept of the best fit straight line with the y-axis has been added to cell "C10".
We can check the results by plotting an XY Scatter chart.
The slope of the line is 2.
The intersection of the line with the y-axis is at -1.
Instead of using the LINEST function you could use the SLOPE and INTERCEPT functions to obtain the same values.
When "const" is FALSE the slope is calculated with an assumption that the Intercept = 0.
This function now only returns a single value and does not have to be entered as an array formula.
This is the only situation when this function does not return more than one value.
When the intercept is zero, the y-values need to be recalculated using the formula "y=mx"
This formula is completely different to "y=mx+c" and therefore whether "const" is true or false has enormous implications on the results returned by this function.
When "stats" is TRUE this function will return additional regression statistics.
Instead of 2 numbers, this function now returns 10 numbers arranged as two columns and five rows.
Also known as Alpha, written as "c" or "b"
This is the ratio of the variance in the data explained by the linear model divided by the variance unexplained by the linear model.
These additional statistics tell you how good the best fit line is.
The correlation coefficient gives a "rough" indicator of a good fit. Values close to 1 are good.
The uncertainties in the slope and intercept are a much better indicator for a "good fit"
Once you know the values of m and b, you can calculate any point on the line by plugging the y- or x-value into that equation. You can also use the TREND function.
You can use the LINEST and INDEX functions to solve this equation.
The residual value is the difference between the value predicted by the equation and the value observed or collected.
If the equation is a close fit then we would expect the residuals to be randomly scattered around zero.
If they display a pattern then it is likely that a better equation exists.
Plotting a graph and then adding a trendline gives you slightly more control as you can provide the value for the intercept.
You can quickly enter the squared symbol by using (Alt + 0178).
You can quickly enter the cubed symbol by using (Alt + 0179). | https://bettersolutions.com/excel/functions/function-linest.htm |
The correlation only indicates the degree and direction of the relationship between two variables. It does not, necessarily connote a cause-effect relationship. Even when there are grounds to believe the causal relationship exits, correlation does not tell us which variable is the cause and which, the effect. For example, the demand for a commodity and its price will generally be found to be correlated, but the question whether demand depends on price or vice-versa; will not be answered by correlation. The dictionary meaning of the ‘regression’ is the act of the returning or going back.
The term regression was first used by Francis Galton in 1877 while studying the relationship between the heights of fathers and sons. “Regression is the measure of the average relationship between two or more variables in terms of the original units of data. ” The line of regression is the line, which gives the best estimate to the values of one variable for any specific values of other variables. For two variables on regression analysis, there are two regression lines. One line as the regression of x on y and other is for regression of y on x. These two regression line show the average relationship between the two variables.
The regression line of y on x gives the most probable value of y for given value of x and the regression line of x and y gives the most probable values of x for the given value of y. For perfect correlation, positive or negative i. e. for r= ±, the two lines coincide i. e. we will find only one straight line. If r=0, i. e. both the variance are independent then the two lines will cut each other at a right angle. In this case the two lines will be ¦to x and y axis. The Graph is given below:- We restrict our discussion to linear relationships only that is the equations to be considered are 1- y=a+bx - x=a+by In equation first x is called the independent variable and y the dependent variable. Conditional on the x value, the equations gives the variation of y. In other words ,it means that corresponding to each value of x ,there is whole conditional probability distribution of y.
Haven’t found the relevant content? Hire a subject expert to help you with Regression Analysis
Similar discussion holds for the equation second, where y acts as independent variable and x as dependent variable. What purpose does regression line serve?
- The first object is to estimate the dependent variable from known values of independent variable. This is possible from regression line.
- The next objective is to obtain a measure of the error involved in using regression line for estimation.
- With the help of regression coefficients we can calculate the correlation coefficient. The square of correlation coefficient (r), is called coefficient of determination, measure the degree of association of correlation that exits between two variables.
What is the difference between correlation and linear regression? Correlation and linear regression are not the same. Consider these differences: Correlation quantifies the degree to which two variables are related. Correlation does not find a best-fit line (that is regression). You simply are computing a correlation coefficient (r) that tells you how much one variable tends to change when the other one does. With correlation you don't have to think about cause and effect. You simply quantify how well two variables relate to each other. With regression, you do have to think about cause and effect as the regression line is determined as the best way to predict Y from X. With correlation, it doesn't matter which of the two variables you call "X" and which you call "Y".
You'll get the same correlation coefficient if you swap the two. With linear regression, the decision of which variable you call "X" and which you call "Y" matters a lot, as you'll get a different best-fit line if you swap the two. The line that best predicts Y from X is not the same as the line that predicts X from Y. Correlation is almost always used when you measure both variables. It rarely is appropriate when one variable is something you experimentally manipulate. With linear regression, the X variable is often something you experimental manipulate (time, concentration... and the Y variable is something you measure. Regression analysis is widely used for prediction (including forecasting of time-series data). Use of regression analysis for prediction has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables.
A large body of techniques for carrying out regression analysis has been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may beinfinite-dimensional. The performance of regression analysis methods in practice depends on the form of the data-generating process, and how it relates to the regression approach being used.
Since the true form of the data-generating process is not known, regression analysis depends to some extent on making assumptions about this process. These assumptions are sometimes (but not always) testable if a large amount of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, when carrying out inference using regression models, especially involving small effects or questions of causality based on observational data, regression methods must be used cautiously as they can easily give misleading results.
Classical assumptions for regression analysis include:
- The sample must be representative of the population for the inference prediction.
- The error is assumed to be a random variable with a mean of zero conditional on the explanatory variables.
- The variables are error-free. If this is not so, modeling may be done using errors-in-variables model techniques.
- The predictors must be linearly independent, i. e. it must not be possible to express any predictor as a linear combination of the others. The errors are uncorrelated, that is, the variance-covariance matrix of the errors is diagonal and each non-zero element is the variance of the error.
- The variance of the error is constant across observations (homoscedasticity). If not, weighted least squares or other methods might be used.
These are sufficient (but not all necessary) conditions for the least-squares estimator to possess desirable properties, in particular, these assumptions imply that the parameter estimates will be unbiased, consistent, and efficient in the class of linear unbiased estimators.
Many of these assumptions may be relaxed in more advanced treatments. Basic Formula of Regression Analysis: X=a+by (Regression line x on y) Y=a+bx (Regression line y on x) 1st – Regression equation of x on y:- 2nd – Regression equation of y on x:
- Regression Coefficient: Case 1st - when x on y means regression coefficient is ‘bxy’ Case 2nd – when y on x means regression coefficient is ‘byx’
- Least Square Estimation: The main object of constructing statistical relationship is to predict or explain the effects on one dependent variable resulting from changes in one or more explanatory variables.
Under the least square criteria, the line of best fit is said to be that which minimizes the sum of the squared residuals between the points of the graph and the points of straight line. The least squares method is the most widely used procedure for developing estimates of the model parameters. The graph of the estimated regression equation for simple linear regression is a straight line approximation to the relationship between y and x. When regression equations obtained directly that is without taking deviation from actual or assumed mean then the two Normal equations are to be solved simultaneously as follows;
For Regression Equation of x on y i. e. x=a+by The two Normal Equations are:- For Regression Equation of y on x i. e. y=a+bx The two Normal Equations are:- Remarks:
- It may be noted that both the regression coefficient ( x on y means bxy and y on x means byx ) cannot exceed 1.
- Both the regression coefficient shall either be positive + or negative -.
- Correlation coefficient (r) will have same sign as that of regression coefficient. | https://phdessay.com/regression-analysis/ |
Technical Report Summary:
As part of a research team led by Professor Nada Basit and Professor Robbie Hott, I conducted a behavioral research project on analyzing impact of time-tracking methodologies in online assessments. As students move to online learning, efforts have been made to streamline instructional and assessment software to reduce distractions. Prior behavioral research has found that visible timers on online assessments are a source of anxiety that can influence performance and outcome. Additional studies on color theory suggest that timer color may be another factor. Through literature review, timer UI design and implementation, and voluntary behavioral studies of undergraduate subjects taking CS 2110 (Software Development Methods) and CS 4750 (Database Systems), we plan to analyze the correlation between various types of virtual timers and exam performance.
STS Research Summary:
This STS research investigates arguments for and against the use of predictive policing technology in the criminal justice system. In the interests of improved efficiency and reduced human error, crime assessment algorithms and other machine learning models are increasingly used to inform societal regulations. However, some researchers assert that historical crime data is biased due to overpolicing, meaning this approach does little more than reinforce systemic problems like racial profiling and the disproportionate targeting of low-income neighborhoods.
The human and social dimensions are important in this research because of the social context that needs to be considered in developing technology that serves public safety and affects the livelihoods of citizens. The Social Construction of Technology (SCOT) framework will be used to analyze the stakes that various social groups have in predictive policing technology. Under the framing of interpretive flexibility, the central tenet of SCOT, I studied each stakeholder's relationship with the technology, the problems they need addressed, and potential solutions this technology can bring.
To conduct this STS research, I analyzed arguments from both sides of the predictive policing debate through a study of case law. I surveyed federal and state court cases from the past ten years (2010-2020) to identify relevant cases, compiled arguments from case briefs, and summarized the current legal boundaries of predictive policing technology. Over time, case law seems to be shifting from more permissive of algorithm usage to more restrictive, as in the landmark case U.S. v Curry (2020). I found that the courts are more favorable towards the use of risk assessment tools like COMPAS to inform sentencing, and are more critical of the use of predictive policing tools, for example, crime hotspots or "heat lists," by law enforcement personnel. Higher courts also tend to prioritize transparency from government agencies.
Through this research, I observed judicial opinions shifting over time towards skepticism of crime prediction algorithms, as more research cast doubt on their efficacy. When considering predictive policing technology and STS research in concert, any efficiencies the technology brings need to be weighed against its adverse effects on civil liberties. While crime prediction and risk assessment algorithms may expedite police work, use of historical crime data without consideration for social context means that this technology may require further development to be effective. | https://libraetd.lib.virginia.edu/public_view/12579t05j |
Click on the presentation title below to download the slides.
Mental Health Matters - Research Overview
Dr. Esther Murphy, Principal Investigator
Disability Service Supports for students with mental health difficulties in higher education
Declan Treanor, Director, Disability Service, Trinity College Dublin
Student Counselling Services: Provision for Students with Mental Health Difficulties
Treasa Fox, Irish Association of University and College Counsellors
Student Central: The Impact of Psychology-Led Supports and Evidence Based Interventions in a Third Level Institution
Rose Ryan, Director of Access Office Maynooth University
Suzanne McCarthy, Educational Psychologist
- 41% increase in students seeking counselling
- Staff cutbacks result in six month waiting lists to see counsellor in third level
- Full and part-time College staff should have mandatory mental health awareness training
- College assessment methods need to become more flexible and open
November 1st, 2016: New research by AHEAD, the Association for Higher Education Access and Disability and the National Learning Network (NLN), a division of the Rehab Group, has identified 12 recommendations to help overcome the serious issues faced by students with mental health difficulties in third level education.
The ‘Mental Health Matters – Mapping Best Practices in Higher Education’ report was carried out to give a voice to students with mental health difficulties and to hear the experiences of professional staff in third level education. Of the 28 Higher Education Institutes (HEI), 22 took part in the report.
Colleges are seeing a 41% increase in the number of students seeking counselling, while staff cutbacks during the austerity years is resulting in students waiting six months to see a counsellor. This is a silent crisis that needs to be addressed. Students with mental health difficulties need to be given the support they deserve.
Two of the key recommendations in this new report to help students include:
Assessment methods
Students with mental health difficulties revealed that presentations are very challenging, causing anxiety and resulting in students describing themselves as a ‘nervous wreck’. The openness of trying out new ways to assess students, such as one-on-one presentations or recording themselves at home, has been welcomed by students. Students agreed these assessment methods are less stressful and help them to fully demonstrate their knowledge.
This report recommends that all courses use assessment methods that give students a choice in how they are examined. Flexibility is not new, but it is also not widespread. Openness to flexible assessment methods can make the difference between a student reaching their potential or failing and dropping out.
Although colleges provide disability awareness training for academic staff, it is on a voluntary basis. This report recommends that mental health awareness training should be made mandatory for full and part-time staff.
Absenteeism support
Time out of college can be a regular feature for students struggling with mental health difficulties. The report found that colleges have a range of responses when students who were not able to attend lectures seek support to catch up. Unreliable access to online lecture notes, the need for additional time, and a lack of understanding of reasons for absenteeism among staff are key issues for students.
One student felt that audio versions of lecture notes would have been beneficial, but that there is a lack of understanding that students with mental health difficulties need this kind of support. A review of the current teaching and learning practices should take place to ensure that institutions are thinking creatively about the learning environment and what will work for individual students. | https://ahead.ie/mentalhealthmatters |
.
O
.
D WITS
Electrical & Information Engineering
09h15
–
09h45
-
Dr Andrew Collier
(Understanding Lightning using Machine Learning Techniques)
09
h45
–
10h15
-
D
r Hugh Hunt
(Observations of lightning events)
10h15
–
10h45
–
Ron Holle
(
Lightning
-
related Safety and Demographics)
10h45
–
11h00
–
Coffee break
11h00
-
12h00
–
Students presentations
(2 x 30
minutes)
(Harry Lee, Brett Terespolsky)
12h00
–
13h00
–
Lunch,
networking
and
collaboration
13h00
–
13h45
–
Dr
Efraim B. Kramer
(
Emergency Medicine and
Lightning)
13h45
–
14h00
-
Morné Gijben
(A Unified Model based Lightning Threat Index for South Africa)
14h00
-
14h30
–
Koos Herselman
(The management of post
-
traumatic stress in lightning victims)
14h30
-
15h00
-
Student
presentations
(2
x 15 minutes)
(
xxxxx, xxxxx
)
15
h00
-
15h15
–
Coffee break
15h15
–
15h45
–
Dr Nhlonipho Nhlabatsi
(The Utilization of Lightning Data at the SA Weather
Service)
15h45
–
16h15
–
Dr Ryan Blumenthal
(Lightning injury mechanisms and mechanisms of death)
16h15
–
16h30
–
D
r Michael David
Grant
-
Concluding remarks
and
the
way forward for LIGHTS
16h3
0
–
Conclusion of proceedings
LIGHTS
2
ABSTRACTS, BIOGRAPHIES AND PHOTOGRAPHS OF SPEAKERS
Andrew
Collier
Dr Andrew Collier is a
Honorary Senior Lecturer at the University of KwaZulu
-
Natal. He also works as a Data
Scientist for Exegetic Analytics. His fields of interest include electromagnetic waves in space plasmas, wave
-
particle interactions, lightning and the application of mach
ine learning techniques in Science and Engineering.
Title:
Understanding Lightning using Machine Learning Techniques
Abstract:
The World Wide Lightning Location Network (WWLLN) provides continuous global coverage of the
Earth's lightning activity in real
time. With around 45 lightning discharges every second, WWLLN produces a
formidable quantity of data every year. Data reduction techniques like Principal Component Analysis (PCA) and
machine learning techniques like Support Vector Machines (SVMs) and Rand
om Forests are applied to
understand the evolution of global patterns of lightning activity and provide some short term predictive power.
Hugh Hunt
Hugh Hunt is a lecturer for the School of Electrical and Information Engineering at the University of
Witwatersrand. He completed his BSc (Eng) Electrical Engineering Degree in 2009 and went on to complete his
MSc (Eng) in Electrical Engineering 2012. He is currently working towards his PhD. His research involves the
fields of both lightning and high volta
ge engineering. He has worked with lightning location systems data,
specifically looking at their use in forensic investigations as well as performing actual testing of insulation and
surge protection using high voltage equipment and procedures.
Abstrac
t:
Observations of lightning events attaching to the Brixton Tower, Johannesburg and the South African
Lightning Detection Network (SALDN) interpretation of these events with specific reference to forensic
investigations.
LIGHTS
3
Ronald L. Holle
Ron
Holle is a meteorological consultant for Vaisala, Inc. Holle has worked extensively in meteorological
education issues, particularly those relating to lightning safety and the demographics of lightning victims and
damages. He has authored or co
-
authored
60 formally
-
reviewed journal papers, 12 books and book chapters,
and 296 informal papers.
Holle has worked with NOAA research laboratories in Norman, Oklahoma; Boulder, Colorado; Coral Gables,
Florida; and Silver Spring, Maryland as well as with Vaisala
, Inc. in Tucson, Arizona. He has analyzed cloud
-
to
-
ground and cloud lightning data from ground
-
based detection networks as they relate to radar echoes, rainfall,
flash floods, and winter weather, as well as compiling lightning climatologies.
He particip
ated in meteorological field programs in Florida and other locations in the U.S., the Caribbean, and
West Africa. He received his B.S. and M.S. degrees in meteorology from Florida State University, and took
additional coursework at the University of Miami
.
Mr. Holle was on the scientific organizing committees of the International Lightning Detection Conferences and
International Lightning Meteorology Conferences in Helsinki, Finland (2004), Tucson (2002, 2006, and 2008),
Orlando (2010), and Broomfield, Co
lorado (2012). He was elected a Fellow of the American Meteorological
Society in 2009, and received the Dr. T. Theodore Fujita Research Achievement Award from the National
Weather Association in 2008.
Title of Paper:
Lightning
-
related Safety and Demograp
hics
Abstract:
The annual number of lightning deaths has been compiled in the U.S. since 1900, and in a few other
developed countries for shorter periods. These time series show a large decrease from 6 deaths per million at
the start of the 20
th
century
to less than one in recent years. The decrease is similar to the population percentage
living in rural areas. Other factors include nearly complete availability of lightning
-
safe buildings and vehicles,
improved medical treatment, and better lightning ed
ucation and awareness of meteorological warnings.
However in many areas of the world, rural labor
-
intensive agriculture is the livelihood of many people who also
live in lightning
-
unsafe dwellings.
The main principle of lightning safety is that only two
certain safe places exist. One is a large substantial often
-
occupied well
-
grounded or otherwise lightning
-
protected building; the other is a fully
-
enclosed metal
-
topped
vehicle. It is emphasized that there are multiple mechanism of lightning injury. The
often
-
considered direct
strike is the least common, and is not the basis for lightning safety advice. Examples of warning methods and
related statistics will be provided.
An overview of the wide variety of applications of lightning detection network dat
a will be presented, including
the latest maps of U.S. and global lightning data. How meteorologists and others use such data will be
described briefly.
LIGHTS
4
Efraim Kramer
Prof Efraim
Kramer is the Head of the Division of Emergency Medicine and Honorary Adjunct Professor of
Exercise Science + Sports Medicine, Faculty of Health Sciences at the University of the Witwatersrand. He is a
member of the FIFA Medical Assessment + Research Cent
re (F
-
MARC) in Zurich and is appointed as the
Football Emergency Medicine Advisor for the FIFA Confederations Cup Brazil 2013 and FIFA World Cup
Brazil 2014. As Medical Officer to FIFA, CAF and SAFA, he is responsible for the provision of medical
services
in the football stadium environment , which is where his interest and responsibility regarding
“Lightning in Football Globally” has relevance.
Title of paper:
Emergency Medicine + Lightning
Introduction for the Chair:
Emergency Medicine healthcare pro
viders, both prehospital and emergency department, are involved in the
lightning injured patient, and associated family, friends and associates, from a prevention, medical management
and post
-
discharge point of view. Unfortunately, the medical fraternity r
emains very much is the Dark Ages
regarding Lightning and its multifaceted impacts regarding morbidity, mortality, medical management and
myths, all of which require active enlightening education. After all, these are the guys that are going to treat the
p
atient either on the field, in the ambulance or in the emergency department.
Abstract
:
The prevention and, if necessary, medical management of lightning injuries in Emergency Medicine presents
challenges in many facets because of the traditional myths
which remain ingrained and the current medical
science which is inadequately trained. Aspects of medical management involving activation of the emergency
medical services, safe speedy response, on
-
scene triage and diagnosis, out
-
of
-
hospital resuscitation,
emergency
department medical management and subsequent rehabilitation are all fraught with challenges that may result in
unintentional, inadequate, inexperienced medical care. This presentation will provide a spectrum of questions
and possible answers to t
his vexing problem.
LIGHTS
5
Morne Gijben
Morné Gijben is a research scientist in the Nowcasting and Very Short
-
Range forecasting group at the South
African Weather Service. He completed his BSc (Hons) in Meteorology in 2010 at the
University of Pretoria.
His fields of research include lightning and convective weather in the 0
-
12 hour forecast scale. He has worked
on topics like anticipating lightning activity from numerical model fields and creating a lightning climatology
for S
outh Africa with data from the South African Lightning Detection Network (SALDN).
Title:
A Unified Model based Lightning Threat Index for South Africa
Abstract:
A Lightning Threat Index (LTI) that uses numerical weather prediction model fields was developed
for the South African region. The LTI provides an outlook map of where the lightning risk can be considered
high. This presentation will demonstrate the perfo
rmance of the LTI against the occurrence of observed
lightning from the South African Lightning Detection Network (SALDN).
Koos Herselman
Koos Herselman (SAC Dip.) Bio
-
As a Stress and Trauma Consultant. Koos works directly with people who
have su
ffered emotional trauma, providing post trauma counselling, grief counselling and stress management
coaching. In addition to this he provides training programs on how to avoid
becoming a victim of crimes such as
hijacking, rape and home invasions. Over the
past 8 years he
has worked with all kinds of people from senior
executives and professionals to the elderly and
children. During this time he has also travelled to other countries
in the Southern African region
to provide post trauma counselling at remote
mines and industrial plants where
major industrial
accidents have occurred. Koos has one major belief that drives him forward in his work, and
that is that human beings have the innate ability to overcome any challenge that they are faced with,
sometimes
just needing some guidance to connect with that ability.
LIGHTS
6
Nhlonipho Nhlabatsi
Dr. Nhlonipho Nhlabatsi
is currently a Senior Manager: Research at the South African Weather Service
(SAWS). He completed his PhD at the University of the Free State and has a number of publications and still an
academic supervisor to a number of PhD and MSc students. He is resp
onsible for research at SAWS at all time
-
scales of which the lightning sub
-
unit is part of.
Title:
The Utilization of Lightning Data at the SA Weather Service
Abstract:
South Africa is a lightning prone country and lightning related deaths in this country are about four
times higher than the global average. Lightning is one of the most spectacular meteorological phenomena and
the most common severe weather event to affec
t people directly. There are roughly 2000 thunderstorms in
progress around the world at any one time, producing about 30 to 100 cloud
-
to
-
ground flashes each second or
about five million flashes a day. Before the installation of the Lightning Detection Netw
ork, South Africa had
no reliable system to observe and monitor this phenomenon
.
Ryan Blumenthal
Dr Ryan Blumenthal: MBChB (Pret), MMed (Med Forens) Pret, FC For Path (SA) Dip For Med (SA) Senior
specialist forensic pathologist at the University of P
retoria’s Department of Forensic Medicine. His chief field of
interest is the pathology of trauma of lightning (keraunopathology). He has been involved in the publication of
numerous articles and textbooks on lightning and electrothermal injuries and has h
elped generate international
standard operating procedures and guidelines for lightning strike fatality and electrocution victims. He has
published widely in the fields of suicide and other areas involving the pathology of trauma. His chief mission in
life
is to advance Forensic Pathology Services both nationally and internationally. Interests outside of forensic
pathology include sleight
-
of
-
hand
-
magic, mountain
-
biking, bird
-
watching, squash, running and novel writing.
Abstract:
A discussion on the various lightning injury mechanisms and what to look for in clinical practice.
LIGHTS
7
Michael David Grant
Dr Michael David Grant Pr. Eng., PhD: Professional Electrical Engineer. Group leader CBI Electric. Recipient
of the Keith
Plowden young achievers award 2011.
He also won best young scientist award 2012 ICLP, Vienna.
Areas of expertise include
,
inter alia,
PV integration with the low
and medium voltage grid, e
xpert in lightning
and syste
m protection
and
knowledge and
experience with renewable energy systems. He is a m
ember of the
South African Institute of Electrical Engineers (council).
Student presentations:
Harry
Lee
BEngSc (BME)
BSc (Eng) Electrical, MSc (Eng) Electrical Candidate ,
University of the Witwatersrand
Yuan
-
chun Harry Lee is a student graduated from the University of
Witwatersrand in 2010 with a Bachelor’s
degree of Engineering Science in
Biomedical Engineering. He then further studied and obtained a Bachelor of
Science
in Electrical Engineering in 2012. He is currently pursuing a Master’s
degree of Science in Electrical
Engineering at the University of Witwatersrand
with a particular interest in lightning injuries.
Abstract:
An investigation on the effects of the
frequency components of the lightning
stroke to the human body
Lightning injuries to the human body can be classified into three main categories:
neurological,
cardiovascular, and external burns. The aim of this research is to investigate the effects of
the
frequency components of the lightning stroke regarding these lightning injuries. Only negative
cloud
-
to
-
ground
lightning and the direct strike scenario is considered. A simple model of the human
body which consists of a
cylindrical conductor is constru
cted in the COMSOL multiphysics
platform. A lightning stroke resembles a
shape which can be estimated by the double exponential
function. This double exponential function is used as
the model of the lightning impulse. The
lightning impulse is separated int
o its basis functions through the use of
the discrete Fourier
Transform. Each of these functions are passed through the human body model at various
contact
points and the results analysed. Properties such as the skin effect, current pathway, current densit
y
and charge transferred are investigated.
LIGHTS
8
Brett Ryan Terespolsky
Brett Terespolsky is an MSc student in the School of Electrical and Information Engineering at the University of
the Witwatersrand. He completed his BSc (Eng
) in Electrical Engineering Degree in 2011. Since then he has
been pursuing a masters degree in lightning research. He also has interests in software engineering and
modelling. This has led to his research in modelling the lightning process as a system of
circuits.
Title:
Circuit model to reproduce the first stroke in a lightning strike
Abstract:
The measurement of lightning currents has been investigated by numerous researchers over more than
five decades. These findings have been used in, amongst other
things, the creation of lightning protection
standards. These standards play a vital role in the design of equipment that can withstand lightning strikes. The
aim of this research is to develop a circuit model that can be used to simulate lightning current
, with particular
focus on applications in lightning protection system studies. The initial research is limited to the first return
stroke described by a Heidler function steepness factor of ten. Ultimately a generic algorithm will be developed
to simulate
any shape lightning current with any electrical load attached.
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The entire section is 3, words. Of course, the dilemma is that what is ethical is not necessarily congruent with a firm's often-stated objective of maximizing profits, especially in the short run.
This example also illustrates how attitudes influence the form that the need takes. Therefore, marketers need to influence consumer behaviour to increase their purchases. Besides, when the price of a good falls, it becomes relatively cheaper than other goods and as a result the consumer is induced to substitute that good for others.
In other words, indifference curve analysis clearly explains why in case of Giffen goods, quantity demanded increases with the rise in price and decreases with the fall in price. There are two types of information searches: The other factors are the external factors and social influences.
At the end of his or her evaluation, the buyer may experience satisfaction or dissatisfaction. The concept of diminishing marginal utility demonstrates that transfer of income from the rich to the poor will increase the economic welfare of the community.
What is consumer involvement and how does it relate to the likelihood of a consumer elaborating on a purchase in their mind.
They went to the store websites or websites of other consumers and researched on how well a product rated. A consumer buying decision process can have up to six stages.
This law has been arrived at by introspection and by observing how people behave. This means that the utility which a consumer derives from a good is the function of the quantity of that good and of that good alone. The internal or psychological factors include: Car costs about Rs.
Also, the there was a camera with all the features that Consumer B was looking for. Your academic paper will be written from scratch.
Another important consideration is reference groups, with these having the potential to influence both needs and wants. In other words, it is assumed in this analysis that utility is cardinally measurable.
The question is how far a consumer goes in purchasing the goods he wants. Adam Smith was greatly perplexed to know why water which is so very essential and useful to life has such a low price indeed no pricewhile diamonds which are quite unnecessary, have such a high price.
Information on consumer behaviour is important to the marketers: An understanding of consumer behavior can lead to improved marketing strategies on the part of firms and organizations, and can also lead to improved public policy.
We have joined the shaded rectangles by a smooth curve which is the curve of marginal utility. In terms of calculus, it can be expressed as: Money represents general purchasing power over all other goods, that is, a man can satisfy all his material wants if he possesses enough money.
If properly understood the law of diminishing marginal utility applies to all objects of desire including money. Postpurchase Behavior Both consumers are relatively satisfied with their cameras. Marginal utility can be expressed as under:. Consumer behaviour is affected by a lot of variables, ranging from personal motivations, needs, attitudes and values, personality characteristics, socio-economic and cultural background, age, sex, professional status to social influences of various kinds exerted.
Determine three (3) aspects of consumer behavior that the physician’s practice management should consider as part of an effective marketing strategy for. B Consumer Behavior Term Paper A Study on Customers From Hell Instructor: Morris.
B. Holbrook In this term paper, I planned to do a study on the behavior of a special consumer-protection legislations to counter the organization or alter the firm’s.
The study of consumer behavior involves elements of economics, the social sciences, and the physical sciences. An endless and diverse field of research and applications, consumer behavior.
Therefore, consumer behavior audits contribute to the development of better marketing strategies, and the development of better products according to the consumers’ desires and demands.
In addition, marketers learn how they can best position their products and segment their markets. Consumer Behaviour Term Paper - Free download as Word Doc .doc), PDF File .pdf), Text File .txt) or read online for free. | https://segaryxemom.michaelferrisjr.com/term-papers-on-consumer-behavior-11260cx.html |
The Midwestern Vascular Surgical Society is pleased to announce the 10th Annual Mock Oral Examination to be held Thursday, September 9, 2021. We urge you to avail this opportunity for your Vascular Surgery Trainees.
The Society will be offering its Mock Orals program in a virtual format from 8:00 AM – 12:30 PM prior to the start of Midwestern Vascular 2021, the Society’s Hybrid 45th Annual Meeting to be held in Chicago.
This is the 10th year that the MVSS will host the Mock Orals Exam for Senior Vascular Fellows and Residents. The Mock Oral Exam provides trainees from across the Midwest an opportunity to experience familiarity with the certifying exam format, gain experience with examiners from outside their training program and receive constructive feedback from examiners to improve their exam-taking skills. Our goal is to provide the Mock Oral Exam to 20 trainees through our Zoom platform.
ELIGIBILITY/APPLICATION PROCESS
- There is limited availability of 20 spots on a first come first serve basis, with priority given to those in their final year of training (i.e. PGY 7 fellowship or 5th year of integrated vascular surgery residency), and to those who have not done the program in the past. Other fellows or residents will be accepted if space allows.
- Contact information for the Program Director will be required at the time of registration. Participation in the program will also require a refundable deposit of $100.00. Failure to attend, or if the Fellow withdraws from participation after July 15, 2021, the deposit will be forfeited. Deposits will be refunded following conclusion of the program.
- The Registration Deadline is Monday, June 28, 2021. However, registration is encouraged early as this program will fill up very quickly and prior to the deadline.
- Trainees should register online by Monday, June 28th by gong to: Registration information will be reviewed for approval by the Education Committee and confirmed following the registration deadline. Point to the button below to Register:
Midwestern Vascular Surgical Society Education Mock Orals Committee
Andrew W. Hoel, MD, Co-Chair, Northwestern Memorial Hospital, Chicago
Brian Lewis, MD, Co-Chair, Medical College of Wisconsin, Milwaukee, WI
Julia B. Wilkinson, MD, Northwestern Regional Medical Group, Winfield, IL
Jihad T. Abbas, MD, University of Toledo Medical Center, Toledo, OH
Paul D. DiMusto, MD, Wisconsin School of Medicine and Public Health
University of Wisconsin, Madison, WI
Irina Shakhnovich, MD, Gundersen Health, LaCrosse, WI
Announcing the 2021 Virtual Medical Student Education Program
The Midwestern Vascular Surgical Society is pleased to announce the 2021 Virtual Medical Student Education Program, “Introduction to Vascular Surgery” to be held on Tuesday, September 7, 2021.
During the past six years of the course, the Society has attracted over 150 medical students from 25 different Midwestern Medical Schools who were interested in learning more about the specialty of Vascular Surgery.
The primary goal of this program is to introduce the specialty of Vascular Surgery as a career choice to medical students from the Midwest region. The program provides a unique opportunity for medical students at all levels to interact with members and leaders of the Midwestern Vascular Surgical Society (MVSS). Vascular Surgery faculty and trainees participating in the program have a particular interest in medical student education and mentorship.
Program content will be delivered virtually. Plans are being made to provide virtual simulation sessions with ‘live’ proctoring of skills.
Visit back for additional information to be available soon. | https://www.midwestvascular.org/annual-meeting/mock-orals-medical-student-programs/ |
Establish and maintain identified solutions in line with enterprise requirements covering design, development, procurement/sourcing and partnering with suppliers/vendors. Manage configuration, test preparation, testing, requirements management and maintenance of business processes, applications, information/data, infrastructure and services.
Establish timely and cost-effective solutions capable of supporting enterprise strategic and operational objectives>
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Design High-Level Solutions
Establish a high-level design specification that translates the proposed solution into business processes, supporting services, applications, infrastructure, and information repositories capable of meeting business and enterprise architecture requirements.
Involve appropriately qualified and experienced users and IT specialists in the design process to make sure that the design provides a solution that optimally uses the proposed IT capabilities to enhance the business process.
Create a design that is compliant with the organization’s design standards, at a level of detail that is appropriate for the solution and development method and consistent with business, enterprise and IT strategies, the enterprise architecture, security plan, and applicable laws, regulations, and contracts.
After quality assurance approval, submit the final high-level design to the project stakeholders and the sponsor/business process owner for approval based on agreed-on criteria. This design will evolve throughout the project as understanding grows.
Design Detailed Solutions Components
Develop Solution Components
Develop business processes, supporting services, applications and infrastructure, and information repositories based on agreed-on specifications and business, functional and technical requirements.
When third-party providers are involved with the solution development, ensure that maintenance, support, development standards, and licensing are addressed and adhered to in contractual obligations.
Track change requests and design, performance, and quality reviews, ensuring active participation of all impacted stakeholders.
Document all solution components according to defined standards and maintain version control over all developed components and associated documentation.
Assess the impact of solution customization and configuration on the performance and efficiency of acquired solutions and on interoperability with existing applications, operating systems, and other infrastructure. Adapt business processes as required to leverage the application capability.
Ensure that responsibilities for using high security or restricted access infrastructure components are clearly defined and understood by those who develop and integrate infrastructure components. Their use should be monitored and evaluated.
Procure Solution Components
Create and maintain a plan for the acquisition of solution components, considering future flexibility for capacity additions, transition costs, risk, and upgrades over the lifetime of the project.
Review and approve all acquisition plans, considering risk, costs, benefits, and technical conformance with enterprise architecture standards.
Assess and document the degree to which acquired solutions require adaptation of the business process to leverage the benefits of the acquired solution.
Follow required approvals at crucial decision points during the procurement processes.
Record receipt of all infrastructure and software acquisitions in an asset inventory.
Build Solutions
Integrate and configure business and IT solution components and information repositories in line with detailed specifications and quality requirements. Consider the role of users, business stakeholders, and the process owner in the configuration of business processes.
Complete and update business process and operational manuals, where necessary, to account for any customization or special conditions unique to the implementation.
Consider all relevant information control requirements in solution component integration and configuration, including implementation of business controls, where appropriate, into an automated application, controls such that processing is accurate, complete, timely, authorized, and auditable.
Implement audit trails during configuration and integration of hardware and infrastructural software to protect resources and ensure availability and integrity.
Consider when the effect of cumulative customizations and configurations (including minor changes that were not subjected to formal design specifications) require a high-level reassessment of the solution and associated functionality.
Ensure the interoperability of solution components with supporting tests, preferably automated.
Configure acquired application software to meet business processing requirements.
Define service catalogs for relevant internal and external target groups based on business requirements.
Perform Quality Assurance
Define a QA plan and practices including, e.g., specification of quality criteria, validation and verification processes, the definition of how quality will be reviewed, necessary qualifications of quality reviewers, and roles and responsibilities for the achievement of quality.
Frequently monitor the solution quality based on project requirements, enterprise policies, adherence to development methodologies, quality management procedures, and acceptance criteria.
Employ code inspection, test-driven development practices, automated testing, continuous integration, walk-throughs, and testing of applications as appropriate. Report on outcomes of the monitoring process and testing to the application software development team and IT management.
Monitor all quality exceptions and address all corrective actions. Maintain a record of all reviews, results, exceptions, and corrections—repeat quality reviews, where appropriate, based on the amount of rework and corrective action.
Prepare for Solution Testing
Execute Solution Testing
Undertake testing of solutions and their components in accordance with the testing plan. Include testers independent from the solution team, with representative business process owners and end-users. Ensure that testing is conducted only within the development and test environments.
Use clearly defined test instructions, as defined in the test plan, and consider the appropriate balance between automated scripted tests and interactive user testing.
Undertake all tests in accordance with the test plan and practices, including the integration of business processes and IT solution components and of non-functional requirements (e.g., security, interoperability, usability).
Identify, log, and classify (e.g., minor, significant, and mission-critical) errors during testing. Repeat tests until all significant errors have been resolved. Ensure that an audit trail of test results is maintained.
Record testing outcomes and communicate results of testing to stakeholders in accordance with the test plan.
Manage Changes to Requirements
Assess the impact of all solution change requests on the solution development, the original business case and the budget, and categorize and prioritize them accordingly.
Track changes to requirements, enabling all stakeholders to monitor, review, and approve the changes. Ensure that the outcomes of the change process are fully understood and agreed on by all the stakeholders and the sponsor/business process owner.
Apply change requests, maintaining the integrity of integration and configuration of solution components. Assess the impact of any major solution upgrade and classify it according to agreed-on objective criteria (such as enterprise requirements), based on the outcome of the analysis of the risk involved (such as the impact on existing systems and processes or security), cost-benefit justification and other requirements.
Maintain Solutions
Develop and execute a plan for the maintenance of solution components that includes periodic reviews against business needs and operational requirements such as patch management, upgrade strategies, risk, vulnerabilities assessment, and security requirements.
Assess the significance of proposed maintenance activity on current solution design, functionality, and/or business processes. Consider risk, user impact, and resource availability. Ensure that the business process owners understand the effect of designating changes as maintenance.
In the event of major changes to existing solutions that result in a significant change in current designs and/or functionality and/or business processes, follow the development process used for new systems. For maintenance updates, use the change management process.
Ensure that the pattern and volume of maintenance activities are analyzed periodically for abnormal trends indicating underlying quality or performance problems, cost/benefit of a major upgrade, or replacement in lieu of maintenance.
For maintenance updates, use the change management process to control all maintenance requests.
Define IT Services and Maintain the Service Portfolio
Propose definitions of the new or changed IT services to ensure that the services are fit for purpose. Document the proposed service definitions in the portfolio list of services to be developed.
Propose new or changed service level options (service times, user satisfaction, availability, performance, capacity, security, continuity, compliance, and usability) to ensure that the IT services are fit for use. Document the proposed service options in the portfolio.
Interface with business relationship management and portfolio management to agree on the proposed service definitions and service level options.
If service change falls within agreed-on approval authority, build the new or changed IT services or service level options. Otherwise, pass the service change to portfolio management for investment review. | https://online-pmo.com/cobit/build-acquire-and-implement/manage-solutions-identification-and-build/ |
1.1 The term “Buyer” shall mean the Company so named in the Purchase Order.
1.2 The term “Supplier” shall mean the person, Firm or Company to whom the Purchase Order is issued.
1.3 The word “Goods” includes all goods covered by the Purchase Order including proprietary items, raw materials, processed materials, fabricated items and services provided.
1.4 The term “Purchase Order” shall mean buyers purchase order which specifies that these Conditions apply to it.
1.5 The “Contract” shall mean the contract between the Buyer and the Supplier consisting of the Purchase Order. These conditions and any other documents (or part thereof) specified in the purchase order.
1.6 The term “Order” shall mean the Purchase Order/Contract as detailed in point’s 1.4 & 1.5.
1.7 The “Company” shall mean AMB Engineering Ltd (hereinafter referred to as AMB).
1.8 The terms “These Conditions” shall mean the Buyers standard Terms and Conditions of Purchase set out in this document including additional requirements specified on the face of the order.
2.1 All contracts of purchase made by AMB shall be deemed to incorporate these Terms & Conditions. No written or printed terms inconsistent with these Conditions or additional thereto shall be binding upon the Company unless expressly accepted in writing by the Company’s representatives.
2.2 The Company shall not be liable in respect of any Orders or instructions other than those issued or confirmed on the Company’s official forms duly signed by the Company’s authorised representatives.
2.3 The Company will incur no obligation in respect of any order until the Company receives the written confirmation of the Supplier in the form of an acknowledgement of the order. If the Supplier should fail to provide such written confirmation, the Company shall have the option of either regarding the Order unconditionally accepted, or withdrawing the same by notice to the Supplier, in which case any costs incurred by the Supplier shall be for the Suppliers account. Acceptance of the Order constitutes a Contract between the Company and the Supplier.
3.1 This order when accepted by the Supplier constitutes the complete and final agreement between the Company and the Supplier. No variation, amendment or alternative understanding in any way purporting to modify the Contract shall be binding upon the Company unless made in writing and signed by the company’s authorised representative.
4.1 The prices stated in the Order are fixed and firm unless otherwise stated.
6.1 The Company accepts no liability for the acceptance of payment for Goods delivered in excess of quantities specified in the Purchase Order unless otherwise agreed and may return such goods to the Seller at no risk or expense to the Company.
7.1 The application of the uniform laws on International Sales shall be governed by the Laws of England and any claim or dispute arising there from shall be subject to the jurisdiction of and determined by English Courts.
8.1 The following sections detail the requirements to be satisfied by suppliers to AMB Engineering Limited. AMB requires that each supplier must comply with the quality requirements set forth within this document and to maintain a Quality Management System that ensure materials, goods and services comply with all our specified requirements.
8.2 These contract requirements are additional to the details on our Purchase Order (which focus on product quantity, logistics, part descriptions, special references, etc.).
9.1 To establish and confirm a supplier’s Quality Assurance requirement for AMB for organisations supplying materials, goods and services that have a direct impact on the specification and or performance of an AMB product.
11.1 Suppliers shall as the terms so require, supply, release and deliver all products in accordance with the Purchase Order and all requirements identified therein.
11.2 AMB require its suppliers to be certified against EN AS 9100 and or EN AS 9120 (current issue) when contracted for Aerospace / Defence work (this is an EN AS 9100 and or EN AS 9120 customer contract requirement). If a supplier’s business is not structured specifically for Aerospace / Defence contracts, then the supplier must be certified against ISO 9001 current issue as a minimum. If a test and or calibration laboratory, the supplier must be ISO 17025 accredited by UKAS.
11.3 Suppliers that do not comply with the above may be used by AMB, provided the supplier’s Quality Management System complies with the following requirements (QA-PR-07) and has been formally approved by AMB management. All certification awarded must be accredited by UKAS (or similar notified body under the mutual recognition agreement (MRA) for international accreditation – refer to EA – EC notified bodies).
11.4 All products shall be supplied strictly in accordance with the purchase order (and technical specification provided). The delivery of incomplete product / shortages is not permissible unless specified on the purchase order or by written authority of AMB.
11.5 When the supplier is manufacturing a product on behalf of AMB, the supplier may only use Special Process Suppliers who are AMB approved. A complete list of AMB approved Special Process Suppliers can be supplied on request.
11.6 Material Stockists / Distributors / Franchised Distributor shall hold as a minimum ISO9001: latest issue Certification. As a minimum, items shall only be procured directly from the manufacturer or approved distributor / franchised distributor.
11.5 In the event that a supplier has its approval against AS9100, AS9120 and / or ISO 9001 removed the supplier must immediately inform AMB in writing stating reason / status of withdrawal.
12.1 Enquiries concerning the content of this document and other referenced documents, or requests for additional copies should be referred to the purchasing representative responsible for the Purchase Order within AMB.
12.2 The requirements of this document and of AMB procedure QA-PR-07 ‘Purchasing’ will be used to provide both existing and potential suppliers with visibility of the current Quality & Standard requirements and expectations of AMB contracts.
12.3 It is the policy of AMB to manufacture and supply products and services, which result in, or contribute to, safe conditions for its customers and the end-users of such products and services. In furtherance of this policy, Suppliers shall establish controls and procedures that ensure that the attention necessary for the achievement of this objective is objectively provided throughout the production in support of their products.
12.4 Suppliers are required to comply in full with the contents of this document. If a supplier cannot comply with any portion of this document, then the supplier must advise AMB in writing. AMB will review the supplier request and advise the supplier of the results in writing. The supplier is responsible for keeping all related documentation on file at their facility. No deviation from this document is acceptable in advance of formal agreement to do so in writing from AMB. Such formal agreement must be retained by the supplier.
12.5 Verbal agreements are un-acceptable.
12.6 Suppliers shall maintain AMB specifications and other Standards at the latest issue and shall review the issue status of specifications on receipt of a Purchase Order and or at least once within a six month period (particularly for repeat contracts).
13.1 All suppliers are expected to have plans to achieve Business (Quality) improvements as part of their continuous improvement programme.
13.2 AMB is dedicated to continuous improvement in the quality and integrity of its services and to the satisfaction of its customer requirements and expectations. Suppliers’ contribution to this approach through the quality and reliability of their products and services is a prerequisite.
13.3 Each supplier shall demonstrate continuous improvement based on pro-active loss-prevention, root cause analysis and effective timely corrective action.
14.1 Any change to the management representative responsible for Quality Management System and / or Inspection within the supplier’s organisation (or group ownership) shall be communicated to AMB. Changes to premises shall be notified sufficiently in advance to AMB.
15.1 Purchase Order amendments shall be subject to review by AMB prior to acceptance. The review shall ensure that copies of all processes and specifications quoted within a Purchase Orders are available, and that, where a supplier is unable to carry out any operations, approved sub-contractors may be identified.
15.2 Where a supplier has more than one site, every site used to produce product for shipment direct to AMB must have AMB approval.
15.3 AMB shall be afforded the right of entry to verify at source and / or upon receipt that purchased product conforms in all respects to specified requirements. This action shall not absolve the supplier of the responsibility for the quality of the delivered product nor preclude its subsequent rejection should other quality issues arise at a later date / time.
15.4 Where the use of a sub-contractor is permitted, the identification and selection shall form a part of the initial contract review. Suppliers may consider / use a sub-contractor suitable given the following circumstances: The sub-contractor is currently approved by AMB.
15.6 Suppliers must reference AMB documentation reference numbers on all Purchase Orders issued in support of activity for AMB (referring their suppliers to the AMB web-site for latest version documentation).
16.1 Failure of components can have major effects on airworthiness, safety, reliability, operational integrity – with related cost impact. All parts are therefore termed “controlled” and should be treated as such (bonding requirements may be appropriate and / or necessary).
16.2 To mitigate the possibility of the inadvertent user of counterfeit parts, the Seller may only purchase components and parts procured directly from the Original Equipment Manufacturers (OEMs) or through the OEMs' authorised distribution chain. If an Independent Distributor is used, the Seller must make available to AMB (if AMB so requests) OEM documentation that authenticates traceability of the components to that applicable OEM.
16.3 If the required items cannot be procured from these sources, use of product without appropriate traceability documentation from independent distributors (brokers) or other sources is not authorised unless first approved in writing by AMB.
NOTE: It is the supplier’s responsibility to check that any sub-contractor is correctly approved prior to use (objective evidence for audit purposes maybe required).
17.1 The supplier shall have no discretionary power to deviate from the specification requirements as detailed with Purchase Order (and supporting documentation). Concessions will only be accepted on receipt from the Supplier of a full “root cause analysis” report detailing the issues and evidence of preventative action. Parts subject to concession must not be delivered to AMB until AMB approves a concession.
Note: Concessions are normally only issued to Suppliers when a product is non-conforming, and the non-conformance does not affect fit, form or functionality.
17.2 No rework shall be permitted on identified non-conforming product without written approval from AMB. Manufacturing records shall clearly record the operation and the results achieved, should re-working under a concession be approved.
17.3 Where the supplier has any reason to suspect non-conformance of any delivered product, then the supplier must immediately notify AMB.
17.4 Scrapped (or non-conforming) components must be physically damaged beyond repair prior to actual disposal (to prevent mixing with conforming product of the same / similar type / model). The AMB management representatives (or their customer) may require a report from the Supplier and / or witness by inspection and of process of damage and / or disposal.
18.1 The Supplier shall be notified of non-conforming supplies found after delivery. AMB will contact the supplier and issue a CAR, (Corrective Action Report), against the parts prior to return.
18.2 Following receipt of a CAR notification the Supplier shall take immediate containment action. The action shall include 100% inspection of all supplier stock or work in progress. This containment action shall be taken within 48 hours of notification from AMB. The supplier shall provide within 14 days results of an investigation into the root cause of the problem and provide corrective action to prevent recurrence. The findings, corrective action and effective date shall be reported to AMB.
19.1 All Suppliers shall monitor the quality and delivery performance of product delivered to AMB. In addition each supplier’s quality and delivery performance is continually monitored by AMB. A supplier whose performance does not achieve and maintain an acceptable level shall be formally notified of their supplier status and may be required to implement improvement actions accordingly. Failure to improve or respond positively to an AMB CAR will result in the withdrawal of supplier approval by AMB.
20.1 All (Quality Management System) records held by Suppliers shall be legible and identifiable to the product involved. Records shall be stored and maintained in such a way that they are readily retrievable in facilities that provide a suitable environment to minimise deterioration or damage and to prevent loss. Records shall be available for evaluation by AMB until such time as AMB authorise disposal in writing.
20.2 Documentation and records applicable to AMB shall not be amended with correction fluid. A single linked line shall delete any revisions and/or correction of errors and will be accompanied by an initial and date.
20.3 Should a supplier cease trading with AMB, quality records shall still be maintained until disposal is authorised by AMB. If the supplier ceases trading completely, or is unable to maintain the records, AMB must be informed so that alternate arrangements can be made to store the records.
20.4 All records shall be retained by the Supplier for a period of 25 years unless otherwise agreed with AMB.
We (name of the supplier) hereby confirm that the whole of the supplies detailed hereon have been manufactured, inspected and tested and conform in all technical and integrity respects with the requirements of the contract order / specification.
Note: * The Supplier shall be able to demonstrate to the satisfaction of AMB that the nominated authorised signatory has controlled usage of the authority (with the technical competence demonstrated by qualification and experience supported by validated CV claims).
21.3 Where the Supplier utilises an automated system for generation and / or authorisation of certificates / records, then those systems shall be subject to robust management and security controls approved by AMB to protect the integrity of the certification process.
21.5 When the purchase order and / or applicable documents do not specify a method of packaging and preservation, it is the supplier’s responsibility to assure that product is preserved and packed using methods and materials that will assure that it is delivered damage free to AMB.
22.1 Electrostatic Sensitive Devices (ESD) must be preserved by the supplier using appropriate ESD packaging materials, and stored under conditions recommend by the manufacturer.
· Assure the shipping address, supplier name, qty, and part number are visible.
· Assure that the packing list, quality documents, and other important information is enclosed, or securely fastened.
23.1 When a FAIR is required with the goods to demonstrate compliance with all the procurement specifications detailed in the design package the following must apply: First Article Inspection Reports shall be in accordance with AS 9102 and or AMB procedure QA-PR-10.
23.2 A copy of the FAIR shall be supplied with the product unless otherwise stated. The supplier shall retain the FAIR as a quality record and they shall not be disposed of without the written permission of AMB. This shall not absolve the supplier of the responsibility for the quality of the delivered product nor preclude its subsequent rejection should other quality issues arise.
24.1 Any person authorised by AMB, including the Customer or Regulatory Authority, shall not be unreasonably refused permission by the supplier to enter any works, warehouse or other premises under the supplier’s control for the purpose of surveillance or inspection of any tools or materials procured or used for the manufacture of the goods or process of manufacture on the completed goods themselves before dispatched to AMB or their customer.
25.1 AMB advises each supplier to have a written business continuity plan to cover disaster recovery and the responsibilities and actions to be taken in the event of an emergency that may affect deliveries to AMB that will bring the supplier on line in the shortest possible time.
26.1 Uncontrolled change within the supply chain can cause deficiency escapes into AMB. It is crucial therefore that all change, no matter how trivial it may appear, is assessed for potential risk and then subject to mitigating actions and control.
1) Change to the manufacturing location, either within a supplier or between suppliers.
1) Changes to the manufacturing location shall be notified to AMB.
2) Changes in components shall be raised with the buyer responsible for the purchase order. The buyer shall take the appropriate action within AMB and inform the Customer. The supplier must not progress with any changes to the component without written agreement from AMB.
· All changes to components storage location shall be subject to a documented risk review prior to being carried out.
· Staff changes within the company’s stores department must be fully trained and supervised until level of competence is assessed and approved as competent.
· Changes to the Stock control computer system, must be documented, risk assessed, audited and checked after changes for example, new operational software is introduced or updated.
All documentation relating to point 3 must be kept indefinitely and made available to AMB on request in writing with reasonable notice following a CAR with relation to supply quality problems.
27.1 All parts shall be clearly traceable back to the original manufacturer of the parts. Where the supplier has purchased a component or assembly, they shall have a copy of the original manufacturer’s certificate of conformance.
27.2 All components and assemblies shall be traceable to the original material identification.
27.3 The traceability system must facilitate the rapid identification of any part delivered and suspected of being defective. Containment action must be implemented immediately to protect the customer from any defects found that affect quality of the product.
28.1 Any special process supplier must be AS9100 or ISO9001 approved or meet the requirements outlined in section 34.0 of this document. The supplier performing the special process must certify that all applicable requirements have been met.
29.1 Adequate, clean well-maintained facilities shall be provided to enable products to be consistently produced in accordance with the requirements of the AMB purchase order.
29.2 Suppliers shall establish a procedure detailing the general workmanship practices for the prevention of Foreign Object Debris.
29.3 Suppliers must not omit any part of any specification except when defined on the purchase order or covered by a non- conforming report authorised by AMB.
29.4 Suppliers providing Shelf life items shall ensure they are correctly labelled with shelf life expiry and suitably packaged. No shelf life items within 6 months of expiry will be accepted.
29.5 Suppliers are expected to establish procedures for identifying adequate statistical techniques for determining process capability of key characteristics, especially when these are identified on the documentation. Such techniques shall demonstrate management ownership and responsibility and be based on recognised industry models.
29.6 Where the supplier uses a sample inspection plan as a means of product acceptance, the plan shall be predicated on industry recognised models, statistically valid and shall preclude the acceptance of known non-conforming product. Documented procedures and records to demonstrate this shall be available.
29.7 All parts supplied to AMB shall be identified in accordance with the requirements of AMB. Suppliers shall maintain records to identify the materials used and the manufacturing and processing history of each batch of parts supplied to AMB. A lot number that enables all associated records to be retrieved shall identify each batch.
30.1 The supplier is required to maintain and provide upon request all inspection records. The records must be at a minimum based on an established/recognised sampling plan.
31.1 Source Inspection will be used by AMB to help develop a new supplier, or a supplier that is having quality issues. Source inspection at a supplier’s site will be imposed by a letter issued from AMB to the supplier. In the event AMB imposes source inspection, only AMB can remove or waive source inspection.
31.2 AMB will also use source inspectors to perform in process checks at a supplier, process audits at a supplier, or corrective action development, or follow up. AMB will select a UKAS and / or other approved inspector.
32.1 If a supplier’s quality system discovers a non-conformance to the AMB Purchase Order, the supplier can submit a request for a concession to the Buyer.
**Requests to use as is, or repair a non-conformance, must be processed using the suppliers own concession request form and signed by AMB.
Note: The supplier is not authorised to dispatch items requiring concession until they have been informed of the applicable Concession Number and the supplier has a copy of the approved concession. This Concession Number must appear on their Certificate of Conformity, each time a delivery is made from the batch that has been approved under Concession.
33.1 If AMB perform a supplier audit and finds a non-conformance a request for corrective action will be issued to the supplier. Corrective actions for issues found during an audit will be documented. Before an audit will be closed out all open audit CARs must be answered by the supplier and accepted by AMB.
34.1 AMB uses AS9100 or ISO 9001 approved special process suppliers. In addition to AS9100 & ISO 9001 approval, the special process supplier must demonstrate the ability to satisfy all applicable requirements. Failure to satisfy any requirement will prevent AMB from using that supplier. Coded welder status is required when requested. | http://www.ambeng.co.uk/tc.htm |
This contest is for landscape (natural environment) photographs with dramatic lighting - this means well-defined shadows and contrast, beautiful colors and atmosphere. There are many factors that can naturally create dramatic lighting, the key is to be in the right place at the right time.
Show us your best landscape images with dramatic lighting/elements which create a strong emotional impact!
Every photo submitted will be available for the crowd to rate once the submissions period has ended. You can see all the images uploaded to a contest, but will need to rate them to see how they’re ranked once the rating period begins.
Some contests on Photocrowd also have a judge. After the submission period closes the judge chooses their favourite images and writes some image reviews. The crowd and judge results will be announced on the same day. | https://www.photocrowd.com/photo-competitions/landscapes-dramatic-lighting-landscape-photo-contest-3769/details/ |
Q:
Computing theory: can a single node be a subgraph?
Can a single node be considered a subgraph?
For example, if I had this graph, G:
X-----Y
and I deleted Y, leaving me with the graph
X
is this a subgraph (induced) of G?
What about the following argument?
Assume a single node can be considered a graph. Any graph is an induced subgraph of itself. Therefore, a single node graph has a single-node induced subgraph.
Though this is only valid if a single node can be considered a graph.
In computing theory, what is the generally accepted norm?
A:
What about the following argument?
Assume a single node can be considered a graph. Any graph is an induced subgraph of itself. Therefore, a single node graph has a single-node induced subgraph.
Though this is only valid if a single node can be considered a graph.
That's completely circular. If a single node can be a graph, you can ask about its subgraphs and, sure, every graph is a subgraph of itself. But if a single node can't be a graph, it doesn't make sense to ask about subgraphs of something that isn't a graph.
In general, a single vertex is considered to be a graph, referred to as the "trivial graph". However, it's something of a special case in that it's often an exception to statements one might wish to make when proving things. For example, every connected graph contains at least one edge... except for the trivial graph; every graph has a proper subgraph... except for the trivial graph; etc. Because of this, writers often exclude the trivial graph from consideration. So, for example, in the "notation" section of a graph theory paper, you often see a statement such as "Except where stated otherwise, we assume that every graph contains at least one edge".
In this respect, asking whether the trivial graph is a graph is a bit like asking whether zero is a natural number. Some people will jump up and down and insist that it is; some people will jump up and down and insist that it isn't; the best plan is to say that it is or isn't according to what makes your life easiest in any particular situation.
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Bedroom furniture has become much easier to move around and assemble with the manufacturing of furniture kits and prefabricated furnishings. Beds have also become much easier to assemble with ready-made rails and slots built into head- and footboards. It will only take a matter of minutes to assemble your bed.
Step 1
Place the headboard against the wall where you want it, and the footboard at the opposite end of room. Lay out your bed rails at 90 degree angles to the headboard on both sides. Verify that the rails are on the right sides of the bed. The vertical sides of the rail should be toward the outside of the bed with the horizontal side facing inward. Lay the middle rail parallel to the headboard and footboard about halfway between them.
Step 2
Attach the middle rail to both side rails. Lift up the locking latch on one side and slide the flanges into the slots. Pull sideways on the center rail to lock the rail into place. Lower the locking mechanism to secure the rail. Repeat the process on the other side of the center rail.
Step 3
With the headboard standing up straight, lift one of the rails and slide the end into the slots on the lower section of the headboard. Push the rail down onto the pins to make sure it locks into place. Repeat the process for the other side of the headboard.
Step 4
Position the footboard at the opposite end of the bed. Lift one of the rails and slide it into the footboard by inserting the end into the slot as you did with the headboard. Repeat the process for the opposite end of the footboard with the remaining rail. Check the plastic feet on the rails and level as necessary with a crescent wrench. | https://www.hunker.com/13403490/how-to-attach-a-headboard-footboard-to-a-metal-frame |
Q:
How do I troubleshoot a UndefinedBehaviorSanitizer error?
I'm solving a leetcode problem where I have to find the longest palindrome within a string and return it. I got the main algorithm written down pretty quickly, and it was passing some simple test cases locally, but when I tried to run it remotely from within leetcode, I got the following error:
Line 1061: Char 9: runtime error: addition of unsigned offset to 0x7fff1f221c60 overflowed to 0x7fff1f221c5f (basic_string.h)
SUMMARY: UndefinedBehaviorSanitizer: undefined-behavior /usr/bin/../lib/gcc/x86_64-linux-gnu/8/../../../../include/c++/8/bits/basic_string.h:1070:9
All of the research that I did in the next few hours led me to believe that I must be accessing or editing some code that was out of bounds of the string. Unfortunately, no matter how thoroughly I check to make sure it's impossible to use an out-of-bounds index, I'm getting the same error.
This is my code as it currently exists:
#include <string>
#include <iostream>
class Solution {
public:
std::string longestPalindrome(std::string s) {
std::string pal = "";
short pal_offset = 0;
for (size_t pivot = 0; pivot < (s.size() - (pal.size() / 2)); ++pivot) {
// Check for odd palindrome at pivot
pal_offset = 0;
// Make sure pivot + next offset doesn't overflow s to the right
// Make sure pivot - next offset doesn't overflow s to the left
if ((pivot + (pal_offset + 1) < s.size()) && (pivot - (pal_offset + 1) >= 0)) {
// Check the next possible offset to see if substring is still a palindrome
while (s[pivot + (pal_offset + 1)] == s[pivot - (pal_offset + 1)]) {
// Confirm that current offset works
++pal_offset;
// Double check that the new offset can't overflow to either side
if (pivot < pal_offset || (pivot + pal_offset) >= s.size())
break;
}
}
// If there is a confirmed offset greater than 0 and that offset is greater than all previous
// offsets
if (pal_offset && pal.size() < (pal_offset * 2) + 1) {
// Gonna be silly and double check here to make sure the bounds of the substring don't
// overflow s from the left or the right
if (pivot - pal_offset >= 0 && (pivot + ((pal_offset * 2) + 1) < s.size())) {
// Stick that new, big palindrome into pal
pal = s.substr((pivot - pal_offset), ((pal_offset * 2) + 1));
}
}
// Check for even palindrome at pivot and pivot + 1
// Why am I starting at -1? Well, let me tell ya. Pull up a chair. In order to be consistent
// with the odd checker, I decied to follow the following algorithm algorithm:
// 1) Check the offset that is one greater than the last known good offset
// 2) If it works, make *that* the last known good offset, and go back to 1
// Because even palindromes start at offset 0 (the pivot is part of the palindrome), we have
// to have the default last known good offset set to -1, so that the 'next' one in the first
// run is 0.
pal_offset = -1;
// Make sure pivot - the next offset doesn't overflow s on the left
// Make sure pivot + 1 + the next offset doesn't overflow s on the right
if ((pivot - (pal_offset + 1) >= 0 ) && ((pivot + 1) + (pal_offset + 1) < s.size())) {
// Check the next possible offset to see if substring is still a palindrome
while (s[pivot - (pal_offset + 1)] == s[(pivot + 1) + (pal_offset + 1)]) {
// If it is a palindrome, increment pal_offset to show the new confirmed offset
++pal_offset;
// Just be really silly and double check that we're not going to be overflowing with
// our next check.
if (pivot < pal_offset || (pivot + pal_offset) >= s.size() - 1)
break;
}
}
// If the greatest confirmed offset is greater than or equal to 0 (remember that an even
// palindrome like "aa" will have a greatest offset of 0) and if the current palindrome is
// larger than any others
if (pal_offset >= 0 && pal.size() < (pal_offset + 1) * 2) {
// Make sure that we are not going to access out of bounds memory here
if ((pivot - pal_offset >= 0) && ((pivot - pal_offset) + (pal_offset + 1) * 2) < s.size()) {
pal = s.substr((pivot - pal_offset), ((pal_offset + 1) * 2));
}
}
}
return pal;
}
};
int main() {
Solution sol;
std::cout << sol.longestPalindrome("babad") << std::endl;
std::cout << sol.longestPalindrome("babbad") << std::endl;
}
I hope the rubber ducky comments aren't too distracting. What can I do to get more information about where this error is coming from? What does it even mean? Is there a straightforward way to fix it?
A:
Two things.
(pivot - (pal_offset + 1) >= 0) will always be true, because pivot is an unsigned type, so the entire expression will be unsigned.
In the while loop inside that if, when pivot == pal_offset (which can happen with an odd length string) you will try to access s[-1], which is illegal (and a possible source of the runtime error you're getting).
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These are some photos I've taken of animals, here and there.
Clicking on the images will give a larger JPG file.
See below for more information on 'my' nearby owls. Last year a pair of owls raised three babies. I figured they might well be back to the same nest this year, and I was right. By March 5 I'd only seen one owl, and I assumed was a female sitting on eggs. (Turns out there are three chicks, and at least one was already hatched. She didn't seem too inclined to fly away when I approached the nest. Right now I'm leaving her mostly alone so she has some peace. I've not see the other half of the pair around either, which makes me a bit nervous when I'm close to the nest.
Here's a shot with the 80-400vr at 400mm.
I've now been taking pictures of the owls for a year with my Nikon 80-400vr. I've been working at getting the sharpest images possible, and I've definitely improved my technique. (See the following section for past history). Today I didn't have very good lighting on the babies in the nest, but I got some of the sharpest images yet that I've taken with the 80-400vr. (You can even see a bee buzzing around just to the right of the owl). This image was taken handheld. Click on it for a larger version.
This shot was taken in the desert near the house with a new Nikon 80-400vr on a D300. I was walking around testing the lens when I came upon an owl. He let me get to a certain distance, then flew away. But not very far. He landed on a saguaro cactus and posed for me. Eventually he flew off, and landed in a small dead tree, so I got another picture of him as the sun went down. (Click picture for larger image).
I moved closer... (Click picture for larger image).
The weather was better (not windy), and I went back out in the desert again to play with the 80-400vr some more. As I was walking in the same area where I saw the owl before, suddenly he flew out of a cactus and perched (somewhat awkwardly) in the top of a palo verde tree. I got several shots of him there before he flew back to the same saguaro as the time before. This could be a giveaway of a nest nearby.
I looked around and quickly found a large stick nest in the arms of a saguaro cactus. Figuring that it was spring, and the owl was sticking close to the nest for a reason, it would not surprise me if there was an egg or baby owl in the nest. I walked carefully closer and got some shots.
This is the baby owl, getting close to fledging. [Sorry about the dust spot, I'm still learning how to wet clean my sensor.] (Click picture for larger image).
There is something about the sound of a rattlesnake rattling at you that kind of makes the hair stand up on the back of your neck. I've only heard it once before - it's kind of like a hose with running water more than a rattle - a sort of a hissing sound.
April 19 - Two owls.
It's pretty cool watching these magnificent birds. I wish I had a 500vr to use with them!.
April 21 - Three owls!
Another visit to the owls, using a tripod on this trip. For the first time I saw two adults, and a baby out of the nest! I had been taking pictures of the adults, but did not see anything in the nest. As I got closer to the nest (and on the way home), I heard a strange clucking sound coming from a tree next to the nest. I looked up to see the baby owl, much to my surprise. I think the clucking was a scared/nervous sound, and it was answered by some hoots from one of the adults. The hooting was a lot closer than they had been a few seconds earlier, and I turned around to see one of the adults had halved the distance between me and where he/she had been sitting. I got the message - "no closer or you might see big claws, up close and personal". I took a couple of shots as best I could, but the baby owl was trying to hide behind branches, and I wasn't about to get closer. (There was no good viewing angle to him anyway).
Here's the baby peeking out from a tree. I was close enough that I had the lens zoomed back to under 300mm. (It definitely seems sharper, but then again, this was taken from the tripod).
April 23 - FIVE owls!
A quick visit to the owls, trying out a monopod for the first time. I was unfortunately in a bit of a hurry, as I got a late start and the sun was getting low. And I had a big surprise as I walked up. Two owls together on a branch in front of the nest, and another one peeking out from the nest. AND they were all juveniles. After I realized that, I looked around and saw the two adults standing on a branch off to one side. I was so excited that I neglected to look at the camera settings, and for some reason I had the camera set to ISO 2000! I realized my mistake too late, and while I got some lower ISO pictures, they were in dim light and did not come out as well as the (very) high ISO ones. It's a shame, because the setting sun lighting was just perfect and I didn't need high ISO.
Here are the two juveniles out on a branch.
And here are the parents.
Here is what it looks like when you walk up to the nest. You can barely see a juvenile owl in the nest peeking out.
I decided to see what the owls were doing in the middle of the day. Previous trips have taken place between 5:30 and 7:00pm. This time I went out just after noon.
Probably shouldn't have bothered, because the lighting was pretty harsh. As an experiment, I tried adding flash to tame the shadows a bit. Not sure it helped any, though you can tell there was a flash because there was a little bit of redeye if you look really closely.
One juvenile was still in the nest, and I didn't see any other owls until I got pretty close to the nest. Suddenly an adult flew out of the tree next to the nest and landed on a saguaro in the distance. The lighting was bad on the chick, so I practiced on the adult instead. It was also very, very windy, and the feathers were blowing a lot in the wind.
This is probably the best shot I got today.
I took my usual walk to the owls in late afternoon. At first I only saw two owls hidden in a tree (perhaps sleeping), but when I got closer, an adult flew out and perched on a distant saguaro. So I concentrated on getting shots of one of the juveniles in the tree, as I didn't see anyone left in the nest. The one juvenile in the tree watched me, but seemed sleepy. Kept closed eyes, with the occasional peek at me.
So I decided to take some pictures of the adult. As I was setting up to take a few shots of him, I heard a commotion, and saw a smaller bird dive-bombing the big owl. Eventually the owl was driven to a lower branch, but the smaller bird kept trying to drive him off. I got a sequence of shots of this once, but haven't decided if the images are good enough to bother posting.
In the meantime, the other adult showed up behind me in another tree, backlit against the sun. While all this was going on, I must have spooked the baby owl in the tree, because he (she?) started clucking at me. As I turned back to him, he moved up a branch, behind the tree. I watched him go up, and found that he was now hiding behind the other two juveniles!
I've been busy in the last week and have not been able to go see the owls. Today I got another chance, so I headed over with tripod and camera. It looked like the area was empty as I walked up, but then two owls flew from one tree to another. I got some handheld shots, but I knew the tripod would provide better results. As I set up the tripod, another owl flew out of a dead tree, leaving just one behind.
After that, I tried getting some Bird In Flight images, by slowly walking toward one or another owl until they flew off. The owls are very smart - they seem to have an uncanny knack of not flying off until you look down. When you look up, they've left one perch, and are in the air toward another.
But you can't simply walk through the desert without looking at where you are walking. Beside the obvious and ever-present problem - cactus, chiefly cholla - there is the possibility of walking on a rattlesnake.
Once again, I stopped to take a picture of an owl, and then looked down to see a rattlesnake within 6 feet. This one was, I think, prettier than the last. As usual, clicking on the image gives you a full-size version.
I've tried to use several of my lenses at one time or another to capture Birds In Flight (BIF), but with very little success. People say that the 80-400vr doesn't auto-focus fast enough to be easily used for BIF. I can't even find the bird in the viewfinder, much less autofocus and track it! I thought I would try something easier, like a rabbit. I still have a lot to learn, and I have a new-found appreciation of those photographers who can get good shots of birds flying.
From one of my first scuba dives, in Cancun in 2007. My wife Connie with a sea turtle. Taken with a little Canon SD630 point-n-shoot in a Canon dive housing about 35 feet down.
This shot was taken from a crowded boat on a river in Costa Rica with a Nikon D200 in October, 2007. This guy's job was to pilot a boat to a suitable riverbank, then hop in the water and entice a crocodile to follow him while teasing him with a dead chicken. He eventually got the crocodile up on shore, and fed the chicken to the crocodile by *dangling the chicken from his mouth*. Again, click on the picture for a larger version. Click here for a sequence of shots of this event Shots taken from a bobbing boat with D200 and the cheap Nikon 70-300g lens. | http://www.cjcphoto.net/misc/misc.html |
LOTUS FLOWER MEDITATION:
Sit in a comfortable and firm position, with the back straight, the eyes closed and a light smile in the expression.
Quiet the body, mind and emotions. Observe your body in stillness, without judging or anticipating, simply be present and enjoy this moment.
Follow the continuous movement of your thoughts. Slowly move away from the randomness of these thoughts and imagine a blank canvas in front of you.
Mentally project the image of a lotus flower in full bloom onto your canvas. Use your creativity to carefully outline its shape, constructing the body of the flower in great detail.
The lotus flower becomes more clear and vivid.
Now visualize each of its petals, immaculately white and velvety. The petals acquire a translucent quality. Notice the texture of the flower and its beauty. Preserve the image of the lotus flower, until the mind settles. Focus and meditate. | https://www.derosemethodgreenwich.org/winter-meditation-challenge-audios/2019/3/3/meditation-challenge-day-1-mabmb-aeppf-clnpw-ejd7c-9lfjg-r4dhx-yfegl-n8jsp-4jpb9-ktgmz-569nx |
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WALLINGFORD — Neighborhoods are transforming into coral reefs teeming with fish fashioned out of household supplies or painted on windows by schoolchildren to encourage each other during the coronavirus crisis.
Art teachers are creating videos showing how to create fish out of readily available materials at home for the district’s #JustKeepSwimming project. The artwork is being compiled into a slideshow — over 500 images as of Thursday — and residents without students at home are encouraged to join.
“By posting the fish it kind of shows a sense of unity that we’re a big school of fish and even though we've been separated by the virus we’re still working together,” said School Superintendent Sal Menzo, who has seen the fish around town.
The effort was started by school social workers worried about students suddenly isolated at home, without their friends and teachers, while adjusting to remote learning.
“When we were forced to socially isolate so suddenly … we didn't have an opportunity to prepare students for such a drastic change,” said Chelsea Polletta, social worker at Mary G. Fritz Elementary School.
Polletta worked with Emily Banach, her counterpart at Rock Hill Elementary School, on the idea to depict the district as a school of fish that keeps swimming together through challenges. The “just keep swimming” line is a reference to the popular movie “Finding Nemo.”
Riding in a recent car parade held by teachers, Polletta saw fish signs and chalk drawings of fish in driveways.
Jack Gonzalez, 7, a first grader at Highland Elementary School, waved a sign “I ♥ Mrs Phillips” from the back of his family’s ATV, which had a few fish painted on it. A second sign attached to the bumper read “#JustKeepSwimming” and “We miss you so much.”
“I miss my teachers, my friends,” he said. While he gets to see classmates in group video calls, Gonzalez is ready to go back to the classroom.
His parents, Elliot and Wanda Gonzalez, said having so many families showing off their fish artwork makes social isolation a little bit easier. | https://www.myrecordjournal.com/News/Wallingford/Wallingford-News/Wallingford-students-decorate-with-fish-in-solidarity.html |
Having watched a lot of Prey streams, I knew the Psychoscope was a big part of the game. That little device that lets you scan alien enemies and work toward getting unlocking their abilities should be top of your wish list when you get in the game.
But, if you do too much extra exploring, you'll be wondering when you actually get a hold of it. If you want to get it fast, you'll need to stay pretty close to the main objectives for a good bit into the game.
After watching the video for the first time in Morgan's office, January will task you with traveling to Dr. Calvino's Office. This will require you to do a bunch of smaller objectives, but after completing this main task, you will have to go back to Morgan's Office and view the rest of the video, after which January will give you a General Access keycard.
Once you get the keycard, it's time to go off the beaten path. No matter where the objective tells you to go, you need to head straight to Pyschotronics. There is an entrance to it in the Talos I Lobby.
Once inside Psychotronics, you'll need to head down a corridor, passing a Security Booth on your right. You'll eventually come to an open entryway into two locker rooms. The locker room on the right is blocked off by cargo requiring Leverage III to get through.
If you don't have Leverage III unlocked, you'll need to travel around the locker room on the left. There are two Phantoms in this room, one of them named. Fight past those two phantoms, and proceed to the other side of the locker rooms.
At this point, you can enter the back entrance of the locker room that was blocked by the Cargo. By the blocked entrance, you'll find a hole in the floor leading to an underground area. Proceed underground and head left. At the end of the hall, you'll find the Pyschoscope on a dead body (in addition to a frozen mimic). | https://www.gamerevolution.com/guides/72269-prey-2017-where-to-find-the-psychoscope |
Studying For Exams
To help you study for finals, the library has extended hours during finals. Please proceed to Hours for specific days and times.
In order to maintain an atmosphere conducive to studying, please be considerate of others:
- If you need to speak to others, go outside of the library
- Please set cell phones to vibrate and take calls in the stairwells or outside of the library
- Food is NOT ALLOWED (even in carrels) – staff will be checking, so please follow the rule
- Even earphones can be loud enough to be distracting to others; be aware of your surroundings
- If others are talking or being disruptive, notify a staff member at the Circulation Desk
- If someone is in your carrel, notify the person that you’re there to study and ask her/him to move; if the person refuses, a staff member is authorized to take appropriate action to remedy the situation. Users who are uncooperative could lose library privileges and/or access.
- If students are talking, staff members are authorized to ask them to stop and/or to leave the library.
In preparation for exams, the Law Library has many old exams on file in print and electronic formats. The print versions are on reserve at the Circulation Desk and can be checked out for four hours. The electronic versions can be accessed through the ICON College of Law Academic Resources page. A complete list of the exams on reserve and on ICON is located at the Circulation Desk.
Student Exam Numbers
The College of Law has a link on the bottom left of its home page: “Find Exam ID.” Click on the link and follow the instructions, and your exam ID will pop up on the screen.
Laptop Exams
If professors permit, students may type exam answers on a laptop using SofTest software, available for $25 at the ISBA Bookstore until Monday, November 25 at 2 p.m. From Tuesday, November 26 until Monday, December 9, students can purchase the software but will pay a late fee of $25; total purchase price $50. Students cannot purchase the software after 2:00 p.m., Monday, December 9.
If using a laptop for your exam(s), you must adhere to the written policies and procedures found on the College of Law website. Proceed to Exam Information for instructions.
Please don’t hesitate to let us know if you need assistance and good luck with exams. | https://library.law.uiowa.edu/article/finals-time |
Meta-learning is a methodology considered with "learning to learn" machine learning algorithms.
( Image credit: Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks )
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Recent progress has demonstrated that such meta-learning methods may exceed scalable human-invented architectures on image classification tasks.
Ranked #3 on Semantic Segmentation on PASCAL VOC 2012 test (using extra training data)
IMAGE CLASSIFICATION META-LEARNING SEMANTIC SEGMENTATION STREET SCENE PARSING
Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task.
If this is not done, the meta-learner can ignore the task training data and learn a single model that performs all of the meta-training tasks zero-shot, but does not adapt effectively to new image classes.
Meta-learning algorithms aim to learn two components: a model that predicts targets for a task, and a base learner that quickly updates that model when given examples from a new task.
To adaptively learn data values jointly with the target task predictor model, we propose a meta learning framework which we name Data Valuation using Reinforcement Learning (DVRL).
To this end, we introduce a method that allows for self-adaptation of learned policies: No-Reward Meta Learning (NoRML).
To address the issue, we propose a novel transfer learning approach based on meta-learning that can automatically learn what knowledge to transfer from the source network to where in the target network.
META-LEARNING SMALL DATA IMAGE CLASSIFICATION TRANSFER LEARNING
In this paper we introduce new Automated Machine Learning (AutoML) techniques motivated by our winning submission to the second ChaLearn AutoML challenge, PoSH Auto-sklearn.
The move from hand-designed features to learned features in machine learning has been wildly successful.
CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. | https://www.paperswithcode.com/task/meta-learning |
From news and speeches to informal chatter on social media, natural language is one of the richest and most underutilized sources of data. Not only does it come in a constant stream, always changing and adapting in context; it also contains information that is not conveyed by traditional data sources. The key to unlocking natural language is through the creative application of text analytics. This practical book presents a data scientist’s approach to building language-aware products with applied machine learning.
You’ll learn robust, repeatable, and scalable techniques for text analysis with Python, including contextual and linguistic feature engineering, vectorization, classification, topic modeling, entity resolution, graph analysis, and visual steering. By the end of the book, you’ll be equipped with practical methods to solve any number of complex real-world problems.
- Preprocess and vectorize text into high-dimensional feature representations
- Perform document classification and topic modeling
- Steer the model selection process with visual diagnostics
- Extract key phrases, named entities, and graph structures to reason about data in text
- Build a dialog framework to enable chatbots and language-driven interaction
- Use Spark to scale processing power and neural networks to scale model complexity
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There are no quotes for this title yet. | https://sclibrary.bibliocommons.com/item/show/1960945146 |
97.1 as a percent
If you are asking “what is 97.1 as a percent?” you are interested in converting the decimal 97.1 to percentage.
The answer: 97.1 is the same as 9710%
Now let’s explain. The good news is that this is the easiest calculation you will perform. In order to express a decimal as a percent you just need to multiply the decimal by hundred (100). That’s it.
In this example you need write the following mathematical expression: 97.1 x 100 = 9710%
When you multiply a decimal by 100 you need to move the decimal point by two digits to the right since there are two zeros in 100. Finally add a percent (%) sign.
There is another way to express a decimal as a percent:
- First shift the decimal point to the right by two digits: 97.1 → 971 → 9710 .
- Second add a percentage (%) sign to get: 9710%
AGAIN ANSWER: 9710%
Find other common decimal to percent conversions with step by step explanations below: | https://rounding.to/decimal-as-a-percent/97-1-as-a-percent/ |
Segmenting and blending sounds can be tricky when students are first learning to read. Reinforcing these skills, particularly with hands-on manipulation of letters, can be a great help for reading development.
Segmenting (separating sounds like /d/ /o/ /g/) and blending (combining sounds like /dog/) are core skills for phonological awareness, and necessary for learning to read.
Assessing Spelling Readiness
Are your students ready to blend and segment sounds? There is a general progression for most students: 1) identifying alliteration and rhyming words 2) counting words in a sentence 3) counting syllables in words 4) identifying onset and rimes 5) recognizing individual phonemes in words 6) manipulate and replace sounds to create new words.
Hands-On Spelling Practice
Using letter tiles or magnetic letters is a great way for students to experience hands-on practice for manipulating letters. You may wish to begin with activities that isolate the first sounds only, and then later progress to ending sounds, and medial sounds. You can find a huge list of phonics activities like the ones pictured below by clicking HERE.
Replacing Letter Sounds
When students are able to identify phonemes in words, they can then move on to substituting sounds to change words and create new words. For example, in the activity shown below, students are asked to spell CVC words such as “cat”, and then asked switch a letter to create a new word like “bat”. The student’s task will be to decide which sound needs to change (first sound in this example – remove the letter C and replace with the letter B). After writing each word, they can discuss spelling patterns (word families) and talk about sounds can be changed at the beginning or ending of words.
You can see the activity above, called Spelling Switcheroo, by clicking HERE. It’s a quick solution to small group intervention because all the letters needed are cut off the bottom of the page to save teacher time – no hunting around for sets of letter tiles! There are five sets included: CVC Words, Blends, Digraphs, Vowel Pairs, and Silent E words. The teacher scripts are included to read aloud as students spell, as shown below: | https://whimsyworkshopteaching.com/ideas/spelling-switcheroo-word-building/ |
Leavened Bakery, specializing in naturally leavened sourdough breads, recently expanded from a wholesale bread bakery to an additional retail location in Gold Beach, Oregon. Bakery owner Meriah Timm describes her new place as an artisan bakery specializing in naturally leavened breads and pastries.
“Leavened is a title that represents my bread and myself,” says Timm, who grew up in Gold Beach and attended Oregon Coast Culinary Institute in Coos Bay, Oregon.
On Dec. 26, she featured challah loaves, along with orange, chocolate cranberry sourdough loaf and chantrelle kouign amann. Her menu includes naturally leavened breads, pastries, desserts and drip coffee from local roaster Nectar of Life Organic Coffee. Her bakery has the capacity to make up to 80 loaves of bread per day, as well as pastries, sourdough bagels and sourdough donuts.
“Breads and pastries are our backbone,” Timm says, adding that her most popular breads are Floyd’s French Batard, Polenta Rosemary and Honey Whole Wheat. | https://www.bakemag.com/articles/12917-oregon-bread-baker-expands-into-retail |
Updated 6/28/19 at 4:45 pm.
Updated 5/3/19.
Updated 5/1/19
Updated 5/1/19.
Updated 7/3/19.
Updated 5/13/19.
Updated 6/28/19 as of 4:45 pm. Commanders, if you are missing audits or minutes, please turn them in ASAP.
Updated 7/3/19 as of 2:00 pm. This is the final PSR for the 2018-2019 administrative year. If you did not make All-State and you think there is an error, please contact Department HQ.
Updated 6/5/19
Updated 5/3/19. Comrades, this report tells what National has on record of which post or auxiliary has donated to the National VMS Program. Please remember that for purposes of All-American, Auxiliary donations ARE NOT considered qualifying - donations must come FROM THE POST. As a reminder, if posts want to achieve All-American Status, they are required to donate to this program in the amount of $50. Lastly, an auxiliary submission for this program DOES NOT give your post credit. Example, if the Auxiliary of Post 23456 submitted a National VMS Donation, Post 23456 WOULD NOT get credit from National for All-American purposes!!! Lastly, the address to submit your $50 is: Veterans and Military Support Programs; 406 W. 34th St., Suite 902; Kansas City, MO 64111!!!
Updated 05/03/19. It is in Excel formatting for you all so that you may sort as necessary. I do have them grouped by District and by Program.
Updated 7/12/19 at 2:45 pm. Note your membership numbers are based upon OMS report from 7/10/19. They may be subject to change. | https://www.vfwca.org/reporting-procedures-and-information/status-reports-1/ |
What is it?
At the center of every artichoke, there lies a tender heart…literally. Artichoke hearts are at the meaty center of the artichoke flower. The heart is surrounded by tender, edible leaves. For a cooked artichoke, the heart can be consumed as is (after scooping out the prickly choke in the middle), but the fleshy, mild texture of the heart also lends itself very well to marinades, roasting, frying and preserving.
Trimmed artichoke hearts are available jarred in marinade, and also frozen. Both types lend an artichoke flavor to dishes without all the work of trimming a whole artichoke.
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Recipe
Rigatoni with Roasted Artichokes, Sun-Dried Tomatoes, and Olives
Tender roasted artichokes and crispy panko add nutty, toasted flavors to a pasta brimming with briny olives and sweet sun-dried tomatoes.
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Recipe
Garlicky Roasted Artichoke Hearts
Panko adds crunch to this Italian-inspired side; it pairs well with a seared flaky fish like cod. The artichokes also add flavor and texture to Pasta with Roasted Artichokes, Sun-Dried…
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Recipe
Raw Artichoke, Portobello, and Fennel Salad
Raw artichokes have a mild, intriguing flavor and firm texture. A quick soak in vinaigrette not only enhances their flavor but also tenderizes them a bit. Be sure to slice…
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Recipe
Spicy Sausage and Artichoke Linguine
Nutty, buttery artichokes balance spicy Italian sausage, while crispy breadcrumbs and creamy mascarpone sauce make the whole dish hard to resist.
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Recipe
Cod with Pancetta, Artichokes, and Olives
Despite the ease of preparation—the fish, sauce, and side dish all cook in one skillet—this is a restaurant-worthy dinner. Serve it with good crusty bread to mop up the sauce.
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Recipe
Pea and Artichoke Dip
Here’s a new take on the classic baked artichoke dip. It may be retro, but it’s always the first to go at parties. Peas give it a beautiful color and…
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Recipe
Pizza Salad
This combination of a warm crispy pizza crust topped with a vinegary chopped salad is such a natural and delicious pairing, you won’t believe you’ve never tried it before. Topping…
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Recipe
Creamy Crab and Artichoke Dip
Splurge on fresh jumbo lump crabmeat for this tasty dip or, for a less expensive option, use pasteurized “special” crabmeat from the canned seafood aisle (Boss or Chicken of the…
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Recipe
Striped Bass en Papillote
Roasting fish in packets (en papillote) allows it to steam in its own juices, intensifying its flavor. Substitute black bass or halibut if striped bass is unavailable. | https://www.finecooking.com/ingredient/artichoke-hearts |
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
DETAILED DESCRIPTION OF THE INVENTION
This invention provides a method of constructing water cooling towers using concrete masonry units (CMUs) more quickly, at lower cost, requiring no heavy construction equipment, resulting in a more durable, fire-resistant, longer lasting and easier to maintain structure than is presently known.
Water cooling towers are well known, and are a common heat-exchange component in large commercial, medical, and industrial HVAC systems, in cooling for industrial processes, and aeration of water for other purposes. Cooling towers are a standard part of new construction of buildings or campuses of buildings. Many existing buildings also need replacement or supplemental cooling towers because of the inadequacy of present cooling towers due to increased demands, higher temperatures, consolidation into campus-wide HVAC systems, or deteriorating performance of existing cooling towers.
An under-performing cooling tower can be a large problem for commercial properties, medical facilities, and industries, affecting the efficiency and therefore the operating costs of HVAC and industrial systems, and affecting the comfort and therefore the satisfaction, health, and productivity of persons. Under such circumstances, existing cooling towers need to either be replaced or be supplemented with new cooling towers. But replacement requires taking an existing cooling tower out of service and waiting for the construction of a new cooling tower to be completed. And supplementation requires finding a new location for the new cooling tower, and then waiting for its construction to be competed.
One common type of industrial cooling tower is a counterflow tower where water falls by gravity through fill media from water nozzles positioned in the upper part of the cooling tower. A water collector pan is positioned below the fill layer. The water is directed to a downstream water basin, from where it is re-circulated back into the spraying nozzles on top. A source of moving air is mounted on or in the cooling tower, directing the cooling air toward the water.
Cooling towers exploit the evaporative cooling of water exposed to air. Therefore they are generally located outside. Cooling towers must provide a very large surface area for water to interact with air. Therefore cooling towers are very large structures—with at least a 20-square-foot footprint and at least 10 feet of height—and some many times that large. Powerful motorized fans are generally required to provide adequate air flow. Water is heavy, and powerful fans are heavy, and therefore cooling towers are heavy structures when in use, and the basic structure of the cooling tower must be capable of withstanding the internal forces of the heavy moving water and heavy moving fan, and the external forces of the outside environment.
Cooling towers must be located outside, take up a lot of space, can be noisy, and might generate some mist or vapor. They are typically placed on the roofs of high-rise buildings or in otherwise out-of-the-way locations on the grounds or the campus. Such locations present problems in the construction and installation of cooling towers. A heavy crane might be necessary—for months—in order to lift construction materials or pump concrete onto a rooftop or into an inaccessible area at ground level. There might be very little adjacent “laydown” or staging area for construction crews, materials, and equipment.
Industrial cooling towers made of wood in the traditional way are susceptible to fire and to rot and early deterioration in the constantly wet cooling-tower environment, requiring proper preparation and constant maintenance throughout the operational life of the cooling tower.
Cooling towers made of steel are known, but are very expensive, very heavy to transport and erect, and require highly skilled workers in the design phase, any pre-fabrication phase, and in the erecting or construction phase, in order to avoid potential failure, improper fitting of components, or even injury to persons and property. Also, steel is subject to rusting and deteriorating in the constantly wet environment if it is not properly prepared and constantly maintained throughout the operational life of the cooling tower.
Cast-concrete cooling towers can be built using the shuttering method, where sections of the building framework are built using wooden forms; then concrete is poured into the forms to make a first lateral row. After the concrete sets, the next lateral layer is formed, filled with concrete, and allowed to set. This process continues until the structure reaches the desired height. The construction of such a tower is a major undertaking requiring many months, even a year, to complete. The logistics and heavy equipment required are extensive. Such traditional towers have underground basins and require extensive engineering and design in advance of construction.
Fordyce and Fritz (U.S. Pat. No. 3,834,681 A) teach an open-frame, prefabricated, concrete cooling tower structure. Furlong, et al. (U.S. Pat. No. 3,917,765 A) teach a cooling tower shell of factory-made pre-cast concrete parts. Curtis (U.S. Pat. No. 5,227,095 A) teaches a cooling tower system consisting of individual modules, which can be built from fiberglass in a factory and then transported to and erected on site. Curtis and Oberlag (U.S. Pat. No. 5,545,356 A) teach a method of constructing a cooling tower structure by casting the concrete walls on site in a horizontal position and then raising the walls to a vertical position—a “tilt-up” construction, or by pre-casting concrete modular wall units off-site and transporting and erecting them on site.
There is some question whether “tilt-up” and some other concrete pre-fabrication methods are capable of producing stable structures generally. For example, concerns about, and even requirements to retrofit, such structures in earthquake-prone areas.
Concrete pre-fabrication, like steel, requires highly skilled workers in the design phase, the pre-fabrication phase, and in the erecting or construction phase, in order to avoid potential failure, improper fitting of components, or even injury to persons and property.
All of the presently known methods of constructing cooling towers have at least one of the disadvantages of being insufficiently durable, too expensive, too difficult to transport, too long to place into operation, too difficult to erect or construct without highly skilled labor and long-term use of heavy machinery, and too difficult to maintain over the operational lifetime of the cooling tower.
Concrete masonry units (CMUs) and proper construction methods and standards for their manufacture and erection are known in other fields of construction. The advantages of CMUs include very low cost, greater strength at lighter weight than cast or pre-cast concrete, and the ability of masons of ordinary skill to quickly build structures according to already well-known methods. In CMU construction, hollow concrete blocks are reinforced with steel rebar or similar material and filled with concrete, mortar, or grout, with construction proceeding layer by layer, continuously, without having to wait for each concrete layer to set.
The present invention provides a cooling tower constructed of multiples of standard concrete masonry units (CMUs) properly reinforced, using standard CMU construction methods and specifications, and using masons of ordinary skill, costing less for construction and maintenance, requiring less heavy equipment, less transportation and lifting of heavy and large components, a smaller construction work site, and requiring significantly less time to construct and make operational.
FIG. 1
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Referring to & the counterflow type of cooling system known in the art comprises, from top to bottom, an optional drift eliminator for the purpose of catching sprays and mists of water and retaining them in the cooling system, a nozzle array that sprays water to maximize the available surface area of water droplets for evaporative cooling, a thick layer of porous fill media to further spread out the water droplets and to prolong their exposure to the cooling stream of air, and a water collector that catches and channels the cooled water but allows the flow of cooling air from below.
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The forced-air counterflow type of cooling system known in the art further comprises a fan driven by a fan motor and surrounded by a fan shroud , with the fan assembly located below the rest of the cooling system, which puts the fan assembly closer to the ground or mounting surface, which is advantageous for maintenance purposes and for weight-distribution purposes. See .
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The forced-air counterflow type of cooling system is necessarily very large, in order to move a great volume of air across a great surface area of water. The cooling system for which a preferred embodiment of this invention is designed is approximately 24 square feet across and 8 feet deep, with an approximately 20-foot fan. In order to move a sufficient amount of air, the fan should be mounted far enough above the ground or mounting surface, and with as few structural restrictions as possible, in order to provide an open chamber allowing sufficient air intake.
Water is heavy, and 20-foot fans are heavy, so cooling systems are heavy. The forced-air counterflow type of cooling system is therefore a very heavy structure that must nevertheless be mounted high off the ground or mounting surface, and remain stable for many years of operation despite internal stresses from the constant movement of water and air and the machinery that moves them, and external stresses from weather, maltreatment, accident, or other circumstances related to the cooling towers being placed outside on rooftops, in parking lots, or in other exposed places.
Every millisecond throughout its several-decades operational life, a cooling-tower structure is required to keep a wet, heavy, shaking machine nine feet higher off the ground than gravity would have it be.
Although a stable cooling tower structure might be achieved by adding to and reinforcing the supporting structure below the level of the fan, adding more material in that area would inevitably reduce the air intake flow. The requirements for strength and stability run counter to the requirements for height and openness. This invention solves that problem.
Cooling towers present another conundrum; they are usually located in places where it is difficult to set up a construction project and difficult to move materials and heavy equipment. This invention solves that problem, too.
Presently known cooling tower structures and methods of construction largely comprise some type of cast concrete or pre-cast, pre-stressed concrete either as large components or as pre-fabricated sections. It is difficult to move large amounts of just-mixed concrete from several trucks at street level up to the rooftop of a tall building, and even where access is not so limited, pouring concrete has to be done in stages and requires a lot of time for completion. Moving large concrete components and pre-fabricated sections to the rooftop of a tall building or other inaccessible or constricted location is similarly difficult and expensive. This invention solves that problem, too.
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The present invention is a cooling tower structure made entirely of multiples of 6 sizes or styles of standard CMU concrete blocks , , , , , , reinforced and installed using standard materials and methods. See . The CMUs are cheaply and readily available everywhere, and a large number of masons everywhere know how to install them properly. CMUs, especially the autoclaved aerated ones, are relatively light for their strength, and can be handled by the single unit or reasonable-sized groups of units, and therefore can be transported, stored, and placed into position much more easily than other building materials.
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In a preferred embodiment, , the cooling tower structure is 30 feet in the longer horizontal dimension, which includes the water basin or reservoir, 26 feet in the shorter horizontal dimension, and 18 feet tall, supporting the fan at about 9 feet off the ground surface and the other cooling-system elements above the fan. This embodiment accommodates a cooling system 24 feet by 24 feet wide and up to 10 feet deep, having a fan size of up to 24 feet, although a 20-foot fan would probably be sufficient. This embodiment uses 1576 8-by-16-by-8-inch CMUs , 26 8-by-8-by-8 CMUs , 234 deep-lintel 16-by-8-by-8 CMUs , 6 corner 16-by-8-by-8 CMUs for terminating some of the bond beams , perforated 8-by-8-by-8 CMUs which allow collected cooled water to flow into the basin , and 209 capping 1-by-8-by-8 CMUs . Other than the reinforcing rods and the cement , mortar, or grout, no other construction materials are needed except for fasteners to support and secure the cooling system in place in the cooling tower.
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In a smaller embodiment, , the cooling tower structure is 18 feet in the longer horizontal dimension, 14 feet in the shorter horizontal dimension, and the same 18 feet tall, supporting the fan at about 9 feet off the ground surface and the other cooling-system elements above the fan. This embodiment accommodates a cooling system 12 feet by 12 feet wide and up to 10 feet deep, having a fan size of up to 12 feet, although a 10-foot fan would probably be sufficient. This smaller embodiment uses 918 8-by-16-by-8-inch CMUs , 27 8-by-8-by-8 CMUs , 126 deep-lintel 16-by-8-by-8 CMUs , 6 corner 16-by-8-by-8 CMUs for terminating some of the bond beams , 19 perforated 8-by-8-by-8 CMUs which allow collected cooled water to flow into the basin , and 119 capping 1-by-8-by-8 CMUs .
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In other embodiments, cooling tower support structures can be built or added onto together, sharing common walls, in several configurations. shows a two-tower configuration having a footprint of 30 feet by 51.3 feet and requiring 2838 of the large CMUs . & show four-tower configurations having footprints of 51.3 feet by 59.3 feet and requiring 5214 of the large CMUs .
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The large, unobstructed open chamber of the invention is made possible by the use of very long bond beams or lintels, spanning, for example, 22 feet each in 3 spans of a preferred embodiment.
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Referring to , the cooling tower structure comprises six lateral bond beams or lintels constructed from deep lintel CMUs having a deep “U” shape that accommodates the placement of a reinforcement bar such as steel rebar in a horizontal orientation spanning and connecting or bonding the units, and filling with cement , mortar, or grout in order to secure the CMUs and the reinforcement bar in place. Where a deep lintel CMU sits over another CMU, such as at a corner, it can be vertically secured by placing a reinforcement bar through a notch in the face of CMU that is mounted downward.
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Referring to , during construction of the lateral bond beams or lintels, the blocks over the span can be temporarily supported with material such as lumber, such as 2-by-4 lumber . Such temporary support is only needed while the cement , mortar, or grout sets up and secures the supporting material. With such a temporary support, the placement of courses of CMUs above the bond beams is allowed to proceed without waiting for any set-up of the bond beam. Alternatively, the bond beams may be constructed on an adjacent flat surface and subsequently hoisted into place.
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illustrates the normal use of the cooling tower structure with the cooling system in place. The fan motor and fan are supported on a fan pedestal which is securely attached to the foundation in order to withstand the weight and the torque of the fan, and which encloses the electrical supply for the fan. In the lower portion , the fan draws air from the large open chamber and blows the air upward against the downward travel of water through the cooling system mounted in the upper portion . Water is taken from the above-ground water basin and is pumped into the nozzle array that sprays water over the porous fill media through which the water droplets travel downward at a pace that is slowed both by the fill media and the counter-flow of air, which prolongs the time available for evaporative cooling. An optional drift eliminator mounted above the nozzle array catches sprays and mists of water and retains them in the cooling system. Finally a water collector that allows the flow of cooling air from below catches and channels the cooled water along its slight slope downward toward and into the water basin from whence the water had come, completing one of the two loops of the system's operation.
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The purpose for cooling the water in the basin is to use that cooled water in one or more heat exchangers that are components of HVAC systems or cooling systems for industrial processes. In the second loop of the system's operation, cooled water is pumped from the basin to the target HVAC or cooling system or systems where it undergoes a heat exchange, and is pumped back into the basin for another iteration of the two loops.
The proper functioning of a cooling tower is critical to the functioning of HVAC systems and other cooling systems. If a cooling tower fails, it must be repaired or replaced. If a cooling tower is under-performing, or is under-specified in light of possibly unforeseen increased needs, it must be either replaced with or supplemented with another cooling tower. And such replacement or supplementation is likely to be needed immediately, where the efficient functioning of an enterprise is being hampered by a broken or under-performing cooling tower. The several months' long construction times of present cooling towers are costly to the enterprises needing new cooling towers.
The cooling-tower structure of the present invention is able to be constructed very quickly, in a matter of only a few days, for several reasons:
The materials, known quantities of six different sizes and styles of standard CMU blocks are universally available at small cost, are available on pallets of manageable size and weight that can be moved with a standard forklift, and can be quickly secured and transported to any job site. The only other materials, rebar and sacks of cement, mortar, or grout, are equally as easily available. There is no waiting period for anything to be pre-fabricated or to be secured and transported from a remote location.
The construction materials can be delivered to the job site—which might be the roof of a tall building—without the delays of arranging special shipments from far away, without arranging and waiting for special equipment such as cranes, and then waiting for permission to block streets with such equipment, and without arranging for the delivery and transfer of mixed concrete for on-site pouring to job sites that are not directly accessible to cement-mixer trucks.
The construction work can be performed by any block mason of average competence and experience, using standard methods. Therefore there is a greater chance that such a block mason will be available no matter the locale or the timing of the construction. Also, the construction work can proceed more quickly by adding more block masons, up to a point, and by adding additional shifts of block masons.
The construction work can proceed continuously to completion without waiting for any curing, drying, or setting up, or waiting for any special personnel or any special tool or material to arrive on site.
The cooling-tower structure that results from the very quick construction time of only a few days, even in difficult locations, is very sturdy, long-lasting, and inherently two-hour fire-rated.
FIG. 10
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The cooling-tower structure of this invention should be constructed on a suitable foundation, where the suitability will be determined by the specific construction site and conditions, which might range from a reinforced-concrete rooftop to a swampy spot of unused ground. illustrates a foundation for the preferred embodiment of , and illustrates a foundation for the smaller alternate embodiment of . In addition to whatever reinforcement and other requirements might be necessary for a particular foundation on a particular site, the foundation should be of a size matching the footprint of the intended cooling-tower structure, which is 30 feet by 26 feet for the preferred embodiment here. Vertical reinforcement bars or rebar should be embedded in the foundation and attached to any horizontal reinforcement within the foundation. The placement of these vertical reinforcement rods is at the corners of the square tower structure under the corner columns , , plus the outer corners of the water basin , plus the eventual location of the fan pedestal , which is at the center of the square formed by the upper portion of the cooling tower, disregarding the water basin .
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The length of the vertical reinforcement bars embedded in the foundation does not have to extend the full height of the cooling tower, and the length is not critical because additional reinforcement bars can be placed in upper courses, as is standard and known in the art.
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The secure attachment of the fan pedestal to the foundation is important because of the weight and the torque generated by the fan in operation.
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Additionally, electrical conduit for electric power to the fan may be incorporated in the foundation and terminated under the location of the fan pedestal , although such electric power can also be run through surface-mounted conduit or by other conforming means.
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Turning now to the invention in more detail, numeral designates the water cooling tower according to the present invention. It should be noted that the water cooling tower is only one example of the structure that can be constructed using the apparatus and method of the present invention. The cooling tower comprises a hollow structure having a foundation , a lower portion supported by the foundation , and an upper portion supported by the lower portion . The exemplary embodiment described herein is of a water cooling tower of counterflow design, where the air flow is directly opposite to the water flow. Air flow first enters an open area beneath the fill media, and is then drawn up vertically. The water is sprayed through pressurized nozzles near the top of the tower, and then flows downward through the fill, opposite to the air flow.
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The lower portion defines an open chamber , where a fan pedestal is mounted. A motorized fan is mounted on top of the fan pedestal , with the fan and motor being protected by a fan shroud . The fan shroud is supported by freestanding rear corner columns and mid corner columns incorporated into the above-ground water basin . A lateral bonding beam separates the lower portion from the upper portion , the lateral bonding beam resting on the four columns of the lower portion .
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51
FIG. 9
A water collector assembly is positioned in the upper portion above the lateral beam . The water collector assembly can be a series of troughs or one large trough configured to direct collected water away from the upper portion . The water collector unit is mounted at an angle to direct water by gravity into a basin located above ground on the foundation . An angle of approximately 2 degrees, or a 4-inch drop over a 24-foot span is sufficient. In an embodiment, the proper mounting angle is created by a spacer shown in that provides a 4-inch rise and that may be made of various material, including concrete or steel, and may be incorporated into the construction of the cooling-tower structure, or into the installation of the cooling system into the tower structure, or may built into the water collector itself.
Pumps, known in the art, are used to circulate water through the cooling tower and from the cooling tower to the HVAC or cooling system or systems served by the cooling tower. Waterproofed piping and connections, also known in the art, can be placed through holes made in the cooling-tower structure and the water basin at the appropriate locations.
16
52
The upper portion defines an open space where the fill media is deposited.
40
53
51
Water is pumped from the basin and sprayed through the nozzle assembly and passes through the fill media before flowing into the water collector unit .
32
34
12
90
The corner columns , are constructed from CMU blocks of 16-inch and 8-inch lengths, in alternating courses, as shown, using construction methods of reinforcement and filling with concrete, mortar, or grout known to block masons of normal skill and competence. Each column provides 40 square inches, in cross section, of support, and each is secured in 5 places to the foundation through the vertical reinforcement bars .
Because the CMU blocks themselves define the structural frame for the concrete, there is no need to wait for the concrete to set in a lower course or layer before placing additional courses on top, and construction can proceed without delay.
32
34
71
72
30
74
79
30
78
90
74
30
30
After the corner columns , are constructed from standard 16-inch and 8-inch CMUs , the lateral bond beams can be constructed from deep lintel CMUs . A temporary support structure can be used to hold the lateral bond beams in place until the concrete , mortar, or grout securing the reinforcement bars sets up. In the alternative, the deep lintel CMUs comprising the bond beams can be assembled on an adjacent flat surface and later hoisted into place. Because the exact materials and dimensions of the bond beams are known in advance, they can be assembled in advance of the time they are needed to be put in place.
30
74
90
78
74
90
77
90
77
The bond beam is constructed from deep lintel CMUs securely bonded together by reinforcement bar and concrete , mortar, or grout, and effectively forming a lintel. Where a deep lintel CMU sits over another CMU, such as at a corner, it can be vertically secured by placing a reinforcement bar through a notch in the face of CMU that is mounted downward. A vertical reinforcement bar is positioned transversely to the horizontal reinforcement bar or bars. The vertical reinforcement member extends through the notch .
The preferred materials of construction are CMU concrete blocks with a waterproof coating applied to the inside walls of the cell and basin to prevent water seeping through the blocks.
The structure of the present invention requires only an above-ground foundation with only a single conduit in the slab for power and controls for the fan. Once the foundation is completed, the blocks will arrive by truck and the block masons can immediately begin installing blocks. A single cell tower can be erected in 3 working days. Multiple cells can be staged with additional block masons and can go up just as quickly. No special equipment (i.e. cranes, forklifts, etc.) are required to erect the tower. A crane will be required to set the water collectors inside the erected tower. The lifts required to install the collectors are less than 1,000 lbs per lift so the size of the crane required is minimal. Everything else will be installed by hand. The total time required to install a working cell is less than two weeks.
Many changes and modifications can be made in the present invention without departing from the spirit thereof. We, therefore pray that our rights to the present invention be limited only by the scope of the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
Reference will now be made to the drawings, wherein like parts are designated by like numerals, and wherein
FIG. 1
is a partially exploded orthogonal perspective view of the invention and of the cooling components housed in the invention.
FIG. 2
is a partially cutaway side perspective view of the invention and of the cooling components housed in the invention shown in place.
FIG. 3
is a low perspective side view of the invention and of the cooling components housed in the invention as in use.
FIG. 4
is a perspective view of the types of CMU components used in the invention.
FIG. 5
is an illustration of the construction method for the deep lintel type of CMU used in the invention.
FIG. 6
is an illustration of the construction methods of the use of reinforcing rebar and of temporarily supporting the deep lintel types of CMUs used in the invention.
FIG. 7
is an orthogonal side view of the invention.
FIG. 8
is an orthogonal top view of the invention.
FIG. 9
is an orthogonal perspective side view of an embodiment of the invention.
FIG. 10
is an orthogonal perspective side view of the foundation and embedded rebar and conduit of an embodiment of the invention.
FIG. 11
is an orthogonal perspective side view of an embodiment of the invention.
FIG. 12
is an orthogonal perspective side view of the foundation and embedded rebar and conduit of an embodiment of the invention.
FIG. 13
is an illustration of the function of the invention in operation.
FIG. 14
is a perspective view of an embodiment of the invention having two connected cooling towers.
FIG. 15
is a perspective view of an embodiment of the invention having four cooling towers connected with the water-basins in the center.
FIG. 16
is a perspective view of an embodiment of the invention having four cooling towers connected with the water basins to the outside. | |
Fun, easy, grain free, low carb, paleo, Halloween snacking!
Prep Time
3
mins
Cook Time
3
mins
Total Time
6
mins
Course:
Appetizer, Snack
Cuisine:
American
Keyword:
keto pizza snacks, low carb pizza, paleo pizza snacks
Calories:
134
kcal
Author:
Stacey
Ingredients
½
Package Uncured
Nitrate Free Salame or Pepperoni
2
tablespoon
Organic Mozzarella * optional
omit for paleo
1
tablespoon
Olive Slices * optional
HOMEMADE PIZZA SAUCE:
3
tablespoon
Organic Tomato Sauce or Tomato Puree
¼
teaspoon
Garlic Powder
¼
teaspoon
Ground Oregano
½
teaspoon
Italian seasonings
Pinch Sea Salt * optional
US Customary
-
Metric
Instructions
Preheat oven to 400 F, and line a baking sheet with parchment paper.
Mix all Sauce ingredients together in small bowl.
Line up Salami, or pepperoni slices on the parchment paper.
Sprinkle a teaspoon of mozzarella in the middle of each Salami slice.
Top each with ½ to 1 teaspoon Sauce.
Top with an olive slice * optional.
Bake for two to three minutes ( or can microwave on just the parchment paper, or microwave safe plate for 8 to 10 seconds).
Cool and Serve.
Notes
Nutrition Information:
Serving size: 4 pizza bites Calories: 134 Fat: 10 g Carbohydrates: 0 g Sugar: 0 g Protein: 8 g
*All nutritional data are estimates based on the products I used*
Nutrition
Serving:
4
pizza bites
|
Calories:
134
kcal
|
Carbohydrates:
0
g
|
Protein:
8
g
|
Fat:
10
g
|
Fiber:
0
g
|
Sugar: | https://beautyandthefoodie.com/wprm_print/recipe/9722 |
During the 2016 and 2017 seasons, the Falcons won a Region 8 conference championship, 13 NJCAA Region 8 awards, 4 USC All-South Region awards, 2 All-American nods, 14 NJCAA All-Academic Awards, and a USC Team Academic award. The Falcon goalkeepers only allowed a total of 17 goals, made 102 saves, and had a 0.835 combined save percent. During that time, Goalkeeper Kristian Shores was named 2x NJCAA All-Region 8 First Team, 2x NJCAA Region 8 Goalkeeper of the Year, 2x to the USC All-South Region Team, and in 2017 was named NJCAA All-American Honorable Mention. In 2017, Manville began working with Orlando City Youth Soccer on the goalkeeper coaching staff.
Manville joined the Daytona State College Women’s Staff after serving as the Assistant Coach at Johnson and Wales University in Denver, Colorado. Manville joined the Wildcats staff at the beginning of the 2015 season and served as both the goalkeeper coach and academic coordinator. “I am excited to have the opportunity to work with Maggie. I know that she will serve as an outstanding resource for our team and her experiences will greatly aid the development of our program,” stated Coach Jones.
In addition to her duties at Johnson and Wales Manville was an active participate in the youth coaching community in Denver. She worked with the Core Goalkeeper Academy training goalkeepers of all levels. Additionally, she worked with numerous youth teams in the Colorado Rapids Youth Soccer Program.
Coach Manville graduated from Eastern Michigan University (EMU) where she was a four-year starting keeper for the Eagles. In 2008, the Eagles finished as runner up in the Mid-American Conference tournament. Manville finished the 2009 season first in the MAC in save percentage (0.909), goals against (0.54), and ranked among the Top 10 DI goalkeepers in NCAA. At EMU, Manville’s career stats rank among the top 3 EMU all-time career saves, save percent, saves in a game, goals against average, games started, wins, shutouts, and she remains number one in career minutes and games played.
Manville earned her Master of Science from Durham University where she was the starting goalkeeper. During her time at Durham she was a member of the British Universities Colleges Sport (BUCS) Futsal National Champions as well as BUCS Football National Champion Runners up. | http://dscfalcons.com/sports/wsoc/coaches/Maggie_Manville |
CROSS-REFERENCE TO RELATED APPLICATIONS
FIELD OF THE INVENTION
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
DETAILED DESCRIPTION OF INVENTION
EXAMPLES
Example 1
1
3
3
Preparation of 2,7-dimethyl-8-(2,4-dimethylphenyl)[1,5-a]-pyrazolo-[1,3,5]-triazin-4(3H)-one (Formula 7, where Y is O, Ris CH, Z is C—CH, Ar is 2,4-dimethylphenyl)
A.1-Cyano-1-(2,4-dimethylphenyl)propan-2-one
B.5-Amino-4-(2,4-dimethylphenyl)-3-methylpyrazole
C.5-Acetamidino-4-(2,4-dimethylphenyl)-3-methylpyrazole, Acetic Acid Salt
D.2,7-dimethyl-8-(2,4-dimethylphenyl)[1,5-a]pyrazolo-[1,3,5]-triazin-4(3H)-one
Example 2
1
3
Preparation of 5-methyl-3-(2,4,6-trimethylphenyl)[1,5-a]-[1,2,3]-triazolo-[1,3,5]-triazin-7(6H)-one (Formula 7, where Y is 0, Ris CH, Z is N, Ar is 2,4,6-trimethylphenyl)
A.1-Phenylmethyl-4-(2,4,6-trimethylphenyl)-5-aminotriazole
B.4-(2,4,6-Trimethylphenyl)-5-aminotriazole
C.4-(2,4,6-Trimethylphenyl)-5-acetamidinotriazole, Acetic Acid Salt
D.5-methyl-3-(2,4,6-trimethylphenyl)[1,5-a][1,2,3]-triazolo-[1,3,5]-triazin-7(4H)-one
Example 3
3
2
3
2
1
3
3
Preparation of 4-(di(carbomethoxy)methyl)-2,7-dimethyl-8-(2,4-dimethylphenyl)[1,5-a]-pyrazolo 1,3,5-triazine (Formula 1, where Ris CH(CHCOCH), Ris CH, Z is C—CH, Ar is 2,4-dimethylphenyl)
A. 4-chloro-2,7-dimethyl-8-(2,4-dichlorophenyl)[1,5-a]-pyrazolo-triazine
B. 4-(di(carbomethoxy)methyl)-2,7-dimethyl-8-(2,4-dimethylphenyl)[1,5-a]-pyrazolo-1,3,5-triazine
Example 6
3
2
3
2
1
3
3
Preparation of 4-(1,3-dimethoxy-2-propylamino)-2,7-dimethyl-8-(2,4-dichlorophenyl)[1,5-a]-pyrazolo 1,3,5-triazine (Formula 1, where Ris NHCH(CHOCH), Ris CH, Z is C—CH, Ar is 2,4-dichlorophenyl)
A. 4-chloro-2,7-dimethyl-8-(2,4-dichlorophenyl)[1,5-a]-pyrazolotriazine
B. 4-(1,3-dimethoxy-2-propylamino)-2,7-dimethyl-8-(2,4-dichlorophenyl)[1,5-a]-pyrazolo-1,3,5-triazine
Example 431
3
3
1
3
3
Preparation of 2,4,7-dimethyl-8-(4-methoxy-2-methylphenyl)[1,5-a]-pyrazolo-1,3,5-triazine (Formula 1, where Ris CH, Ris CH, Z is C—CH, Ar is 2,4-dimethylphenyl)
Example 432
3
7-hydroxy-5-methyl-3-(2-chloro-4-methylphenyl)pyrazolo[1,5-a]pyrimidine (Formula 1 where A is CH, R1 is Me, Ris OH, Z is C-Me, Ar is 2-chloro-4-methylphenyl)
Example 433
3
7-chloro-5-methyl-3-(2-chloro-4-methylphenyl)pyrazolo[1,5-a]pyrimidine (Formula 1 where A is CH, R1 is Me, Ris Cl, Z is C-Me, Ar is 2-chloro-4-methylphenyl)
Example 434
7-(pentyl-3-amino)-5-methyl-3-(2-chloro-4-methylphenyl)pyrazolo[1,5-a]pyrimidine (Formula 1 where A is CH, R1 is Me, R3 is pentyl-3-amino, Z is C-Me, Ar is 2-chloro-4-methylphenyl)
The present application is a continuation of Ser. No. 09/930,782, filed on Aug. 16, 2001 now abandoned, which is a divisional of Ser. No. 09/014,734, filed Jan. 28, 1998, now U.S. Pat. No. 6,313,124, and claims benefit of Ser. No. 60/023,290, filed Jul. 24, 1996, the contents all of which are incorporated herein by reference.
This invention relates a treatment of psychiatric disorders and neurological diseases including major depression, anxiety-related disorders, post-traumatic stress disorder, supranuclear palsy and feeding disorders as well as treatment of immunological, cardiovascular or heart-related diseases and colonic hypersensitivity associated with psychopathological disturbance and stress, by administration of certain [1,5-a]pyrazolo-1,3,5-triazines, [1,5-a]-1,2,3-triazolo-1,3,5-triazines, [1,5-a]-pyrazolo-pyrimidines and [1,5-a]-1,2,3-triazolo-pyrimidines.
Proc. Nat. Acad. Sci
USA
Science
Rec. Prog. Horm. Res.
Persp. Behav. Med.
J. Neurosci.
Physiological Reviews
Life Sci.
Corticotropin releasing factor (herein referred to as CRF), a 41 amino acid peptide, is the primary physiological regulator of proopiomelanocortin(POMC)-derived peptide secretion from the anterior pituitary gland [J. Rivier et al., . () 80:4851 (1983); W. Vale et al., 213:1394 (1981)]. In addition to its endocrine role at the pituitary gland, immunohistochemical localization of CRF has demonstrated that the hormone has a broad extrahypothalamic distribution in the central nervous system and produces a wide spectrum of autonomic, electrophysiological and behavioral effects consistent with a neurotransmitter or neuromodulator role in brain [W. Vale et al., 39:245 (1983); G. F. Koob, 2:39 (1985); E. B. De Souza et al., 5:3189 (1985)]. There is also evidence that CRF plays a significant role in integrating the response of the immune system to physiological, psychological, and immunological stressors [J. E. Blalock, 69:1 (1989); J. E. Morley, 41:527 (1987)].
Hosp. Practice
Clinical data provide evidence that CRF has a role in psychiatric disorders and neurological diseases including depression, anxiety-related disorders and feeding disorders. A role for CRF has also been postulated in the etiology and pathophysiology of Alzheimer's disease, Parkinson's disease, Huntington's disease, progressive supranuclear palsy and amyotrophic lateral sclerosis as they relate to the dysfunction of CRF neurons in the central nervous system [for review see E. B. De Souza, 23:59 (1988)].
Science
Am. J. Psychiatry
Biol. Psychiatry
Biol Psychiatry
Arch. Gen. Psychiatry
Am J. Psychiatry
Psychoneuroendocrinology
New Eng. J. Med.
Arch. Gen. Psychiatry
Neuropsychopharmacology
In affective disorder, or major depression, the concentration of CRF is significantly increased in the cerebral spinal fluid (CSF) of drug-free individuals [C. B. Nemeroff et al., 226:1342 (1984); C. M. Banki et al., 144:873 (1987); R. D. France et al., 28:86 (1988); M. Arato et al., 25:355 (1989)]. Furthermore, the density of CRF receptors is significantly decreased in the frontal cortex of suicide victims, consistent with a hypersecretion of CRF [C. B. Nemeroff et al., 45:577 (1988)]. In addition, there is a blunted adrenocorticotropin (ACTH) response to CRF (i.v. administered) observed in depressed patients [P. W. Gold et al., 141:619 (1984); F. Holsboer et al., 9:147 (1984); P. W. Gold et al., 314:1129 (1986)]. Preclinical studies in rats and non-human primates provide additional support for the hypothesis that hypersecretion of CRF may be involved in the symptoms seen in human depression [R. M. Sapolsky, 46:1047 (1989)]. There is preliminary evidence that tricyclic antidepressants can alter CRF levels and thus modulate the numbers of CRF receptors in brain [Grigoriadis et al., 2:53 (1989)].
Life Sci.
Regul. Peptides
Horm. Behav.
Brain Research Reviews
Psychopharmacology
Psychopharmacology
Psychopharmacology
Psychopharmacology
There has also been a role postulated for CRF in the etiology of anxiety-related disorders. CRF produces anxiogenic effects in animals and interactions between benzodiazepine/non-benzodiazepine anxiolytics and CRF have been demonstrated in a variety of behavioral anxiety models [D. R. Britton et al., 31:363 (1982); C. W. Berridge and A. J. Dunn 16:83 (1986)]. Preliminary studies using the putative CRF receptor antagonist a-helical ovine CRF (9-41) in a variety of behavioral paradigms demonstrate that the antagonist produces “anxiolytic-like” effects that are qualitatively similar to the benzodiazepines [C. W. Berridge and A. J. Dunn 21:393 (1987), 15:71 (1990)]. Neurochemical, endocrine and receptor binding studies have all demonstrated interactions between CRF and benzodiazepine anxiolytics providing further evidence for the involvement of CRF in these disorders. Chlordiazepoxide attenuates the “anxiogenic” effects of CRF in both the conflict test [K. T. Britton et al., 86:170 (1985); K. T. Britton et al., 94:306 (1988)] and in the acoustic startle test [N. R. Swerdlow et al., 88:147 (1986)] in rats. The benzodiazepine receptor antagonist (Ro15-1788), which was without behavioral activity alone in the operant conflict test, reversed the effects of CRF in a dose-dependent manner while the benzodiazepine inverse agonist (FG7142) enhanced the actions of CRF [K. T. Britton et al., 94:306 (1988)].
9-41
Corticotropin
Releasing Factor: Basic and Clinical Studies of a Neuropeptide
The mechanisms and sites of action through which the standard anxiolytics and antidepressants produce their therapeutic effects remain to be elucidated. It has been hypothesized however, that they are involved in the suppression of the CRF hypersecretion that is observed in these disorders. Of particular interest is that preliminary studies examining the effects of a CRF receptor antagonist (α-helical CRF) in a variety of behavioral paradigms have demonstrated that the CRF antagonist produces “anxiolytic-like” effects qualitatively similar to the benzodiazepines [for review see G. F. Koob and K. T. Britton, In: -, E. B. De Souza and C. B. Nemeroff eds., CRC Press p221 (1990)].
Several publications describe corticotropin releasing factor antagonist compounds and their use to treat psychiatric disorders and neurological diseases. Examples of such publications include DuPont Merck PCT application US94/11050, Pfizer WO 95/33750, Pfizer WO 95/34563, Pfizer WO 95/33727 and Pfizer EP 0778 277 A1.
Insofar as is known, [1,5-a]-pyrazolo-1,3,5-triazines, [1,5-a]-1,2,3-triazolo-1,3,5-triazines, [1,5-a]-pyrazolo-pyrimidines and [1,5-a]1,2,3-triazolo-pyrimidines, have not been previously reported as corticotropin releasing factor antagonist compounds useful in the treatment of psychiatric disorders and neurological diseases. However, there have been publications which teach some of these compounds for other uses.
For instance, EP 0 269 859 (Ostuka, 1988) discloses pyrazolotriazine compounds of the formula:
1
2
3
where Ris OH or alkanoyl, Ris H, OH, or SH, and Ris an unsaturated heterocyclic group, naphthyl or substituted phenyl, and states that the compounds have xanthine oxidase inhibitory activity and are useful for treatment of gout.
EP 0 594 149 (Ostuka, 1994) discloses pyrazolotriazine and pyrazolopyrimidine compounds of the formula:
0
3
1
2
where A is CH or N, Rand Rare H or alkyl, and Rand Rare H, alkyl, alkoxyl, alkylthio, nitro, etc., and states that the compounds inhibit androgen and are useful in treatment of benign prostatic hypertrophy and prostatic carcinoma.
U.S. Pat. No. 3,910,907 (ICI, 1975) discloses pyrazolotriazines of the formula:
3
2
5
6
5
6
5
3
6
4
6
5
3
6
4
3
6
4
3
2
5
6
5
3
7
3
7
3
4
9
2
5
2
where R1 is CH, CHor CH, X is H, CH, m-CHCH, CN, COOEt, Cl, I or Br, Y is H, CH, o-CHCH, or p-CHCH, and Z is OH, H, CH, CH, CH, n-CH, i-CH, SH, SCH, NHCH, or N(CH), and states that the compounds are c-AMP phosphodiesterase inhibitors useful as bronchodilators.
U.S. Pat. No. 3,995,039 discloses pyrazolotriazines of the formula:
1
2
3
where Ris H or alkyl, Ris H or alkyl, Ris H, alkyl, alkanoyl, carbamoyl, or lower alkylcarbamoyl, and R is pyridyl, pyrimidinyl, or pyrazinyl, and states that the compounds are useful as bronchodilators.
U.S. Pat. No. 5,137,887 discloses pyrazolotriazines of the formula:
where R is lower alkoxy, and teaches that the compounds are xanthine oxidase inhibitors and are useful for treatment of gout.
U.S. Pat. No. 4,892,576 discloses pyrazolotriazines of the formula:
6
8
9
where X is O or S, Ar is a phenyl, naphthyl, pyridyl or thienyl group, R–Rare H, alkyl, etc., and Ris H, alkyl, phenyl, etc. The patent states that the compounds are useful as herbicides and plant growth regulants.
U.S. Pat. No. 5,484,760 and WO 92/10098 discloses herbicidal compositions containing, among other things, a herbicidal compound of the formula:
3
3
4
2
5
2
6
7
1
2
where A can be N, B can be CR, Rcan be phenyl or substituted phenyl, etc., R is —N(R)SORor —SON(R)Rand Rand Rcan be taken together to form
where X, Y and Z are H, alkyl, acyl, etc. and D is O or S.
U.S. Pat. No. 3,910,907 and Senga et al., J. Med. Chem., 1982, 25, 243–249, disclose triazolotriazines cAMP phosphodiesterase inhibitors of the formula:
3
2
5
6
5
3
7
3
7
3
4
9
2
5
2
3
1
3
2
5
where Z is H, OH, CH, CH, CH, n-CH, iso-CH, SH, SCH, NH(n-CH), or N(CH), R is H or CH, and Ris CHor CH. The reference lists eight therapeutic areas where inhibitors of cAMP phosphodiesterase could have utility: asthma, diabetes mellitus, female fertility control, male infertility, psoriasis, thrombosis, anxiety, and hypertension.
WO95/35298 (Otsuka, 1995) discloses pyrazolopyrimidines and states that they are useful as analgesics. The compounds are represented by the formula:
1
2
3
4
5
6
where Q is carbonyl or sulfonyl, n is 0 or 1, A is a single bond, alkylene or alkenylene, Ris H, alkyl, etc., Ris naphthyl, cycloalkyl, heteroaryl, substituted phenyl or phenoxy, Ris H, alkyl or phenyl, Ris H, alkyl, alkoxycarbonyl, phenylalkyl, optionally phenylthio-substituted phenyl, or halogen, Rand Rare H or alkyl.
EP 0 591 528 (Otsuka, 1991) discloses antiinflammatory use of pyrazolopyrimidines represented by the formula:
1
2
3
4
5
6
7
8
6
7
8
where R, R, Rand Rare H, carboxyl, alkoxycarbonyl, optionally substituted alkyl, cycloalkyl, or phenyl, Ris SRor NRR, Ris pyridyl or optionally substituted phenyl, and Rand Rare H or optionally substituted phenyl.
Springer et al, J. Med. Chem., 1976, vol. 19, no. 2, 291–296 and Springer U.S. Pat. Nos. 4,021,556 and 3,920,652 disclose pyrazolopyrimidines of the formula:
where R can be phenyl, substituted phenyl or pyridyl, and their use to treat gout, based on their ability to inhibit xanthine oxidase.
Joshi et al., J. Prakt. Chemie, 321, 2, 1979, 341–344, discloses compounds of the formula:
1
2
3
2
5
6
4
3
2
5
3
6
4
where Ris CF, CF, or CHF, and Ris CH, CH, CF, or CHF.
Maquestiau et al., Bull. Soc. Belg., vol. 101, no. 2, 1992, pages 131–136 discloses a pyrazolo[1,5-a]pyrimidine of the formula:
Ibrahim et al., Arch. Pharm. (weinheim) 320, 487–491 (1987) discloses pyrazolo[1,5-a]pyrimidines of the formula:
where R is NH2 or OH and Ar is 4-phenyl-3-cyano-2-aminopyrid-2-yl.
Other references which disclose azolopyrimidines inclued EP 0 511 528 (Otsuka, 1992), U.S. Pat. No. 4,997,940 (Dow, 1991), EP 0 374 448 (Nissan, 1990), U.S. Pat. No. 4,621,556 (ICN, 1997), EP 0 531 901 (Fujisawa, 1993), U.S. Pat. No. 4,567,263 (BASF, 1986), EP 0 662 477 (Isagro, 1995), DE 4 243 279 (Bayer, 1994), U.S. Pat. No. 5,397,774 (Upjohn, 1995), EP 0 521 622 (Upjohn, 1993), WO 94/109017 (Upjohn, 1994), J. Med. Chem., 24, 610–613 (1981), and J. Het. Chem., 22, 601 (1985).
In accordance with one aspect, the present invention provides novel compounds, pharmaceutical compositions and methods which may be used in the treatment of affective disorder, anxiety, depression, irritable bowel syndrome, post-traumatic stress disorder, supranuclear palsy, immune suppression, Alzheimer's disease, gastrointestinal disease, anorexia nervosa or other feeding disorder, drug or alcohol withdrawal symptoms, drug addiction, inflammatory disorder, fertility problems, disorders, the treatment of which can be effected or facilitated by antagonizing CRF, including but not limited to disorders induced or facilitated by CRF, or a disorder selected from inflammatory disorders such as rheumatoid arthritis and osteoarthritis, pain, asthma, psoriasis and allergies; generalized anxiety disorder; panic, phobias, obsessive-compulsive disorder; post-traumatic stress disorder; sleep disorders induced by stress; pain perception such as fibromyalgia; mood disorders such as depression, including major depression, single episode depression, recurrent depression, child abuse induced depression, and postpartum depression; dysthemia; bipolar disorders; cyclothymia; fatigue syndrome; stress-induced headache; cancer, human immunodeficiency virus (HIV) infections; neurodegenerative diseases such as Alzheimer's disease, Parkinson's disease and Huntington's disease; gastrointestinal diseases such as ulcers, irritable bowel syndrome, Crohn's disease, spastic colon, diarrhea, and post operative ilius and colonic hypersensitivity associated by psychopathological disturbances or stress; eating disorders such as anorexia and bulimia nervosa; hemorrhagic stress; stress-induced psychotic episodes; euthyroid sick syndrome; syndrome of inappropriate antidiarrhetic hormone (ADH); obesity; infertility; head traumas; spinal cord trauma; ischemic neuronal damage (e.g., cerebral ischemia such as cerebral hippocampal ischemia); excitotoxic neuronal damage; epilepsy; cardiovascular and hear related disorders including hypertension, tachycardia and congestive heart failure; stroke; immune dysfunctions including stress induced immune dysfunctions (e.g., stress induced fevers, porcine stress syndrome, bovine shipping fever, equine paroxysmal fibrillation, and dysfunctions induced by confinement in chickens, sheering stress in sheep or human-animal interaction related stress in dogs); muscular spasms; urinary incontinence; senile dementia of the Alzheimer's type; multiinfarct dementia; amyotrophic lateral sclerosis; chemical dependencies and addictions (e.g., dependencies on alcohol, cocaine, heroin, benzodiazepines, or other drugs); drug and alcohol withdrawal symptoms; osteoporosis; psychosocial dwarfism and hypoglycemia in a mammal.
The present invention provides novel compounds which bind to corticotropin releasing factor receptors, thereby altering the anxiogenic effects of CRF secretion. The compounds of the present invention are useful for the treatment of psychiatric disorders and neurological diseases, anxiety-related disorders, post-traumatic stress disorder, supranuclear palsy and feeding disorders as well as treatment of immunological, cardiovascular or heart-related diseases and colonic hypersensitivity associated with psychopathological disturbance and stress in a mammal.
According to another aspect, the present invention provides novel compounds of Formulae (1) and (2) (described below) which are useful as antagonists of the corticotropin releasing factor. The compounds of the present invention exhibit activity as corticotropin releasing factor antagonists and appear to suppress CRF hypersecretion. The present invention also includes pharmaceutical compositions containing such compounds of Formulae (1) and (2), and methods of using such compounds for the suppression of CRF hypersecretion, and/or for the treatment of anxiogenic disorders.
According to yet another aspect of the invention, the compounds provided by this invention (and especially labelled compounds of this invention) are also useful as standards and reagents in determining the ability of a potential pharmaceutical to bind to the CRF receptor.
The present invention comprises a method of treating affective disorder, anxiety, depression, headache, irritable bowel syndrome, post-traumatic stress disorder, supranuclear palsy, immune suppression, Alzheimer's disease, gastrointestinal diseases, anorexia nervosa or other feeding disorder, drug addiction, drug or alcohol withdrawal symptoms, inflammatory diseases, cardiovascular or heart-related diseases, fertility problems, human immunodeficiency virus infections, hemorrhagic stress, obesity, infertility, head and spinal cord traumas, epilepsy, stroke, ulcers, amyotrophic lateral sclerosis, hypoglycemia or a disorder the treatment of which can be effected or facilitated by antagonizing CRF, including but not limited to disorders induced or facilitated by CRF, in mammals comprising administering to the mammal a therapeutically effective amount of a compound of Formulae (1) or (2):
A is N or CR;
2
Z is N or CR;
4
Ar is selected from phenyl, naphthyl, pyridyl, pyrimidinyl, triazinyl, furanyl, thienyl, benzothienyl, benzofuranyl, 2,3-dihydrobenzofuranyl, 2,3-dihydrobenzothienyl, indanyl, 1,2-benzopyranyl, 3,4-dihydro-1,2-benzopyranyl, tetralinyl, each Ar optionally substituted with 1 to 5 Rgroups and each Ar is attached to an unsaturated carbon atom;
1
4
2
4
2
4
3
6
4
7
1
4
R is independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, halo, CN, C–Chaloalkyl;
1
9
10
9
10
9
10
11
12
1
4
2
4
2
4
1
4
1
12
2
12
2
10
3
6
4
10
1
4
n
Ris independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, halo, CN, C–Chaloalkyl, C–Chydroxyalkyl, C–Calkoxyalkyl, C–Ccyanoalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NRR, C–Calkyl-NRR, NRCOR, OR, SH or S(O)R;
2
6
7
9
10
6
7
6
7
7
12
1
4
2
4
2
4
3
6
4
10
1
4
n
n
1
4
n
Ris selected from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Chydroxyalkyl, halo, CN, —NRR, NRCOR, —NRS(O)R, S(O)NRR, C–Chaloalkyl, —OR, SH or —S(O)R;
3
7
13
7
7
13
8
7
7
8
6
7
8
13
6
7
6a
7a
7
6
6
7
n
2
2
2
—H, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, NRR, N(OR)R, CONRR, aryl, heteroaryl and heterocyclyl, or
1
10
2
10
2
10
3
8
5
8
4
12
6
10
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkenyl, C–Ccycloalkylalkyl or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl and heterocyclyl;
Ris selected from:
4
6
7
8
7
8
7
7
7
6
7
9
7
7
7
6
7
8
7
8
7
7
7
6
7
7
9
7
7
1
10
2
10
2
10
3
6
4
12
2
1
4
2
2
n
1
10
2
10
2
10
3
6
4
12
1
4
2
2
2
n
Ris independently selected at each occurrence from: C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NO, halo, CN, C–Chaloalkyl, NRR, NRCOR, NRCOR, COR, OR, CONRR, CO(NOR)R, COR, or S(O)R, where each such C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl and C–Ccycloalkylalkyl are optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, NO, halo, CN, NRR, NRCOR, NRCOR, COROR, CONRR, COR, CO(NOR)R, or S(O)R;
6
7
6a
7a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
1
4
6
7
6a
7a
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups;
Rand R, Rand Rare independently selected at each occurrence from:
8
1
4
Ris independently selected at each occurrence from H or C–Calkyl;
9
10
1
4
3
6
Rand Rare independently selected at each occurrence from H, C–Calkyl, or C–Ccycloalkyl;
11
1
4
1
4
3
6
Ris selected from H, C–Calkyl, C–Chaloalkyl, or C–Ccycloalkyl;
12
1
4
1
4
Ris C–Calkyl or C–Chaloalkyl;
13
1
4
1
4
2
8
3
6
4
12
1
4
1
4
Ris selected from C–Calkyl, C–Chaloalkyl, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, aryl, aryl(C–Calkyl)-, heteroaryl or heteroaryl(C–Calkyl)-;
14
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
1
10
3
10
3
10
3
8
4
12
1
6
3
6
1
4
n
2
2
2
1
6
1
6
1
6
Ris selected from C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, or C–Ccycloalkylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, and C–Calkylthio, C–Calkylsulfinyl and C–Calkylsulfonyl;
15
16
15
15
1
6
3
10
4
16
n
Rand Rare independently selected at each occurrence from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, except that for S(O)R, Rcannot be H;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
aryl is phenyl or naphthyl, each optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
heteroaryl is pyridyl, pyrimidinyl, triazinyl, furanyl, pyranyl, quinolinyl, isoquinolinyl, thienyl, imidazolyl, thiazolyl, indolyl, pyrrolyl, oxazolyl, benzofuranyl, benzothienyl, benzothiazolyl, isoxazolyl, pyrazolyl, 2,3-dihydrobenzothienyl or 2,3-dihydrobenzofuranyl, each being optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR; heterocyclyl is saturated or partially saturated
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
15
16
16
15
heteroaryl, optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
n is independently at each occurrence 0, 1 or 2.
and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof, wherein:
4
Preferred methods of the present invention are methods in wherein in the compound of Formulae (1) or (2), Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, each optionally substituted with 1 to 4 Rsubstituents.
2
1
2
3
6a
7a
3
Further preferred methods of the above invention are methods wherein, in the compound of Formulae (1) or (2), A is N, Z is CR, Ar is 2,4-dichlorophenyl, 2,4-dimethylphenyl or 2,4,6-trimethylphenyl, Rand Rare CH, and Ris NRR.
The present invention comprises compounds of Formulae (1) or (2):
A is N or CR;
2
Z is N or CR;
4
Ar is selected from phenyl, naphthyl, pyridyl, pyrimidinyl, triazinyl, furanyl, thienyl, benzothienyl, benzofuranyl, 2,3-dihydrobenzofuranyl, 2,3-dihydrobenzothienyl, indanyl, 1,2-benzopyranyl, 3,4-dihydro-1,2-benzopyranyl, tetralinyl, each Ar optionally substituted with 1 to 5 Rgroups and each Ar is attached to an unsaturated carbon atom;
1
4
2
4
2
4
3
6
4
7
1
4
R is independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, halo, CN, C–Chaloalkyl;
1
9
10
9
10
9
10
11
12
1
4
2
4
2
4
1
4
1
12
2
12
2
10
3
6
4
10
1
4
n
Ris independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, halo, CN, C–Chaloalkyl, C–Chydroxyalkyl, C–Calkoxyalkyl, C–Ccyanoalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NRR, C–Calkyl-NRR, NRCOR, OR, SH or S(O)R;
2
6
7
9
10
6
7
6
7
7
12
1
4
2
4
2
4
3
6
4
10
1
4
n
n
1
4
n
Ris selected from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Chydroxyalkyl, halo, CN, —NRR, NRCOR, —NRS(O)R, S(O)NRR, C–Chaloalkyl, —OR, SH or —S(O)R;
3
7
13
7
7
13
8
7
7
8
6
7
8
13
6
7
6a
7a
7
6
6
7
n
2
2
2
—H, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, NRR, N(OR)R, CONRR, aryl, heteroaryl and heterocyclyl, or
1
10
2
10
2
10
3
8
5
8
4
12
6
10
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkenyl, C–Ccycloalkylalkyl or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl and heterocyclyl;
Ris selected from:
4
6
7
8
7
8
7
7
7
6
7
9
7
7
7
6
7
8
7
8
7
7
7
6
7
7
9
7
7
1
10
2
10
2
10
3
6
4
12
2
1
4
2
2
n
1
10
2
10
2
10
3
6
4
12
1
4
2
2
2
n
Ris independently selected at each occurrence from: C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NO, halo, CN, C–Chaloalkyl, NRR, NRCOR, NRCOR, COR, OR, CONRR, CO(NOR)R, COR, or S(O)R, where each such C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl and C–Ccycloalkylalkyl are optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, NO, halo, CN, NRR, NRCOR, NRCOR, COROR, CONRR, COR, CO(NOR)R, or S(O)R;
6
7
6a
7a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
1
4
6
7
6a
7a
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups;
Rand R, Rand Rare independently selected at each occurrence from:
8
1
4
Ris independently selected at each occurrence from H or C–Calkyl;
9
10
1
4
3
6
Rand Rare independently selected at each occurrence from H, C–Calkyl, or C–Ccycloalkyl;
11
1
4
1
4
3
6
Ris selected from H, C–Calkyl, C–Chaloalkyl, or C–Ccycloalkyl;
12
1
4
1
4
Ris C–Calkyl or C–Chaloalkyl;
13
1
4
1
4
2
8
3
6
4
12
1
4
1
4
Ris selected from C–Calkyl, C–Chaloalkyl, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, aryl, aryl(C–Calkyl)-, heteroaryl or heteroaryl(C–Calkyl)-;
14
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
1
10
3
10
3
10
3
8
4
12
1
6
3
6
1
4
n
2
2
2
1
6
1
6
1
6
Ris selected from C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, or C–Ccycloalkylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, and C–Calkylthio, C–Calkylsulfinyl and C–Calkylsulfonyl;
15
16
15
15
1
6
3
10
4
16
n
Rand Rare independently selected at each occurrence from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, except that for S(O)R, Rcannot be H;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
aryl is phenyl or naphthyl, each optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
heteroaryl is pyridyl, pyrimidinyl, triazinyl, furanyl, pyranyl, quinolinyl, isoquinolinyl, thienyl, imidazolyl, thiazolyl, indolyl, pyrrolyl, oxazolyl, benzofuranyl, benzothienyl, benzothiazolyl, isoxazolyl, pyrazolyl, 2,3-dihydrobenzothienyl or 2,3-dihydrobenzofuranyl, each being optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
15
16
16
15
heterocyclyl is saturated or partially saturated heteroaryl, optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
n is independently at each occurrence 0, 1 or 2,
2
2
3
7
13
7
1
(1) when A is N, Z is CR, Ris H, Ris —ORor —OCOR, and Ris H, then Ris not H, OH or SH;
2
1
2
3
3
2
5
3
2
5
6
5
3
7
3
7
3
4
9
2
5
2
3
(2) when A is N, Z is CR, Ris CHor CH, Ris H, and Ris OH, H, CH, CH, CH, n-CH, i-CH, SH, SCH, NHCH, or N(CH), then Ar is not phenyl or m-CH-phenyl;
2
2
3
6a
7a
6a
7a
(3) when A is N, Z is CR, Ris H, and Ar is pyridyl, pyrimidinyl or pyrazinyl, and Ris NRR, then Rand Rare not H or alkyl;
2
2
6
7
3
2
(4) when A is N, Z is CR, and Ris SONRR, then Ris not OH or SH;
2
2
6
7
6
7
2
2
(5) when A is CR and Z is CR, then Ris not —NRSORor —SONRR;
2
2
6
7
6
7
3
2
2
(6) when A is N, Z is CRand Ris —NRSORor —SONRR, then Ris not OH or SH;
2
1
2
3
3
2
5
6
5
3
7
3
7
3
4
9
2
5
2
(7) when A is N, Z is CR, Ris methyl or ethyl, Ris H, and Ris H, OH, CH, CH, CH, n-CH, iso-CH, SH, SCH, NH(n-CH), or N(CH), then Ar is not unsubstituted phenyl or m-methylphenyl;
2
2
3
8
7
7
1
4
1
4
1
4
(8) when A is CR, Z is CR, Ris H, phenyl or alkyl, Ris NRCORand Ar is phenyl or phenyl substituted with phenylthio, then Ris not aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocycly(C–Calkyl);
2
2
3
13
6a
7a
13
6a
7a
(9) when A is CR, Z is CR, Ris H or alkyl, Ar is phenyl, and Ris SRor NRR, then Ris not aryl or heteroaryl and Rand Rare not H or aryl; or
2
1
11
2
3
7
7
11
3
3
(10) when A is CH, Z is CR, Ris OR, Ris H, Ris OR, and Rand Rare both H, then Ar is not phenyl, p-Br-phenyl, p-Cl-phenyl, p-NHCOCH-phenyl, p-CH-phenyl, pyridyl or naphthyl;
2
2
3
3
2
5
3
6
4
1
3
2
5
(11) when A is CH, Z is CR, Ris H, Ar is unsubstituted phenyl, and Ris CH, CH, CFor CHF, then R, is not CFor CF;
2
2
1
3
(12) when A is CR, R is H, Z is CR, Ris OH, and Rand Rare H, then Ar is not phenyl;
2
2
1
3
2
3
(13) when A is CR, R is H, Z is CR, Ris OH or NH, Rand Rare CH, then Ar is not 4-phenyl-3-cyano-2-aminopyrid-2-yl.
with the provisos that:
and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein:
1
3
6a
7a
6a
7a
1
3
6a
7a
7a
6a
1
4
1
12
1
4
2
1
4
1
4
3
6
1
4
1
12
1
4
2
1
4
1
4
3
6
Preferred compounds of the above invention are compounds of Formulae (1) and (2) and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof with the additional provisos that: (1) when A is N, Ris H, C–Calkyl, halo, CN, C–Chydroxyalkyl, C–Calkoxyalkyl or SO(C–Calkyl), Ris NRRand Ris unsubstituted C–Calkyl, then Ris not phenyl, naphthyl, thienyl, benzothienyl, pyridyl, quinolyl, pyrazinyl, furanyl, benzofuranyl, benzothiazolyl, indolyl or C–Ccycloalkyl; and (2) A is N, Ris H, C–Calkyl, halo, CN, C–Chydroxyalkyl, C–Calkoxyalkyl or SO(C–Calkyl), Ris NRRand Ris unsubstituted C–Calkyl, then Ris not phenyl, naphthyl, thienyl, benzothienyl, pyridyl, quinolyl, pyrazinyl, furanyl, benzofuranyl, benzothiazolyl, indolyl or C–Ccycloalkyl.
4
Preferred compounds of the above invention also include compounds of Formulae (1) and (2) and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, each optionally substituted with 1 to 4 Rsubstituents.
2
1
2
3
6a
7a
3
Preferred compounds of the above invention also include compounds of Formulae (1) and (2) and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein A is N, Z is CR, Ar is 2,4-dichlorophenyl, 2,4-dimethylphenyl or 2,4,6-trimethylphenyl, Rand Rare CH, and Ris NRR.
More preferred compounds of the above invention are compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein A is N.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
4
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl and each Ar is optionally substituted with 1 to 4 Rsubstituents.
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ris NRRor OR.
4
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents, and Ris NRRor OR.
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Z is CR.
4
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl and each Ar is optionally substituted with 1 to 4 Rsubstituents.
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ris NRRor OR.
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
Ris independently selected from:
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl); and
7a
—H,
5
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
1
4
6
7
6a
7a
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups.
Ris independently selected at each occurrence from:
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
7a
1
4
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl or C–Ccycloalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl, and -aryl or heteroaryl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare identical and are selected from:
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
Ris selected from:
7a
1
4
1
4
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl and each such C–Calkyl is substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
Ris selected from:
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
7a
3
6
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Ccycloalkyl, each such C–Ccycloalkyl optionally substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
-aryl,
-heteroaryl or
6a
7a
1
4
-heterocyclyl,
and the other of Rand Ris unsubstituted C–Calkyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein one of Rand Ris selected from:
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare independently H or C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
4
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents, and Ris NRRor OR.
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
Ris independently selected from:
7a
—H,
5
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
1
4
6
7
6a
7a
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups.
Ris independently selected at each occurrence from:
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
7a
1
4
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl or C–Ccycloalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl, and -aryl or heteroaryl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare identical and are selected from:
6a
7a
1
4
1
4
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R—COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare identical and are
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
7a
1
4
1
4
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl and each such C–Calkyl is substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
Ris:
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ris selected from:
6a
7a
3
6
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Ccycloalkyl, each such C–Ccycloalkyl optionally substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
-aryl,
-heteroaryl or
6a
7a
1
4
-heterocyclyl,
and the other of Rand Ris unsubstituted C–Calkyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein one of Rand Ris selected from:
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare independently H or C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
4
—Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents,
3
6a
7a
7
—Ris NRRor ORand
1
2
1
4
3
6
4
10
—Rand Rare independently selected from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
Ris independently selected from:
7a
—H,
5
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
1
4
6
7
6a
7a
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups.
Ris independently selected at each occurrence from:
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
7a
1
4
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl or C–Ccycloalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl, and -aryl or heteroaryl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare identical and are selected from:
6a
7a
1
4
1
4
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare identical and are
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
Ris selected from:
7a
1
4
1
4
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl and each such C–Calkyl is substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
Ris:
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
7a
3
6
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Ccycloalkyl, each such C–Ccycloalkyl optionally substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
-aryl,
-heteroaryl or
6a
7a
1
4
-heterocyclyl,
and the other of Rand Ris unsubstituted C–Calkyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein one of Rand Ris selected from:
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare independently H or C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
Specifically preferred compounds of the above invention are compounds of Formula (50)
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(n-Pr), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
a compound of Formula (50) wherein Ris —N(Et)(n-Bu), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris -(n-Pr)(CHcPr), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
a compound of Formula (50) wherein Ris —NHCH(Et)(n-Bu), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et)(CHOMe), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris C, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOEt), Ris Cl, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Cl, Ris H, Ris C, Ris H and Ris H;
3
4a
1
4b
4c
1
4d
4e
a compound of Formula (50) wherein Ris —N(Me)(Ph), Ris C, Ris H, Ris C, Ris H and Ris H;
3
4a
1
4b
4c
1
4d
4e
2
a compound of Formula (50) wherein Ris —N(n-Pr), Ris C, Ris H, Ris C, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
a compound of Formula (50) wherein Ris —NHCH(Et)(n-Pr), Ris C, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et)(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
a compound of Formula (50) wherein Ris —OEt, Ris C, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(CHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Me)(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —OCH(Et)(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(n-Pr)(CHc-Pr), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(Me)(CHN(Me)), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(cPr)(CHCHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(n-Pr)(CHCHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(n-Bu)(CHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris NHCH(Et)(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et)(CHOMe), Ris Br, Ris H Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOEt), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHCHOMe)(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
a compound of Formula (50) wherein Ris morpholino, Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4c
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
a compound of Formula (50) wherein Ris —NH(c-Pr), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris NHCH(CHOMe), Ris CN, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(c-Pr)(CHCHCN), Ris Me, Ris H, Ris Me, Ris H and Ris Me;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NCH(CHOMe), Ris Me, Ris H, Ris Br, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(CHCHOMe), Ris Me, Ris H, Ris Br, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris OMe, Ris Me and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris OMe, Ris Me and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris OMe, Ris Me and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein a compound of Formula (50) wherein Ris —N(Et), Ris Me, Ris H, Ris OMe, Ris Me and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Cl, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et)(CHOMe), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(CHCHOMe), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(c-Pr)(CHCHCN), Ris Me, Ris H, Ris OMe, Ris Me and Ris H;
3
4a
1
4b
4c
1
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(cPr)(CHCHCN), Ris C, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
2
a compound of Formula (50) wherein Ris (S)—NHCH(CHOMe)(CHCHOMe), Ris Cl, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(CHCHOMe), Ris Cl, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris Br, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris Br, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —NH(CHOMe)(CH-iPr), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris H, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris NMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(n-Pr), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(CHOEt)(Et), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(CHCHOMe), Ris Me, Ris H, Ris NMe2, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Me, Ris H, Ris Br, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Cl, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris NMe2, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris (S)—NHCH(CHOMe)(CHCHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(CHCHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris (S)—NHCH(CHOMe)(CHCHOMe), Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOMe)(CHCHOMe), Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(c-Pr)(CHCHCN), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
a compound of Formula (50) wherein Ris —NH(Et)(CHCN), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Me, Ris Me, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe)(CHCHOH), Ris Cl, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris Me, Ris Me, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et), Ris Me, Ris Me, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
a compound of Formula (50) wherein Ris —N(CHc-Pr) (n-Pr), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(c-Pr) (CHCHCN), Ris Me, Ris Me, Ris OMe, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH (Et), Ris C, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Cl, Ris H, Ris OMe, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris —N(CHCHOMe), Ris C, Ris H, Ris OMe, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —NHCH(Et)(CHOMe), Ris C, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (50) wherein Ris —N(Et), Ris Cl, Ris H, Ris CN, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
a compound of Formula (50) wherein Ris —N(c-Pr)(CHCHCN), Ris C, Ris H, Ris OMe, Ris H and Ris H;
3
4a
1
4b
4c
1
4d
4e
2
2
a compound of Formula (50) wherein Ris —NHCH(CHOH), Ris C, Ris H, Ris C, Ris H and Ris H; and
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (50) wherein Ris N(CHCHOMe), Ris Me, Ris H, Ris OMe, Ris H and Ris H.
and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof, selected from the group consisting of:
More specifically preferred is 4-(bis-(2-methoxyethyl)amino)-2,7-dimethyl-8-(2-methyl-4-methoxyphenyl)-[1,5-a]-pyrazolo-1,3,5-triazine and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
More specifically preferred is 4(bis-(2-methoxyethyl)amino)-2,7-dimethyl-8-(2,5-dimethyl-4-methoxyphenyl)-[1,5-a]-pyrazolo-1,3,5-triazine and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
More preferred are compounds of the above invention are compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein A is CR.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
4
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl and each Ar is optionally substituted with 1 to 4 Rsubstituents.
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ris NRRor OR.
4
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents, and Ris NRRor OR.
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Z is CR.
4
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl and each Ar is optionally substituted with 1 to 4 Rsubstituents.
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ris NRRor OR.
4
3
6a
7a
7
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents, and Ris NRRor OR.
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare independently H or C–Calkyl, and each such C–Calkyl is optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
4
—Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents,
3
6a
7a
7
—Ris NRRor ORand
1
2
1
4
3
6
4
10
—Rand Rare independently selected from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl.
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
More preferred compounds of the above invention also include compounds and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof wherein Rand Rare independently H or C–Calkyl, and each such C–Calkyl is optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
Specifically preferred compounds of the above invention are compounds of Formula (51)
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(n-Pr), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris N(CHCHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(c-Pr)(CHCHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —N(CHCHOMe), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —NHCH(CHOMe), Ris Cl, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Cl, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —N(Et), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(n-Pr) (CHCHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(n-Bu)(CHCHCN), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(n-Pr)(CHOMe), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris (S)—NH(CHCHOMe)CHOMe, Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —NH(CHCHOMe)CHOMe, Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —N(CHCHOMe), Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
a compound of Formula (51) wherein Ris —NH(Et), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(n-Pr), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
2
a compound of Formula (51) wherein Ris —NHCH(CHOMe), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris (S)—NH(CHCHOMe)CHOMe, Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —NH(CHCHOMe)CHOMe, Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(n-Pr)(CHCHCN), Ris Me, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —N(Et), Ris Me, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris (S)—NH(CHCHOMe)CHOMe, Ris Cl, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —NH(CHCHOMe)CHOMe, Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —N(Et), Ris Cl, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(c-Pr)(CHCHCN), Ris Me, Ris H, Ris OMe, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(c-Pr)(CHCHCN), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH (n-Pr)(CHOMe), Ris Me, Ris H, Ris OMe, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH (n-Pr)(CHOMe), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Br, Ris H, Ris OMe, Ris OMe and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —N(CHCHOMe), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —NHCH(CHOMe), Ris Br, Ris H, Ris OMe, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —N(Et), Ris Me, Ris H, Ris Cl, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —N(Et), Ris Cl, Ris H, Ris OMe, Ris OMe and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Cl, Ris H, Ris OMe, Ris OMe and Ris H;
3
4a
1
4b
4c
1
4d
4e
2
2
2
a compound of Formula (51) wherein Ris —N(CHCHOMe), Ris C, Ris H, Ris C, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —NHCH(CHOMe), Ris C, Ris H, Ris Cl, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(Pr)(CHCHCN), Ris C, Ris H, Ris Cl, Ris H and Ris H;
3
4a
1
4b
4c
1
4d
4e
a compound of Formula (51) wherein Ris —N(Bu)(Et), Ris C, Ris H, Ris C, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et)CHOMe, Ris C, Ris H, Ris Cl, Ris H and Ris H;
3
4a
1
4b
4c
1
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris C, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris Me, Ris H and Ris H;
3
4a
1
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris C, Ris H, Ris Me, Ris H and Ris H;
3
4a
4b
4c
1
4d
4e
2
a compound of Formula (51) wherein Ris —NHCH(Et), Ris Me, Ris H, Ris C, Ris H and Ris H;
3
4a
4b
4c
4d
4e
2
a compound of Formula (51) wherein Ris —NEt, Ris Me, Ris H, Ris OMe, Ris H and Ris H; and
3
4a
4b
4c
4d
4e
2
2
a compound of Formula (51) wherein Ris —N(Pr)(CHCHCN), Ris Me, Ris H, Ris OMe, Ris H and Ris H.
and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof selected from the group consisting of:
More specifically preferred is 7-(3-pentylamino)-2,5-dimethyl-3-(2-methyl-4-methoxyphenyl)-[1,5-a]-pyrazolopyrimidine and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
More specifically preferred is 7-(Diethylamino)-2,5-dimethyl-3-(2-methyl-4-methoxyphenyl-[1,5-a]-pyrazolopyrimidine and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
More specifically preferred is 7-(N-(3-cyanopropyl)-N-propylamino)-2,5-dimethyl-3-(2,4-dimethylphenyl)-[1,5-a]-pyrazolopyrimidine and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt or pro-drug forms thereof.
The present invention also provides pharmaceutical compositions comprising compounds of Formulae (1) and (2) and a pharmaceutically acceptable carrier.
The present invention still further comprises a method of treating affective disorder, anxiety, depression, headache, irritable bowel syndrome, post-traumatic stress disorder, supranuclear palsy, immune suppression, Alzheimer's disease, gastrointestinal diseases, anorexia nervosa or other feeding disorder, drug addiction, drug or alcohol withdrawal symptoms, inflammatory diseases, cardiovascular or heart-related diseases, fertility problems, human immunodeficiency virus infections, hemorrhagic stress, obesity, infertility, head and spinal cord traumas, epilepsy, stroke, ulcers, amyotrophic lateral sclerosis, hypoglycemia or a disorder the treatment of which can be effected or facilitated by antagonizing CRF, including but not limited to disorders induced or facilitated by CRF, in mammals comprising administering to the mammal a therapeutically effective amount of a compound of Formulae (1) or (2):
2
Z is N or CR;
4
Ar is selected from phenyl, naphthyl, pyridyl, pyrimidinyl, triazinyl, furanyl, thienyl, benzothienyl, benzofuranyl, 2,3-dihydrobenzofuranyl, 2,3-dihydrobenzothienyl, indanyl, 1,2-benzopyranyl, 3,4-dihydro-1,2-benzopyranyl, tetralinyl, each Ar optionally substituted with 1 to 5 Rgroups and each Ar is attached to an unsaturated carbon atom;
1
9
10
9
10
9
10
11
12
1
4
2
4
2
4
1
4
1
12
2
12
2
10
3
6
4
10
1
4
n
Ris independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, halo, CN, C–Chaloalkyl, C–Chydroxyalkyl, C–Calkoxyalkyl, C–Ccyanoalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NRR, C–Calkyl-NRR, NRCOR, OR, SH or S(O)R;
2
6
7
9
10
6
7
6
7
7
12
1
4
2
4
2
4
3
6
4
10
1
4
n
n
1
4
n
Ris selected from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Chydroxyalkyl, halo, CN, —NRR, NRCOR, —NRS(O)R, S(O)NRR, C–Chaloalkyl, —OR, SH or —S(O)R;
3
7
13
7
7
13
8
7
7
8
6
7
8
13
6
7
6a
7a
7
6
6
7
n
2
2
2
—H, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, NRR, N(OR)R, CONRR, aryl, heteroaryl and heterocyclyl, or
1
10
2
10
2
10
3
8
5
8
4
12
6
10
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkenyl, C–Ccycloalkylalkyl or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl and heterocyclyl;
Ris selected from:
4
6
7
8
7
8
7
7
7
6
7
9
7
7
7
6
7
8
7
8
7
7
7
6
7
7
9
7
7
1
10
2
10
2
10
3
6
4
12
2
1
4
2
2
n
1
10
2
10
2
10
3
6
4
12
1
4
2
2
2
n
Ris independently selected at each occurrence from: C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NO, halo, CN, C–Chaloalkyl, NRR, NRCOR, NRCOR, COR, OR, CONRR, C(NOR)R, COR, or S(O)R, where each such C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl and C–Ccycloalkylalkyl are optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, NO, halo, CN, NRR, NRCOR, NRCOR, COROR, CONRR, COR, CO(NOR)R, or S(O)R;
6
7
6a
7a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
R, R, Rand Rare independently selected at each occurrence from:
6
7
6a
7a
1
4
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups;
8
1
4
Ris independently selected at each occurrence from H or C–Calkyl;
9
10
1
4
3
6
Rand Rare independently selected at each occurrence from H, C–Calkyl, or C–Ccycloalkyl;
11
1
4
1
4
3
6
Ris selected from H, C–Calkyl, C–Chaloalkyl, or C–Ccycloalkyl;
12
1
4
1
4
Ris C–Calkyl or C–Chaloalkyl;
13
1
4
1
4
2
8
3
6
4
12
1
4
1
4
Ris selected from C–Calkyl, C–Chaloalkyl, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, aryl, aryl(C–Calkyl)-, heteroaryl or heteroaryl(C–Calkyl)-;
14
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
1
10
3
10
3
10
3
8
4
12
1
6
3
6
1
4
n
2
2
2
1
6
1
6
1
6
Ris selected from C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, or C–Ccycloalkylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, and C–Calkylthio, C–Calkylsulfinyl and C–Calkylsulfonyl;
15
16
15
15
1
6
3
10
4
16
n
Rand Rare independently selected at each occurrence from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, except that for S(O)R, Rcannot be H;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
aryl is phenyl or naphthyl, each optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)RCOR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCORNRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
heteroaryl is pyridyl, pyrimidinyl, triazinyl, furanyl, pyranyl, quinolinyl, isoquinolinyl, thienyl, imidazolyl, thiazolyl, indolyl, pyrrolyl, oxazolyl, benzofuranyl, benzothienyl, benzothiazolyl, isoxazolyl, pyrazolyl, 2,3-dihydrobenzothienyl or 2,3-dihydrobenzofuranyl, each being optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
15
16
16
15
heterocyclyl is saturated or partially saturated heteroaryl, optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
n is independently at each occurrence 0, 1 or 2;
2
3
6
7
6a
7a
7
with the proviso that when Z is CR, then Ris not NRR, NRRor OR.
and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof, wherein:
4
Further preferred methods of the present invention are methods wherein in the compound of Formulae (1) or (2), Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, each optionally substituted with 1 to 4 Rsubstituents.
2
1
2
3
6a
7a
3
Further preferred methods of the present invention are methods wherein in the compound of Formulae (1) or (2), A is N, Z is CR, Ar is 2,4-dichlorophenyl, 2,4-dimethylphenyl or 2,4,6-trimethylphenyl, Rand Rare CH, and Ris NRR.
The present invention further comprises compounds of Formulae (1) or (2):
2
Z is N or CR;
4
Ar is selected from phenyl, naphthyl, pyridyl, pyrimidinyl, triazinyl, furanyl, thienyl, benzothienyl, benzofuranyl, 2,3-dihydrobenzofuranyl, 2,3-dihydrobenzothienyl, indanyl, 1,2-benzopyranyl, 3,4-dihydro-1,2-benzopyranyl, tetralinyl, each Ar optionally substituted with 1 to 5 Rgroups and each Ar is attached to an unsaturated carbon atom;
1
9
10
9
10
9
10
11
12
1
4
2
4
2
4
1
4
1
12
2
12
2
10
3
6
4
10
1
4
n
Ris independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, halo, CN, C–Chaloalkyl, C–Chydroxyalkyl, C–Calkoxyalkyl, C–Ccyanoalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NRR, C–Calkyl-NRR, NRCOR, OR, SH or S(O)R;
2
6
7
9
10
6
7
6
7
7
12
1
4
2
4
2
4
3
6
4
10
1
4
n
n
1
4
n
Ris selected from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Chydroxyalkyl, halo, CN, —NRR, NRCOR, —NRS(O)R, S(O)NRR, C–Chaloalkyl, —OR, SH or —S(O)R;
3
7
13
7
7
13
8
7
7
8
6
7
8
13
6
7
6a
7a
7
6
6
7
n
2
2
2
—H, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, NRR, N(OR)R, CONRR, aryl, heteroaryl and heterocyclyl, or
1
10
2
10
2
10
3
8
5
8
4
12
6
10
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkenyl, C–Ccycloalkylalkyl or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl and heterocyclyl;
Ris selected from:
4
6
7
8
7
8
7
7
7
6
7
9
7
7
7
6
7
8
7
8
7
7
7
6
7
7
9
7
7
1
10
2
10
2
10
3
6
4
12
2
1
4
2
2
n
1
10
2
10
2
10
3
6
4
12
1
4
2
2
2
n
Ris independently selected at each occurrence from: C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, NO, halo, CN, C–Chaloalkyl, NRR, NRCOR, NRCOR, COR, OR, CONRR, CO(NOR)R, COR, or S(O)R, where each such C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl and C–Ccycloalkylalkyl are optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, NO, halo, CN, NRR, NRCOR, NRCOR, COROR, CONRR, COR, CO(NOR)R, or S(O)R;
6
7
6a
7a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
R, R, Rand Rare independently selected at each occurrence from:
6
7
6a
7a
1
4
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups;
8
1
4
Ris independently selected at each occurrence from H or C–Calkyl;
9
10
1
4
3
6
Rand Rare independently selected at each occurrence from H, C–Calkyl, or C–Ccycloalkyl;
11
1
4
1
4
3
6
Ris selected from H, C–Calkyl, C–Chaloalkyl, or C–Ccycloalkyl;
12
1
4
1
4
Ris C–Calkyl or C–Chaloalkyl;
13
1
4
1
4
2
8
3
6
4
12
1
4
1
4
Ris selected from C–Calkyl, C–Chaloalkyl, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, aryl, aryl(C–Calkyl)-, heteroaryl or heteroaryl(C–Calkyl)-;
14
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
1
10
3
10
3
10
3
8
4
12
1
6
3
6
1
4
n
2
2
2
1
6
1
6
1
6
Ris selected from C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, or C–Ccycloalkylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, and C–Calkylthio, C–Calkylsulfinyl and C–Calkylsulfonyl;
15
16
15
15
1
6
3
10
4
16
n
Rand Rare independently selected at each occurrence from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, except that for S(O)R, Rcannot be H;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
aryl is phenyl or naphthyl, each optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
16
15
16
15
heteroaryl is pyridyl, pyrimidinyl, triazinyl, furanyl, pyranyl, quinolinyl, isoquinolinyl, thienyl, imidazolyl, thiazolyl, indolyl, pyrrolyl, oxazolyl, benzofuranyl, benzothienyl, benzothiazolyl, isoxazolyl, pyrazolyl, 2,3-dihydrobenzothienyl or 2,3-dihydrobenzofuranyl, each being optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
1
6
3
6
1
4
n
2
2
2
15
15
15
15
15
8
15
15
8
16
15
8
15
15
16
16
15
heterocyclyl is saturated or partially saturated heteroaryl, optionally substituted with 1 to 5 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, and CONRR;
n is independently at each occurrence 0, 1 or 2;
2
2
3
13
7
1
(1) when Z is CRand Ris H and Ris OCORand Ris H, then Ris not H, OH or SH;
2
1
2
3
3
2
5
3
2
5
6
5
3
7
3
7
3
3
(2) when Z is CRand Ris CHor CHand Ris H, and Ris H, CH, CH, CH, n-CH, i-CH, SH or SCH, then Ar is not phenyl or m-CH-phenyl;
2
2
6
7
6
7
3
2
2
(3) when Z is CRand Ris —NRSORor —SONRR, then Ris not SH; and
2
3
6
7
6a
7a
7
(4) when Z is CR, then Ris not NRR, NRRor OR.
with the provisos that:
and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein:
1
2
4
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, each optionally substituted with 1 to 4 Rsubstituents.
1
2
The present invention further provides for a pharmaceutical composition comprising a pharmaceutically acceptable carrier and a therapeutically effective amount of a compound of formula () or .
Further preferred compounds of the present invention include compounds of Formula (2) and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof.
2
4
Further preferred compounds of the present invention include compounds of formula () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl and each Ar is optionally substituted with 1 to 4 Rsubstituents.
2
3
6a
7a
7
Further preferred compounds of the present invention include compounds of formula () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ris NRRor OR.
2
4
3
6a
7a
7
Further preferred compounds of the present invention include compounds of formula () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents, and Ris NRRor OR.
1
2
2
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Z is CR.
1
4
Further preferred compounds of the present invention include compounds of formula () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl and each Ar is optionally substituted with 1 to 4 Rsubstituents.
1
2
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
1
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl); and
Ris independently selected from:
7a
—H,
5
10
3
10
3
10
1
10
2
8
3
6
4
12
5
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
Ris independently selected at each occurrence from:
6
7
6a
7a
1
4
alternatively, NRRand NRRare independently piperidine, pyrrolidine, piperazine, N-methylpiperazine, morpholine or thiomorpholine, each optionally substituted with 1–3 C–Calkyl groups.
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein:
1
2
6a
7a
1
4
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl or C–Ccycloalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, —COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl, and -aryl or heteroaryl.
Rand Rare identical and are selected from:
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein:
1
2
6a
—H,
1
10
3
10
3
10
1
10
2
8
3
6
4
12
1
10
6
14
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl, C–Calkenyl, C–Calkynyl, C–Chaloalkyl with 1–10 halogens, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Ccycloalkenyl, or C–Ccycloalkenylalkyl, each optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
Ris selected from:
7a
1
4
1
4
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Calkyl and each such C–Calkyl is substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
Ris selected from:
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein:
1
2
6a
7a
3
6
3
6
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
—C–Ccycloalkyl, each such C–Ccycloalkyl optionally substituted with 1–3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
-aryl,
-heteroaryl or
6a
7a
1
4
-heterocyclyl,
and the other of Rand Ris unsubstituted C–Calkyl.
one of Rand Ris selected from:
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein:
1
2
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
Further preferred compounds of the present invention include compounds of formula () of () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Rand Rare independently H or C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
1
2
4
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents.
1
2
4
—Ar is phenyl, pyridyl or 2,3-dihydrobenzofuranyl, and each Ar is optionally substituted with 1 to 4 Rsubstituents,
1
2
1
4
3
6
4
10
—Rand Rare independently selected from H, C–Calkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl.
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein
1
2
6a
7a
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
1
10
1
10
1
6
3
6
1
4
n
2
2
2
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Rand Rare independently H or C–Calkyl, each such C–Calkyl optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), RCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl.
1
2
1
1
4
2
4
2
4
1
4
1
12
2
12
3
6
4
10
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ris independently selected at each occurrence from H, C–Calkyl, C–Calkenyl, C–Calkynyl, halo, CN, C–Chaloalkyl, C–Chydroxyalkyl, C–Calkoxyalkyl, C–Ccycloalkyl, C–Ccycloalkylalkyl.
1
2
2
6
7
7
1
4
2
4
2
4
3
6
4
10
1
4
1
4
Further preferred compounds of the present invention include compounds formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ris selected from H, C–Calkyl, C–Calkenyl, C–Calkynyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, C–Chydroxyalkyl, halo, CN, —NRR, C–Chaloalkyl, —OR.
1
2
4
6
7
7
7
6
7
7
7
7
1
10
2
10
3
6
4
12
1
4
1
10
2
10
2
3
6
4
12
1
4
2
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ris independently selected at each occurrence from: C–Calkyl, C–Calkenyl, C–Ccycloalkyl, C–Ccycloalkylalkyl, halo, CN, C–Chaloalkyl, NRR, COR, OR, where each such C–Calkyl, C–Calkenyl, C–C–Ccycloalkyl and C–Ccycloalkylalkyl are optionally substituted with 1 to 3 substituents independently selected at each occurrence from C–Calkyl, NRR, COROR, COR.
1
2
4
6
7
1
10
1
4
Further preferred compounds of the present invention include compounds of formula () or () and isomers thereof, stereoisomeric forms thereof, or mixtures of stereoisomeric forms thereof, and pharmaceutically acceptable salt forms thereof wherein Ris independently selected at each occurrence from: H, C–Calkyl, C–Calkoxy, halo, CN and —NRR.
1
2
The present invention further provides for a pharmaceutical composition comprising a pharmaceutically acceptable carrier and a therapeutically effective amount of a compound of formula () or ().
1
2
The present invention further provides for a method of treating affective disorder, anxiety, depression, headache, irritable bowel syndrome, posttraumatic stress disorder, supranuclear palsy, immune suppression, Alzheimer's disease, gastrointestinal diseases, anorexia nervosa or other feeding disorder, drug addiction, drug or alcohol withdrawal symptoms, inflammatory diseases, cardiovascular or heart-related diseases, fertility problems, human immunodeficiency virus infections, hemorrhagic stress, obesity, infertility, head and spinal cord traumas, epilepsy, stroke, ulcers, amyotrophic lateral sclerosis, hypoglycemia or a disorder the treatment of which can be effected or facilitated by antagonizing CRF, including but not limited to disorders induced or facilitated by CRF, in mammals comprising administering to the mammal a therapeutically effective amount of a compound of formula () or ().
Many compounds of this invention have one or more asymmetric centers or planes. Unless otherwise indicated, all chiral (enantiomeric and diastereomeric) and racemic forms are included in the present invention. Many geometric isomers of olefins, C═N double bonds, and the like can also be present in the compounds, and all such stable isomers are contemplated in the present invention. The compounds may be isolated in optically active or racemic forms. It is well known in the art how to prepare optically active forms, such as by resolution of racemic forms or by synthesis from optically active starting materials. All chiral, (enantiomeric and diastereomeric) and racemic forms and all geometric isomeric forms of a structure are intended, unless the specific stereochemistry or isomer form is specifically indicated.
The term “alkyl” includes both branched and straight-chain alkyl having the specified number of carbon atoms. Commonly used abbreviations have the following meanings: Me is methyl, Et is ethyl, Pr is propyl, Bu is butyl. As is conventional, in a chemical structure drawing, a straight single bond attached to an atom at one end but with no atom designation at the other end indicates the presence of a methyl group at the unattached end of the bond. The prefix “n” means a straight chain alkyl. The prefix “c” means a cycloalkyl. The prefix “(S)” means the S enantiomer and the prefix “(R)” means the R enantiomer. Alkenyl” includes hydrocarbon chains of either a straight or branched configuration and one or more unsaturated carbon—carbon bonds which may occur in any stable point along the chain, such as ethenyl, propenyl, and the like. “Alkynyl” includes hydrocarbon chains of either a straight or branched configuration and one or more triple carbon—carbon bonds which may occur in any stable point along the chain, such as ethynyl, propynyl and the like. “Haloalkyl” is intended to include both branched and straight-chain alkyl having the specified number of carbon atoms, substituted with 1 or more halogen; “alkoxy” represents an alkyl group of indicated number of carbon atoms attached through an oxygen bridge; “cycloalkyl” is intended to include saturated ring groups, including mono-,bi- or poly-cyclic ring systems, such as cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, and so forth. “Halo” or “halogen” includes fluoro, chloro, bromo, and iodo.
The term “substituted”, as used herein, means that one or more hydrogen on the designated atom is replaced with a selection from the indicated group, provided that the designated atom's normal valency is not exceeded, and that the substitution results in a stable compound. When a substitent is keto (i.e., ═O), then 2 hydrogens on the atom are replaced.
Combinations of substituents and/or variables are permissible only if such combinations result in stable compounds. By “stable compound” or “stable structure” is meant a compound that is sufficiently robust to survive isolation to a useful degree of purity from a reaction mixture, and formulation into an efficacious therapeutic agent.
The term “appropriate amino acid protecting group” means any group known in the art of organic synthesis for the protection of amine or carboxylic acid groups. Such amine protecting groups include those listed in Greene and Wuts, “Protective Groups in Organic Synthesis” John Wiley & Sons, New York (1991) and “The Peptides: Analysis, Synthesis, Biology, Vol. 3, Academic Press, New York (1981), the disclosure of which is hereby incorporated by reference. Any amine protecting group known in the art can be used. Examples of amine protecting groups include, but are not limited to, the following: 1) acyl types such as formyl, trifluoroacetyl, phthalyl, and p-toluenesulfonyl; 2) aromatic carbamate types such as benzyloxycarbonyl (Cbz) and substituted benzyloxycarbonyls, 1-(p-biphenyl)-1-methylethoxycarbonyl, and 9-fluorenylmethyloxycarbonyl (Fmoc); 3) aliphatic carbamate types such as tert-butyloxycarbonyl (Boc), ethoxycarbonyl, diisopropylmethoxycarbonyl, and allyloxycarbonyl; 4) cyclic alkyl carbamate types such as cyclopentyloxycarbonyl and adamantyloxycarbonyl; 5) alkyl types such as triphenylmethyl and benzyl; 6) trialkylsilane such as trimethylsilane; and 7) thiol containing types such as phenylthiocarbonyl and dithiasuccinoyl.
The term “pharmaceutically acceptable salts” includes acid or base salts of the compounds of Formulae (1) and (2). Examples of pharmaceutically acceptable salts include, but are not limited to, mineral or organic acid salts of basic residues such as amines; alkali or organic salts of acidic residues such as carboxylic acids; and the like.
Remington's Pharmaceutical Sciences,
Pharmaceutically acceptable salts of the compounds of the invention can be prepared by reacting the free acid or base forms of these compounds with a stoichiometric amount of the appropriate base or acid in water or in an organic solvent, or in a mixture of the two; generally, nonaqueous media like ether, ethyl acetate, ethanol, isopropanol, or acetonitrile are preferred. Lists of suitable salts are found in 17th ed., Mack Publishing Company, Easton, Pa., 1985, p. 1418, the disclosure of which is hereby incorporated by reference.
“Prodrugs” are considered to be any covalently bonded carriers which release the active parent drug of formula (I) or (II) in vivo when such prodrug is administered to a mammalian subject. Prodrugs of the compounds of formula (I) and (II) are prepared by modifying functional groups present in the compounds in such a way that the modifications are cleaved, either in routine manipulation or in vivo, to the parent compounds. Prodrugs include compounds wherein hydroxy, amine, or sulfhydryl groups are bonded to any group that, when administered to a mammalian subject, cleaves to form a free hydroxyl, amino, or sulfhydryl group, respectively. Examples of prodrugs include, but are not limited to, acetate, formate and benzoate derivatives of alcohol and amine functional groups in the compounds of formulas (I) and (II); and the like.
The term “therapeutically effective amount” of a compound of this invention means an amount effective to antagonize abnormal level of CRF or treat the symptoms of affective disorder, anxiety or depression in a host.
Syntheses
Some compounds of Formula (1) may be prepared from intermediate compounds of Formula (7), using the procedures outlined in Scheme 1:
2
3
3
5
3
3
5
Compounds of Formula (7) (where Y is O) may be treated with a halogenating agent or sulfonylating agent in the presence or absence of a base in the presence or absence of an inert solvent at reaction temperatures ranging from −80° C. to 250° C. to give products of Formula (8) (where X is halogen, alkanesulfonyloxy, arylsulfonyloxy or haloalkane-sulfonyloxy). Halogenating agents include, but are not limited to, SOCl, POCl, PCl, PCl, POBr, PBror PBr. Sulfonylating agents include, but are not limited to, alkanesulfonyl halides or anhydrides (such as methanesulfonyl chloride or methanesulfonic acid anhydride), arylsulfonyl halides or anhydrides (such as p-toluenesulfonyl chloride or anhydride) or haloalkylsulfonyl halides or anhydrides (preferably trifluoromethanesulfonic anhydride). Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine or triethylamine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from −20° C. to 100° C.
3
3
3
7
7
2
Compounds of Formula (8) may be reacted with compounds of Formula RH (where Ris defined as above except Ris not SH, COR, COR, aryl or heteroaryl) in the presence or absence of a base in the presence or absence of an inert solvent at reaction temperatures ranging from −80 to 250° C. to generate compounds of Formula (1). Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons) (preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bicarbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from 0° C. to 140° C.
Scheme 2 delineates the procedures for converting intermediate compounds of Formula (7) (where Y is S) to some compounds of Formula (1).
13
13
13
Compounds of Formula (7) (where Y is S) may be treated with an alkylating agent RX (where Ris defined as above, except Ris not aryl or heteroaryl) in the presence or absence of a base in the presence or absence of an inert solvent at reaction temperatures ranging from −80° C. to 250° C. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal hydroxides, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (prefereably N,N-di-isopropyl-N-ethyl amine or triethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from −80° C. to 100° C.
3
13
3
3
13
3
13
3
13
3
n
n
Comprehensive Organic Synthesis
Compounds of Formula (12) (Formula (1) where Ris SR) may then be reacted with compounds of Formula RH to give compounds of Formula (1), using the same conditions and reagents as were used for the conversion of compounds of Formula (8) to compounds of Formula (1) as outlined for Scheme 1 above. Alternatively, compounds of Formula (12) (Formula (1) where Ris SR) may be oxidized to compounds of Formula (13) (Formula (1) where Ris S(O)R, n is 1,2) by treatment with an oxidizing agent in the presence of an inert solvent at temperatures ranging from −80° C. to 250° C. Oxidizing agents include, but are not limited to, hydrogen peroxide, alkane or aryl peracids (preferably peracetic acid or m-chloroperbenzoic acid), dioxirane, oxone, or sodium periodate. Inert solvents may include, but are not limited to, alkanones (3 to 10 carbons, preferably acetone), water, alkyl alcohols (1 to 6 carbons), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane) or combinations thereof. The choices of oxidant and solvent are known to those skilled in the art (cf. Uemura, S., Oxidation of Sulfur, Selenium and Tellurium, in , Trost, B. M. ed., (Elmsford, N.Y.: Pergamon Press, 1991), 7, 762–769). Preferred reaction temperatures range from −20° C. to 100° C. Compounds of Formula (13) (Formula (1) where Ris S(O)Rn is 1,2) may then be reacted with compounds of Formula RH to give compounds of Formula (1), using the same conditions and reagents as were used for the conversion of compounds of Formula (8) to compounds of Formula (1) as outlined for Scheme (1) above.
3
8
7
7
8
6
7
8
13
6
7
8
7
2
2
2
Compounds of Formula (1), where Rmay be —NRCOR, —N(COR), —NRCONRR, —NRCOR, —NRR, NRSOR, may be prepared from compounds of Formula (7), where Y is NH, by the procedures depicted in Scheme 3.
3
8
7
7
8
6
7
8
13
6
7
8
7
2
2
2
1
10
1
10
2
8
3
6
4
12
1
4
1
4
1
4
1
10
1
10
2
8
3
6
4
12
1
4
1
4
1
4
1
10
1
10
2
8
3
6
4
12
1
4
1
4
1
4
Reaction of compounds of Formula (7), where Y is NH, with alkylating agents, sulfonylating agents or acylating agents or sequential reactions with combinations thereof, in the presence or absence of a base in an inert solvent at reaction temperatures ranging from −80° C. to 250° C. may afford compounds of Formula (1), where Rmay be —NRCOR, —N(COR), —NRCONRR, —NRCOR, —NRR, —NRSOR. Alkylating agents may include, but are not limited to, C–Calkyl -halides, -tosylates, -mesylates or -triflates; C–Chaloalkyl(1–10 halogens)-halides, -tosylates, -mesylates or -triflates; C–Calkoxyalkyl-halides, -tosylates, -mesylates or -triflates; C–Ccycloalkyl-halides, -tosylates, -mesylates or -triflates; C–Ccycloalkylalkyl-halides, -tosylates, -mesylates or -triflates; aryl(C–Calkyl)-halides, -tosylates, -mesylates or -triflates; heteroaryl(C–Calkyl)-halides, -tosylates, -mesylates or -triflates; or heterocyclyl(C–Calkyl)-halides, -tosylates, -mesylates or -triflates. Acylating agents may include, but are not limited to, C–Calkanoyl halides or anhydrides, C–Chaloalkanoyl halides or anhydrides with 1–10 halogens, C–Calkoxyalkanoyl halides or anhydrides, C–Ccycloalkanoyl halides or anhydrides, C–Ccycloalkylalkanoyl halides or anhydrides, aroyl halides or anhydrides, aryl(C–C) alkanoyl halides or anhydrides, heteroaroyl halides or anhydrides, heteroaryl(C–C) alkanoyl halides or anhydrides, heterocyclylcarboxylic acid halides or anhydrides or heterocyclyl(C–C) alkanoyl halides or anhydrides. Sulfonylating agents include, but are not limited to, C–Calkylsulfonyl halides or anhydrides, C–Chaloalkylsulfonyl halides or anhydrides with 1–10 halogens, C–Calkoxyalkylsulfonyl halides or anhydrides, C–Ccycloalkylsulfonyl halides or anhydrides, C–Ccycloalkylalkylsulfonyl halides or anhydrides, arylsulfonyl halides or anhydrides, aryl(C–Calkyl)-, heteroarylsulfonyl halides or anhydrides, heteroaryl(C–Calkyl)sulfonyl halides or anhydrides, heterocyclylsulfonyl halides or anhydrides or heterocyclyl(C–Calkyl)sulfonyl halides or anhydrides. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (prefereably di-isopropylethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from 0° C. to 100° C.
2
Scheme 4 delineates procedures, which may be employed to prepare intermediate compounds of Formula (7), where Y is O, S and Z is CR.
2
2
b
2
b
Compounds of the formula ArCHCN are reacted with compounds of the formula RCOR, where Ris defined above and Ris halogen, cyano, lower alkoxy (1 to 6 carbons) or lower alkanoyloxy (1 to 6 carbons), in the presence of a base in an inert solvent at reaction temperatures ranging from −78° C. to 200° C. to afford compounds of Formula (3). Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal hydroxides, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), water, dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from 0° C. to 100° C.
c
Compounds of Formula (3) may be treated with hydrazine-hydrate in the presence of an inert solvent at temperatures ranging from 0° C. to 200° C., preferably 70° C. to 150° C., to produce compounds of Formula (4). Inert solvents may include, but are not limited to, water, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Compounds of Formula (4) may be reacted with compounds of Formula (5) (where Ris alkyl (1–6 carbons)) in the presence or absence of an acid in the presence of an inert solvent at temperatures ranging from 0° C. to 200° C. to produce compounds of Formula (6). Acids may include, but are not limited to alkanoic acids of 2 to 10 carbons (preferably acetic acid), haloalkanoic acids (2–10 carbons, 1–10 halogens, such as trifluoroacetic acid), arylsulfonic acids (preferably p-toluenesulfonic acid or benzenesulfonic acid), alkanesulfonic acids of 1 to 10 carbons (preferably methanesulfonic acid), hydrochloric acid, sulfuric acid or phosphoric acid. Stoichiometric or catalytic amounts of such acids may be used. Inert solvents may include, but are not limited to, water, alkanenitriles (1 to 6 carbons, preferably acetonitrile), halocarbons of 1 to 6 carbons and 1 to 6 halogens (preferably dichloromethane or chloroform), alkyl alcohols of 1 to 10 carbons (preferably ethanol), dialkyl ethers (4 to 12 carbons, preferably diethyl ether or di-isopropylether) or cyclic ethers such as dioxan or tetrahydrofuran. Preferred temperatures range from ambient temperature to 100° C.
d
d
2
Compounds of Formula (6) may be converted to intermediate compounds of Formula (7) by treatment with compounds C═Y(R)(where Y is O or S and Ris halogen (preferably chlorine), alkoxy (1 to 4 carbons) or alkylthio (1 to 4 carbons)) in the presence or absence of a base in an inert solvent at reaction temperatures from −50° C. to 200° C. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkali metal carbonates, alkali metal hydroxides, trialkyl amines (preferably N,N-diisopropyl-N-ethyl amine or triethylamine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred temperatures are 0° C. to 150° C.
Intermediate compounds of Formula (7), where Z is N, may be synthesized according the methods
2
2
3
2
q
q
2
Compounds of ArCHCN are reacted with compounds of Formula RCHN(where Ris a phenyl group optionally substituted by H, alkyl (1 to 6 carbons) or alkoxy (1 to 6 carbons) in the presence or absence of a base in an inert solvent at temperatures ranging from 0° C. to 200° C. to generate compounds of Formula (9). Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide, sodium ethoxide or potassium t-butoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal hydroxides, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine or triethylamine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from ambient temperature to 100° C. Compounds of Formula (9) may be treated with a reducing agent in an inert solvent at 100° C. to 100° C. to afford products of Formula (10). Reducing agents include, but are not limited to, (a) hydrogen gas in combination with noble metal catalysts such as Pd-on-carbon, PtO, Pt-on-carbon, Rh-on-alumina or Raney nickel, (b) alkali metals (preferably sodium) in combination with liquid ammonia or (c) ceric ammonium nitrate. Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), water, dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). The preferred reaction temperatures are −50° C. to 60° C. Compounds of Formula (9) are then converted to compounds of Formula (7) (where Z is N) via intermediates of Formula (11) using the reagents and reaction conditions outlined in Scheme 4 for the conversion of compounds of Formula (4) to compounds of Formula (7) (where Z is CR).
Compounds of Formula (1) may also be prepared from compounds of Formula (7) (where Y is O, S and Z is defined above) as outlined in Scheme 6:
3
2
5
Compounds of Formula (7) may be reacted with compounds of Formula RH in the presence of a dehydrating agent in an inert solvent at reaction temperatures ranging from 0° C. to 250° C. Dehydrating agents include, but are not limited to, PO, molecular sieves or inorganic or organic acids. Acids may include, but are not limited to alkanoic acids of 2 to 10 carbons (preferably acetic acid), arylsulfonic acids (preferably p-toluenesulfonic acid or benzenesulfonic acid), alkanesulfonic acids of 1 to 10 carbons (preferably methanesulfonic acid), hydrochloric acid, sulfuric acid or phosphoric acid. Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably glyme or diglyme), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or halocarbons of 1 to 10 carbons and 1 to 10 halogens (preferably chloroform). Preferred reaction temperatures range from ambient temperature to 150° C.
Some compounds of Formula (1) (where A is N) may also be prepared by the methods shown in Scheme 7:
3
e
e
3
Intermediate compounds of Formula (14), where Z is defined above, may be reacted with compounds of Formula RC(OR), where Rmay be alkyl (1 to 6 carbons) in the presence or absence of an acid in an inert solvent at temperatures ranging from 0° C. to 250° C. Acids may include, but are not limited to alkanoic acids of 2 to 10 carbons (preferably acetic acid), arylsulfonic acids (preferably p-toluenesulfonic acid or benzenesulfonic acid), alkanesulfonic acids of 1 to 10 carbons (preferably methanesulfonic acid), hydrochloric acid, sulfuric acid or phosphoric acid. Stoichiometric or catalytic amounts of such acids may be used. Inert solvents may include, but are not limited to, lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from 50° C. to 150° C.
Intermediate compounds of Formula (7) may also be synthesized by the reactions displayed in Scheme 8.
6
7
3
3
2
2
2
3
4
2
3
2
2
2
3
2
Compounds of Formula (15), (where Y is OH, SH, NRR; Z is defined above, X is Br, Cl, I, OSCFor B(OR″″)and R″″ is H or alkyl (1 to 6 carbons)) may be reacted with a compound of Formula ArM (where M is halogen, alkali metal, ZnCl, ZnBr, ZnI, MgBr, MgCl, MgI, CeCl, CeBror copper halides) in the presence or absence of an organometallic catalyst in the presence or absence of a base in an inert solvents at temperatures ranging from −100° C. to 200° C. Those skilled in the art will recognize that the reagents ArM may be generated in situ. Organometallic catalysts include, but are not limited to, palladium phosphine complexes (such as Pd(PPh)), palladium halides or alkanoates (such as PdCl(PPh)or Pd(OAc)) or nickel complexes (such as NiCl(PPh)). Bases may include, but are not limited to, alkali metal carbonates or trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine or triethylamine). Inert solvents may include, but are not limited to, dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or water. Preferred reaction temperatures range from 80° C. to 100° C.
Comprehensive Organic Synthesis
Comprehensive Organic Synthesis
Comprehensive Organic Synthesis
2
The choices of M and X are known to those skilled in the art (of Imamoto, T., Organocerium Reagents in , Trost, B. M. ed., (Elmsford, N.Y.: Pergamon Press, 1991), 1, 231–250; Knochel, P., Organozinc, Organocadmium and Organomercury Reagents in , Trost, B. M. ed., (Elmsford, N.Y.: Pergamon Press, 1991), 1, 211–230; Knight, D. W., Coupling Reactions between spCarbon Centers, in , Trost, B. M. ed., (Elmsford, N.Y.: Pergamon Press, 1991), 3, 481–520).
Compounds of Formula (1) may also be prepared using the methods shown in Scheme 9.
1
3
3
3
2
2
2
3
4
2
3
2
2
2
3
2
Comprehensive Organic Synthesis
Compounds of Formula (16), where A, Z, Rand Rare defined above and X is Br, Cl, I, OSCFor B(OR″″)and R″″ is H or alkyl (1 to 6 carbons)) may be reacted with a compound of Formula ArM (where M is halogen, alkali metal, ZnCl, ZnBr, ZnI, MgBr, MgCl, MgI, CeCl, CeBror copper halides) in the presence or absence of an organometallic catalyst in the presence or absence of a base in an inert solvents at temperatures ranging from −100° C. to 200° C. Those skilled in the art will recognize that the reagents ArM may be generated in situ (see the above references in ). Organometallic catalysts include, but are not limited to, palladium phosphine complexes (such as Pd(PPh)), palladium halides or alkanoates (such as PdCl(PPh)or Pd(OAc)) or nickel complexes (such as NiCl(PPh)). Bases may include, but are not limited to, alkali metal carbonates or trialkyl amines (preferably N,N-diisopropyl-N-ethyl amine or triethylamine). Inert solvents may include, but are not limited to, dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or water. Preferred reaction temperatures range from 80° C. to 100° C.
2
1
2
Intermediate compounds of Formula (7)(where Y is O, S, NH, Z is CRand R, Rand Ar are defined as above) may be prepared as illustrated in Scheme 10.
2
2
Compounds of Formula (3) may be reacted with compounds of Formula HNNH(C═Y)NH, where Y is O, S or NH, in the presence or absence of a base or acid in an inert solvent at temperatures from 0° C. to 250° C. to produce compounds of Formula (17). Acids may include, but are not limited to alkanoic acids of 2 to 10 carbons (preferably acetic acid), arylsulfonic acids (preferably p-toluenesulfonic acid or benzenesulfonic acid), alkanesulfonic acids of 1 to 10 carbons (preferably methanesulfonic acid), hydrochloric acid, sulfuric acid or phosphoric acid. Stoichiometric or catalytic amounts of such acids may be used. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine or triethylamine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 6 carbons), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane).
3
e
e
3
Preferred reaction temperatures range from 0° C. to 150° C. Compounds of Formula (17) may then be reacted with compounds of Formula RC(OR), where Rmay be alkyl (1 to 6 carbons) in the presence or absence of an acid in an inert solvent at temperatures ranging from 0° C. to 250° C. Acids may include, but are not limited to alkanoic acids of 2 to 10 carbons (preferably acetic acid), arylsulfonic acids (preferably p-toluenesulfonic acid or benzenesulfonic acid), alkanesulfonic acids of 1 to 10 carbons (preferably methanesulfonic acid), hydrochloric acid, sulfuric acid or phosphoric acid. Stoichiometric or catalytic amounts of such acids may be used. Inert solvents may include, but are not limited to, lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from 50° C. to 150° C.
3
7
7
8
7
6
7
3
7
8
7
6
7
2
2
2
2
In Scheme 11, the procedures which may be used to convert compounds of Formula (1), where Ris COR, COR, NRCORand CONRR, to other compounds of Formula (1), where Ris CH(OH)R, CHOH, NRCHRand CHNRRby treatment with a reducing agent in an inert solvent at temperatures ranging from −80° C. to 250° C.
Reducing agents include, but are not limited to, alkali metal or alkaline earth metal borohydrides (preferably lithium or sodium borohydride), borane, dialkylboranes (such as di-isoamylborane), alkali metal aluminum hydrides (preferably lithium aluminum hydride), alkali metal (trialkoxy)aluminum hydrides, or dialkyl aluminum hydrides (such as di-isobutylaluminum hydride). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 6 carbons), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from −80° C. to 100° C.
3
7
7
3
7
7
2
2
In Scheme 12, the procedures are shown which may be used to convert compounds of Formula (1), where Ris CORor COR, to other compounds of Formula (1), where Ris C(OH)(R)by treatment with a reagent of Formula RM in an inert solvent at temperatures ranging from −80° C. to 250° C.
2
2
M is halogen, alkali metal, ZnCl, ZnBr, ZnI, MgBr, MgCl, MgI, CeCl, CeBror copper halides. Inert solvents may include, but are not limited to, dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from −80° C. to 100° C.
3
8
7
7
8
6
7
8
13
6
7
8
7
2
2
2
Compounds of Formula (1), where Rmay be —NRCOR, —N(COR), —NRCONRR, —NRCOR, —NRR, —NRSOR, may be synthesized as depicted in Scheme 13.
1
Reaction of compounds of Formula (18), where R and Rare defined above, with compounds of Formula (4) or (10) in the presence or absence of base in an inert solvent may produce compounds of Formula (19) at temperatures ranging from −50° C. to 250° C. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons) (preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (prefereably di-isopropylethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from 0° C. to 100° C.
3
8
7
7
8
6
7
8
13
6
7
8
7
2
2
2
1
10
1
10
2
8
3
6
4
12
1
4
1
4
1
4
1
10
1
10
2
8
3
6
4
12
1
4
1
4
1
4
1
10
1
10
2
8
3
6
4
12
1
4
1
4
1
4
Compounds of Formula (19) may then be reacted with alkylating agents, sulfonylating agents or acylating agents or sequential reactions with combinations thereof, in the presence or absence of a base in an inert solvent at reaction temperatures ranging from −80° C. to 250° C. may afford compounds of Formula (1), where Rmay be —NRCOR, —N(COR), —NRCONRR, —NRCOR, —NRR, —NRSOR. Alkylating agents may include, but are not limited to, C–Calkyl -halides, -tosylates, -mesylates or -triflates; C–Chaloalkyl(1–10 halogens)-halides, -tosylates, -mesylates or -triflates; C–Calkoxyalkyl-halides, -tosylates, -mesylates or -triflates; C–Ccycloalkyl-halides, -tosylates, -mesylates or -triflates; C–Ccycloalkylalkyl-halides, -tosylates, -mesylates or -triflates; aryl(C–Calkyl)-halides, -tosylates, -mesylates or -triflates; heteroaryl(C–Calkyl)-halides, -tosylates, -mesylates or -triflates; or heterocyclyl(C–Calkyl)-halides, -tosylates, mesylates or -triflates. Acylating agents may include, but are not limited to, C–Calkanoyl halides or anhydrides, C–Chaloalkanoyl halides or anhydrides with 1–10 halogens, C–Calkoxyalkanoyl halides or anhydrides, C–Ccycloalkanoyl halides or anhydrides, C–Ccycloalkylalkanoyl halides or anhydrides, aroyl halides or anhydrides, aryl(C–C) alkanoyl halides or anhydrides, heteroaroyl halides or anhydrides, heteroaryl(C–C) alkanoyl halides or anhydrides, heterocyclylcarboxylic acid halides or anhydrides or heterocyclyl(C–C) alkanoyl halides or anhydrides. Sulfonylating agents include, but are not limited to, C–Calkylsulfonyl halides or anhydrides, C–Chaloalkylsulfonyl halides or anhydrides with 1–10 halogens, C–Calkoxyalkylsulfonyl halides or anhydrides, C–Ccycloalkylsulfonyl halides or anhydrides, C–Ccycloalkylalkylsulfonyl halides or anhydrides, arylsulfonyl halides or anhydrides, aryl(C–Calkyl)-, heteroarylsulfonyl halides or anhydrides, heteroaryl(C–Calkyl)sulfonyl halides or anhydrides, heterocyclylsulfonyl halides or anhydrides or heterocyclyl(C–Calkyl)sulfonyl halides or anhydrides. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (prefereably di-isopropylethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic-ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from 0° C. to 100° C.
Compounds of Formula (1), where A is CR and R is defined above, may be synthesized by the methods depicted in Scheme 14.
1
3
Compounds of Formula (4) or (10) may be treated with compounds of Formula (20), where Rand Rare defined above in the presence or absence of base in an inert solvent at temperatures ranging from 0° C. to 250° C. to give compounds of Formula (1), where A is CR and R is defined above. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably di-isopropylethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from 0° C. to 100° C. Alternatively, compounds of Formula (1) where A is CR and R is defined above, may be synthesized through intermediates (22) and (23).
1
2
3
3
5
3
3
5
Compounds of Formula (4) or (10) may be treated with compounds of Formula (21), where Ris defined above and Re is alkyl (1–6 carbons), in the presence or absence of base in an inert solvent at temperatures ranging from 0° C. to 250° C. to give compounds of Formula (1), where A is CR and R is defined above. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (prefereably di-isopropylethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide) or aromatic hydrocarbons (preferably benzene or toluene). Preferred reaction temperatures range from 0° C. to 100° C. Compounds of Formula (22) may be treated with a halogenating agent or sulfonylating agent in the presence or absence of a base in the presence or absence of an inert solvent at reaction temperatures ranging from −80° C. to 250° C. to give products of Formula (23) (where X is halogen, alkanesulfonyloxy, arylsulfonyloxy or haloalkane-sulfonyloxy). Halogenating agents include, but are not limited to, SOCl, POCl, PCl, PCl, POBr, PBror PBr. Sulfonylating agents include, but are not limited to, alkanesulfonyl halides or anhydrides (such as methanesulfonyl chloride or methanesulfonic acid anhydride), arylsulfonyl halides or anhydrides (such as p-toluenesulfonyl chloride or anhydride) or haloalkylsulfonyl halides or anhydrides (preferably trifluoromethanesulfonic anhydride). Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine or triethylamine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from −20° C. to 100° C.
3
3
3
7
7
2
Compounds of Formula (23) may be reacted with compounds of Formula RH (where Ris defined as above except Ris not SH, COR, COR, aryl or heteroaryl) in the presence or absence of a base in the presence or absence of an inert solvent at reaction temperatures ranging from −80° C. to 250° C. to generate compounds of Formula (1). Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal carbonates, alkali metal bicarbonates, alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, alkyl alcohols (1 to 8 carbons, preferably methanol or ethanol), lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from 0° C. to 140° C.
Some compounds of Formula (1) may also be prepared using the methods shown in Scheme 15.
c
e
e
d
1
1
d
A compound of Formula (24) (Ris a lower alkyl group and Ar is defined as above) may be reacted with hydrazine in the presence or absence of an inert solvent to afford an intermediate of Formula (25), where Ar is defined as above. The conditions employed are similar to those used for the preparation of intermediate of Formula (4) from compound of Formula (3) in Scheme 4. Compounds of Formula (25), where A is N, may be reacted with reagents of the formula RC(═NH)OR, where Ris defined above and Ris a lower alkyl group) in the presence or absence of an acid in an inert solvent, followed by reaction with a compound of formula YisC(R)2 (where Y is O or S and Ris halogen (preferably chlorine), alkoxy (1 to 4 carbons) or alkylthio (1 to 4 carbons)) in the presence or absence of a base in an inert solvent to give compounds of Formula (27) (where A is N and Y is O, S). The conditions for these transformations are the same as those employed for the conversions of compound of Formula (4) to compound of Formula (7) in Scheme 4.
1
1
3
2
2
c
c
Alternatively, compounds of Formula (25), where A is CR, may be reacted with compounds of the formula R(C═O)CHR(C═Y)OR(where Rand R are defined as above and Ris a lower alkyl group) to give a compound of Formula (27) (where A is CR) using conditions similar to those employed for the conversion of compounds of Formula (21) to compounds of Formula (22) in Scheme 14. Intermediates of Formula (27) (where Y is O) may be treated with halogenating agents or sulfonylating agents in the presence or absence of a base in an inert solvent, followed by reaction with RH or RH in the presence or absence of a base in an inert solvent to give compounds of Formula (1) (where Z is CR).
3
2
2
3
3
2
It will be recognized by those skilled in the art that various combinations of halogenating agents, sulfonylating agents, RH or RH may be used in different orders of reaction sequences in Scheme 15 to afford compounds of Formula (1). For example, in some cases, it may be desirable to react compounds with stoichiometric amounts of halogenating agents or sulfonylating agents, react with RH (or RH), then repeat the reaction with halogenating agents or sulfonylating agents and react with RH (or RH) to give compounds of Formula (1). The reaction conditions and reagents used for these conversions are similar to the ones employed for the conversion of intermediate compounds of Formulae (22) to (23) to (1) in Scheme 14 (for A is CR) or the conversion of intermediate compounds of Formulae (7) to (8) to (1) in Scheme 1 (where A is N).
f
f
3
Alternatively, compounds of Formula (27) (where Y is S) may be converted to compounds of Formula (1) in Scheme 15. Intermediate compounds of Formula (27) may be alkylated with a compound RX (where Ris lower alkyl and X is halogen, alkanesulfonyloxy or haloalkanesulfonyloxy) in an inert solvent, (then optionally oxidized with an oxidizing agent in an inert solvent) and then reacted with RH in the presence or absence of a base in an inert solvent to give a compound of Formula (1). The conditions and reagents employed are similar to those used in the conversion of intermediate compounds of Formulae (7) to (12) (or to (13)) to compounds of Formula (1) in Scheme 2.
2
2
c
3
c
1
1
Compounds of Formula (1) may be prepared from compounds of Formula (24), using an alternate route as depicted in Scheme 15. Compounds of Formula (24) may be converted to compounds of Formula (27) via reaction with compounds of formula NHNH(C═NH)NHin the presence or absence of an acid in an inert solvent, followed by reaction with compounds RC(OR)(where Ris lower alkyl and Ris defined as above), using the conditions employed for the conversion of compounds of Formulae (3) to (17) to (7) in Scheme 10.
Some compounds of Formula (2) may be prepared by the methods illustrated in Scheme 16.
14
14
3
f
f
3
Compounds of Formula (27b) may be treated with various alkylating agents RX (where Ris defined above and X is halogen, alkanesulfonyloxy or haloalkanesulfonyloxy) in the presence or absence of a base in an inert solvent to afford structures of Formula (28). Compounds of Formula (28) (Y is O) may then be converted to compounds of Formula (2) by treatment with halogenating agents or sulfonylating agents in the presence or absence of a base in an inert solvent, followed by reaction with RH in the presence or absence of a base in an inert solvent to give compounds of Formula (2). The reaction conditions used for these conversions are similar to the ones employed for the conversion of intermediate compounds (22) to (23) to (1) in Scheme 14 (for A is CR) or the conversion of intermediate compounds of Formulae (7) to (8) to (1) in Scheme 1 (where A is N). Alternatively, compounds of Formula (28) (Y is S) may be alkylated with a compound RX (where Ris lower alkyl and X is halogen, alkanesulfonyloxy or haloalkanesulfonyloxy) in an inert solvent, (then optionally oxidized with an oxidizing agent in an inert solvent) and then reacted with RH in the presence or absence of a base in an inert solvent to give a compound of Formula (1). The conditions and reagents employed are similar to those used in the conversion of intermediate compounds of Formulae (7) to (12) (or to (13)) to compounds of Formula (1) in Scheme 2.
14
14
7
Compounds of Formula (1), where Z is COH, may be converted to compounds of Formula (2) as illustrated in Scheme 16. Treatment with various alkylating agents RX (where Ris defined above and X is halogen, alkanesulfonyloxy or haloalkanesulfonyloxy) in the presence or absence of a base in an inert solvent to afford structures (2). It will be recognized by one skilled in the art that the methods used in Scheme 16 may also be used to prepare compounds of Formula (1) where Z is COR.
For Scheme 16, the terms “base” and “inert solvent” may have the meanings given below. Bases may include, but are not limited to, alkali metal hydrides (preferably sodium hydride), alkali metal alkoxides (1 to 6 carbons)(preferably sodium methoxide or sodium ethoxide), alkaline earth metal hydrides, alkali metal dialkylamides (preferably lithium di-isopropylamide), alkali metal bis(trialkylsilyl)amides (preferably sodium bis(trimethylsilyl)amide), trialkyl amines (preferably N,N-di-isopropyl-N-ethyl amine or triethylamine) or aromatic amines (preferably pyridine). Inert solvents may include, but are not limited to, lower alkanenitriles (1 to 6 carbons, preferably acetonitrile), dialkyl ethers (preferably diethyl ether), cyclic ethers (preferably tetrahydrofuran or 1,4-dioxane), N,N-dialkylformamides (preferably dimethylformamide), N,N-dialkylacetamides (preferably dimethylacetamide), cyclic amides (preferably N-methylpyrrolidin-2-one), dialkylsulfoxides (preferably dimethylsulfoxide), aromatic hydrocarbons (preferably benzene or toluene) or haloalkanes of 1 to 10 carbons and 1 to 10 halogens (preferably dichloromethane). Preferred reaction temperatures range from −20° C. to 100° C.
3
Analytical data were recorded for the compounds described below using the following general procedures. Proton NMR spectra were recorded on an IBM-Bruker FT-NMR (300 MHz); chemical shifts were recorded in ppm (δ) from an internal tetramethysilane standard in deuterochloroform or deuterodimethylsulfoxide as specified below. Mass spectra (MS) or high resolution mass spectra (HRMS) were recorded on a Finnegan MAT 8230 spectrometer (using chemi-ionization (CI) with NHas the carrier gas or gas chromatography (GC) as specified below) or a Hewlett Packard 5988A model spectrometer. Melting points were recorded on a Buchi Model 510 melting point apparatus and are uncorrected. Boiling points are uncorrected. All pH determinations during workup were made with indicator paper.
Purification of Laboratory Chemicals,
Reagents were purchased from commercial sources and, where necessary, purified prior to use according to the general procedures outlined by D. Perrin and W. L. F. Armarego, 3rd ed., (New York: Pergamon Press, 1988). Chromatography was performed on silica gel using the solvent systems indicated below. For mixed solvent systems, the volume ratios are given. Otherwise, parts and percentages are by weight.
The following examples are provided to describe the invention in further detail. These examples, which set forth the best mode presently contemplated for carrying out the invention, are intended to illustrate and not to limit the invention.
4
3
Sodium pellets (9.8 g, 0.43 mol) were added portionwise to a solution of 2,4-dimethylphenylacetonitrile (48 g, 0.33 mol) in ethyl acetate (150 mL) at ambient temperature. The reaction mixture was heated to reflux temperature and stirred for 16 hours. The resulting suspension was cooled to room temperature and filtered. The collected precipitate was washed with copious amounts of ether and then air-dried. The solid was dissolved in water and a 1N HCl solution was added until the pH=5−6. The mixture was extracted with ethyl acetate (3×200 mL); the combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo to afford a white solid (45.7 g, 74% yield): NMR (CDCl,300 MHz):; CI-MS: 188 (M+H).
4
3
A mixture of 1-cyano-1-(2,4-dimethylphenyl)propan-2-one (43.8 g, 0.23 mol), hydrazine-hydrate (22 mL, 0.46 mol), glacial acetic acid (45 mL, 0.78 mol) and toluene (500 mL) were stirred at reflux temperature for 18 hours in an apparatus fitted with a Dean-Stark trap. The reaction mixture was cooled to ambient temperature and solvent was removed in vacuo. The residue was dissolved in 6N HCl and the resulting solution was extracted with ether three times. A concentrated ammonium hydroxide solution was added to the aqueous layer until pH=11. The resulting semi-solution was extracted three times with ethyl acetate. The combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo to give a pale brown viscous oil (34.6 g, 75% yield): NMR (CDCl,300 MHz): 7.10 (s, 1H), 7.05 (d, 2H, J=1), 2.37 (s, 3H), 2.10 (s, 3H); CI-MS: 202 (M+H).
4
Ethyl acetamidate hydrochloride (60 g, 0.48 mol) was added quickly to a rapidly stirred mixture of potassium carbonate (69.5 g, 0.50 mol), dichloromethane (120 mL) and water (350 mL). The layers were separated and the aqueous layer was extracted with dichloromethane (2×120 mL). The combined organic layers were dried over MgSOand filtered. Solvent was removed by simple distillation and the pot residue, a clear pale yellow liquid, (35.0 g) was used without further purification.
6
Glacial acetic acid (9.7 mL, 0.17 mol) was added to a stirred mixture of 5-amino-4-(2,4-dimethylphenyl)-3-methylpyrazole (34 g, 0.17 mol), ethyl acetamidate (22 g, 0.25 mol) and acetonitrile (500 mL). The resulting reaction mixture was stirred at room temperature for 3 days; at the end of which time, it was concentrated in vacuo to about one-third of its original volume. The resulting suspension was filtered and the collected solid was washed with copious amounts of ether. The white solid was dried in vacuo (31.4 g, 61% yield): NMR (DMSO-d, 300 MHz): 7.00 (s, 1H), 6.90 (dd, 2H, J=7, 1), 2.28 (s, 3H), 2.08 (s, 3H), 2.00 (s, 3H), 1.90 (s, 3H), 1.81 (s, 3H); CI-MS: 243 (M+H).
4
3
Sodium pellets (23 g, 1 mol) were added portionwise to ethanol (500 mL) with vigorous stirring. After all the sodium reacted, 5-acetamidino-4-(2,4-dimethylphenyl)-3-methylpyrazole, acetic acid salt (31.2 g, 0.1 mol) and diethyl carbonate (97 mL, 0.8 mol) were added. The resulting reaction mixture was heated to reflux temperature and stirred for 18 hours. The mix was cooled to room temperature and solvent was removed in vacuo. The residue was dissolved in water and a 1N HCl solution was added slowly until pH=5–6. The aqueous layer was extracted with ethyl acetate three times; the combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo to give a pale tan solid (26 g, 98% yield): NMR (CDCl,300 MHz): 7.15(s, 1H), 7.09 (s, 2H), 2.45 (s, 3H), 2.39 (s, 3H), 2.30 (s, 3H); CI-MS: 269 (M+H).
4
3
A mixture of 2,4,6-trimethylbenzyl cyanide (1.0 g, 6.3 mmol), benzyl azide (0.92 g, 6.9 mmol) and potassium t-butoxide (0.78 g, 6.9 mmol) in tetrahydrofuran (10 mL) was stirred at ambient temperature for 2.5 days. The resulting suspension was diluted with water and extracted three times with ethyl acetate. The combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo to give a brown oil. Trituration with ether and filtration afforded a yellow solid (1.12 g, 61% yield): NMR (CDCl,300 MHz):7.60–7.30 (m, 5H), 7.30–7.20 (m, 2H), 5.50 (s, 2H), 3.18 (br s, 2H), 2.30 (s, 3H), 2.10 (s, 6H); CI-MS: 293 (M+H).
4
Sodium (500 mg, 22 mmol) was added with stirring to a mixture of liquid ammonia (30 mL) and 1-phenylmethyl-4-(2,4,6-trimethylphenyl)-5-aminotriazole (1.1 g, 3.8 mmol). The reaction mixture was stirred until a dark green color persisted. An ammonium chloride solution (mL) was added and the mixture was stirred while warming to ambient temperature over 16 hours. The residue was treated with a 1M HCl solution and filtered. The aqueous layer was basified with a concentrated ammonium hydroxide solution (pH=9) and then extracted with ethyl acetate three times. The combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo to give a yellow solid (520 mg), which was homogeneous by thin layer chromatography (ethyl acetate):
3
NMR (CDCl,300 MHz): 6.97 (s, 2H), 3.68–3.50 (br.s, 2H), 2.32 (s, 3H), 2.10 (s, 6H); CI-MS: 203 (M+H).
6
A mixture of 4-(2,4,6-trimethylphenyl)-5-aminotriazole (400 mg, 1.98 mmol), ethyl acetamidate 261 mg, 3 mmol) and glacial acetic acid (0.1 mL, 1.98 mmol) in acetonitrile (6 mL) was stirred at ambient temperature for 4 hours. The resulting suspension was filtered and the collected solid was washed with copious amounts of ether. Drying in vacuo afforded a white solid (490 mg, 82% yield): NMR (DMSO-d,300 MHz):7.90–7.70 (br s, 0.5H), 7.50–7.20 (br. s, 0.5H), 6.90 (s, 2H), 6.90 (s, 2H), 3.50–3.10 (br s, 3H), 2.30–2.20 (br s, 3H), 2.05 (d, 1H, J=7), 1.96 (s, 6H), 1.87 (s, 6H); CI-MS: 244 (M+H).
4
3
Sodium (368 mg, 16.2 mmol) was added with stirring to ethanol (10 mL) at room temperature. After the sodium had reacted, 4-(2,4,6-trimethylphenyl)-5-acetamidino-triazole, acetic acid salt (490 mg, 1.6 mmol) and diethyl carbonate (1.6 mL, 13 mmol) were added. The reaction mixture was stirred at reflux temperature for 5 hours, then cooled to room temperature. The reaction mixture was diluted with water; a 1N HCl solution was added until pH=5−6 and three extractions with ethyl acetate were performed. The combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo to give a yellow residue. Trituration with ether and filtration afforded a yellow solid (300 mg, 69% yield): NMR (CDCl,300 MHz): 6.98 (s, 2H), 2.55 (s, 3H), 2.35 (s, 3H), 2.10 (s, 6H); CI-MS: 270 (M+H).
4
f
3
A mixture of 2,7-dimethyl-8-(2,4-dimethylphenyl)[1,5-a]-pyrazolo-1,3,5-triazin-4-one (Example 1, 1.38 g, 4.5 mmol), N,N-dimethylaniline (1 mL, 8 mmol) and phosphorus oxychloride (10 mL) was stirred at reflux temperature for 48 hours. The excess phosphorus oxychloride was removed in vacuo. The residue was poured onto ice-water, stirred briefly and extracted quickly with ethyl acetate three times. The combined organic layers were washed with ice water, then dried over MgSOand filtered. Solvent was removed in vacuo to give a brown oil. Flash column chromatography (ethyl acetate:hexanes::1:4) gave one fraction (R=0.5) Solvent was removed in vacuo to afford a yellow oil (1.0 g, 68% yield): NMR (CDCl,300 MHz): 7.55 (d, 1H, J=1), 7.38 (dd, 1H, J=7,1), 7.30 (d, 1H, J=7), 2.68 (s, 3H), 2.45 (s, 3H); CI-MS: 327 (M+H).
4
3
Sodium hydride (60% in oil, 80 mg, 2 mmol) was washed with hexanes twice, decanted after each washing and taken up in anhydrous tetrahydrofuran (THF, 1 mL). A solution of diethyl malonate (0.32 g, 2 mmol) in THF (2 mL) was added dropwise over 5 min, during which time vigorous gas evolution ensued. A solution of 4-chloro-2,7-dimethyl-8-(2,4-dichlorophenyl)[1,5-a]pyrazolotriazine (0.5 g, 1.75 mmol) in THF (2 mL) was added and the reaction mixture was then stirred under a nitrogen atmosphere for 48 hours. The resulting suspension was poured onto water and extracted three times with ethyl acetate. The combined organic layers were washed once with brine, dried over MgSOand filtered. Solvent was removed in vacuo to give a brown oil. Column chromatography (ethyl acetate:hexanes::1:9) afforded, after removal of solvent in vacuo, a pale yellow solid (Rf=0.2, 250 mg, 35% yield): mp 50–52° C.; NMR (CDCl, 300 MHz): 12.35 (br.s, 1H, 7.15–7.00 (m, 3H), 4.40 (q, 2H, J=7), 4.30 (q, 2H, J=7), 2.4, 2.35, 2.3, 2.2, 2.1 (5 s, 12H), 1.4 (t, 3H, J=7), 1.35–1.25 (m, 3H); CI-HRMS: Calcd: 411.2032, Found: 411.2023.
4
3
A mixture of 2,7-dimethyl-8-(2,4 dimethylphenyl)[1,5-a]-pyrazolo-1,3,5-triazin-4-one (Example 1, 1.38 g, 4.5 mmol), N,N-dimethylaniline (1 mL, 8 mmol) and phosphorus oxychloride (10 mL) was stirred at reflux temperature for 48 hours. The excess phosphorus oxychloride was removed in vacuo. The residue was poured onto ice-water, stirred briefly and extracted quickly with ethyl acetate three times. The combined organic layers were washed with ice water, then dried over MgSOand filtered. Solvent was removed in vacuo to give a brown oil. Flash column chromatography (ethyl acetate:hexanes::1:4) gave one fraction (Rf=0.5) Solvent was removed in vacuo to afford a yellow oil (1.0 g, 68% yield): NMR (CDCl,300 MHz): 7.55 (d, 1H, J=1), 7.38 (dd, 1H, J=7,1), 7.30 (d, 1H, J=7), 2.68 (s, 3H), 2.45 (s, 3H); CI-MS: 327 (M+H).
4
2
2
3
3
18
21
2
5
2
A mixture of 4-chloro-2,7-dimethyl-8-(2,4-dichlorophenyl)[1,5-a]-pyrazolo-1,3,5-triazine (Part A, 570 mg, 1.74 mmol), 1,3-dimethoxypropyl-2-aminopropane (25 mg, 2.08 mmol) and ethanol (10 mL) was stirred at ambient temperature for 18 hours. The reaction mixture was poured onto water (25 mL) and extracted three times with ethyl acetate. The combined organic layers were dried over MgSOand filtered. Solvent was removed in vacuo. Column chromatography (CHCl:CHOH::50:1) afforded one fraction. Removal of solvent in vacuo gave a solid (250 mg, 35% yield): mp 118–120° C.; NMR (CDCl,300 MHz): 7.50 (s, 1H), 7.28 (dd, 2H, J=8,1), 6.75 (d, 1H, J=8), 4.70–4.58 (m, 1H), 3.70–3.55 (m, 4H), 3.43 (s, 6H), 2.50 (s, 3H), 2.35 (s, 3H); CI-HRMS: Calcd: 409.1072, Found: 409.1085; Analysis Calcd. for CHClNO: C, 52.69, H, 5.17, N, 17.07, Cl, 17.28; Found: C, 52.82, H, 5.06, N, 16.77, Cl, 17.50.
Using the above procedures and modifications known to one skilled in the art of organic synthesis, the following additional examples of Tables 1–4 may be prepared.
The examples delineated in TABLE 1 may be prepared by the methods outlined in Examples 1, 2, 3 or 6. Commonly used abbreviations are: Ph is phenyl, Pr is propyl, Me is methyl, Et is ethyl, Bu is butyl, Ex is Example.
TABLE 1
<chemistry id="CHEM-US-00039" num="00039"><img id="EMI-C00039" he="23.20mm" wi="24.64mm" file="US07094782-20060822-C00039.TIF" alt="embedded image" img-content="table" img-format="tif" /></chemistry>
Ex.
Z
R<sub>3</sub>
Ar
mp(° C.)
6<sup>a</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
118–120
7<sup>b</sup>
C—Me
NHCHPr<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
114–116
8<sup>c</sup>
C—Me
NEtBu
2,4-Cl<sub>2</sub>—Ph
oil
9<sup>d</sup>
C—Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Cl<sub>2</sub>—Ph
oil
10<sup>e</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
oil
11<sup>f</sup>
C—Me
NH-3-heptyl
2,4-Cl<sub>2</sub>—Ph
90–92
12<sup>g</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
179–181
13<sup>h</sup>
C—Me
NEt<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
133–134
14<sup>i</sup>
C—Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
oil
15<sup>j</sup>
C—Me
NH-3-pentyl
2,4-Cl<sub>2</sub>—Ph
139–140
16<sup>k</sup>
C—Me
NMePh
2,4-Cl<sub>2</sub>—Ph
60–62
17<sup>l</sup>
C—Me
NPr<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
oil
18<sup>m</sup>
C—Me
NH-3-hexyl
2,4-Cl<sub>2</sub>—Ph
130–132
19
C—Me
morpholino
2,4-Cl<sub>2</sub>—Ph
20
C—Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
21
C—Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
22
C—Me
NH-4-tetrahydropyranyl
2,4-Cl<sub>2</sub>—Ph
23
C—Me
NH-cyclopentyl
2,4-Cl<sub>2</sub>—Ph
24
C—Me
1,2,3,4-tetrahydro-
2,4-Cl<sub>2</sub>—Ph
isoquinolinyl
25
C—Me
CH<sub>2</sub>-(1,2,3,4-tetrahydro-
2,4-Cl<sub>2</sub>—Ph
isoquinolinyl)
26<sup>n</sup>
C—Me
OEt
2,4-Cl<sub>2</sub>—Ph
141–143
27
C—Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
28
C—Me
OCH<sub>2</sub>Ph
2,4-Cl<sub>2</sub>—Ph
29
C—Me
O-3-pentyl
2,4-Cl<sub>2</sub>—Ph
30
C—Me
SEt
2,4-Cl<sub>2</sub>—Ph
31
C—Me
S(O)Et
2,4-Cl<sub>2</sub>—Ph
32
C—Me
SO<sub>2</sub>Et
2,4-Cl<sub>2</sub>—Ph
33
C—Me
CH(CO<sub>2</sub>Et)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
34
C—Me
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
35
C—Me
CH(Et)CH<sub>2</sub>OH
2,4-Cl<sub>2</sub>—Ph
36
C—Me
CH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
37
C—Me
CONMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
38
C—Me
COCH<sub>3</sub>
2,4-Cl<sub>2</sub>—Ph
39
C—Me
CH(OH)CH<sub>3</sub>
2,4-Cl<sub>2</sub>—Ph
40
C—Me
C(OH)Ph-3-pyridyl
2,4-Cl<sub>2</sub>—Ph
41
C—Me
Ph
2,4-Cl<sub>2</sub>—Ph
42
C—Me
2-CF<sub>3</sub>—Ph
2,4-Cl<sub>2</sub>—Ph
43
C—Me
2-Ph—Ph
2,4-Cl<sub>2</sub>—Ph
44
C—Me
3-pentyl
2,4-Cl<sub>2</sub>—Ph
45
C—Me
cyclobutyl
2,4-Cl<sub>2</sub>—Ph
46
C—Me
3-pyridyl
2,4-Cl<sub>2</sub>—Ph
47
C—Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
48
C—Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
49<sup>o</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
125–127
50
C—Me
NHCHPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
51
C—Me
NEtBu
2,4,6-Me<sub>3</sub>—Ph
52
C—Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4,6-Me<sub>3</sub>—Ph
53<sup>ae</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
123–124
54
C—Me
NH-3-heptyl
2,4,6-Me<sub>3</sub>—Ph
55<sup>ac</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
145–146
56<sup>ah</sup>
C—Me
NEt<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
88–90
57<sup>ai</sup>
C—Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
132–134
58<sup>ad</sup>
C—Me
NH-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
134–135
59
C—Me
NMePh
2,4,6-Me<sub>3</sub>—Ph
60
C—Me
NPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
61
C—Me
NH-3-hexyl
2,4,6-Me<sub>3</sub>—Ph
62
C—Me
morpholino
2,4,6-Me<sub>3</sub>—Ph
63
C—Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
64
C—Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
65
C—Me
NH-4-tetrahydropyranyl
2,4,6-Me<sub>3</sub>—Ph
66
C—Me
NH-cyclopentyl
2,4,6-Me<sub>3</sub>—Ph
67
C—Me
1,2,3,4-tetrahydro-
2,4,6-Me<sub>3</sub>—Ph
isoquinolinyl
68
C—Me
CH<sub>2</sub>-(1,2,3,4-tetrahydro-
2,4,6-Me<sub>3</sub>—Ph
isoquinolinyl)
69
C—Me
OEt
2,4,6-Me<sub>3</sub>—Ph
70
C—Me
OCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
71
C—Me
OCH<sub>2</sub>Ph
2,4,6-Me<sub>3</sub>—Ph
72
C—Me
O-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
73
C—Me
SEt
2,4,6-Me<sub>3</sub>—Ph
74
C—Me
S(O)Et
2,4,6-Me<sub>3</sub>—Ph
75
C—Me
SO<sub>2</sub>Et
2,4,6-Me<sub>3</sub>—Ph
76
C—Me
CH(CO<sub>2</sub>Et)2
2,4,6-Me<sub>3</sub>—Ph
77
C—Me
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
78
C—Me
CH(Et)CH<sub>2</sub>OH
2,4,6-Me<sub>3</sub>—Ph
79
C—Me
CH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
80
C—Me
CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
81
C—Me
COCH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
82
C—Me
CH(OH)CH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
83
C—Me
C(OH)Ph-3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
84
C—Me
Ph
2,4,6-Me<sub>3</sub>—Ph
85
C—Me
2-CF<sub>3</sub>—Ph
2,4,6-Me<sub>3</sub>—Ph
86
C—Me
2-Ph-Ph
2,4,6-Me<sub>3</sub>—Ph
87
C—Me
3-pentyl
2,4,6-Me<sub>3</sub>—Ph
88
C—Me
cyclobutyl
2,4,6-Me<sub>3</sub>—Ph
89
C—Me
3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
90
C—Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
91
C—Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
92<sup>p</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
44–45
93<sup>q</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
oil
94<sup>r</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
102–104
95<sup>s</sup>
C—Me
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
102–104
96<sup>t</sup>
C—Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
oil
97<sup>u</sup>
C—Me
N(CH<sub>2</sub>CN)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
148–150
98<sup>v</sup>
C—Me
NHCH(Me)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
102–104
99<sup>w</sup>
C—Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
oil
100<sup>x</sup>
C—Me
NPr-c-C<sub>3</sub>H<sub>5</sub>
2,4-Me<sub>2</sub>—Ph
oil
101<sup>y</sup>
C—Me
NHCH(Me)CH<sub>2</sub>NMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
47–48
202<sup>z</sup>
C—Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
117–118
103<sup>aa</sup>
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
oil
104<sup>ab</sup>
C—Me
N(Bu)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
oil
105
C—Me
NHCHPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
106
C—Me
NEtBu
2,4-Me<sub>2</sub>—Ph
107
C—Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Me<sub>2</sub>—Ph
108
C—Me
NH-3-heptyl
2,4-Me<sub>2</sub>—Ph
109
C—Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
110
C—Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
111
C—Me
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
112
C—Me
NMePh
2,4-Me<sub>2</sub>—Ph
113
C—Me
NPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
114
C—Me
NH-3-hexyl
2,4-Me<sub>2</sub>—Ph
115
C—Me
morpholino
2,4-Me<sub>2</sub>—Ph
116
C—Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
117
C—Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
118
C—Me
NH-4-tetrahydropyranyl
2,4-Me<sub>2</sub>—Ph
119
C—Me
NH-cyclopentyl
2,4-Me<sub>2</sub>—Ph
120
C—Me
1,2,3,4-tetrahydro-
2,4-Me<sub>2</sub>—Ph
isoquinolinyl
121
C—Me
CH<sub>2</sub>-(1,2,3,4-tetrahydro-
2,4-Me<sub>2</sub>—Ph
isoquinolinyl)
122
C—Me
OEt
2,4-Me<sub>2</sub>—Ph
123
C—Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
124
C—Me
OCH<sub>2</sub>Ph
2,4-Me<sub>2</sub>—Ph
125
C—Me
O-3-pentyl
2,4-Me<sub>2</sub>—Ph
126
C—Me
SEt
2,4-Me<sub>2</sub>—Ph
127
C—Me
S(O)Et
2,4-Me<sub>2</sub>—Ph
128
C—Me
SO<sub>2</sub>Et
2,4-Me<sub>2</sub>—Ph
3
C—Me
CH(CO<sub>2</sub>Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
50–52
129
C—Me
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
130
C—Me
CH(Et)CH<sub>2</sub>OH
2,4-Me<sub>2</sub>—Ph
131
C—Me
CH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
132
C—Me
CH(Et)CH<sub>2</sub>OEt
2,4-Me<sub>2</sub>—Ph
133
C—Me
CONMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
134
C—Me
COCH<sub>3</sub>
2,4-Me<sub>2</sub>—Ph
135
C—Me
CH(OH)CH<sub>3</sub>
2,4-Me<sub>2</sub>—Ph
136
C—Me
C(OH)Ph-3-pyridyl
2,4-Me<sub>2</sub>—Ph
137
C—Me
Ph
2,4-Me<sub>2</sub>—Ph
138
C—Me
2-CF<sub>3</sub>—Ph
2,4-Me<sub>2</sub>—Ph
139
C—Me
2-Ph—Ph
2,4-Me<sub>2</sub>—Ph
140
C—Me
3-pentyl
2,4-Me<sub>2</sub>—Ph
141
C—Me
cyclobutyl
2,4-Me<sub>2</sub>—Ph
142
C—Me
3-pyridyl
2,4-Me<sub>2</sub>—Ph
143
C—Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
144
C—Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
145<sup>bc</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-MeO—Ph
45–46
146<sup>bd</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-MeO—Ph
oil
147<sup>be</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-MeO—Ph
86–88
148<sup>bf</sup>
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-MeO—Ph
oil
149
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-MeO—Ph
150<sup>af</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeO—Ph
88–90
151<sup>al</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeO—Ph
oil
152<sup>ag</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-MeO—Ph
95–97
153
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-MeO—Ph
154
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-MeO—Ph
155
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-NMe<sub>2</sub>—Ph
156
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-NMe<sub>2</sub>—Ph
oil
157
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-NMe<sub>2</sub>—Ph
158
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-NMe<sub>2</sub>—Ph
159
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-NMe<sub>2</sub>—Ph
160
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-NMe<sub>2</sub>—Ph
161
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-NMe<sub>2</sub>—Ph
162
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-NMe<sub>2</sub>—Ph
163
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-NMe<sub>2</sub>—Ph
164
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-NMe<sub>2</sub>—Ph
165
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-i-Pr—Ph
166
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-i-Pr—Ph
167
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-i-Pr—Ph
168
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-i-Pr—Ph
169
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-i-Pr—Ph
170
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-Me—Ph
171
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-Me—Ph
172
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-Me—Ph
173
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-Me—Ph
174
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-Me—Ph
175<sup>ar</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-Br—Ph
108–109
176
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-Br—Ph
177
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
178
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-Br—Ph
179
C—Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
180
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-Me<sub>2</sub>—Ph
181
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-Me<sub>2</sub>—Ph
182
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-Br-2,6-(Me)<sub>2</sub>—Ph
183
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-Br-2,6-(Me)<sub>2</sub>—Ph
184
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
185
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
186
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-CF<sub>3</sub>—Ph
187
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-CF<sub>3</sub>—Ph
188
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>—Ph
189
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>—Ph
190
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>—Ph
191
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>—Ph
192
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
193
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
194
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-(COMe)-2-Br—Ph
195
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-(COMe)-2-Br—Ph
196
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>-pyrid-3-yl
197
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>-pyrid-3-yl
198
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-(Br)<sub>2</sub>—Ph
199
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-(Br)<sub>2</sub>—Ph
200
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
201
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
202
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
203
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
204
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
205
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
206
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SO<sub>2</sub>Me—Ph
207
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SO<sub>2</sub>Me—Ph
208
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-I-4-i-Pr—Ph
209
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-I-4-i-Pr—Ph
210
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-N(Me)<sub>2</sub>-6-MeO—Ph
211
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-N(Me)<sub>2</sub>-6-MeO—Ph
212
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-[SMe]2-Ph
213
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-[SMe]2-Ph
214
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-[SO<sub>2</sub>Me]2-Ph
215
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-[SO<sub>2</sub>Me 2-Ph
216
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
217
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
218
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
219
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
220
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-N(Me)<sub>2</sub>-4-Me—Ph
221
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-N(Me)<sub>2</sub>-4-Me—Ph
222
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeS-4,6-(Me)<sub>2</sub>—Ph
223
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeS-4,6-(Me)<sub>2</sub>—Ph
224
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-(CH<sub>3</sub>CO)-4,6-(Me)<sub>2</sub>—Ph
225
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-(CH<sub>3</sub>CO)-4,6-(Me)<sub>2</sub>—Ph
226
H
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
227
H
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
228
CF3
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
229
CF3
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
230
N
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
231
N
NHCHPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
232
N
NEtBu
2,4,6-Me<sub>3</sub>—Ph
233
N
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4,6-Me<sub>3</sub>—Ph
234
N
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
235
N
NH-3-heptyl
2,4,6-Me<sub>3</sub>—Ph
236
N
NHCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
237
N
NEt<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
238
N
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
239
N
NH-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
240
N
NMePh
2,4,6-Me<sub>3</sub>—Ph
241
N
NPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
242
N
NH-3-hexyl
2,4,6-Me<sub>3</sub>—Ph
243
N
morpholino
2,4,6-Me<sub>3</sub>—Ph
244
N
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
245
N
NHCH (CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
246
N
NH-4-tetrahydropyranyl
2,4,6-Me<sub>3</sub>—Ph
247
N
NH-cyclopentyl
2,4,6-Me<sub>3</sub>—Ph
248
N
1,2,3,4-tetrahydro-
2,4,6-Me<sub>3</sub>—Ph
isoquinolinyl
249
N
CH<sub>2</sub>-(1,2,3,4-tetrahydro-
2,4,6-Me<sub>3</sub>—Ph
isoquinolinyl)
250
N
OEt
2,4,6-Me<sub>3</sub>—Ph
251
N
OCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
252
N
OCH<sub>2</sub>Ph
2,4,6-Me<sub>3</sub>—Ph
253
N
O-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
254
N
SEt
2,4,6-Me<sub>3</sub>—Ph
255
N
S(O)Et
2,4,6-Me<sub>3</sub>—Ph
256
N
SO<sub>2</sub>Et
2,4,6-Me<sub>3</sub>—Ph
257
N
CH(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
258
N
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
259
N
CH(Et)CH<sub>2</sub>OH
2,4,6-Me<sub>3</sub>—Ph
260
N
CH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
261
N
CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
262
N
COCH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
263
N
CH(OH)CH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
264
N
C(OH)Ph-3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
265
N
Ph
2,4,6-Me<sub>3</sub>—Ph
266
N
2-CF<sub>3</sub>—Ph
2,4,6-Me<sub>3</sub>—Ph
267
N
2-Ph—Ph
2,4,6-Me<sub>3</sub>—Ph
268
N
3-pentyl
2,4,6-Me<sub>3</sub>—Ph
269
N
cyclobutyl
2,4,6-Me<sub>3</sub>—Ph
270
N
3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
271
N
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
272
N
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
273
N
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
274
N
NHCHPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
275
N
NEtBu
2,4-Me<sub>2</sub>—Ph
276
N
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Me<sub>2</sub>—Ph
277
N
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
278
N
NH-3-heptyl
2,4-Me<sub>2</sub>—Ph
279
N
NHCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
280
N
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
281
N
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
282
N
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
283
N
NMePh
2,4-Me<sub>2</sub>—Ph
284
N
NPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
285
N
NH-3-hexyl
2,4-Me<sub>2</sub>—Ph
286
N
morpholino
2,4-Me<sub>2</sub>—Ph
287
N
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
288
N
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
289
N
NH-4-tetrahydropyranyl
2,4-Me<sub>2</sub>—Ph
290
N
NH-cyclopentyl
2,4-Me<sub>2</sub>—Ph
291
N
1,2,3,4-tetrahydro-
2,4-Me<sub>2</sub>—Ph
isoquinolinyl
292
N
CH<sub>2</sub>-(1,2,3,4-tetrahydro-
2,4-Me<sub>2</sub>—Ph
isoquinolinyl)
293
N
OEt
2,4-Me<sub>2</sub>—Ph
294
N
OCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
295
N
OCH<sub>2</sub>Ph
2,4-Me<sub>2</sub>—Ph
296
N
O-3-pentyl
2,4-Me<sub>2</sub>—Ph
297
N
SEt
2,4-Me<sub>2</sub>—Ph
298
N
S(O)Et
2,4-Me<sub>2</sub>—Ph
299
N
SO<sub>2</sub>Et
2,4-Me<sub>2</sub>—Ph
300
N
CH(CO<sub>2</sub>Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
301
N
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
302
N
CH(Et)CH<sub>2</sub>OH
2,4-Me<sub>2</sub>—Ph
303
N
CH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
304
N
CONMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
305
N
COCH<sub>3</sub>
2,4-Me<sub>2</sub>—Ph
306
N
CH(OH)CH<sub>3</sub>
2,4-Me<sub>2</sub>—Ph
307
N
C(OH)Ph-3-pyridyl
2,4-Me<sub>2</sub>—Ph
308
N
Ph
2,4-Me<sub>2</sub>—Ph
309
N
2-CF<sub>3</sub>—Ph
2,4-Me<sub>2</sub>—Ph
310
N
2-Ph—Ph
2,4-Me<sub>2</sub>—Ph
311
N
3-pentyl
2,4-Me<sub>2</sub>—Ph
312
N
cyclobutyl
2,4-Me<sub>2</sub>—Ph
313
N
3-pyridyl
2,4-Me<sub>2</sub>—Ph
314
N
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
315
N
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
316<sup>an</sup>
C—Me
NEt<sub>2</sub>
2-Br-4-MeO—Ph
oil
317<sup>am</sup>
C—Me
NH-3-pentyl
2-Br-4-MeO—Ph
oil
318<sup>aj</sup>
C—Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
101–103
319<sup>ao</sup>
C—Me
NH(c-C<sub>3</sub>H<sub>5</sub>)
2,4-Me<sub>2</sub>—Ph
oil
320<sup>ak</sup>
C—Me
morpholino
2,4,6-Me<sub>3</sub>—Ph
139–141
321<sup>ap</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-CN-4-Me—Ph
152–153
322<sup>aq</sup>
C—Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4,6-Me<sub>3</sub>—Ph
149–151
324<sup>as</sup>
C—Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
115–117
325<sup>at</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
55–57
326<sup>au</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
72
327<sup>av</sup>
C—Me
NH-3-pentyl
2,5-Me<sub>2</sub>-4-MeO—Ph
45–47
328<sup>aw</sup>
C—Me
NEt<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
oil
329<sup>ax</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MePh
80–81
330<sup>ay</sup>
C—Me
NCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MePh
77–79
331<sup>az</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MePh
oil
332<sup>ba</sup>
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)CH<sub>2</sub>OMe
2-Cl-4-MePh
139–140
333<sup>bb</sup>
C—Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,5-Me<sub>2</sub>-4-MeOPh
120–122
334<sup>bg</sup>
C—Me
NEt<sub>2</sub>
2-Me-4-MeOPh
oil
335<sup>bh</sup>
C—Me
OEt
2-Me-4-MeOPh
oil
336<sup>bi</sup>
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)CH<sub>2</sub>OMe
2-Me-4-MeOPh
oil
337<sup>bj</sup>
C—Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-MeOPh
129
338<sup>bk</sup>
C—Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OEt)<sub>2</sub>
2-Me-4-MeOPh
amorph.
339
C—Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Cl<sub>2</sub>—Ph
109–110
340
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
93–94
341
C—Me
NH-3-pentyl
2-Me-4-BrPh
118–119
342
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-BrPh
oil
343
C—Me
NHCH(CH<sub>2</sub>-iPr)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
oil
344
C—Me
NHCH(Pr)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
94–95
345
C—Me
NHCH(Et)CH<sub>2</sub>OEt
2,4-Me<sub>2</sub>—Ph
76–77
346
C—Me
NHCH(CH<sub>2</sub>OMe)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-Me<sub>2</sub>NPh
oil
347
C—Me
NEt<sub>2</sub>
2-Me-4-ClPh
oil
348
C—Me
NH-3-pentyl
2-Me-4-ClPh
122–124
349
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-ClPh
oil
350
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-ClPh
122–123
351
C—Me
NEt<sub>2</sub>
2-Me-4-ClPh
oil
352
C—Me
NEt<sub>2</sub>
2-Cl-4-MePh
oil
353
C—Me
NH-3-pentyl
2-Cl-4-MePh
120–121
354
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
355<sup>bl</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
oil
356<sup>bm</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MeOPh
108–110
357<sup>bn</sup>
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4-MeOPh
127–129
358<sup>bo</sup>
C—Me
NEt<sub>2</sub>
2-Cl-4-MeOPh
oil
359<sup>bp</sup>
C—Me
NH-3-pentyl
2-Cl-4-MeOPh
77–79
360
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
361
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
362
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
363
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
364
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
365
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
366
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
367
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
368
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
369
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4,5-(MeO)<sub>2</sub>Ph
370
C—Me
NEt<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
371
C—Me
NH-3-pentyl
2-Cl-4,5-(MeO)<sub>2</sub>Ph
372
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
373
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
374<sup>bq</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
137–138
375
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
376<sup>br</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
147–148
377
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4,5-(MeO)<sub>2</sub>Ph
378<sup>bs</sup>
C—Me
NEt<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
52–58
379
C—Me
NH-3-pentyl
2-Br-4,5-(MeO)<sub>2</sub>Ph
380
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
381
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
382
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
383
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
384
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4,6-(MeO)<sub>2</sub>Ph
385
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4,6-(MeO)<sub>2</sub>Ph
386
C—Me
NEt<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
387
C—Me
NH-3-pentyl
2-Cl-4,6-(MeO)<sub>2</sub>Ph
388
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,6-(MeO)<sub>2</sub>Ph
389
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,6-(MeO)<sub>2</sub>Ph
390
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
391
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
392
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
393
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4,6-(MeO)<sub>2</sub>Ph
395
C—Me
NEt<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
396
C—Me
NH-3-pentyl
2-Me-4,6-(MeO)<sub>2</sub>Ph
397
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
398
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
399
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4,6-(MeO)<sub>2</sub>Ph
400
C—Me
NEt<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>Ph
401
C—Me
NH-3-pentyl
2-Br-4,6-(MeO)<sub>2</sub>Ph
402
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,6-(MeO)<sub>2</sub>Ph
403
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,6-(MeO)<sub>2</sub>Ph
404
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
405
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
406
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
407
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
408
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
409
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
410
C—Me
NEt<sub>2</sub>
2-MeO-4-MePh
411
C—Me
NH-3-pentyl
2-MeO-4-MePh
412
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
413
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
414
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
415
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
416
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
417
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
418
C—Me
NEt<sub>2</sub>
2-MeO-4-MePh
419
C—Me
NH-3-pentyl
2-MeO-4-MePh
420
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
421
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
423<sup>bt</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
oil
424
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
425
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-ClPh
426
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-ClPh
427
C—Me
NEt<sub>2</sub>
2-MeO-4-ClPh
428
C—Me
NH-3-pentyl
2-MeO-4-ClPh
429
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-ClPh
430
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me0-4-ClPh
Notes for Table 1:
a) Analysis Calcd: C, 52.69, H, 5.17, N, 17.07, Cl, 17.28; Found: C, 52.82, H, 5.06, N, 16.77, Cl, 17.50.
3
b) CI-HRMS: Calcd: 406.1565, Found: 405.1573 (M+H); Analysis Calcd: C, 59.11; H, 6.20; N, 17.23; Cl: 17.45; Found: C, 59.93; H, 6.34; N, 16.50; Cl: 16.95; NMR (CDCl, 300 MHz): 0.95 (t, J=8, 4H), 1.30–1.40 (m, 4H), 1.50–1.75 (m, 4H), 2.35 (s, 3H), 2.48 (s, 3H), 4.30–4.45 (m, 1H), 6.15 (d, J=8, 1H), 7.30 (s, 2H), 7.50 (s, 1H)
3
c) CI-HRMS: Calcd: 392.1409, Found: 392.1388 (M+H); NMR (CDCl, 300 MHz): 1.00 (t, J=8, 3H), 1.35 (t, J=8, 3H), 1.41 (q, J=8, 2H), 1.65–1.85 (m, 2H), 2.30 (s, 3H), 2.40 (s, 3H), 3.85–4.20 (m, 4H), 7.30 (s, 2H), 7.50 (s, 1H).
3
d) CI-HRMS: Calcd: 404.1409, Found: 404.1408 (M+H); NMR(CDCl, 300 MHz): 0.35–0.45 (m, 2H), 0.52–0.62 (m, 2H), 0.98 (t, J=8, 3H), 1.70–1.90 (m, 2H), 2.30 (s, 3H), 2.40 (s, 3H), 3.85–4.02 (m, 2H), 4.02–4.20 (m, 2H), 7.30 (s, 2H), 7.50 (s, 1H).
3
e) CI-HRMS: Calcd: 424.1307, Found: 424.1307 (M+H): NMR (CDCl, 300 MHz): 2.28 (s, 3H), 2.40 (s, 3H), 3.40 (s, 6H), 3.75 (t, J=8, 4H), 4.20–4.45 (m, 4H), 7.30 (s, 2H), 7.50 (s, 1H).
3
f) CI-HRMS: Calcd: 406.1565, Found: 406.1578 (M+H); NMR (CDCl, 300 MHz): 0.90 (t, J=8, 3H), 1.00 (t, J=8, 3H), 1.28–1.45 (m, 4H), 1.50–1.80 (m, 4H), 2.35 (s, 3H), 2.50 (s, 3H), 4.20–4.35 (m, 1H), 6.10–6.23 (m, 1H), 7.30 (s, 2H), 7.50 (s, 1H).
3
g) CI-HRMS: Calcd: 394.1201, Found: 394.1209 (M+H); NMR (CDCl, 300 MHz): 1.02 (t, J=8, 3H), 1.65–1.90 (m, 2H), 2.35 (s, 3H), 2.48 (s, 3H), 3.40 (s, 3H), 3.50–3.60 (m, 2H), 4.35–4.45 (brs, 1H), 6.50–6.60 (m, 1H), 7.30 (s, 2H), 7.50 (s, 1H).
3
h) CI-HRMS: Calcd: 364.1096, Found: 364.1093 (M+H); Analysis: Calcd: C, 56.05; H, 5.27; N, 19.23; Cl: 19.46; Found: C, 55.96; H, 5.24; N, 18.93; Cl: 19.25; NMR (CDCl, 300 MHz): 1.35 (t, J=8, 6H), 2.30 (3, 3H), 2.40 (s, 3H), 3.95–4.15 (m, 4H), 7.30 (s, 2H), 7.50 (d, J=1, 1H).
3
i) CI-HRMS: Calcd: 438.1464, Found: 438.1454 (M+H); NMR (CDCl, 300 MHz): 1.22 (t, J=8, 6H), 2.35 (s, 3H), 2.47 (s, 3H), 3.39 (q, J=8, 4H), 3.65 (dd, J=8, 1, 2H), 3.73 (dd, J=8, 1, 2H), 4.55–4.65 (m, 1H), 6.75 (d, J=8, 1H), 7.30 (d, J=1, 2H), 7.50 (s, 1H).
3
j) CI-HRMS: Calcd: 378.1252, Found: 378.1249 (M+H); Analysis: Calcd: C, 57.15; H, 5.61; N, 18.51; Cl: 18.74; Found: C, 57.56; H, 5.65; N, 18.35; Cl: 18.45; NMR (CDCl, 300 MHz): 1.00 (t, J=8, 6H), 1.55–1.70 (m, 2H), 1.70–1.85 (m, 2H), 2.35 (s, 3H), 2.50 (s, 3H), 4.15–4.25 (m, 1H), 6.18 (d, J=8, 1H), 7.30 (s, 2H), 7.50 (s, 1H).
3
k) CI-HRMS: Calcd: 398.0939, Found: 398.0922 (M+H); Analysis: Calcd: C, 60.31; H, 4.30; N, 17.58; Cl: 17.80; Found: C, 60.29; H, 4.59; N, 17.09; Cl: 17.57; NMR (CDCl, 300 MHz): 2.05 (s, 3H), 2.50 (s, 3H), 3.78 (s, 3H), 7.20–7.45 (m, 7H), 7.50 (d, J=1, 1H).
3
l) CI-HRMS: Calcd: 392.1409, Found: 392.1391 (M+H); NMR (CDCl, 300 MHz): 0.98 (t, J=8, 6H), 1.70–1.85 (m, 4H), 2.30 (s, 3H), 2.40 (s, 3H), 3.80–4.10 (m, 4H), 7.30 (s, 2H), 7.50 (d, J=1, 1H).
3
m) CI-HRMS: Calcd: 392.1409, Found: 392.1415 (M+H); Analysis: Calcd: C, 58.17; H, 5.92; N, 17.85; Cl: 18.07; Found: C, 58.41; H, 5.85: N, 18.10; Cl: 17.75; NMR (CDCl, 300 MHz): 0.90–1.05 (m, 6H), 1.35–1.55 (m, 2H), 1.55–1.85 (m, 4H), 2.35 (s, 3H), 2.48 (s, 3H), 4.20–4.35 (m, 1H), 6.15 (d, J=8, 1H), 7.30 (s, 2H), 7.50 (d, J=1, 1H).
3
n) CI-HRMS: Calcd: 337.0623, Found: 337.0689 (M+H); Analysis: Calcd: C, 53.43; H, 4.18; N, 16.62; Cl: 21.03, Found: C, 53.56; H, 4.33; N, 16.56; Cl: 20.75; NMR (CDCl, 300 MHz): 1.60 (t, J=8, 3H), 2.40 (s, 3H), 2.55 (s, 3H), 4.80 (q, J=8, 2H), 7.30 (d, J=8, 1H), 7.35 (dd, J=8, 1, 1H), 7.55 (d, J=1, 1H)
3
o) CI-HRMS: Calcd: 383.2321, Found: 383.2309 (M+H); NMR (CDCl, 300 MHz): 2.00 (s, 6H), 2.20 (s, 3H), 2.30 (s, 3H), 2.45 (s, 3H), 3.45 (s, 6H), 3.61 (dd, J=8, 8, 2H), 3.70 (dd, J=8, 8, 2H), 4.60–4.70 (m, 1H), 6.70 (d, J=8, 1H), 6.94 (s, 2H).
3
p) CI-HRMS: Calcd: 370.2243, Found: 370.2246 (M+H); Analysis: Calcd: C, 65.02; H, 7.38; N, 18.96; Found: C, 65.22; H, 7.39; N, 18.71; NMR (CDCl, 300 MHz): 2.18 (s, 3H), 2.30 (s, 3H), 2.45 (s, 3H), 3.45 (s, 6H), 3.60 (dd, J=8, 8, 2H), 3.69 (dd, J=8, 8, 2H), 4.60–4.70 (m, 1H), 6.70 (d, J=8, 1H), 7.05 (d, J=8, 1H), 7.07 (d, J=8, 1H), 7.10 (s, 1H).
3
q) CI-HRMS: Calcd: 384.2400, Found: 384.2393 (M+H); NMR (CDCl, 300 MHz): 2.16 (s, 3H), 2.25 (s, 3H), 2.35 (s, 3H), 2.39 (s, 3H), 3.40 (s, 6H), 3.77 (t, J=8, 4H), 4.20–4.45 (m, 4H), 7.02 (d, J=8, 1H) 7.05 (s, 1H), 7.10 (d, J=7, 1H).
3
r) CI-HRMS: Calcd: 354.2294, Found: 354.2271 (M+H); Analysis: Calcd: C, 67.96; H, 7.71; N, 19.81; Found: C, 67.56; H, 7.37; N, 19.60; NMR (CDCl, 300 MHz): 1.03 (t, J=8, 3H), 1.65–1.88 (m, 2H), 2.17 (s, 3H), 2.30 (s, 3H), 2.35 (s, 3H), 2.45 (s, 3H), 3.40 (s, 3H), 3.50–3.62 (m, 2H), 4.30–4.45 (m, 1H), 6.51 (d, J=8, 1H), 7.04 (d, J=8, 1H), 7.10 (d, J=8, 1H), 7.12 (s, 1H).
3
s) CI-HRMS: Calcd: 338.2345, Found: 338.2332 (M+H); Analysis: Calcd: C, 71.18; H, 8.06; N, 20.75; Found: C, 71.43; H, 7.80; N, 20.70; NMR (CDCl, 300 MHz): 1.00 (t, J=8, 6H), 1.55–1.70 (m, 2H), 1.70–1.85 (m, 2H), 2.19 (s, 3H), 2.30 (s, 3H), 2.35 (s, 3H), 2.46 (s, 3H), 4.15–4.26 (m, 1H), 6.17 (d, J=8, 1H), 7.06 (d, J=8, 1H), 7.10 (d, J=1, 1H), 7.13 (s, 1H).
3
t) CI-HRMS: Calcd: 324.2188, Found: 324.2188 (M+H); NMR (CDCl, 300 MHz): 1.25 (t, J=8, 6H), 2.16 (s, 3H), 2.28 (s, 3H), 2.35 (s, 3H), 2.40 (s, 3H), 3.95–4.20 (m, 4H), 7.05 (dd, J=8, 1, 1H), 7.07 (s, 1H), 7.10 (d, J=1, 1H)
3
u) CI-HRMS: Calcd: 346.1780, Found: 346.1785 (M+H); Analysis: Calcd: C, 66.07; H, 5.54; N, 28.39; Found: C, 66.07; H, 5.60; N, 27.81; NMR (CDCl, 300 MHz): 2.15 (s, 3H), 2.32 (s, 3H) 2.17 (s, 3H), 2.52 (s, 3H), 5.25–5.35 (m, 4H), 7.08 (s, 2H), 7.15 (s, 1H).
3
v) CI-HRMS: Calcd: 340.2137, Found: 340.2137 (M+H); Analysis: Calcd: C, 67.23; H, 7.42; N, 20.63; Found:C, 67.11; H, 7.39; N, 20.26; NMR (CDCl, 300 MHz): 1.40 (d, J=8, 3H), 2.16 (s, 3H), 2.32 (s, 3H), 2.35 (s, 3H), 2.47 (s, 3H), 3.42 (s, 3H), 3.50–3.60 (m, 2H), 4.50–4.15 (m, 1H), 6.56 (d, J=8, 1H), 7.00–7.15 (m, 3H).
3
w) CI-HRMS: Calcd: 355.2134, Found: 355.2134 (M+H); NMR (CDCl, 300 MHz): 1.05 (t, J=8, 3H), 1.85–2.00 (m, 2H), 2.17 (s, 3H), 2.36 (s, 6H), 2.50 (s, 3H), 3.41 (s, 3H), 3.45 (dd, J=8, 3, 1H), 3.82 (dd, J=8, 1, 1H), 5.70–5.80 (m, 1H), 7.00–7.20 (m, 3H).
3
x) CI-HRMS: Calcd: 364.2501, Found: 364.2501 (M+H); NMR (CDCl, 300 MHz): 0.35–0.43 (m, 2H), 0.50–0.60 (m, 2H), 0.98 (t, J=8, 3H), 1.20–1.30 (m, 1H), 1.72–1.90 (m, 2H), 2.18 (s, 3H) 2.28 (s, 3H), 2.35 (s, 3H), 2.40 (s, 3H), 3.88–4.03 (m, 2H), 4.03–4.20 (m, 2H), 7.00–7.15 (m, 3H).
3
y) CI-HRMS: Calcd: 353.2454, Found: 353.2454 (M+H); Analysis: Calcd: C, 68.15; H, 8.02; N, 23.84; Found: C, 67.43; H, 7.81; N, 23.45; NMR (CDCl, 300 MHz): 1.38 (d, J=8, 3H), 2.18 (s, 3H), 2.30–2.40 (m, 12H), 2.47 93, 3H), 2.60–2.75 (m, 2H), 4.30–4.50 (m, 1H), 6.60–6.70 (m, 1H), 7.00–7.15 (m, 3H).
3
z) CI-HRMS: Calcd: 361.2140, Found: 361.2128 (M+H); NMR (CDCl, 300 MHz): 0.75–0.83 (m, 2H), 1.00–1.10 (m, 2H), 2.17 (s, 3H), 2.30 (s, 3H), 2.36 (s, 3H), 2.47 (s, 3H), 2.85 (t, J=8, 2H), 3.30–3.40 (m, 1H), 4.40–4.55 (m, 2H), 7.00–7.18 (m, 3H).
3
aa) CI-HRMS: Calcd: 363.2297, Found: 363.2311 (M+H); NMR (CDCl, 300 MHz): 1.01 (t, 3H, J=8), 1.75–1.90 (m,2H), 2.15 (s,3H), 2.19 (s, 3H), 2.35 (s, 3H), 2.40 (s, 3H), 2.40 (s, 3H), 2.98 (t, 2H, J=8), 3.97–4.15 (m, 2H), 4.15–4.30 (m, 2H), 7.03(d, 1H, 1H), 7.08 (d, 1H, J=8), 7.10 (s, 1H).
3
ab) CI-HRMS: Calcd: 363.2297, Found: 363.2295 (M+H); NMR (CDCl, 300 MHz): 1.01 (t, 3H, J=8), 1.35–1.55 (m, 2H), 1.75–1.90 (m, 2H), 2.15 (s, 3H), 2.30 (s, 3H), 2.36 (s, 3H), 2.46 (s, 3H), 4.10–4.30 (m, 2H), 4.95–5.10 (br s, 2H), 7.05 (d, 1H, J=8), 7.10 (d, 1H, J=8), 7.15 (s, 1H).
3
ac) CI-HRMS: Calcd: 368.2450, Found: 368.2436; Analysis: Calcd: C, 68.62, H, 7.95, N, 19.06; Found: C, 68.73, H, 7.97, N, 19.09; NMR (CDCl, 300 MHz): 1.05 (t, J=8, 3H), 1.70–1.90 (m, 2H), 2.01 (d, J=3, 6H), 2.20 (s, 3H), 2.30 (s, 3H), 2.46, 2.465 (s, s, 3H), 3.42, 3.48 (s, s, 3H), 3.53–3.63 (m, 2H), 4.35–4.45 (m, 1H), 6.73 (d, J=8, 1H), 6.97 (s, 2H).
3
(ad) CI-HRMS: Calcd: 352.2501, Found: 352.2500 (M+H): Analysis: Calcd: C, 71.76; H, 8.33; N: 19.92, Found: C, 71.55; H, 8.15; N, 19.28; NMR (CDCl, 300 MHz): 1.01(t, J=8, 6H), 1.58–1.70 (m, 2H), 1.70–1.85 (m, 2H), 2.02 (s, 6H), 2.19 (s, 3H), 2.45 (s, 3H), 4.12–4.28 (m, 1H), 6.18 (d, J=8, 1H), 6.95 (s, 2H).
3
(ae) CI-HRMS: Calcd: 398.2556, Found: 398.2551 (M+H); Analysis: Calcd: C, 66.47; H, 7.86; N, 17.62, Found: C, 66.74; H, 7.79; N, 17.70; NMR (CDCl, 300 MHz): 2.00 (s, 6H), 2.12 (s, 3H), 2.30 (s, 3H), 2.37 (s, 3H), 3.40 (s, 6H), 3.78 (t, J=8, 4H), 4.25–4.40 (m, 4H), 6.93 (s, 2H).
3
(af) CI-HRMS: Calcd: 450.1141, Found: 450.1133 (M+H); Analysis: Calcd: C, 50.67; H, 5.37; N, 15.55; Br: 17.74; Found: C, 52.36; H, 5.84; N, 14.90; Br: 17.44; NMR (CDCl, 300 MHz): 2.32 (s, 3H), 2.57 (s, 3H), 3.42 (s, 6H), 3.60 (q, J=8, 2H), 3.69 (q, J=8, 2H), 3.82 (s, 3H), 4.60–4.70 (m, 1H), 6.73 (d, J=8, 1H), 6.93 (dd, J=8, 1, 1H), 7.22 (d, J=8, 1H).
3
ag) CI-HRMS: Calcd: 434.1192, Found: 434.1169 (M+H); Analysis: Calcd: C, 52.54; H, 5.58; N, 16.12; Br: 18.40; Found: C, 52.57; H, 5.60; N, 15.98; Br: 18.22; NMR (CDCl, 300 MHz): 1.00–1.07 (m, 3H), 1.65–1.85 (m, 2H), 2.35 (s, 3H), 2.46, 2.47 (s, s, 3H), 3.40, 3.45 (s, s, 3H), 3.83 (s, 3H), 4.35–4.45 (m, 1H), 6.55 (d, J=8, 1H), 6.92 (dd, J=8, 1, 1H) 7.20–7.30 (m, 2H).
3
ah) CI-HRMS: Calcd: 337.2266, Found: 337.2251 (M+H); Analysis: Calcd: C, 70.18; H, 8.06; N, 20.75; Found: C, 70.69; H, 7.66; N: 20.34; NMR (CDCl, 300 MHz): 1.35 (t, J=8, 6H), 2.01 (s, 6H), 2.15 (s, 3H), 2.30 (s, 3H), 2.38 (s, 3H), 4.07 (q, J=8, 4H), 6.93 (s, 2H).
3
ai) CI-HRMS: Calcd: 412.2713, Found: 412.2687 (M+H); Analysis: Calcd: C, 67.13; H, 8.08; N, 17.02; Found: C, 67.22; H, 7.85; N, 17.13; NMR (CDCl, 300 MHz):1.24 (t, J=8, 6H), 2.00 (s, 6H), 2.20 (s, 3H), 2.30 (s, 3H), 2.43 (s, 3H), 3.60 (q, J=8, 4H), 3.66 (dd, J=8, 3, 2H), 3.75 (dd, J=8, 3, 2H), 4.55–4.65 (m, 1H), 6.75 (d, J=8, 1H), 6.95 (s, 2H).
3
aj) CI-HRMS: Calcd: 398.2556, Found: 398.2545 (M+H); Analysis: Calcd: C, 66.47; H, 7.86; N, 17.62; Found: C, 66.87; H, 7.62; N, 17.75; NMR (CDCl, 300 MHz): 1.95–2.10 (m, 8H), 2.20 (s, 3H), 2.32 (s, 3H), 2.44 (s, 3H), 3.38 (s, 3H), 3.42 (s, 3H), 3.50–3.70 (m, 4H), 4.58–4.70 (m, 1H), 6.87 (d, J=8, 1H), 6.95 (s, 2H).
3
ak) CI-HRMS: Calcd: 338.1981, Found: 338.1971 (M+H); Analysis: Calcd: C, 67.63; H, 6.87; N, 20.06; Found: C, 67.67; H, 6.82; N, 20.31; NMR (CDCl, 300 MHz): 2.15 (s, 3H), 2.29 (s, 3H), 2.35 (s, 3H), 2.43 (s, 3H), 3.90 (t, J=8, 4H), 4.35–4.45 (m, 4H), 7.00–7.15 (m, 3H).
3
al) CI-HRMS: Calcd: 464.1297, Found: 464.1297 (M+H); NMR (CDCl, 300 MHz): 2.28 (s, 3H), 2.40 (s, 3H), 3.40 (s, 6H), 3.75 (t, J=8, 4H), 3.83 (s, 3H), 4.20–4.50 (m, 4H), 6.93 (dd, J=8, 1, 1H), 7.20 (s, 1H), 7.24 (d, J=1, 1H).
3
am) CI-HRMS: Calcd: 418.1242, Found: 418.1223 (M+H); NMR (CDCl, 300 MHz): 1.00 (t, d, J=8, 1, 6H), 1.55–1.75 (m, 4H), 2.34 (s, 3H), 2.49 (s, 3H), 2.84 (s, 3H), 4.15–4.27 (m, 1H), 6.19 (d, J=8, 1H), 6.93 (dd, J=8, 1, 1H), 7.21–7.30 (m, 2H).
3
an) CI-HRMS: Calcd: 404.1086, Found: 404.1079(M+H); NMR (CDCl, 300 MHz): 1.35 (t, J=8, 6H), 2.28 (s, 3H), 2.40 (s, 3H), 3.83 (s, 3H), 3.90–4.08 (m, 2H), 4.08–4.20 (m, 2H), 6.92 (dd, J=8, 1, 1H), 7.20–7.25 (m, 2H).
3
ao) CI-HRMS: Calcd: 308.1875, Found: 308.1872 (M+H); NMR (CDCl, 300 MHz): 0.75–0.80 (m, 2H), 0.93–1.00 (m, 2H), 2.16 (s, 3H), 2.28 (s, 3H), 2.35 (s, 3H), 2.53 (s, 3H), 3.00–3.10 (m, 1H), 6.50–6.55 (m, 1H), 7.00–7.15 (m, 3H).
3
ap) CI-HRMS: Calcd: 397.1988, Found: 397.1984 (M+H); NMR (CDCl, 300 MHz): 2.43 (s, 3H), 2.50 (s, 3H), 3.43 (s, 3H), 3.61 (dd, J=8, 8, 2H), 3.69 (dd,J=8, 8, 2H), 3.88 (s, 3H), 4.58–4.70 (m, 1H), 6.75 (d, J=8, 1H), 7.20 (dd, J=8, 1, 1H), 7.25 (d, J=1, 1H), 7.40 (s, 1H).
3
aq) CI-HRMS: Calcd: 375.2297, Found: 375.2286 (M+H); Analysis: Calcd: C, 70.56; H, 7.01; N, 22.44; Found: C, 70.49; H, 6.99; N, 22.45; NMR (CDCl, 300 MHz): 0.79–0.85 (m, 2H), 1.00–1.05 (m, 1H), 2.00 (s, 6H), 2.19 (s, 3H), 2.32 (s, 3H), 2.44 (s, 3H), 2.84 (t, J=8, 2H), 3.30–3.40 (m, 1H), 4.50 (t, J=8, 2H), 6.95 (s, 2H).
3
ar) CI-HRMS: Calcd: 434.1192, Found: 434.1189 (M+H); Analysis: Calcd: C, 52.54; H, 5.58; N, 16.12; Br: 18.40; Found: C, 52.75; H, 5.59; N, 16.09; Br: 18.67; NMR (CDCl, 300 MHz): 2.19 (s, 3H), 2.30 (s, 3H), 2.47 (s, 3H), 3.43 (s, 6H), 3.60 (dd, J=8, 8, 2H), 3.70 (dd, J=8,8, 2H), 4.58–4.70 (m, 1H), 6.71 (d, J=8, 1H), 7.08 (d, J=8, 1H), 7.37 (dd, J=8, 1, 1H), 7.45 (d, J=1, 1H).
3
as) CI-HRMS: Calcd: 448.1348, Found: 448.1332 (M+H); Analysis: Calcd: C, 53.58; H, 5.85; N, 16.62; Br: 17.82; Found: C, 53.68; H, 5.74; N, 15.52; Br: 13.03; NMR (CDCl, 300 MHz): 1.95–2.10 (m, 2H), 2.20 (s, 3H), 2.30 (s, 3H), 2.47 (s, 3H), 3.38 (s, 3H), 3.41 (s, 3H), 3.50–3.67 (m, 4H), 4.55–4.70 (m, 1H), 6.89 (d, J=8, 1H), 7.05 (d, J=8, 1H), 7.35 (dd, J=8, 1, 1H), 7.47 (d, J=1, 1H).
3
at) CI-HRMS: Calcd: 400.2349, Found: 400.2348 (M+H); Analysis: Calcd: C: C, 63.14; H, 7.32; N, 17.53; Found: C, 63.40; H, 7.08; N, 17.14; NMR (CDCl, 300 MHz): 2.16 (s, 3H), 2.20 (s, 3H), 2.30 (s, 3H), 2.46 (s, 3H), 3.42 (s, 6H), 3.60 (q, J=8, 2H), 3.70 (q, J=8, 2H), 3.85 (s, 3H), 4.59–4.70 (m, 1H), 6.70 (d, J=8, 1H), 6.76 (s, 1H), 6.96 (s, 1H).
3
au) CI-HRMS: Calcd: 414.2505, Found: 414.2493 (M+H); NMR (CDCl, 300 MHz): 2.15 (s, 3H), 2.19 (s, 3H), 2.25 (s, 3H), 2.40 (s, 3H), 3.40 (s, 6H), 3.76 (t, J=8, 4H), 3.84 (s, 3H), 4.20–4.45 (m, 4H), 6.77 (s, 1H), 6.93 (s, 1H).
3
av) CI-HRMS: Calcd: 368.2450, Found: 368.2447 (M+H); NMR (CDCl, 300 MHz): 1.00 (t, J=8, 6H), 1.55–1.85 (m, 4H), 2.19 (s, 3H), 2.20 (s, 3H), 2.30 (s, 3H), 2.47 (s, 3H), 3.88 (s, 3H), 4.10–4.30 (m, 1H), 6.15 (d, J=8, 1H), 6.78 (s, 1H), 6.98 (s, 1H).
3
aw) CI-HRMS: Calcd: 353.2216, Found: 353.2197 (M+H); NMR (CDCl, 300 MHz): 1.35 (t, J=8, 6H), 2.17 (s, 3H), 2.19 (s, 3H), 2.28 (s, 3H), 2.40 (s, 3H), 3.85 (s, 3H), 3.90–4.20 (m, 4H), 6.78 (s, 1H), 6.95 (s, 1H).
3
ax) CI-HRMS: Calcd: 390.1697, Found: 390.1688 (M+H); Analysis: Calcd: C, 58.53; H, 6.20; N, 17.96; Cl: 9.09; Found: C, 58.95; H, 6.28; N, 17.73; Cl: 9.15; NMR (CDCl, 300 MHz): 2.35 (s, 3H), 2.37 (s, 3H), 2.48 (s, 3H), 3.42 (s, 6H), 3.60 (dd, J=8, 8, 2H) 3.68 (dd, J=8, 8, 2H), 4.59–4.72 (m, 1H), 6.72 (d, J=8, 1H), 7.12 (d, J=8, 1H), 7.23 (d, J=8, 1H), 7.32 (s, 1H).
3
ay) CI-HRMS: Calcd: 374.1748, Found: 374.1735 (M+H); Analysis: Calcd: C, 61.04; H, 6.47; N, 18.73; Cl: 9.48; Found: C, 61.47; H, 6.54; N, 18.23; Cl: 9.61; NMR (CDCl,300 MHz): 1.01 (t, J=8, 3H), 1.62–1.88 (m, 4H), 2.35 (s, 3H), 2.37 (s, 3H), 2.48 (d, J=1, 3H), 3.40, 3.45 (s, s, 3H), 3.50–3.64 (m, 2H), 4.38–4.47 (m, 1H), 6.53 (d, J=8, 1H), 7.12 (d, J=8, 1H), 7.07 (d, J=8, 1H), 7.12 (s, 1H).
3
az) CI-HRMS: Calcd: 404.1853, Found: 404.1839 (M+H); NMR (CDCl, 300 MHz): 2.29 (s, 3H), 2.38 (s, 3H), 2.40 (s, 3H), 3.40 (s, 6H), 3.76 (t, J=8, 4H), 4.20–4.45 (m, 4H), 7.11 (d, J=8, 1H), 7.22 (d, J=8, 1H), 7.31 (s, 1H).
3
ba) CI-HRMS: Calcd: 404.1853, Found: 404.1859 (M+H); Analysis: C, 59.47; H, 6.50; N, 17.34; Cl: 8.79; Found: C, 59.73; H, 6.46; N, 17.10; Cl: 8.73; NMR (CDCl, 300 MHz): 1.95–2.08 (m, 2H), 2.35 (s, 3H), 2.38 (s, 3H), 2.46 (s, 3H), 3.38 (s, 3H), 3.41 (s, 3H), 3.50–3.65 (m, 4H), 4.56–4.70 (m, 1H), 6.85 (d, J=8, 1H), 7.12 (d, J=8, 1H), 7.45 (d, J=8, 1H), 7.32 (s, 1H).
3
bb) CI-HRMS: Calcd: 391.2246, Found: 391.2258 (M+H); Analysis: C, 67.67; H, 6.71; N, 21.52; Found: C: 67.93; H, 6.70; N, 21.48; NMR (CDCl, 300 MHz): 0.76–0.84 (m, 2H), 0.84–0.91 (m, 2H), 1.00–1.08 (m, 2H), 2.15 (s, 3H), 2.20 (s, 3H), 2.29 (s, 3H), 2.45 (s, 3H), 2.85 (t, J=8, 2H), 3.28–3.30 (m, 1H), 3.85 (s, 3H), 6.78 (s, 1H), 6.95 (s, 1H).
3
bc) CI-HRMS: Calcd: 386.2192, Found: 386.2181 (M+H); Analysis: C, 62.32; H, 7.06; N, 18.17; Found: C: 62.48; H, 6.83; N, 18.15; NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=8), 6.9 (d, 1H, J=1), 6.8 (dd, 1H, J=8,1), 6.7 (br. d, 1H, J=8), 4.7–4.6 (m, 1H), 3.85 (s, 3H), 3.70–3.55 (m, 4H), 3.45 (s, 6H), 2.5 (s, 3H), 2.3 (s, 3H), 2.15 (s, 3H).
3
bd) CI-HRMS: Calcd: 400.2349, Found: 400.2336 (M+H); NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=7), 6.85 (d, 1H, J=1), 6.75 (dd, 1H, J=7,1), 4.45–4.25 (br.s, 4H), 3.75 (t, 4H, J=7), 3.4 (s, 6H), 2.4 (s, 3H), 2.25 (s, 3H), 2.15 (s, 3H).
3
be) CI-HRMS: Calcd: 370.2243, Found: 370.2247 (M+H); Analysis: C, 65.02; H, 7.38; N, 18.96; Found: C: 65.28; H, 7.27; N, 18.71; NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=8), 6.85 (d, 1H, J=1), 6.8 (dd, 1H, J=8,1), 6.5 (br. d, 1H, J=1), 4.5–4.3 (m, 1H), 3.85 (s, 3H), 3.65–3.5 (m, 2H), 3.4 (s, 2H), 2.5 (s, 3H), 2.3 (s, 3H), 2.2 (s, 3H), 1.9–1.7 (m, 2H), 1.05 (t, 3H, J=7).
3
bf) CI-HRMS: Calcd: 379.2246, Found: 379.2248 (M+H); NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=8), 6.85 (d, 1H, J=1), 6.8 (dd, 1H, J=8,1), 4.3–4.0 (m, 4H), 3.85 (s, 3H), 3.0 (t, 2H, J=7), 2.45 (s, 3H), 2.3 (s, 3H), 2.2 (s, 3H), 1.9–1.8 (m, 2H) 1.0 (t, 3H, J=7).
3
bg) CI-HRMS: Calcd: 340.2137, Found: 340.2122 (M+H); NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=8), 6.85 (d, 1H, J=1), 6.75 (dd, 1H, J=8,1), 4.2–4.0 (br.m, 4H), 3.85 (s, 3H, 2.4 (s, 3H), 2.3 (s, 3H), 2.2 (s, 3H), 1.35 (t, 6H, J=7).
bh) CI-HRMS: Calcd: 313.1665, Found: 313.6664 (M+H).
3
bi) CI-HRMS: Calcd: 400.2349, Found: 400.2346 (M+H); NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=7), 6.9–6.75 (m, 3H), 4.7–4.55 (m, 1H), 3.8 (s, 3H), 3,7–3.5 (m, 4H), 3.45 (s, 3H), 3.35 (s, 3H), 2.5 (s, 3H), 2.3 (s, 3H), 2.2 (s, 3H), 2.1–1.95 (m, 2H).
3
bj) CI-HRMS: Calcd: 377.2090, Found: 377.2092 (M+H); Analysis: C, 67.00; H, 6.44; N, 22.32; Found: C: 67.35; H, 6.44; N, 22.23; NMR (CDCl, 300 MHz): 7.1 (d, 1H, J=8), 6.9 (d, 1H, J=1), 6.8 (dd, 1H, J=8,1), 4.55–4.4 (m, 2H), 3.85 (s, 3H), 3.4–3.3 (m, 1H), 2.85 (t, 2H, J=7), 2.5 (s, 3H), 2.3 (s, 3H), 2.2 (s, 3H), 1.11.0 (m, 2H), 0.85–0.75 (m, 2H).
3
bk) CI-HRMS: Calcd: 413.2427, Found: 413.2416 (M+H); NMR (CDCl, 300 Hz): 7.1 (d, 1H, J=8), 6.85 (d, 1H, J=1), 6.75 (dd, 1H, J=8,1), 4.6 (m, 1H), 3.85 (s, 3H), 3.75–3.6(m, 4H), 3.6 (q, 4H, J=7), 2.5 (s, 3H), 2.3 s, 3H), 2.2 (s, 3H), 1.25 (t, 6H, J=7).
bl) CI-HRMS: Calcd: 420.1802, Found: 420.1825(M+H);
bm) CI-HRMS: Calcd: 390.1697, Found: 390.1707(M+H);
bn) CI-HRMS: Calcd: 397.1465, Found: 397.1462(M+H);
bo) CI-HRMS: Calcd: 360.1513, Found: 360.1514(M+H);
bp) CI-HRMS: Calcd: 374.1748, Found: 374.1737(M+H);
bq) CI-HRMS: Calcd: 479.1155, Found: 479.1154(M+H);
br) CI-HRMS: Calcd: 463.1219, Found: 463.1211(M+H); Analysis Calcd: C, 51.96, H, 5.23, N, 15.15, Br: 17.28; Found: C, 52.29, H, 5.62, N, 14.79, Br: 17.47
79
bs) CI-HRMS: Calcd: 433.1113, Found: 433.1114(M, Br);
3
3
bt) NH—CI MS: Calcd: 406, Found: 406 (M+H)+; NMR (CDCl, 300 MHz):δ7.28 (d, J=10 Hz, 1H), 7.03 (d, J=8 Hz, 1H), 6.96 (s, 1H), 6.7 (d, J=9, 1H), 4.63 (m, 1H), 3.79 (s, 3H), 3.6 (m, 4H), 3.42 (s, 6H), 2.47 (s, 3H), 2.32 (s, 3H).
3
4
3
3
5-Acetamidino-4-(4-methoxy-2-methylphenyl)-3-methylpyrazole, acetic acid salt (602 mg, 2 mmol) was mixed with a saturated NaHCOsolution (10 mL). The aqueous mixture was extracted with EtOAc three times. The combined organic layers were dried over MgSO, filtered and concentrated in vacuo. The residue was taken up in toluene (10 mL) and trimethyl orthoacetate (0.36 g, 3 mmol) was added to the suspension. The reaction mixture was heated to reflux temperature under a nitrogen atmosphere and stirred for 16 hours. After being cooled to ambient temperature, the reaction mixture was concentrated in vacuo to give an oily solid. Column chromatography (CHCl:MeOH::9:1) afforded, after removal of solvent in vacuo, a yellow viscous oil (Rf=0.6, 210 mg, 37% yield): NMR (CDCl, 300 MHz): 7.15 (d, 1H, J=8), 6.9 (d, 1H, J=1), 6.85 (dd, 1H, J=8,1), 3.85 (s, 3H), 2.95 (s, 3H), 2.65 (s, 3H), 2.4 (s, 3H), 2.15 (s, 3H); CI-HRMS: Calcd: 283.1559, Found: 283.1554 (M+H).
3
5-Amino-4-(2-chloro-4-methylphenyl)-3-methylpyrazole (1.86 g, 8.4 mmol) was dissolved in glacial acetic acid (30 mL) with stirring. Ethyl acetoacetate (1.18 mL, 9.2 mmol) was then added dropwise to the resulting solution. The reaction mixture was then heated to reflux temperature and stirred for 16 hours, then cooled to room temperature. Ether (100 mL) was added and the resulting precipitate was collected by filtration. Drying in vacuo afforded a white solid (1.0 g, 42% yield): NMR (CDCl, 300 Hz): 8.70 (br.s 1H), 7.29 (s, 1H), 7.21–7.09 (m, 2H), 5.62 (s, 1H), 2.35 (s, 6H), 2.29 (s, 3H); CI-MS: 288 (M+H).
3
A mixture of 7-hydroxy-5-methyl-3-(2-chloro-4-methylphenyl)-pyrazolo[1,5-a]pyrimidine (1.0 g, 3.5 mmol), phosphorus oxychloride (2.7 g, 1.64 mL, 17.4 mmol), N,N-diethylaniline (0.63 g, 0.7 mL, 4.2 mmol) and toluene (20 mL) was stirred at reflux temperature for 3 hours, then it was cooled to ambient temperature. The volatiles were removed in vacuo. Flash chromatography (EtOAc:hexane::1:2) on the residue gave 7-chloro-5-methyl-3-(2-chloro-4-methylphenyl)pyrazolo[1,5-a]pyrimidine (900 mg, 84% yield) as a yellow oil: NMR (CDCl, 300 Hz): 7.35 (s, 1H), 7.28–7.26 (m, 1H), 71.6 (d, 1H, J=7), 6.80 (s, 1H), 2.55 (s, 3H), 2.45 (s, 3H), 2.40 (s, 3H); CI-MS: 306 (M+H).
1
6
3
6
1
4
n
2
2
2
15
13
15
15
13
8
15
15
8
16
15
8
13
16
15
16
15
each occurrence from C–Calkyl, C–Ccycloalkyl, halo, C–Chaloalkyl, cyano, OR, SH, S(O)R, COR, COR, OC(O)R, NRCOR, N(COR), NRCONRR, NRCOR, NRR, CONRR, aryl, heteroaryl or heterocyclyl,
1
4
1
4
1
4
4
3
2
25
4
-aryl, aryl(C–Calkyl), heteroaryl, heteroaryl(C–Calkyl), heterocyclyl or heterocyclyl(C–Calkyl);
3-pentylamine (394 mg, 6.5 mmol) and 7-chloro-5-methyl-3-(2-chloro-4-methylphenyl)pyrazolo[1,5-a]pyrimidine (200 mg, 0.65 mmol) in dimethylsulfoxide (DMSO, 10 mL) was stirred at 150° C. for 2 hours; then it was cooled to ambient temperature. The reaction mixture was then poured onto water (100 mL) and mixed. Three extractions with dichloromethane, washing the combined organic layers with brine, drying over MgSO, filtration and removal of solvent in vacuo produced a yellow solid. Flash chromatography (EtOAc:hexanes::1:4) afforded a white solid (140 mg, 60% yield): mp 139–141° C.; NMR (CDCl, 300 Hz):7.32 (s, 1H), 7.27 (d, 1H, J=8), 7.12 (d, 1H, J=7), 6.02 (d, 1H, J=9), 5.78 (s, 1H), 3.50–3.39 (m, 1H), 2.45 (s, 3H), 2.36 (s, 6H), 1.82–1.60 (m, 4H), 1.01 (t, 6H, J=8); Analysis Calcd for COOHClN: C, 67.31, H, 7.06, N, 15.70, Cl: 9.93; Found: C, 67.32, H, 6.95, N, 15.50, Cl, 9.93.
A solution of substituents independently selected at
The examples delineated in TABLE 2 may be prepared by the methods outlined in Examples 1A, 1B, 432, 433, 434. Commonly used abbreviations are: Ph is phenyl, Pr is propyl, Me is methyl, Et is ethyl, Bu is butyl, Ex is Example, EtOAc is ethyl acetate.
TABLE 2
<chemistry id="CHEM-US-00040" num="00040"><img id="EMI-C00040" he="23.20mm" wi="24.64mm" file="US07094782-20060822-C00040.TIF" alt="embedded image" img-content="table" img-format="tif" /></chemistry>
Ex.
Z
R<sub>3</sub>
Ar
mp(° C.)
435<sup>b</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
71–73
436<sup>c</sup>
C—Me
N(Bu)Et
2,4-Cl<sub>2</sub>—Ph
86–87
437<sup>d</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
110–111
438<sup>e</sup>
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Cl<sub>2</sub>—Ph
83–85
439<sup>f</sup>
C—Me
NH-3-pentyl
2,4-Cl<sub>2</sub>—Ph
175–176
440<sup>g</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
107
441<sup>h</sup>
C—Me
NHCH(Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
oil
442<sup>i</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
103–105
443<sup>j</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
87–89
444<sup>k</sup>
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
133 (dec)
445<sup>l</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl,4-MePh
77–78
446<sup>m</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl,4-MePh
131–133
447<sup>n</sup>
C—Me
NHCH(Et)<sub>2</sub>
2-Cl,4-MePh
139–141
448<sup>o</sup>
C—Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
92–94
449<sup>p</sup>
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
143–144
450<sup>q</sup>
C—Me
N(Bu)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
115–117
451<sup>r</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
oil
452<sup>s</sup>
C—Me
NHCH(Et)<sub>2</sub>
2-Me,4-MeOPh
104–106
453<sup>t</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me,4-MeOPh
115–116
454<sup>u</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me,4-MeOPh
oil
455<sup>v</sup>
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)—(CH<sub>2</sub>OMe)
2-Me,4-MeOPh
oil
456<sup>w</sup>
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)—(CH<sub>2</sub>OMe)
2,4-Me<sub>2</sub>—Ph
oil
457<sup>x</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me,4-ClPh
oil
458<sup>y</sup>
C—Me
NHEt
2,4-Me<sub>2</sub>—Ph
oil
459<sup>z</sup>
C—Me
NHCH(Et)<sub>2</sub>
2-Me,4-ClPh
94–96
460<sup>aa</sup>
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me,4-ClPh
113–114
461<sup>ab</sup>
C—Me
N(Ac)Et
2,4-Me<sub>2</sub>—Ph
oil
462<sup>ac</sup>
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)—(CH<sub>2</sub>OMe)
2-Me,4-ClPh
oil
463<sup>ad</sup>
C—Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me,4-MeOPh
118–119
464<sup>ae</sup>
C—Me
NEt<sub>2</sub>
2-Me,4-MeOPh
97–99
465<sup>af</sup>
C—Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)—(CH<sub>2</sub>OMe)
2-Cl,4-MePh
101–103
466<sup>ag</sup>
C—Me
NEt<sub>2</sub>
2-Cl,4-MePh
129–130
467<sup>ah</sup>
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me,4-MeOPh
177–178
468<sup>ai</sup>
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl,4-MePh
162–163
469<sup>aj</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me,4-MeOPh
oil
470<sup>ak</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl,4-MePh
111–113
471
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
472
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
473
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MeOPh
474
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4-MeOPh
475
C—Me
NEt<sub>2</sub>
2-Cl-4-MeOPh
476
C—Me
NH-3-pentyl
2-Cl-4-MeOPh
477
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
478
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
479
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
480
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
481
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
482
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
483
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
484
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
485
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
486
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4,5-(MeO)<sub>2</sub>Ph
487
C—Me
NEt<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
99–101
488
C—Me
NH-3-pentyl
2-Cl-4,5-(MeO)<sub>2</sub>Ph
169–170
489
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
490
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
491
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
90–93
492
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
110
493
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
494
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4,5-(MeO)<sub>2</sub>Ph
495
C—Me
NEt<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
496
C—Me
NH-3-pentyl
2-Br-4,5-(MeO)<sub>2</sub>Ph
497
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
498
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
499
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
500
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
501
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4,6-(MeO)<sub>2</sub>Ph
502
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4,6-(MeO)<sub>2</sub>Ph
503
C—Me
NEt<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
504
C—Me
NH-3-pentyl
2-Cl-4,6-(MeO)<sub>2</sub>Ph
505
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,6-(MeO)<sub>2</sub>Ph
506
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,6-(MeO)<sub>2</sub>Ph
507
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
508
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
509
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
510
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4,6-(MeO)<sub>2</sub>Ph
511
C—Me
NEt<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
512
C—Me
NH-3-pentyl
2-Me-4,6-(MeO)<sub>2</sub>Ph
513
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
514
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
515
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4,6-(MeO)<sub>2</sub>Ph
516
C—Me
NEt<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>Ph
517
C—Me
NH-3-pentyl
2-Br-4,6-(MeO)<sub>2</sub>Ph
518
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,6-(MeO)<sub>2</sub>Ph
519
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4,6-(MeO)<sub>2</sub>Ph
520
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
521
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
522
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
523
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
524
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
525
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
526
C—Me
NEt<sub>2</sub>
2-MeO-4-MePh
527
C—Me
NH-3-pentyl
2-MeO-4-MePh
528
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
529
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
530
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
531
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
532
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
533
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
534
C—Me
NEt<sub>2</sub>
2-MeO-4-MePh
535
C—Me
NH-3-pentyl
2-MeO-4-MePh
536
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
537
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
538
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
539
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
540
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-ClPh
541
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-ClPh
542
C—Me
NEt<sub>2</sub>
2-MeO-4-ClPh
543
C—Me
NH-3-pentyl
2-MeO-4-ClPh
544
C—Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-ClPh
545
C—Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-ClPh
Notes for Table 2:
b) CI-HRMS: Calcd: 423.1355; Found: 423.1337 (M+H).
c) Analysis: Calcd: C, 61.38, H, 6.18, N, 14.32: Found: C, 61.54, H, 6.12, N, 14.37.
d) Analysis: Calcd: C, 58.02, H, 5.65, N, 14.24; Found: C, 58.11, H, 5.52, N, 14.26.
e) Analysis: Calcd: C, 59.71, H, 5.26, N, 14.85; Found: C, 59.94, H, 5.09, N, 17.23.
f) Analysis: Calcd: C, 60.48, H, 5.89, N, 14.85, Found: C, 60.62, H, 5.88, N, 14.82.
h) CI-HRMS: Calcd: 337.2388; Found: 337.2392 (M+H).
i) Analysis: Calcd: C, 68.45, H, 7.669, N, 15.21, Found: C, 68.35, H, 7.49 N, 14.91.
j) Analysis: Calcd: C, 69.08, H, 7.915, N, 14.65, Found: C, 68.85, H, 7.83, N, 14.54.
k) Analysis: Calcd: C, 73.51, H, 7.01, N, 19.48, Found: C, 71.57, H, 7.15, N, 19.12.
l) CI-HRMS: Calcd: 403.1899; Found: 403.1901 (M+H).
m) Analysis: Calcd: C, 61.77, H, 6.49, N, 14.41, Cl. 9.13; Found: C, 61.90, H, 6.66, N, 13.62, Cl, 9.25.
n) Analysis: Calcd: C, 67.31, H, 7.06, N, 15.70, Cl. 9.93; Found: C, 67.32, H, 6.95, N, 15.50, Cl, 9.93.
o) Analysis: Calcd:. C, 74.50, H, 8.14, N, 17.38, Found: C, 74.43, H, 7.59, N, 17.16.
p) Analysis: Calcd: C, 73.10, H, 7.54, N, 19.37, Found: C, 73.18, H, 7.59, N, 18.81.
q) Analysis: Calcd: C, 73.57, H, 7.78, N, 18.65, Found: C, 73.55, H, 7.79, N, 18.64.
r) CI-HRMS: Calcd: 353.2333; Found: 353.2341 (M+H).
s) Analysis: Calcd: C, 71.56, H, 8.02, N, 15.90, Found: C, 71.45, H, 7.99, N, 15.88.
t) Analysis: Calcd: C, 65.60, H, 7.34, N, 14.57, Found: C, 65.42, H, 7.24, N, 14.37.
u) CI-HRMS: Calcd: 399.2398; Found: 399.2396 (M+H).
v) CI-HRMS: Calcd: 399.2398; Found: 399.2396 (M+H).
w) CI-HRMS: Calcd: 383.2450; Found: 383.2447 (M+H).
x) CI-HRMS: Calcd: 403.1887; Found: 403.1901 (M+H).
y) CI-HRMS: Calcd: 295.1919; Found: 295.1923 (M+H).
z) Analysis: Calcd: C, 67.31, H, 7.06, N, 15.70, Found: C, 67.12, H, 6.86, N, 15.53.
aa) Analysis: Calcd: C, 61.77, H, 6.49, N, 14.41, Cl, 9.13; Found: C, 62.06, H, 6.37, N, 14.25, Cl, 9.12.
ab) CI-HRMS: Calcd: 337.2017; Found: 337.2028 (M+H).
ac) CI-HRMS: Calcd: 403.1893; Found: 403.1901 (M+H).
ad) Analysis: Calcd: C, 70.00, H, 7.22, N, 18.55, Found: C, 70.05, H, 7.22, N, 18.36.
ae) Analysis: Calcd: C, 70.98, H, 7.74, N, 16.55, Found: C, 71.15, H, 7.46, N, 16.56.
ag) Analysis: Calcd: C, 66.59, H, 6.76, N, 16.34, Found: C, 66.69, H, 6.82, N, 16.20.
ah) Analysis: Calcd: C, 70.38, H, 6.71, N, 18.65, Found: C, 70.35, H, 6.82, N, 18.83.
ai) Analysis: Calcd: C, 66.39, H, 5.85, N, 18.44, Cl, 9.33; Found: C, 66.29, H, 5.51, N, 18.36, Cl, 9.31.
aj) CI-HRMS: Calcd: 369.2278; Found: 369.2291 (M+H).
ak) Analysis: Calcd: C, 64.42, H, 6.77, N, 15.02, Found: C, 64.59, H, 6.51, N, 14.81.
The examples delineated in TABLE 3 may be prepared by the methods outlined in Examples 1, 2, 3 or 6. Commonly used abbreviations are: Ph is phenyl, Pr is propyl, Me is methyl, Et is ethyl, Bu is butyl, Ex is Example.
TABLE 3
<chemistry id="CHEM-US-00041" num="00041"><img id="EMI-C00041" he="23.20mm" wi="24.64mm" file="US07094782-20060822-C00041.TIF" alt="embedded image" img-content="table" img-format="tif" /></chemistry>
Ex.
Z
R<sub>3</sub>
Ar
mp(° C.)
546<sup>a</sup>
C—Me
NHCH(Et)<sub>2</sub>
2-Me-4-Me<sub>2</sub>N—Ph
164–166
547<sup>b</sup>
C—Me
S—NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)—CH<sub>2</sub>OMe
2,4-Me2-Ph
oil
548<sup>c</sup>
C—Me
S—NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)—CH<sub>2</sub>OMe
2-Me-4-Cl—Ph
oil
549<sup>d</sup>
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-Cl—Ph
115–116
550<sup>e</sup>
C—Me
NHCH(Et)CH<sub>2</sub>CN
2-Me-4-Cl—Ph
131–132
551<sup>f</sup>
C—Me
N(Et)<sub>2</sub>
2,3-Me<sub>2</sub>-4-OMe—Ph
oil
552<sup>g</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)CH<sub>2</sub>CH<sub>2</sub>OH
2,4-Cl<sub>2</sub>—Ph
oil
553<sup>h</sup>
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,3-Me<sub>2</sub>-4-OMe—Ph
oil
554<sup>i</sup>
C—Me
NHCH(Et)<sub>2</sub>
2,3-Me<sub>2</sub>-4-OMePh
123–124
555<sup>j</sup>
C—Me
N(CH<sub>2</sub>—c-Pr)Pr
2-Me-4-Cl—Ph
oil
556<sup>k</sup>
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,3-Me<sub>2</sub>-4-OMePh
158–160
557
C—Me
N(c-Pr)Et
2-Cl-4-OMePh
558
C—Me
N(c-Pr)Me
2-Cl-4-OMePh
559
C—Me
N(c-Pr)Pr
2-Cl-4-OMePh
560
C—Me
N(c-Pr)Bu
2-Cl-4-OMePh
561<sup>l</sup>
C—Me
N(Et)<sub>2</sub>
2-Cl-4-CN—Ph
115–117
562
C—Me
N(c-Pr)<sub>2</sub>
2-Cl-4-OMe
127–129
563<sup>m</sup>
C—Me
NHCH(CH<sub>2</sub>OH)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
128–129
564
C—Me
N(c-Pr)Et
2-Br-4,5-(MeO)2Ph
565
C—Me
N(c-Pr)Me
2-Br-4,5-(MeO)2Ph
566
C—Me
NH-c-Pr
2-Me-4-MeOPh
126–128
567
C—Me
NHCH(Et)CH2OH
2-Me-4-MeOPh
60–62
568
C—Me
NMe<sub>2</sub>
2-Br-4,5-(MeO)2Ph
569
C—Me
NHCH(Et)<sub>2</sub>
2-Me-4-MeOPh
103–105
570
C—Me
N(c-Pr)Et
2-Me-4-MeOPh
173–174
571
C—Me
NH-2-pentyl
2,4-Cl<sub>2</sub>—Ph
118–120
572
C—Me
NHCH(Et)CH2CN
2,4-Cl<sub>2</sub>—Ph
141–142
573
C—Me
NHCH(Pr)CH2OMe
2,4-Cl<sub>2</sub>—Ph
87–88
574
C—Me
NHCH(CH2-iPr)CH2OMe
2,4-Cl<sub>2</sub>—Ph
amorphous
575
C—Me
NH-2-butyl
2,4-Me<sub>2</sub>—Ph
oil
576
C—Me
NH-2-pentyl
2,4-Me<sub>2</sub>—Ph
oil
577
C—Me
NH-2-hexyl
2,4-Me<sub>2</sub>—Ph
oil
578
C—Me
NHCH(i-Pr)Me
2,4-Me<sub>2</sub>—Ph
oil
579
C—Me
NHCH(Me)CH2-iPr
2,4-Me<sub>2</sub>—Ph
oil
580
C—Me
NHCH(Me)-c-C6H11
2,4-Me<sub>2</sub>—Ph
oil
581
C—Me
NH-2-indanyl
2,4-Me<sub>2</sub>—Ph
oil
582
C—Me
NH-1-indanyl
2,4-Me<sub>2</sub>—Ph
oil
583
C—Me
NHCH(Me)Ph
2,4-Me<sub>2</sub>—Ph
oil
584
C—Me
NHCH(Me)CH<sub>2</sub>—(4-ClPh)
2,4-Me<sub>2</sub>—Ph
oil
585
C—Me
NHCH(Me)CH<sub>2</sub>COCH<sub>3</sub>
2,4-Me<sub>2</sub>—Ph
oil
586
C—Me
NHCH(Ph)CH<sub>2</sub>Ph
2,4-Me<sub>2</sub>—Ph
oil
587
C—Me
NHCH(Me)(CH<sub>2</sub>)3NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
oil
588
C—Me
NH—(2-Ph-c-C<sub>3</sub>H<sub>4</sub>)
2,4-Me<sub>2</sub>—Ph
oil
589
C—Me
NHCH(Et)CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
119–120
590
C—Me
NH-3-hexyl
2,4-Me<sub>2</sub>—Ph
oil
591<sup>n</sup>
C—Me
NEt<sub>2</sub>
2-MeO-4-ClPh
oil
592<sup>o</sup>
C—Me
NHCH(Et)<sub>2</sub>
2-MeO-4-ClPh
oil
593<sup>p</sup>
C—Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-ClPh
oil
594
C—Me
NMe<sub>2</sub>
2-MeO-4-ClPh
oil
595<sup>q</sup>
C—Me
NHCH(Et)<sub>2</sub>
2-OMe-4-MePh
oil
596<sup>r</sup>
C—Me
NEt<sub>2</sub>
2-OMe-4-MePh
oil
597<sup>s</sup>
C-c-Pr
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
oil
598
C—Me
N(c-Pr)Et
2,4-Me<sub>2</sub>—Ph
599
C—Me
N(c-Pr)Et
2,4-Cl<sub>2</sub>—Ph
600
C—Me
N(c-Pr)Et
2,4,6-Me<sub>3</sub>—Ph
601
C—Me
N(c-Pr)Et
2-Me-4-Cl—Ph
602
C—Me
N(c-Pr)Et
2-Cl-4-Me—Ph
603
C—Me
NHCH(c-Pr)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
604
C—Me
NHCH(c-Pr)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
605
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Me-4-Cl—Ph
606
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Cl-4-Me—Ph
607
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Me-4-OMe—Ph
608
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Cl-4-OMe—Ph
609
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-5-F—OMePh
610
C—Me
NEt<sub>2</sub>
2-Cl-5-F—OMePh
611
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-5-F—OMePh
612
C—Me
NHCH(Et)<sub>2</sub>
2-Cl-5-F—OMePh
613
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-5-F—OMePh
614
C—Me
NEt<sub>2</sub>
2,6-Me<sub>2</sub>-pyrid-3-yl
615
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,6-Me<sub>2</sub>-pyrid-3-yl
616
C—Me
NHCH(Et)<sub>2</sub>
2,6-Me<sub>2</sub>-pyrid-3-yl
617
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-Me<sub>2</sub>-pyrid-3-yl
618
C—OH
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
619
C—OH
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
620
C—OH
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
621
C—OH
NHCH(Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
623
C—OH
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
624
C—NEt<sub>2</sub>
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
625
C—NEt<sub>2</sub>
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
626
C—NEt<sub>2</sub>
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
627
C—NEt<sub>2</sub>
NHCH(Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
628
C—NEt<sub>2</sub>
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
629
C—Me
NHCH(Et)<sub>2</sub>
2-Me-4-CN—Ph
630
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-CN—Ph
Notes for Table 3:
a) CI-HRMS: Calcd:367.2610, Found: 367.2607 (M+H);
b) CI-HRMS: Calcd:384.2400, Found: 384.2393 (M+H);
c) CI-HRMS: Calcd:404.1853, Found: 404.1844 (M+H);
d) CI-HRMS: Calcd:381.1594, Found: 381.1596 (M+H); Analysis: Calcd: C, 63.07, H, 5.57, N, 22.07, Cl, 9.32; Found: C, 63.40, H, 5.55, N, 21.96, Cl: 9.15
e) CI-HRMS: Calcd:369.1594, Found: 369.1576 (M+H);
f) CI-HRMS: Calcd:354.2216, Found: 354.2211 (M+H);
g) CI-HRMS: Calcd:410.1072, Found: 410.1075 (M+H);
h) CI-HRMS: Calcd:414.2427, Found: 414.2427(M+H);
i) CI-HRMS: Calcd:368.2372, Found: 368.2372(M+H);
j) CI-HRMS: Calcd:384.1955, Found: 384.1947(M+H);
k) CI-HRMS: Calcd:391.2168, Found: 391.2160(M+H);
l) CI-HRMS: Calcd:335.1984, Found: 335.1961(M+H);
m) CI-HRMS: Calcd:382.0759, Found: 382.0765(M+H);
3
n) NH-CI MS: Calcd: 360, Found: 360 (M+H)+
3
3
o) NH-CI MS: Calcd: 374, Found: 374 (M+H)+; NMR (CDCl, 300 MHz):δ7.29 (d, J=8.4 Hz, 1H), 7.04 (dd, J=1.8, 8 Hz, 1H), 6.96 (d, J=1.8 Hz, 1H), 6.15 (d, J=10, 1H), 4.19 (m, 1H), 3.81 (s, 3H), 2.47 (s, 3H), 2.32 (s, 3H), 1.65 (m, 4H), 0.99 (t, J=7.32 Hz, 6H)
3
3
p) NH-CI MS: Calcd: 390, Found: 390 (M+H)+; NMR (CDCl, 300 MHz): δ7.28 (d, J=8 Hz, 1H), 7.03 (d, J=8 Hz, 1H), 6.96 (s, 1H), 6.52 (d, J=9 Hz, 1H), 4.36 (m, 1H), 3.8 (s, 3H), 3.55 (m, 2H), 3.39 (s, 3H), 2.47 (s, 3H), 2.32 (s, 3H), 1.76 (m, 2H), 1.01 (t, J=7.32 Hz, 3H).
q) CI-HRMS: Calcd: 354.2294, Found: 354.2279 (M+H)+
r) CI-HRMS: Calcd: 340.2137, Found: 340.2138 (M+H)+
s) CI-HRMS: Calcd: 436.1307, Found: 436.1296 (M+H)+
The examples delineated in TABLE 4 may be prepared by the methods outlined in Examples 1A, 1B, 432, 433, 434. Commonly used abbreviations are: Ph is phenyl, Pr is propyl, Me is methyl, Et is ethyl, Bu is butyl, Ex is Example, EtOAc is ethyl acetate.
TABLE 4
<chemistry id="CHEM-US-00042" num="00042"><img id="EMI-C00042" he="23.20mm" wi="24.64mm" file="US07094782-20060822-C00042.TIF" alt="embedded image" img-content="table" img-format="tif" /></chemistry>
Ex.
Z
R<sub>3</sub>
Ar
mp (° C.)
631
C—Me
NHCH(Et)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
160–161
632
C—Me
NHCH(Et)<sub>2</sub>
2-Br-4-MeOPh
110–111
633
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeOPh
74–76
634
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeOPh
128–130
635
C—Me
N(Et)<sub>2</sub>
2-Me-4-ClPh
113–114
636
C—Me
N(c-Pr)Et
2,4-Cl<sub>2</sub>Ph
637
C—Me
N(c-Pr)Et
2,4-Me<sub>2</sub>Ph
638
C—Me
N(c-Pr)Et
2,4,6-Me<sub>3</sub>Ph
639
C—Me
N(c-Pr)Et
2-Me-4-MeOPh
640
C—Me
N(c-Pr)Et
2-Cl-4-MeOPh
641
C—Me
N(c-Pr)Et
2-Cl-4-MePh
642
C—Me
N(c-Pr)Et
2-Me-4-ClPh
643
C—Me
NHCH(c-Pr)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
644
C—Me
NHCH(c-Pr)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
645
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Me-4-Cl—Ph
646
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Cl-4-Me—Ph
647
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Me-4-OMe—Ph
648
C—Me
NHCH(c-Pr)<sub>2</sub>
2-Cl-4-OMe—Ph
649
C—Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-5-F-OMePh
650
C—Me
NEt<sub>2</sub>
2-Cl-5-F-OMePh
651
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-5-F-OMePh
652
C—Me
NHCH(Et)<sub>2</sub>
2-Cl-5-F-OMePh
653
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-5-F-OMePh
654
C—Me
NEt<sub>2</sub>
2,6-Me<sub>2</sub>-pyrid-3-yl
655
C—Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,6-Me<sub>2</sub>-pyrid-3-yl
656
C—Me
NHCH(Et)<sub>2</sub>
2,6-Me<sub>2</sub>-pyrid-3-y1
657
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-Me<sub>2</sub>-pyrid-3-yl
658
C—OH
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
659
C—OH
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
660
C—OH
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
661
C—OH
NHCH(Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
662
C—OH
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
663
C—NEt<sub>2</sub>
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
664
C—NEt<sub>2</sub>
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
665
C—NEt<sub>2</sub>
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
666
C—NEt<sub>2</sub>
NHCH(Et)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
667
C—NEt<sub>2</sub>
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
668
C—Me
NHCH(Et)<sub>2</sub>
2-Me-4-CN—Ph
669
C—Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-CN—Ph
The examples in Tables 5 or 6 may be prepared by the methods illustrated in Examples 1A, 1B, 2, 3, 6, 431, 432, 433, 434 or by appropriate combinations thereof. Commonly used abbreviations are: Ph is phenyl, Pr is propyl, Me is methyl, Et is ethyl, Bu is butyl, Ex is Example.
TABLE 5
<chemistry id="CHEM-US-00043" num="00043"><img id="EMI-C00043" he="23.20mm" wi="30.06mm" file="US07094782-20060822-C00043.TIF" alt="embedded image" img-content="table" img-format="tif" /></chemistry>
Ex.
R<sub>14</sub>
R<sub>3</sub>
Ar
670
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
671
Me
NHCHPr<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
672
Me
NEtBu
2,4-Cl<sub>2</sub>—Ph
673
Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Cl<sub>2</sub>—Ph
674
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
675
Me
NH-3-heptyl
2,4-Cl<sub>2</sub>—Ph
676
Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
677
Me
NEt<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
678
Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
679
Me
NH-3-pentyl
2,4-Cl<sub>2</sub>—Ph
680
Me
NMePh
2,4-Cl<sub>2</sub>—Ph
681
Me
NPr<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
682
Me
NH-3-hexyl
2,4-Cl<sub>2</sub>—Ph
683
Me
morpholino
2,4-Cl<sub>2</sub>—Ph
684
Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
685
Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
686
Me
NH-4-tetrahydropyranyl
2,4-Cl<sub>2</sub>—Ph
687
Me
NH-cyclopentyl
2,4-Cl<sub>2</sub>—Ph
688
Me
OEt
2,4-Cl<sub>2</sub>—Ph
689
Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
690
Me
OCH<sub>2</sub>Ph
2,4-Cl<sub>2</sub>—Ph
691
Me
O-3-pentyl
2,4-Cl<sub>2</sub>—Ph
692
Me
SEt
2,4-Cl<sub>2</sub>—Ph
693
Me
S(O)Et
2,4-Cl<sub>2</sub>—Ph
694
Me
SO<sub>2</sub>Et
2,4-Cl<sub>2</sub>—Ph
695
Me
Ph
2,4-Cl<sub>2</sub>—Ph
696
Me
2-CF<sub>3</sub>—Ph
2,4-Cl<sub>2</sub>—Ph
697
Me
2-Ph—Ph
2,4-Cl<sub>2</sub>—Ph
698
Me
3-pentyl
2,4-Cl<sub>2</sub>—Ph
699
Me
cyclobutyl
2,4-Cl<sub>2</sub>—Ph
700
Me
3-pyridyl
2,4-Cl<sub>2</sub>—Ph
701
Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
702
Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
703
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
704
Me
NHCHPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
705
Me
NEtBu
2,4,6-Me<sub>3</sub>—Ph
706
Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4,6-Me<sub>3</sub>—Ph
707
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
708
Me
NH-3-heptyl
2,4,6-Me<sub>3</sub>—Ph
709
Me
NHCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
710
Me
NEt<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
711
Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
712
Me
NH-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
713
Me
NMePh
2,4,6-Me<sub>3</sub>—Ph
714
Me
NPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
715
Me
NH-3-hexyl
2,4,6-Me<sub>3</sub>—Ph
716
Me
morpholino
2,4,6-Me<sub>3</sub>—Ph
717
Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
718
Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
719
Me
NH-4-tetrahydropyranyl
2,4,6-Me<sub>3</sub>—Ph
720
Me
NH-cyclopentyl
2,4,6-Me<sub>3</sub>—Ph
721
Me
OEt
2,4,6-Me<sub>3</sub>—Ph
722
Me
OCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
723
Me
OCH<sub>2</sub>Ph
2,4,6-Me<sub>3</sub>—Ph
724
Me
O-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
725
Me
SEt
2,4,6-Me<sub>3</sub>—Ph
726
Me
S(O)Et
2,4,6-Me<sub>3</sub>—Ph
727
Me
SO<sub>2</sub>Et
2,4,6-Me<sub>3</sub>—Ph
728
Me
CH(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
729
Me
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
730
Me
CH(Et)CH<sub>2</sub>OH
2,4,6-Me<sub>3</sub>—Ph
731
Me
CH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
732
Me
CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
733
Me
COCH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
734
Me
CH(OH)CH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
735
Me
C(OH)Ph-3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
736
Me
Ph
2,4,6-Me<sub>3</sub>—Ph
737
Me
2-Ph—Ph
2,4,6-Me<sub>3</sub>—Ph
738
Me
3-pentyl
2,4,6-Me<sub>3</sub>—Ph
739
Me
cyclobutyl
2,4,6-Me<sub>3</sub>—Ph
740
Me
3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
741
Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
742
Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
743
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
744
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
745
Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
746
Me
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
747
Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
748
Me
N(CH<sub>2</sub>CN)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
749
Me
NHCH(Me) CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
750
Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
751
Me
NPr-c-C<sub>3</sub>H<sub>5</sub>
2,4-Me<sub>2</sub>—Ph
752
Me
NHCH(Me)CH<sub>2</sub>NMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
753
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
754
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
755
Me
N(Bu)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
756
Me
NHCHPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
757
Me
NEtBu
2,4-Me<sub>2</sub>—Ph
758
Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Me<sub>2</sub>—Ph
759
Me
NH-3-heptyl
2,4-Me<sub>2</sub>—Ph
760
Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
761
Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
762
Me
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
763
Me
NMePh
2,4-Me<sub>2</sub>—Ph
764
Me
NPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
765
Me
NH-3-hexyl
2,4-Me<sub>2</sub>—Ph
766
Me
morpholino
2,4-Me<sub>2</sub>—Ph
767
Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
768
Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
769
Me
NH-4-tetrahydropyranyl
2,4-Me<sub>2</sub>—Ph
770
Me
NH-cyclopentyl
2,4-Me<sub>2</sub>—Ph
771
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-MeO—Ph
772
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-MeO—Ph
773
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-MeO—Ph
774
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-MeO—Ph
775
Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-MeO—Ph
776
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeO—Ph
777
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeO—Ph
778
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-MeO—Ph
779
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-MeO—Ph
780
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-MeO—Ph
781
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-NMe<sub>2</sub>—Ph
782
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-NMe<sub>2</sub>—Ph
783
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-NMe<sub>2</sub>—Ph
784
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-NMe<sub>2</sub>—Ph
785
Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-NMe<sub>2</sub>—Ph
786
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-NMe<sub>2</sub>—Ph
787
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-NMe<sub>2</sub>—Ph
788
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-NMe<sub>2</sub>—Ph
789
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-NMe<sub>2</sub>—Ph
790
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-NMe<sub>2</sub>—Ph
791
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-i-Pr—Ph
792
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-i-Pr—Ph
793
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-i-Pr—Ph
794
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-i-Pr—Ph
795
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-i-Pr—Ph
796
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-Me—Ph
797
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-Me—Ph
798
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-Me—Ph
799
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-Me—Ph
800
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-Me—Ph
801
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-Br—Ph
802
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-Br—Ph
803
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
804
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-Br—Ph
805
Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
806
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-Me<sub>2</sub>—Ph
807
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-Me<sub>2</sub>—Ph
808
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-Br-2,6-(Me)<sub>2</sub>—Ph
809
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-Br-2,6-(Me)<sub>2</sub>—Ph
810
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
811
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
812
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-CF<sub>3</sub>—Ph
813
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-CF<sub>3</sub>—Ph
814
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>—Ph
815
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>—Ph
816
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>—Ph
817
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>—Ph
818
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
819
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
820
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-(COMe)-2-Br—Ph
821
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-(COMe)-2-Br—Ph
822
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>-pyrid-3-yl
823
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>-pyrid-3-yl
824
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-(Br)<sub>2</sub>—Ph
825
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-(Br)<sub>2</sub>—Ph
826
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
827
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
828
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
829
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
830
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
831
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
832
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SO<sub>2</sub>Me—Ph
833
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SO<sub>2</sub>Me—Ph
834
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-I-4-i-Pr—Ph
835
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-I-4-i-Pr—Ph
836
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-N(Me)<sub>2</sub>-6-MeO—Ph
837
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-N(Me)<sub>2</sub>-6-MeO—Ph
838
Me
NEt<sub>2</sub>
2-Br-4-MeO—Ph
839
Me
NH-3-pentyl
2-Br-4-MeO—Ph
840
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-CN-4-Me—Ph
841
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4,6-Me<sub>3</sub>—Ph
842
Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)-
2-Me-4-Br—Ph
CH<sub>2</sub>OMe
843
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
844
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
845
Me
NH-3-pentyl
2,5-Me<sub>2</sub>-4-MeO—Ph
846
Me
NEt<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
847
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MePh
848
Me
NCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MePh
849
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MePh
850
Me
(S)—NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)-
2-Cl-4-MePh
CH<sub>2</sub>OMe
851
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,5-Me<sub>2</sub>-4-MeOPh
852
Me
NEt<sub>2</sub>
2-Me-4-MeOPh
853
Me
OEt
2-Me-4-MeOPh
854
Me
(S)—NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)-
2-Me-4-MeOPh
CH<sub>2</sub>OMe
855
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-MeOPh
856
Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OEt)<sub>2</sub>
2-Me-4-MeOPh
857
Me
N(c-C<sub>3</sub>H<sub>5</sub>) CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Cl<sub>2</sub>—Ph
858
Me
NEt<sub>2</sub>
2-Me-4-ClPh
859
Me
NH-3-pentyl
2-Me-4-ClPh
860
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-ClPh
861
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-ClPh
862
Me
NEt<sub>2</sub>
2-Me-4-ClPh
863
Me
NEt<sub>2</sub>
2-Cl-4-MePh
864
Me
NH-3-pentyl
2-Cl-4-MePh
865
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
866
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
867
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MeOPh
868
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4-MeOPh
869
Me
NEt<sub>2</sub>
2-Cl-4-MeOPh
870
Me
NH-3-pentyl
2-Cl-4-MeOPh
871
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
872
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
873
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
874
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
875
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
876
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
877
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
878
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
879
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
880
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4,5-(MeO)<sub>2</sub>Ph
881
Me
NEt<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
882
Me
NH-3-pentyl
2-Cl-4,5-(MeO)<sub>2</sub>Ph
883
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
884
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
885
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
886
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
887
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
888
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4,5-(MeO)<sub>2</sub>Ph
889
Me
NEt<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
890
Me
NH-3-pentyl
2-Br-4,5-(MeO)<sub>2</sub>Ph
891
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
892
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
893
Me
NEt<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
894
Me
NH-3-pentyl
2-Cl-4,6-(MeO)<sub>2</sub>Ph
895
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
896
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
897
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
898
Me
NEt<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
899
Me
NH-3-pentyl
2-Me-4,6-(MeO)<sub>2</sub>Ph
900
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
901
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
902
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
903
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
904
Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
905
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
906
Me
NEt<sub>2</sub>
2-MeO-4-MePh
907
Me
NH-3-pentyl
2-MeO-4-MePh
908
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
909
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
910
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
911
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
912
Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
913
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
914
Me
NEt<sub>2</sub>
2-MeO-4-MePh
915
Me
NH-3-pentyl
2-MeO-4-MePh
916
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
917
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
918
Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-ClPh
919
Me
NEt<sub>2</sub>
2-MeO-4-ClPh
920
Me
NH-3-pentyl
2-MeO-4-ClPh
TABLE 6
<chemistry id="CHEM-US-00044" num="00044"><img id="EMI-C00044" he="23.20mm" wi="30.06mm" file="US07094782-20060822-C00044.TIF" alt="embedded image" img-content="table" img-format="tif" /></chemistry>
Ex.
R<sub>14</sub>
R<sub>3</sub>
Ar
921
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
922
Me
NHCHPr<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
923
Me
NEtBu
2,4-Cl<sub>2</sub>—Ph
924
Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Cl<sub>2</sub>—Ph
925
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
926
Me
NH-3-heptyl
2,4-Cl<sub>2</sub>—Ph
927
Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
928
Me
NEt<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
929
Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
930
Me
NH-3-pentyl
2,4-Cl<sub>2</sub>—Ph
931
Me
NMePh
2,4-Cl<sub>2</sub>—Ph
932
Me
NPr<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
933
Me
NH-3-hexyl
2,4-Cl<sub>2</sub>—Ph
934
Me
morpholino
2,4-Cl<sub>2</sub>—Ph
935
Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
936
Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
937
Me
NH-4-tetrahydropyranyl
2,4-Cl<sub>2</sub>—Ph
938
Me
NH-cyclopentyl
2,4-Cl<sub>2</sub>—Ph
939
Me
OEt
2,4-Cl<sub>2</sub>—Ph
940
Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Cl<sub>2</sub>—Ph
941
Me
OCH<sub>2</sub>Ph
2,4-Cl<sub>2</sub>—Ph
942
Me
O-3-pentyl
2,4-Cl<sub>2</sub>—Ph
943
Me
SEt
2,4-Cl<sub>2</sub>—Ph
944
Me
S(O)Et
2,4-Cl<sub>2</sub>—Ph
945
Me
SO<sub>2</sub>Et
2,4-Cl<sub>2</sub>—Ph
946
Me
Ph
2,4-Cl<sub>2</sub>—Ph
947
Me
2-CF<sub>3</sub>—Ph
2,4-Cl<sub>2</sub>—Ph
948
Me
2-Ph—Ph
2,4-Cl<sub>2</sub>—Ph
949
Me
3-pentyl
2,4-Cl<sub>2</sub>—Ph
950
Me
cyclobutyl
2,4-Cl<sub>2</sub>—Ph
951
Me
3-pyridyl
2,4-Cl<sub>2</sub>—Ph
952
Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
953
Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4-Cl<sub>2</sub>—Ph
954
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
955
Me
NHCHPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
956
Me
NEtBu
2,4,6-Me<sub>3</sub>—Ph
957
Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4,6-Me<sub>3</sub>—Ph
958
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
959
Me
NH-3-heptyl
2,4,6-Me<sub>3</sub>—Ph
960
Me
NHCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
961
Me
NEt<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
962
Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
963
Me
NH-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
964
Me
NMePh
2,4,6-Me<sub>3</sub>—Ph
965
Me
NPr<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
966
Me
NH-3-hexyl
2,4,6-Me<sub>3</sub>—Ph
967
Me
morpholino
2,4,6-Me<sub>3</sub>—Ph
968
Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
969
Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
970
Me
NH-4-tetrahydropyranyl
2,4,6-Me<sub>3</sub>—Ph
971
Me
NE-cyclopentyl
2,4,6-Me<sub>3</sub>—Ph
972
Me
OEt
2,4,6-Me<sub>3</sub>—Ph
973
Me
OCH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
974
Me
OCH<sub>2</sub>Ph
2,4,6-Me<sub>3</sub>—Ph
975
Me
O-3-pentyl
2,4,6-Me<sub>3</sub>—Ph
976
Me
SEt
2,4,6-Me<sub>3</sub>—Ph
977
Me
S(O)Et
2,4,6-Me<sub>3</sub>—Ph
978
Me
SO<sub>2</sub>Et
2,4,6-Me<sub>3</sub>—Ph
979
Me
CH(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
980
Me
C(Et)(CO<sub>2</sub>Et)<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
981
Me
CH(Et)CH<sub>2</sub>OH
2,4,6-Me<sub>3</sub>—Ph
982
Me
CH(Et)CH<sub>2</sub>OMe
2,4,6-Me<sub>3</sub>—Ph
983
Me
CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
984
Me
COCH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
985
Me
CH(OH)CH<sub>3</sub>
2,4,6-Me<sub>3</sub>—Ph
986
Me
C(OH)Ph-3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
987
Me
Ph
2,4,6-Me<sub>3</sub>—Ph
988
Me
2-Ph—Ph
2,4,6-Me<sub>3</sub>—Ph
989
Me
3-pentyl
2,4,6-Me<sub>3</sub>—Ph
990
Me
cyclobutyl
2,4,6-Me<sub>3</sub>—Ph
991
Me
3-pyridyl
2,4,6-Me<sub>3</sub>—Ph
992
Me
CH(Et)CH<sub>2</sub>CONMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
993
Me
CH(Et)CH<sub>2</sub>CH<sub>2</sub>NMe<sub>2</sub>
2,4,6-Me<sub>3</sub>—Ph
994
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
995
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
996
Me
NHCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
997
Me
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
998
Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
999
Me
N(CH<sub>2</sub>CN)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
1000
Me
NHCH(Me)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
1001
Me
OCH(Et)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
1002
Me
NPr-c-C<sub>3</sub>H<sub>5</sub>
2,4-Me<sub>2</sub>—Ph
1003
Me
NHCH(Me)CH<sub>2</sub>NMe<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
1004
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
1005
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
1006
Me
N(Bu)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Me<sub>2</sub>—Ph
1007
Me
NHCHPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
1008
Me
NEtBu
2,4-Me<sub>2</sub>—Ph
1009
Me
NPr(CH<sub>2</sub>-c-C<sub>3</sub>H<sub>5</sub>)
2,4-Me<sub>2</sub>—Ph
1010
Me
NH-3-heptyl
2,4-Me<sub>2</sub>—Ph
1011
Me
NEt<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
1012
Me
NHCH(CH<sub>2</sub>OEt)<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
1013
Me
NH-3-pentyl
2,4-Me<sub>2</sub>—Ph
1014
Me
NMePh
2,4-Me<sub>2</sub>—Ph
1015
Me
NPr<sub>2</sub>
2,4-Me<sub>2</sub>—Ph
1016
Me
NH-3-hexyl
2,4-Me<sub>2</sub>—Ph
1017
Me
morpholino
2,4-Me<sub>2</sub>—Ph
1018
Me
N(CH<sub>2</sub>Ph)CH<sub>2</sub>CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
1019
Me
NHCH(CH<sub>2</sub>Ph)CH<sub>2</sub>OMe
2,4-Me<sub>2</sub>—Ph
1020
Me
NH-4-tetrahydropyranyl
2,4-Me<sub>2</sub>—Ph
1021
Me
NH-cyclopentyl
2,4-Me<sub>2</sub>—Ph
1022
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-MeO—Ph
1023
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-MeO—Ph
1024
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-MeO—Ph
1025
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-MeO—Ph
1026
Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-MeO—Ph
1027
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeO—Ph
1028
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-MeO—Ph
1029
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-MeO—Ph
1030
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-MeO—Ph
1031
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-MeO—Ph
1032
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-NMe<sub>2</sub>—Ph
1033
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-NMe<sub>2</sub>—Ph
1034
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-NMe<sub>2</sub>—Ph
1035
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-NMe<sub>2</sub>—Ph
1036
Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-NMe<sub>2</sub>—Ph
1037
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-NMe<sub>2</sub>—Ph
1038
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-NMe<sub>2</sub>—Ph
1039
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-NMe<sub>2</sub>—Ph
1040
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-NMe<sub>2</sub>—Ph
1041
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-NMe<sub>2</sub>—Ph
1042
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-i-Pr—Ph
1043
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-i-Pr—Ph
1044
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-i-Pr—Ph
1045
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-i-Pr—Ph
1046
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-i-Pr—Ph
1047
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-Me—Ph
1048
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-Me—Ph
1049
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4-Me—Ph
1050
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4-Me—Ph
1051
Me
OCH(Et)CH<sub>2</sub>OMe
2-Br-4-Me—Ph
1052
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-Br—Ph
1053
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-Br—Ph
1054
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
1055
Me
N(Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-Br—Ph
1056
Me
OCH(Et)CH<sub>2</sub>OMe
2-Me-4-Br—Ph
1057
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-Me<sub>2</sub>—Ph
1058
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-Me<sub>2</sub>—Ph
1059
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-Br-2,6-(Me)<sub>2</sub>—Ph
1060
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-Br-2,6-(Me)<sub>2</sub>—Ph
1061
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
1062
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
1063
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-CF<sub>3</sub>—Ph
1064
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-CF<sub>3</sub>—Ph
1065
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>—Ph
1066
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,6-(MeO)<sub>2</sub>—Ph
1067
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>—Ph
1068
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>—Ph
1069
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
1070
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
1071
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-(COMe)-2-Br—Ph
1072
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-(COMe)-2-Br—Ph
1073
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>-pyrid-3-yl
1074
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4,6-Me<sub>3</sub>-pyrid-3-yl
1075
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,4-(Br)<sub>2</sub>—Ph
1076
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,4-(Br)<sub>2</sub>—Ph
1077
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
1078
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SMe—Ph
1079
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
1080
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
4-i-Pr-2-SO<sub>2</sub>Me—Ph
1081
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
1082
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SMe—Ph
1083
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SO<sub>2</sub>Me—Ph
1084
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,6-(Me)<sub>2</sub>-4-SO<sub>2</sub>Me—Ph
1085
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-I-4-i-Pr—Ph
1086
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-I-4-i-Pr—Ph
1087
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-N(Me)<sub>2</sub>-6-MeO—Ph
1088
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4-N(Me)<sub>2</sub>-6-MeO—Ph
1089
Me
NEt<sub>2</sub>
2-Br-4-MeO—Ph
1090
Me
NH-3-pentyl
2-Br-4-MeO—Ph
1091
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-CN-4-Me—Ph
1092
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4,6-Me<sub>3</sub>—Ph
1093
Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)
2-Me-4-Br—Ph
CH<sub>2</sub>OMe
1094
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
1095
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
1096
Me
NH-3-pentyl
2,5-Me<sub>2</sub>-4-MeO—Ph
1097
Me
NEt<sub>2</sub>
2,5-Me<sub>2</sub>-4-MeO—Ph
1098
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MePh
1099
Me
NCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MePh
1100
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MePh
1101
Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)
2-Cl-4-MePh
CH<sub>2</sub>OMe
1102
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,5-Me<sub>2</sub>-4-MeOPh
1103
Me
NEt<sub>2</sub>
2-Me-4-MeOPh
1104
Me
OEt
2-Me-4-MeOPh
1105
Me
(S)-NHCH(CH<sub>2</sub>CH<sub>2</sub>OMe)
2-Me-4-MeOPh
CH<sub>2</sub>OMe
1106
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2-Me-4-MeOPh
1107
Me
NHCH(CH<sub>2</sub>CH<sub>2</sub>OEt)<sub>2</sub>
2-Me-4-MeOPh
1108
Me
N(c-C<sub>3</sub>H<sub>5</sub>)CH<sub>2</sub>CH<sub>2</sub>CN
2,4-Cl<sub>2</sub>—Ph
1109
Me
NEt<sub>2</sub>
2-Me-4-ClPh
1110
Me
NH-3-pentyl
2-Me-4-ClPh
1111
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-ClPh
1112
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4-ClPh
1113
Me
NEt<sub>2</sub>
2-Me-4-ClPh
1114
Me
NEt<sub>2</sub>
2-Cl-4-MePh
1115
Me
NH-3-pentyl
2-Cl-4-MePh
1116
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
1117
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4-MeOPh
1118
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4-MeOPh
1119
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4-MeOPh
1120
Me
NEt<sub>2</sub>
2-Cl-4-MeOPh
1121
Me
NH-3-pentyl
2-Cl-4-MeOPh
1123
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
1124
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4-MeOPh
1125
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
1126
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Br-4-MeOPh
1127
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
1128
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
1129
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1130
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1131
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1132
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1133
Me
NEt<sub>2</sub>
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1134
Me
NH-3-pentyl
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1135
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1136
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Cl-4,5-(MeO)<sub>2</sub>Ph
1137
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
1138
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
1139
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Br-4,5-(MeO)<sub>2</sub>Ph
1140
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-Br-4,5-(MeO)<sub>2</sub>Ph
1141
Me
NEt<sub>2</sub>
2-Br-4,5-(MeO)<sub>2</sub>Ph
1142
Me
NH-3-pentyl
2-Br-4,5-(MeO)<sub>2</sub>Ph
1143
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
1144
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
1145
Me
NEt<sub>2</sub>
2-Cl-4,6-(MeO)<sub>2</sub>Ph
1146
Me
NH-3-pentyl
2-Cl-4,6-(MeO)<sub>2</sub>Ph
1147
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
1148
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
1149
Me
NHCH(Et)CH<sub>2</sub>OMe
2-Me-4,6-(MeO)<sub>2</sub>Ph
1150
Me
NEt<sub>2</sub>
2-Me-4,6-(MeO)<sub>2</sub>Ph
1151
Me
NH-3-pentyl
2-Me-4,6-(MeO)<sub>2</sub>Ph
1152
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
1153
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-Me-4-MeOPh
1154
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
1155
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
1156
Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
1157
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
1158
Me
NEt<sub>2</sub>
2-MeO-4-MePh
1159
Me
NH-3-pentyl
2-MeO-4-MePh
1160
Me
NHCH(Et)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
1161
Me
NHCH(Me)CH<sub>2</sub>CH<sub>2</sub>OMe
2-MeO-4-MePh
1162
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
1163
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-MePh
1164
Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-MePh
1165
Me
N(c-Pr)CH<sub>2</sub>CH<sub>2</sub>CN
2-MeO-4-MePh
1166
Me
NEt<sub>2</sub>
2-MeO-4-MePh
1167
Me
NH-3-pentyl
2-MeO-4-MePh
1168
Me
NHCH(CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
1169
Me
N(CH<sub>2</sub>CH<sub>2</sub>OMe)<sub>2</sub>
2-MeO-4-ClPh
1170
Me
NHCH(Et)CH<sub>2</sub>OMe
2-MeO-4-ClPh
1171
Me
NEt<sub>2</sub>
2-MeO-4-ClPh
1172
Me
NH-3-pentyl
2-MeO-4-ClPh
Utility
CRF-R1 Receptor Binding Assay for the Evaluation of Biological Activity
The following is a description of the isolation of cell membranes containing cloned human CRF-R1 receptors for use in the standard binding assay as well as a description of the assay itself.
8
Messenger RNA was isolated from human hippocampus. The mRNA was reverse transcribed using oligo (dt) 12–18 and the coding region was amplified by PCR from start to stop codons. The resulting PCR fragment was cloned into the EcoRV site of pGEMV, from whence the insert was reclaimed using XhoI+XbaI and cloned into the XhoI+XbaI sites of vector pm3ar (which contains a CMV promoter, the SV40 ‘t’ splice and early poly A signals, an Epstein-Barr viral origin of replication, and a hygromycin selectable marker). The resulting expression vector, called phchCRFR was transfected in 293EBNA cells and cells retaining the episome were selected in the presence of 400 μM hygromycin. Cells surviving 4 weeks of selection in hygromycin were pooled, adapted to growth in suspension and used to generate membranes for the binding assay described below. Individual aliquots containing approximately 1×10of the suspended cells were then centrifuged to form a pellet and frozen.
2
For the binding assay a frozen pellet described above containing 293EBNA cells transfected with hCRFR1 receptors is homogenized in 10 ml of ice cold tissue buffer (50 mM HEPES buffer pH 7.0, containing 10 mM MgCl, 2 mM EGTA, 1 μg/l aprotinin, 1 μg/ml leupeptin and 1 μg/ml pepstatin). The homogenate is centrifuged at 40,000×g for 12 min and the resulting pellet rehomogenized in 10 ml of tissue buffer. After another centrifugation at 40,000×g for 12 min, the pellet is resuspended to a protein concentration of 360 μg/ml to be used in the assay.
−10
−5
125
125
Binding assays are performed in 96 well plates; each well having a 300 μl capacity. To each well is added 50 μl of test drug dilutions (final concentration of drugs range from 10–10M), 100 μl of I-ovine-CRF (I-o-CRF) (final concentration 150 pM) and 150 μl of the cell homogenate described above. Plates are then allowed to incubate at room temperature for 2 hours before filtering the incubate over GF/F filters (presoaked with 0.3% polyethyleneimine) using an appropriate cell harvester. Filters are rinsed 2 times with ice cold assay buffer before removing individual filters and assessing them for radioactivity on a gamma counter.
125
Anal. Biochem.
Curves of the inhibition of I-o-CRF binding to cell membranes at various dilutions of test drug are analyzed by the iterative curve fitting program LIGAND [P. J. Munson and D. Rodbard, 107:220 (1980), which provides Ki values for inhibition which are then used to assess biological activity.
i
A compound is considered to be active if it has a Kvalue of less than about 10000 nM for the inhibition of CRF.
Inhibition of CRF-Stimulated Adenylate Cyclase Activity
Synapse
2
−9
6m
32
3
32
32
Inhibition of CRF-stimulated adenylate cyclase activity can be performed as described by G. Battaglia et al. 1:572 (1987). Briefly, assays are carried out at 37° C. for 10 min in 200 ml of buffer containing 100 mM Tris-HCl (pH 7.4 at 37° C.), 10 mM MgCl, 0.4 mM EGTA, 0.1% BSA, 1 mM isobutylmethylxanthine (IBMX), 250 units/ml phosphocreatine kinase, 5 mM creatine phosphate, 100 mM guanosine 5′-triphosphate, 100 nM oCRF, antagonist peptides (concentration range 10to 10) and 0.8 mg original wet weight tissue (approximately 40–60 mg protein). Reactions are initiated by the addition of 1 mM ATP/P]ATP (approximately 2–4 mCi/tube) and terminated by the addition of 100 ml of 50 mM Tris-HCL, 45 mM ATP and 2% sodium dodecyl sulfate. In order to monitor the recovery of cAMP, 1 μl of [H]cAMP (approximately 40,000 dpm) is added to each tube prior to separation. The separation of [P]cAMP from [P]ATP is performed by sequential elution over Dowex and alumina columns.
In vivo Biological Assay
Brain Research Reviews
The in vivo activity of the compounds of the present invention can be assessed using any one of the biological assays available and accepted within the art. Illustrative of these tests include the Acoustic Startle Assay, the Stair Climbing Test, and the Chronic Administration Assay. These and other models useful for the testing of compounds of the present invention have been outlined in C. W. Berridge and A. J. Dunn 15:71 (1990).
Compounds may be tested in any species of rodent or small mammal.
Compounds of this invention have utility in the treatment of inbalances associated with abnormal levels of corticotropin releasing factor in patients suffering from depression, affective disorders, and/or anxiety.
Compounds of this invention can be administered to treat these abnormalities by means that produce contact of the active agent with the agent's site of action in the body of a mammal. The compounds can be administered by any conventional means available for use in conjunction with pharmaceuticals either as individual therapeutic agent or in combination of therapeutic agents. They can be administered alone, but will generally be administered with a pharmaceutical carrier selected on the basis of the chosen route of administration and standard pharmaceutical practice.
The dosage administered will vary depending on the use and known factors such as pharmacodynamic character of the particular agent, and its mode and route of administration; the recipient's age, weight, and health; nature and extent of symptoms; kind of concurrent treatment; frequency of treatment; and desired effect. For use in the treatment of said diseases or conditions, the compounds of this invention can be orally administered daily at a dosage of the active ingredient of 0.002 to 200 mg/kg of body weight. Ordinarily, a dose of 0.01 to 10 mg/kg in divided doses one to four times a day, or in sustained release formulation will be effective in obtaining the desired pharmacological effect.
Dosage forms (compositions) suitable for administration contain from about 1 mg to about 100 mg of active ingredient per unit. In these pharmaceutical compositions, the active ingredient will ordinarily be present in an amount of about 0.5 to 95% by weight based on the total weight of the composition.
The active ingredient can be administered orally is solid dosage forms, such as capsules, tablets and powders; or in liquid forms such as elixirs, syrups, and/or suspensions. The compounds of this invention can also be administered parenterally in sterile liquid dose formulations.
Gelatin capsules can be used to contain the active ingredient and a suitable carrier such as but not limited to lactose, starch, magnesium stearate, steric acid, or cellulose derivatives. Similar diluents can be used to make compressed tablets. Both tablets and capsules can be manufactured as sustained release products to provide for continuous release of medication over a period of time. Compressed tablets can be sugarcoated or film-coated to mask any unpleasant taste, or used to protect the active ingredients from the atmosphere, or to allow selective disintegration of the tablet in the gastrointestinal tract.
Liquid dose forms for oral administration can contain coloring or flavoring agents to increase patient acceptance.
In general, water, pharmaceutically acceptable oils, saline, aqueous dextrose (glucose), and related sugar solutions and glycols, such as propylene glycol or polyethylene glycol, are suitable carriers for parenteral solutions. Solutions for parenteral administration preferably contain a water soluble salt of the active ingredient, suitable stabilizing agents, and if necessary, butter substances. Antioxidizing agents, such as sodium bisulfite, sodium sulfite, or ascorbic acid, either alone or in combination, are suitable stabilizing agents. Also used are citric acid and its salts, and EDTA. In addition, parenteral solutions can contain preservatives such as benzalkonium chloride, methyl- or propyl-paraben, and chlorobutanol.
Suitable pharmaceutical carriers are described in “Remington's Pharmaceutical Sciences”, A. Osol, a standard reference in the field.
Useful pharmaceutical dosage-forms for administration of the compounds of this invention can be illustrated as follows:
Capsules
A large number of units capsules are prepared by filling standard two-piece hard gelatin capsules each with 100 mg of powdered active ingredient, 150 mg lactose, 50 mg cellulose, and 6 mg magnesium stearate.
Soft Gelatin Capsules
A mixture of active ingredient in a digestible oil such as soybean, cottonseed oil, or olive oil is prepared and injected by means of a positive displacement was pumped into gelatin to form soft gelatin capsules containing 100 mg of the active ingredient. The capsules were washed and dried.
Tablets
A large number of tablets are prepared by conventional procedures so that the dosage unit was 100 mg active ingredient, 0.2 mg of colloidal silicon dioxide, 5 mg of magnesium stearate, 275 mg of microcrystalline cellulose, 11 mg of starch, and 98.8 mg lactose. Appropriate coatings may be applied to increase palatability or delayed adsorption.
The compounds of this invention may also be used as reagents or standards in the biochemical study of neurological function, dysfunction, and disease.
Although the present invention has been described and exemplified in terms of certain preferred embodiments, other embodiments will be apparent to those skilled in the art. The invention is, therefore, not limited to the particular embodiments described and exemplified, but is capable of modification or variation without departing from the spirit of the invention, the full scope of which is delineated by the appended claims. | |
Amortization is writing down the loan’s value and intangible assets like goodwill, trademark, copyright, etc. It is similar to depreciation, but this term is for intangible assets.
In amortization, only intangible assets can be amortized. However, if the intangible asset has an indefinite or unlimited lifespan, it can be amortized.
So, in this article, you will learn and understand the amortization, importance, and formula to calculate amortization.
Table of contents
Amortization is a method of spreading the value of a loan and the cost of intangible assets over time. It may refer to two completely different financial processes: amortization of intangible assets and loans.
Intangible assets are not physical, but they add value to your business. Examples of intangible assets are
It refers to paying off debt over time in a regular installment of interest and outstanding loan principal. Examples of amortization loans are
The formula to calculate a monthly principal amount due on the amortized loan is as under
TMP= Total monthly payment
OLB=outstanding loan balance
Typically, If you want to calculate the total monthly payment, the formula will be as follow:
i=Monthly interest rate
n=Number of payments
The accounting treatment for amortization is similar to the accounting treatment of depreciation. Accumulated amortization is a contra asset that is why it is recorded in the balance sheet as it reduces the value of intangible assets shown on the balance sheet. Similarly, amortization expense is an income statement item so, it will be recorded as an expense in the income statement.
Let’s understand the accounting for amortization through example.
The ABC company has spent $200,000 to acquire a patent for 10 years. Therefore, It is an intangible asset and should be amortized over five years before its expiration. The entry to record amortization for each year would be:
The following formula can calculate amortization expenses:
Initial value-residual value/ lifespan = Amortization expenses.
In this formula, you have to subtract the residual value of the assets from their initial value and divide them by the asset’s lifespan. If the asset has no residual value, divide the initial value by the life span. The result you can amortize each year.
Let’s understand amortization through example.
Assume company XYZ purchases a patent for $10,000. The accountant recorded the patent in accounts at its cost value. So, It also determined the useful life of the patent to be 10 years.
At the end of the year, XYZ company records the amortization expense for the patent.
The amortization expense will be $2,000 ($10,000/10 years) each year. The company uses a double-entry system under:
Amortization expenses=Initial value-residual value/ lifespan
10,000/10
Amortization expenses = 1,000
NOTE: In the above example the asset has zero residual value so we divide the initial value by lifespan.
Amortization helps in managing the intangible asset of the business. It is crucial because it assists investors and businesses in understanding and forecasting their costs on time.
In addition, this can be useful for deducting interest payments for tax purposes. Moreover, it can reduce a business’s taxable income and tax liability while giving investors a better understanding of the true learning of the company. | https://invyce.com/amortization-and-its-accounting-treatment/ |
The embodiment of the invention provides a method and device for processing aggressive traffic, electronic equipment and storage equipment, and relates to the technical field of network security. The method is applied to a terminal and comprises the steps of firstly, processing a cache region of the terminal according to a preset segmentation mode, obtaining a plurality of sub-cache regions, wherein each sub-cache region comprises an attack cache region; then, when an original message is received, processing the original message according to a preset filtering strategy to obtain a to-be-cached attack message, and distributing a target sub-cache region for the attack message according to a preset load balancing algorithm; and finally, caching the attack message to an attack cache region of the target sub-cache region. According to the method for processing the aggressive traffic provided by the embodiment of the invention, the aggressive traffic is prevented from attacking and occupying all cache spaces provided by a host or a server from multiple aspects, so that flooding attacks are effectively restrained. | |
2009 June VHF Contest
June is just not our contest! If it wasn’t so much fun just to get out and make contacts I’d think seriously about skipping it next year. Once again this turned out to be a 6 meter contest due to E skip! That puts most rovers at a disadvantage due to a small 6m antenna, limited power, and reduced activity on the upper bands. To make maters worse, the tropo to the NE was limited to short haul only (150-200 Miles) for most of the contest. For those of us who participate for the thrill of the VHF and above contacts, Saturday was a big bust score wise! Working 6m on E skip just isn’t as much fun as making a 370 mile contact on 2304 or 3456 with 1 watt!
We decided to run the Rover on our old route one more time starting in FM27 and working our way up to FM28 then FM29 and FM18 on Saturday. Normally FM27 costs us an extra 2 hours of travel plus fuel to pick up just a few contacts. This time we made sure some of the Multi-Multi’s and big gun single ops knew we were starting. The sky opened up about 10 miles from our destination in Crisfield. To make matters worse the 1296 Amplifier was shutting down due to high SWR! We had to shut it off and run 8 watts on 1296 for the rest of the contest. The contact count for this grid was up slightly but not really enough to make it worth while. The thunder storms seemed to follow us around all afternoon and evening.
With the poor results from Saturday we decided just to run out to Sideling Hill in FM09 on Sunday and call it a day. We’ll save the gas money for August or September.
There were a couple of high points of the trip. We managed once again to complete with K1RZ on all 8 bands from every grid! That included 1296 with a bad antenna and 3456 with 1 watt at 140 miles. We also completed with WA2FGK up to 2304 at 212 miles from FM09.
We’ll be out looking for good uW Tropo in August and September.
73, | https://www.k3lfo.org/?m=200907 |
Sun:
↑ 07:20AM ↓ 04:57PM (9h 38m)
More info
Tokyo
03:04AM
Beijing
02:04AM
Moscow
09:04PM
Paris
07:04PM
London
06:04PM
New York
01:04PM
Los Angeles
10:04AM
Time zone
Currently Atlantic Standard Time (AST), UTC -4
Daylight saving time (Atlantic Daylight Time (ADT), UTC -3) starts March 8, 2020
The IANA time zone identifier for Saint John is America/Moncton.
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Sunrise, sunset, day length and solar time for Saint John
Sunrise: 07:20AM
Sunset: 04:57PM
Day length: 9h 38m
Solar noon: 12:09PM
The current local time in Saint John is 9 minutes ahead of apparent solar time.
Time difference
from Saint John
Los Angeles
:
−4 hours
New York
:
−1
London
:
+4 hours
UTC
:
+4 hours
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:
+5 hours
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+7 hours
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+7 hours
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+8 hours
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+12 hours
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+12 hours
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+13 hours
Sydney
: | https://time.is/Saint_John,_Canada |
---
abstract: 'Isotropic-Nematic and Nematic-Nematic transitions from a homogeneous base state of a suspension of high aspect ratio, rod-like magnetic particles are studied for both Maier-Saupe and the Onsager excluded volume potentials. A combination of classical linear stability and asymptotic analyses provides insight into possible nematic states emanating from both the isotropic and nematic non-polarized equilibrium states. Local analytical results close to critical points in conjunction with global numerical results (Bhandar, 2002) yields a unified picture of the bifurcation diagram and provides a convenient base state to study effects of external orienting fields.'
author:
- 'Gopinath A., Mahadevan L., and Armstrong R. C.,§'
title: Transitions to Nematic states in homogeneous suspensions of high aspect ratio magnetic rods
---
Recently, a kinetic theory based model for dispersions of acicular magnetic particles was developed$^{1,2}$ using ideas grounded in classical models for liquid-crystalline polymers$^{3}$. Effects of Brownian motion, anisotropic hydrodynamic drag, a steric force chosen to be of the Maier - Saupe form and a mean-field magnetic potential were included. Both continuum descriptions obtained via closure approximations and the diffusion equation were solved numerically for some parameter ranges$^{1,2}$. The focus of this article is on obtaining a theoretical characterization of transitions to nematic states from a homogeneous base state of a suspension of slender high aspect ratio magnetic particles. Combining local asymptotic and stability analysis near critical points with global numerical results, we obtain a physically convenient point of departure for investigations of external aligning fields. Both the Maier-Saupe and the Onsager potentials are considered. Results for the Maier-Saupe potential are in excellent agreement with available numerical solutions of the equations and complement recent investigations on the classical Doi model$^{4}$.
The particles in the homogeneous dispersion are modeled as two point masses connected by a rigid massless rod of length L and diameter $d$ with inherent magnetic dipoles, the magnetic moment being along the axis$^{1,2}$. We envisage a situation in which $d$ and $L$ are kept constant and the concentration of the rods can be varied. The orientation of the rod is specified by the unit vector $\bf u$ along the axis from one specified bead to another. In the mean-field approximation it suffices to consider one test particle in a sea of others. Denoting the orientation distribution function by $f({\bf u},t)$, one writes for the case of constant diffusivity in scaled form$^{6}$ $${\partial {f} \over \partial{t}} = \Re_{\bf u} {\boldsymbol{\cdot}}(\Re_{\bf u}
f + f \Re_{\bf u} (V_{EV} + V_{M})).$$ Here $\Re_{{\bf u}}(.)$ is the rotation operator and the potentials are measured in units of $k_{b}T$. We define the average of a quantity, ${\bf X}({\bf u})$, as $ \langle{\bf
X}({\bf u})\rangle \equiv \int {\bf X}({\bf u}) \: f({\bf u})d{\bf
u}$. The excluded volume intermolecular potential for a Maier-Saupe (MS) or Onsager (O) potential can then be written as $$V_{EV}({\bf u}) = \int \beta_{MS/O}({\bf u},{\bf
u}') \: f({\bf u}',t) \: d{\bf u}',$$ where, $ \beta_{MS}({\bf u},{\bf u}') = - \Pi_{MS} ({\bf u} \cdot
{\bf u}')^{2}$, $\Pi_{MS}$ being a phenomenological constant proportional to the concentration of rods, $N$ and $\beta_{O}({\bf
u},{\bf u}') = 2NL^{2}d \: |{\bf u} \times {\bf u}'| $. The total potential due to the mean magnetic field, $ V_{M}$, can be written$^{2}$ $$V_{M}= - {(3/2)} \mathcal{B}' \langle{\bf u}{\bf u}\rangle:{\bf
u}{\bf u} - \mathcal{A}'{\bf u}{\boldsymbol{\cdot}}\langle{\bf u}\rangle +
{\mathcal{A}}_{o} + {\mathcal{B}}_{o}$$ The first term reflects a net magnetic interaction potential due to average order$^{1,2}$, the second term is the mean field approximation to the dipole-dipole interaction between particles and ${\mathcal{A}}_{o}$ and ${\mathcal{B}}_{o}$ are constants independent of ${\bf u}$.
Equations (1)-(3) do not involve any preferred direction for orientation of possible nematic states and so we choose to employ an expansion for $f({\bf u},t)$ in terms of spherical harmonic functions $Y_{l}^{m}({\bf u}) = Y^{m}_{l}(\theta,\phi)$. where $ {\bf u} = (\sin{\theta}\sin{\phi})\:{\bf
e}_{x}+(\sin{\theta}\cos{\phi})\:{\bf e}_{y}+(\cos{\theta})\:{\bf
e}_{z}$ and ${\bf e}_{z}$ is the axis from which $\theta$ is measured. Since $f$ is real valued, we can write $$f({\bf u},t) = \sum_{l=0}^{\infty} \sum_{m=-l}^{+l} b_{l}^{m}(t)
Y_{l}^{m}({\bf u}),$$ where $ b_{l}^{-m}(t) = (-1)^{m} \overline{b_{l}^{m}(t)} $ for all $
m \geq 0$ (the over-bar denotes complex conjugation) and $b^{0}_{0}=(4 \pi)^{-1/2}$ $\forall$ $t$ due to the normalization condition. Nematic states with fore-aft symmetry satisfy $f({\bf
u})=f(-{\bf u})$, and for these $l$ is restricted to the set of even integers. The macroscopic state of the suspension can be quantified by three variables - the structure tensor, ${\bf S} \equiv
\langle{\bf u}{\bf u}\rangle - {{\mbox{\boldmath
$\delta$}}}/3 $, the concomitant scalar structure factor $ S_{e} \equiv 9({\bf S}{\boldsymbol{\cdot}}{\bf S}{\boldsymbol{\cdot}}{\bf
S})/2]^{1 / 3}$ and the mean polarity ${\bf J} \equiv \langle{\bf
u}\rangle$. We now specify the two inner products, $ \langle
Y^{m}_{l} | f \rangle \equiv \int \overline{Y_{l}^{m}({\bf u})} \:
f({\bf u},t) \: d{\bf u}$, and $ \langle l_{1},m_{1} | l_{2},m_{2} |
l_{3},m_{3} \rangle \equiv \int \overline{Y_{l_{1}}^{m_{1}}({\bf
u})} \: Y_{l_{2}}^{m_{2}}({\bf u}) \:Y^{m_{3}}_{l_{3}}({\bf u})
\:d{\bf u}$ and functions $ d_{2n}= [\pi (4n+1)(2n-3)!!(2n-1)!!]
[2^{(2n+2)}n!(n+1)!]^{-1} $ and $ c_{o}(l') =
[(l'-1){(l'-3)!!}^{2}][(l'+2){(l'!!)}^{2}]^{-1}.$
Using these definitions with (4) we can write (2) as $$V_{MS} = - {3 \over 2}U ({8\pi \over 15}) \sum_{l'=0}^{\infty}
\sum_{m'=-l'}^{l'} \delta_{l',2} Y_{l'}^{m'}({\bf
u})b_{l'}^{m'},$$ and $$V_{O} = - 4 \pi U \sum_{l'=1}^{\infty}\sum_{m'=-2l'}^{+2l'} {d_{2l'}
\over (4l'+1)} Y_{2l'}^{m'}({\bf u})b_{2l'}^{m'}$$ with $U=2NL^{2}d$. In writing (5) and (6) we have ignored constants linear in $U$ and independent of ${\bf u}$. The expressions are the same as those for non-magnetizable rods because the excluded volume potential is just dependent on [*geometrical*]{} symmetries. Parameters $\mathcal{A}'$ and $\mathcal{B}'$ in (3) are proportional to the number density of the particles, and can be rewritten as $\mathcal{A}'=\mathcal{A}U$ and $\mathcal{B}'=\mathcal{B}U$. Henceforth $U$, $\mathcal{A}$ and $\mathcal{B}$ are treated as three independent parameters. Combining (1), (4), (5) and (6) and using appropriate inner products we get the following evolution equation for the modes $b_{l}^{m}$, $${d{b_{l}^{m}} \over dt} = -l(l+1)\: b_{l}^{m} - \sum_{p=0}^{\infty}
\sum_{q=-p}^{+p} (\sigma_{EV}+ \sigma_{M}),$$ where $$\sigma_{M} = {4 \pi U} \sum_{l'=0}^{\infty} \sum_{m'=-l'}^{+l'}
b_{p}^{q} b_{l'}^{m'} ({{\mathcal{B} \delta_{l',2}} \over 5} +
{{\mathcal{A} \delta_{l',1}} \over 3}) \Psi$$ and $\sigma_{EV}$ depends on the nature of the excluded volume potential, $$\sigma_{MS} = {{4 \pi U} \over 5} \sum_{l'=0}^{\infty}
\sum_{m'=-l'}^{+l'} b_{p}^{q} b_{l'}^{m'} \delta_{l',2} \Psi,$$ $$\sigma_{O} = {4 \pi U}\sum_{l'=0}^{\infty} \sum_{m'=-2l'}^{+2l'}
{d_{2l'} \over 4l'+1} b_{p}^{q} b_{l'}^{m'} \Psi.$$ The function $\Psi =\Psi(l,m,p,q,l',m')$ is given by $$\Psi (l,m,p,q,l',m') = - m m' \langle l,m | p,q | l',m' \rangle$$ $$-{1 \over 2} ({{ [l(l+1) -m(m+1)]\over {
[l'(l'+1)-m'(m'+1)]^{-1}}}})^{1 \over 2} \langle l,m+1 | p,q |
l',m'+1 \rangle$$ $$-{1 \over 2} ({{ [l(l+1) -m(m-1)]\over {
[l'(l'+1)-m'(m'-1)]^{-1}}}})^{1 \over 2} \langle l,m-1 | p,q |
l',m'-1 \rangle$$
It is clear from equations (7)-(11) that nematic branches corresponding to $(\mathcal{A}=0$, $\mathcal{B} \geq 0)$ and thus $J=0$ form a subset of possible stationary solutions to (7). It is also clear that $(S =0, J \neq 0)$ states are un-physical.
A linear stability analysis of (7) about the isotropic state, $f_{o}({\bf{u}})=(4\pi)^{-1}$ is readily performed using $b_{l}^{m}=(b_{l}^{m})_{o}+\epsilon {b}_{l}^{'m} +
O(\epsilon^{2})$, $\epsilon \ll 1 $ being a suitable amplitude, and retaining terms through $O(\epsilon)$. The growth rates or eigenvalues, $\lambda_{l}^{m}$, corresponding to the disturbance $Y_{l}^{m}({\bf u})$ can be obtained from the linearized equations. For the Maier-Saupe potential we get the following eigenvalues (for odd and even $l$ respectively) $
(\lambda_{l}^{m})_{MS} = -l(l+1)(1-\delta_{l,1}\mathcal{A}U/3)$, and $(\lambda_{l}^{m})_{MS} =
-l(l+1)(1-U(1+\mathcal{B})\delta_{l,2}/5)$, indicating that there are two critical points on the $S=0$ isotropic branch. The first critical point satisfies $(1+\mathcal{B})U_{c}^{a} = 5$. The critical eigenvalue is [*five fold*]{} degenerate with the associated destabilizing eigenvectors being linear combinations of $Y_{2}^{m}$, $m=-2,-1,0,1,2$. The second critical point satisfies $U_{c}^{b}=3\mathcal{A}^{-1}$ and the critical eigenvalues that change sign at this point are [*three-fold*]{} degenerate and correspond to the eigenvectors $Y_{1}^{m}$, $m=-1,0,1$. In Figure (1) we plot these analytical predictions and compare them to numerically obtained solutions[@Bhandar] for the case $\mathcal{B}=1$. We note that for fixed and finite $\mathcal{B}$, as $\mathcal{A} \rightarrow \infty$, $U_{c}^{b} \rightarrow 0$. As $\mathcal{A}$ decreases from very large values, $U_{c}^{b} <
U_{c}^{a}$ initially and then, beyond a critical value of $\mathcal{A}$, we get $U_{c}^{b} > U_{c}^{a}$. For $\mathcal{B}=1$, the two critical points coincide for $\mathcal{A}=1.2$. Detailed numerical calculations show that for $U_{c}^{b}<U_{c}^{a}$, the branch is prolate, otherwise it is an oblate branch. For the Onsager potential we find (for odd and even $l$ respectively) $ {(\lambda_{l}^{m})_{O}} = - l(l+1)
(1-\mathcal{A}U \delta_{l,1}/3)$, and ${(\lambda_{l}^{m})_{O}} =
-l(l+1)(1-U(1+\mathcal{B})\delta_{k,1}/5 + U \pi c_{o}(l)/2)$. Thus for odd $l$, as for the Maier-Saupe potential, there is one critical point on the $S=0$ line, $U_{c}^{b}$, which is the same as before. The destabilizing eigenvectors are the $3$ independent components of $Y_{1}^{m}({\bf u})$. Let us denote the critical points for even $l$ by $U_{c}^{a}(l)$ such that the critical eigenvectors at each point are the $2l+1$ independent components of $Y_{l}^{m}({\bf u})$. The first critical point occurs at $U_{c}^{a}(2)= (\pi c_{o}(2)/2 + \mathcal{B}/5)^{-1}$ and corresponds to the eigenvector set $Y_{2}^{m}({\bf u})$. Higher order bifurcations occur at $U_{c}^{b}(l) = 2(\pi c_{o}(l))^{-1}$ for $l \geq 4$ $(k=2,3,..)$.
We now concentrate on bifurcations of $J > 0$ branches from the non-trivial $J=0$ nematic states for the specific case of a Maier-Saupe inter-molecular potential. As a point of departure to frame our discussion, we focus on the vicinity of the critical concentration given by $U_{c}^{a}=U_{c}^{b}$ and study the bifurcating branches as $\mathcal{A}$ and $U$ are varied with $\mathcal{B}$ held fixed.
Since the equations (1), (3), (7), (8) and (9) with $\mathcal{A}=0$ exhibit rotational symmetry, we consider a base nematic state of the form (3) with coefficients $(b_{l}^{m})_{o}$ real and non-zero only if both $l$ and $m$ are even. From (1), (3) and (8) it is clear that the potential $U$ and the parameter $\mathcal{B}$ can be combined into one dimensionless factor, $W=U(1+ \mathcal{B})$. Consider a base nematic state with director ${\bf n}={\bf e}_{z}$ such that $\cos{\theta} = ({\bf
u}{\boldsymbol{\cdot}}{\bf n})$. Then the steady, uniaxial solution for this nematic is given by $ f(\theta) ={\exp{(3W S_{e}
\cos{2\theta}/4)}}/P $, where $P$ is a normalizing constant. This yields $${{2 S_{e} + 1} \over 3} = (\int_{0}^{1} \exp{({3 \over 2} W S_{e}
t^{2})} t^{2} dt)(\int_{0}^{1} \exp{({3 \over 2} W S_{e} t^{2})}
dt)^{-1}$$ plotted in Figure (2a). The solid lines are linearly stable branches. The oblate phase where the rods are oriented randomly in the $({ {\mbox{\boldmath
$\delta$}}}- {\bf n}{\bf n})$ plane, is unstable to director fluctuations but stable if these are artificially suppressed - this is exemplified by the open circles which denote solutions obtained in integrating (1) in [*time*]{} in the subspace mentioned above$^{4}$. Brownian dynamics simulations of the system for the Maier-Saupe potential$^{5}$ and $\mathcal{B}_{m}=0$ indicate that results using time integration for [*short times*]{} can yield an [*apparently stable*]{} oblate phase, thus mimicking for short times the effect of a pinned director. However long time integration of the stochastic system leads to the oblate branch being destabilized by symmetry breaking perturbations. We expect similar considerations to hold for ${\mathcal{B}} \geq 0$.
For later analysis we need an expression for the solution curve close to the critical point $W=5$. An regular perturbation expansion in the small parameter, $\hat{W}\equiv W-5$ indicates that along the nematic branches, we have the approximate relationship $$S_{e}(\hat{W}) \approx -{7 \over 25} {\hat{W}'} + {119 \over 625}
{\hat{W}}^{'2} -{29981 \over 171875}{\hat{W}}^{'3} +
O(\hat{W}^{'4}),$$ also plotted in Figure (2a) as the dash-dot line. We expect this to be accurate close to the critical point only. The structure factor for this nematic state has the form ${\bf S}_{o} = -S_{e}(W){\bf
S}^{(1)}/3 $, with $(S^{(1)}_{xx}=S^{(1)}_{yy}=-S^{(1)}_{zz}/2)$. The eigenvalues obtained from (7) corresponding to the destabilizing eigenvectors, $Y_{2}^{m}$, are shown in Figure (2b). There are five eigenvalues that are zero at $U_{c}^{a}$. The one corresponding to $Y_{2}^{0}$ (the structure parameter mode) has multiplicity of $1$. The other four correspond to director fluctuations and occur as two pairs, one of which is identically zero. Since there are two independent ways to rotate a director on a sphere, we expect two neutral eigen-directions.
We now impose small perturbations to the base state, $b_{l}^{'m}$, comprised only of even $m$ modes while $l$ can be both even and odd. The equation for the growth of mode $b_{1}^{'0}$ with $\Psi_{(1)} =
\Psi(1,0,2,0,1,0)=1/\sqrt{(5\pi)}$ and $\Psi_{(2)}=\Psi(1,0,1,0,2,0)
= -3/\sqrt{(5\pi)}$ is: $${d{b_{1}^{'0}} \over dt} = -2\: b_{1}^{'0} (1- { U \mathcal{A}
\over 3} + {{2 \pi U \mathcal{A}} \over 3} (b_{2}^{0})_{o}
\Psi_{(1)}$$ $$- {{4 \pi U} \over {5(1+\mathcal{B})}} \sum_{p=0}^{\infty}
\sum_{q=-p}^{+p} \sum_{m'=-2}^{2} b_{p}^{'q} (b_{2}^{m'})_{o}
\Psi(1,0,p,q,2,m'))$$ Close to criticality, the $b_{1}^{'0}$ mode dominates and so the $p=3$ term in (13) can be ignored to leading order. Setting the growth rate to zero yields the following equation for $\mathcal{A}^{c}(\mathcal{B},U)$ valid for small $S_{e}$, $$[1+{2 \pi \over 5}(1+\mathcal{B})U(b_{2}^{0})_{o}\Psi_{(2)}] = {U
\mathcal{A}^{c} \over 3} (1-2 \pi (b_{2}^{0})_{o}\Psi_{(1)}).$$ To obtain local information about the nature of the $J>0$ branches close to the critical point $U_{c}^{a}=U_{c}^{b}$, we expand all quantities in terms of a small parameter $\delta$ that denotes the [*distance*]{} from the critical point measured along the $(J=0)$ nematic branches - to obtain (a) $ U=5 (1+\mathcal{B})^{-1}(1+
\delta \hat{U})$, (b) $ \mathcal{A}^{c}=3 (1+
\mathcal{B})(1+\delta \hat{\mathcal{A}}^{c})/5$ and (c) $
(b_{2}^{0})_{o} = \delta (\hat{b_{2}^{0}})_{o} \approx \delta U'
(d/d\hat{U})_{0}(\hat{b_{2}^{0}})_{o} = \delta k_{m}\hat{U} $ with the slope $k_{m} = -7\sqrt{5}(10\sqrt{\pi})^{-1}$. Substituting these expressions in (14) yields at $O(\delta)$ $$\hat{\mathcal{A}}^{c} = (2 \pi (\Psi_{(1)}+\Psi_{(2)})k_{m} -1
)\hat{U} = {9 \over 5} \hat{U}$$ Thus, close to the critical point as as we move along the prolate (with $\hat{U}$ locally decreasing), $\hat{\mathcal{A}}^{c}$ decreases as well. Similarly, as one moves along the oblate towards more higher values of $U$ ($\hat{U}$ increases), $\hat{\mathcal{A}}^{c}$ increases. In short, critical points on the $(J=0$, $S_{e} <0)$ oblate state have $\mathcal{A}^{c} > 1.2$ and on the $(J=0$, $S_{e} > 0)$ prolate state satisfy $\mathcal{A}^{c}
<1.2$.
Our analysis yields insight about the behavior close to the critical point. Crucially, we find that it accords with numerical solutions far from the critical point obtained by Bhandar$^{1}$ for the specific case $\mathcal{B}=1$. Combining our local analytic results with these global numerical results, we obtain the bifurcation scenario illustrated in Figure 3. Let us recast the results in terms of the dependence of $\mathcal{A}^{c}$ on the scalar structure parameter. For a fixed value of $\mathcal{A}$, there are two critical points at which the $J=0$ branch becomes unstable to disturbances comprised of $Y_{1}^{0}$ components. One of them is always on the $S_{e}=0$ isotropic branch and the other is always on the $(S_{e} \neq 0 , J=0) $ nematic solution. When $\mathcal{A} < 1.2$, the $J>0$ branches bifurcate at one point in the segment $(S_{e}=0$, $U>5/2)$ and at one point in the the prolate branch $(J=0$ , $ S_{e}>0$. Even though the $J=0$ nematic prolate has a turning point at $U \approx 2.245$, the salient qualitative results of the local analysis holds even far from the critical point.
Consider now the effects of an imposed external magnetic field ${\bf H}$ modeled by adding a term to the potential to (1) and (3) that is proportional to ${\bf u}{\boldsymbol{\cdot}}{\bf H}$. Such a field breaks the rotational degeneracy of the system inherent in (1). We anticipate that for a fixed values of $U$, $\mathcal{A}$ and $\mathcal{B}$, the degree of order $S$ as well as the extent of average polarization $J$ change continuously with $H$. The transition from an isotropic to nematic state is replaced by a transition from a weakly aligned (paranematic) state to a strongly aligned state. Our results provide a mathematically convenient and physically relevant starting point to investigate these scenarios.
### Acknowledgements {#acknowledgements .unnumbered}
AG thanks Dr. Bhandar for providing a copy of the dissertation from which the simulation data used for comparison (in Figure 1) was obtained.
[6]{}
A. S. Bhandar, A constitutive theory for magnetic dispersions, PhD Dissertation, The University of Alabama (2002).
A. S. Bhandar, and J. M. Weist, Mesoscale constitutive modeling of magnetic dispersions, J. Colloid Interface Sci., , 371 (2003).
R. G. Larson and H. C. Öttinger, Orientation distribution function for rod-like polymers, Macromolecules, , 6270 (1991).
A. Gopinath, R. C. Armstrong and R. A. Brown, Observations on the eigenspectrum of the linearized Doi equation and application to numerical simulations of liquid crystal suspensions, J. Chem. Physics, (12), 6093 (2004).
C. I. Siettos, M. D. Graham and I. G. Kevrekidis, Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation, J. Chem. Phys., (22), 10149 (2003).
The assumption of constant diffusivity is reasonable as we are concerned only with equilibrium nematic states.
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The number of snacks a person with diabetes should eat during the day depends largely on their eating preferences, weight-management goals and the timing of major meals. People with diabetes can eat snacks throughout the day for a number of reasons—simply enjoying a mid-morning snack or planning them into their day for better blood glucose control. Exactly how many snacks you should eat—and when you eat them—is very individualized. Meeting with a registered dietitian or certified diabetes educator is the best way to make sure your diabetes meal plan meets your needs. However, here are a few basic guidelines that can be helpful when planning snacks.
1. How many hours pass between meals?
In general, people with diabetes who want to optimize blood glucose control should not go longer than five hours without eating. If you consistently eat your main meals every four to five hours, then you may not need any snacks between meals. However, if your main meals are generally spaced out at longer intervals, snacking between meals can help you achieve your best blood glucose control. This is common during a typical workday in which you eat lunch at noon but don't leave work until 5 p.m. In this case, you likely won't be eating your evening meal until after 5 p.m.—well past the 5-hour guideline—and an afternoon snack would be recommended.
2. When do you prefer to eat?
Do you find you are usually yearning for a snack between meals? If so, you're better off planning these snacks into your daily meal plan rather than eating the additional calories and carbohydrates in these snacks on a whim (which can hinder your weight-loss and blood sugar control goals). Planning snacks into your daily routine better accounts for the calories and carbohydrates in the snack as part of your total goal for the day. For example, if you eat 1,500 calories in a day, they can be divided among three meals and two snacks, three meals and one snack, or three meals and three snacks, or just among three meals—it is really up to you! But be careful: When you eat more often, you need to be more conscientious about portion sizes.
3. Is your blood sugar low before bedtime?
For those looking to optimize blood sugar control, eating a snack one to two hours before bedtime can sometimes improve blood sugar control and prevent nighttime hypoglycemia (low blood sugar), though not everyone will experience this benefit, according to recent research. A 2003 study published in the journal Diabetes Care suggests that people with diabetes who have blood glucose levels over 180 mg/dL before bed should not eat a bedtime snack, but those with blood glucose levels below 126 mg/dL at bedtime should have a snack (roughly 15 grams of carbohydrates and 100 calories) to prevent late-night lows.
Talk to your doctor or diabetes educator about whether or not a bedtime snack is right for your diabetes care plan. And remember, even though the blood glucose control benefits can vary from person to person, an evening snack can also be part of a diabetes meal plan simply because you enjoy an evening snack—again, it’s up to you!
How to Plan Your Snacks
People with diabetes should follow a daily meal plan to achieve specific calorie and carbohydrate goals for each meal, and snacks are no exception. In general, a diabetes-friendly snack should contain 15 to 30 grams of carbohydrates and between 100 to 200 calories. If you are planning several snacks in addition to your meals, consider using the lower end of the recommendation: 15 grams of carbohydrates and 100 calories. Adding one ounce (7 grams) of protein to your snack is optional. At one time, people with diabetes were encouraged to eat protein with each snack, because it was thought to "level out" increases in blood sugar after a meal. Recent research, however, does not support this theory, so eating protein at every snack is not a must for everyone—although it can increase feelings of fullness after eating, which is beneficial.
What to Eat: Diabetes-Friendly Snack Ideas
So how do you meet these calorie and nutrition goals in a healthful way? Here are several diabetes-friendly snack ideas that meet the nutritional criteria above. Select a snack that fits into your daily meal plan for calories and carbohydrates but also meets your personal taste preferences. Keep in mind that different foods and food combinations (carbs, protein and fat) affect every individual's blood sugar levels differently. The following chart merely shows some options, but you'll still need to monitor your blood sugar response and find the best food combinations for you.
If you have trouble selecting appropriate snacks or practicing portion control, pre-packaged meal replacements (including snack bars and shakes) can be a smart solution for some. In their Evidence Analysis Library, the Academy of Nutrition and Dietetics (formerly the American Dietetic Association) states that "substituting one or two daily meals or snacks with meal replacements is a successful weight loss and weight maintenance strategy." Not all energy bars or weight-loss shakes will meet the needs of people with diabetes, so look for products designed specifically for diabetics, and be sure to read labels to determine if the product you're considering meets your nutritional needs.
Here are a few examples of daily eating schedules that include one to three snacks.
As you can see, snacks can be especially beneficial for people with diabetes, and there really are endless options that can help you stay within your daily nutritional goals.
Source
Adult Weight Management Meal Replacements, American Dietetic Association Evidence Library, accessed September 2011.
Diabetes Care, January 2003.
For more specific information or help, talk to your health care provider. The American Diabetes Association's National Call Center also offers live advice from 8:30 a.m. to 8 p.m. EST, Monday through Friday at 1-800-DIABETES or 1-800-342-2383. | https://www.sparkpeople.com/resource/nutrition_articles.asp?id=1588 |
AS A SOPHOMORE: Emerged as a likely candidate to fill the 4x400-meter relay voids left by departed seniors Ryan Postel and Jordan Powell ... set two career bests during the indoor campaign ... earned a BIG EAST qualification in the 500 meters by posting a time of 1:04.45 at the Blue and Gold Invitational ... ran 48.98 over 400 meters at the Notre Dame Invitational for his second BIG EAST mark ... took 12th in the preliminaries of the 500 meters at the BIG EAST indoor meet ... ran his first career 800-meter race outdoors at the Mike Poehlein Invitational ... ran 1:55.15 for second place ... top 400-meter performance of the outdoor season came at the BIG EAST Championship, where he ran 49.38 to finish 16th (second of four on the team) in the prelims.
AS A FRESHMAN: Showed promise in the middle distance group ... concentrated on the 500 meters during the indoor season ... top performance came early in the season at the Blue and Gold Invitational (1:06.58) ... shifted to the 400 meters during the outdoor campaign ... ran 50.55 at the Notre Dame Spring Opener ... broke the 50-second mark at the Miami (Ohio) Invitational, running 49.71 ... again lowered his time at the Central Collegiates with a time of 49.44 ... established his personal-best mark at the Hillsdale Gina Relays, running 49.30.
HIGH SCHOOL AND PERSONAL: Earned three varsity letters in both indoor and outdoor track and another in cross country during his career at Seton Hall Prep ... earned All-American honors as a member of Seton Hall Prep's 4x400-meter relay team that finished fourth at Nike Outdoor Nationals (3:13.88) ... the 4x400 relay also won the New Jersey state indoor championship and earned an indoor and outdoor national ranking ... his 4x800 team also earned a national ranking in his senior season (7:46) ... outdoor track team MVP and 400-meter conference champion in 2004 ... qualified for two Championship of America races at the 2005 Penn Relays (4x400, 4x800), the first New Jersey team to accomplish such a feat in over 20 years ... personal bests include 48.00 in the 400 meters and 1:53.6 in the 800 meters ... member of National Honor Society and Spanish Honor Society ... grandfather, Joseph Colleran, played hockey at Boston College ... oldest of three children ... born Feb. 14, 1987 in Hinsdale, Ill. ... enrolled in the Mendoza College of Business. | http://www.und.com/sports/c-track/mtt/buzaid_billy00.html |
Rupert Grint's height is 5 feet and 8 inches. That's 68 inches tall.
Or in metric units, Rupert Grint is 173 centimetres. That's 1 metre and 73 centimetres.
Rupert Grint is 2 centimetres (1 inches) taller than the average celebrity (the average is 171 centimetres, 5 feet 7 inches or 67 inches tall).
How tall is Rupert Grint compared to the average person? | https://socelebrity.com/height/rupert-grint |
Q:
Matlab to Python Stat Equation
I was wondering if anybody could help me translate the following code from MatLab into Python. The equation is used for determining the 99% Confidence Interval of a truncated normal distribution.
function sigma = var_truncNormal( a, b, mu, sigma, data )
x1 = (a-mu)/sigma * normpdf( a, mu, sigma );
x2 = (b-mu)/sigma * normpdf( b, mu, sigma );
cx = normcdf( b, mu, sigma) - normcdf( a, mu, sigma );
yhat = var( data(data>(mu-3000)&data<(mu+3000)) );
sigma2 = yhat/((1+(x1-x2)/cx - ((x1-x2)/cx)^2));
sigma = sqrt( sigma2 );
return;
function ci99 = GetCI99( data )
mu = median( data );
sigma = std( data );
fprintf( 1, 'initial sigma = %.1f\n', sigma );
sigma = var_truncNormal( mu-3000, mu+3000, mu, sigma, data );
fprintf( 1, 'updated sigma = %.1f\n', sigma );
sigma = var_truncNormal( mu-3000, mu+3000, mu, sigma, data );
fprintf( 1, 'updated sigma = %.1f\n', sigma );
ci99 = 2*mu-norminv( 0.01, mu, sigma );
figure( 'visible', 'off' );
hist( data, 5000:200:20000 );
axis( [5000 35000 0 550] );
hold;
[n2, xx] = ksdensity( data, 'npoints', 100 );
plot( xx, n2*length(data)*200, 'r' );
hdl = plot( xx, normpdf( xx, mu, sigma )*length(data)*200, 'k' );
set( hdl, 'linewidth', 2 );
line( [ci99 ci99], [0 550] );
print( '-dpdf', 'testFigure' );
close;
return;
I would appreciate any help.
A:
I think you will be very happy going from matlab to python/numpy. You just have to go through it line by line.
For example the first line of your function:
x1 = (a-mu)/sigma * normpdf( a, mu, sigma );
The normpdf in python is: 1/(sigma*sqrt(2*pi))exp(-1(a-mu)**2/2*sigma**2).
So we can define a little function in python:
a = numpy.array([3,4,5,2,2,2,1,3,3,3,3])
mu = 3.1
sigma = .7
def normpdf_python(x, mu, sigma):
return 1/(sigma*sqrt(2*pi))*exp(-1*(x-mu)**2/2*sigma**2)
x1 = (a-mu)/sigma*normpdf_python(a,mu,sigma)
Numpy/Scipy has a deep set of statistical packages, you should always check for pre-existing functions that do what you need. In this case http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm pdf(x, loc=0, scale=1) is close, but might not be enough as it is defined as:
norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
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Coding Interview Question: Find the median of two sorted arrays. Click for the solution.
Coding Interview Question: Implement a priority queue. Click for the solution.
Coding Interview Question: Given a binary search tree, print out the elements of the tree in order without using recursion. Click for the solution.
Coding Interview Question: Given a list of items, find the maximum value you can generate from the items. Click for the solution.
Coding Interview Question: Given a matrix, find the path from top left to bottom right with the greatest product. Click for the solution.
Coding Interview Question: Given an array of integers where each value 1 <= x <= len(array), write a function that finds all the duplicates in the array. Click for the solution.
Coding Interview Question: Write an autocomplete class that returns all dictionary words with a given prefix. Click for the solution.
Coding Interview Question: Given a list of packages to build, determine a valid order in which to build the packages. Click for the solution.
Coding Interview Question: Given an unsorted array, find the length of the longest sequence of consecutive numbers in the array. Click for the solution.
Coding Interview Question: Given a matrix, update it so that if any cell is true, all the cells in that row and column are true. Click for the solution. | https://www.byte-by-byte.com/tag/medium/ |
Q:
moving average and errors - Matlab
I have a series of data x,y and I am trying to find the moving average. The x data numbers are integers from 1 to 100 while the y data are numbers from 0.01 to 1 and they also have a standard deviation y_dev (which we derive because the experiment is repeated several times).
I am trying to find the moving average using the 20 closest neighbors (using Matlab):
num_data=length(x)
mov_average=y
for i=11,num_data-10 % we leave the data in the edges the same
ind1(i)=i-10
ind2(i)=i+10
mov_average(i)=mean(y(ind1(i):ind2(i)));
end
The above way derives the moving average but I do not know how to use the standard deviation that I have for each y data point because some data points have much larger standard deviations than others which means they are not as reliable as others (so they probably weigh less). How can i include the standard deviation for each data point in the above calculation?
Thank you.
A:
Say you have a vector a. Then another way of writing mean(a) as a weighted average is a*wts', where wts = ones(1,numel(a))/numel(a). In your case, you have a = y(ind1(i):ind2(i)).
It sounds like what you're wanting to use is a weighted moving average, where your weights wts are no longer identical, but are chosen using the standard deviation of the corresponding values.
Assuming the vector sd holds the standard deviations, here's one way of doing this:
num_data=length(x)
mov_average=y
for i=11,num_data-10
ind1(i)=i-10
ind2(i)=i+10
sds = 1./sd(ind1(i):ind2(i)); % smaller sd -> larger weight
wts = sds./sum(sds); % weights should sum to 1
mov_average(i) = y*wts';
end
Here, the values with smaller standard deviations will contribute larger weights.
An alternative idea is to calculate the simple moving average of both y and your standard deviations sd, and then plot them alongside one another.
wts = ones(1,10)/10;
y_mean = conv(y, wts, 'valid'); % moving avg of y
y_lb = y + conv(sd, wts, 'valid'); % moving avg of lower bound on y
y_ub = y - conv(sd, wts, 'valid'); % moving avg of upper bound on y
This has the advantage of being more statistically interpretable than choosing weights as a function of the standard deviations.
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The Concordia Lutheran Ministries family has a history of giving selflessly when a disaster occurs and people are in need. The recent catastrophe in Japan was no different, as Haven residents used the "most scholarly" of activities to raise money for the tsunami victims.
On March 30, Haven II resident and former librarian Lorraine Kesterson held a Spelling Bee in the Haven II Chapel. What separated this contest from others was that residents were able to sponsor one of the eight contestants, with all sponsorship dollars being donated to the Disaster Relief Fund for Japan (through the Lutheran Church Missouri Synod World Relief and Human Care).
Between sponsorships and straight donations, the Haven residents raised nearly $750 at the event, which was standing room only. The best speller on this particular day was Haven II resident Betty Mason, another former librarian.
It's stories like this that give us reason to hope and smile. It should be noted that this event was led and coordinated by Haven residents, with minimal support from the staff.
For more information on Concordia Haven Apartments, visit http://www.concordiahaven.org/, call 724.352.5378 or e-mail here. For more on LCMS World Relief visit http://www.lcms.org/. | https://www.concordialm.org/blog/concordia-residents-raise-funds-for-tsunami-victims |
The winners of the Delaware lottery will be revealed next week
DELAWARE — The winners are coming — and they’ll be in white shirts.
Delaware’s lottery office will announce its winners on Wednesday, the first day of the new season, when the lottery’s three-day drawing is underway.
The winners are expected to be announced by 3 p.m.
EST, said Craig Stier, spokesman for the lottery.
He declined to give any other details.
The lottery office said the winning numbers will be announced at 2:30 p.M.
EST on Thursday.
The winning numbers include the number of the winner, the winning ticket and the winning number of tickets in each group.
The first winner will be determined in a lottery drawing on Feb. 3, according to lottery officials.
If there are more than five winners, the winner will receive the prize.
The last lottery drawing will be held on June 1.
The next draw will be on July 7, with a winner chosen on June 28.
The winner of the lottery will not be obligated to participate in the drawing or participate in any other activities in the event of a tie, lottery officials said.
Lottery officials said they would not be sharing the names of the winning lottery numbers.
The Delaware Lottery was created in 1876.
The lottery is one of the oldest in the United States.
The state has not had a lottery since the 1930s.
The prize money is paid to the winner in the lottery and is then deposited in the state’s General Fund. | https://tutkugyo.com/2021/07/19/the-winners-of-the-delaware-lottery-will-be-revealed-next-week/ |
1. Technical Field
This invention relates generally to executing a section of code on an all-or-nothing basis, such that the entire section of code is executed and committed to memory, or none of the section of code is executed and committed to memory. The invention relates more particularly to software locking approaches and hardware transactional approaches to such execution of code on an all-or-nothing basis.
2. Description of the Prior Art
In multiple-processor computing systems, more than one processor may attempt to affect the same memory at the same time. For instance, a number of transactions, which may be read or write requests or responses to resources such as memory, may vie for the same memory at the same time. If each transaction is allowed unfettered access to the same memory, the results can include corrupting the integrity of the data stored in this memory. For example, one transaction may read a given memory line, act upon the value read, and then write a new value to the memory line. While the transaction is acting upon the value it read from the memory line, another transaction may write a different value to the memory line. When the first transaction writes its new value to the memory line, the second transaction may not realize that its value has been overwritten.
One approach to ensuring that a number of transactions are not attempting to process the same memory at the same time is to use a software locking approach. In a software locking approach, a transaction must first successfully obtain a lock on the relevant lines of memory before it is able to process the data stored in these memory lines. If two transactions are attempting to process the same memory line, then one transaction will initially win the lock, and be able to process the memory line before the second transaction does. Thus, the transactions are implicitly serialized, so that they do not try to compete for the same memory line at the same time. A disadvantage to using the software locking approach is that it can add overhead to the processing of transactions that in most cases is unnecessary, since most of the time there will be no contention for desired memory lines. This can cause degradation in performance of the entire system.
Another approach to ensuring that a number of transactions are not attempting to process the same memory at the same time is to use a hardware transactional memory approach. In a hardware transactional memory approach, the hardware of a system, specifically its processors, have the ability to process sections of code as transactional memory. Transactional memory can thus be considered as a way to bracket a code section such that it becomes a large, multi-argument load link/store conditional (LL/SC) transaction. The code section is executed speculatively, and the decision to commit the changes is deferred until the end of the section of code. If there has been any interference with any of the data used by the code section, such as the memory lines, cache lines, and so on, being used by the code section, then the entire transaction is aborted. Otherwise, the entire transaction is committed to memory, and the changes memory to the relevant memory and caches lines are effected.
While the hardware transactional memory approach is faster in performance than the software locking approach, it nevertheless suffers from some disadvantages. For the hardware transactional memory approach to work, the operations performed by the relevant section of code are accomplished within a cache before being committed to memory. However, if the cache is not large enough, or does not have great enough associativity, then the approach will fail. This is because the entire section of code will not be able to be completely executed speculatively before the processing effects of the code section are committed to memory. That is, the hardware transactional memory approach, while advantageous in performance as compared to the software locking approach, is not as widespread in its potential application as is the software locking approach. For these and other reasons, therefore, there is a need for the present invention.
| |
A cool electronic device emits a small amount of energy in a vacuum, and it’s called an electron.
The energy is called the valence electron.
A liquid, such as water, will have a higher energy output.
The higher the valance electron, the more energy is released.
How much energy does an electron produce?
A good way to determine how much energy is being emitted by an electronic device is to measure its energy at different temperature and pressure levels.
The key is to look at how much the energy is produced at a particular temperature and to calculate how much is being absorbed.
The most commonly used measurement of energy output is called a “temperature coefficient,” which is a measurement of how much heat is released as a result of the energy being emitted.
This temperature coefficient is measured by the valentine function, which measures the change in energy when the temperature of the object increases and decreases.
Temperature coefficients can be very useful, but they aren’t exact, so they should only be used for precise measurements.
The standard method for calculating temperature coefficients is to use the value of the temperature coefficient (in degrees Celsius) for the material being measured.
This is done by measuring how much water molecules in the object react to the heat, as well as the number of molecules in an individual atom of the material.
These reactions can be measured using a method called the Kullback–Leibler–Yudkowsky method.
The Kullbacks and the Yudkowsks are the most common and standard methods for temperature measurements.
It’s also known as the “kool-aid method,” and it measures the temperature at which the reaction is occurring.
In this method, a small sample of a material is placed under a high pressure of water, which then freezes into a liquid.
The molecules of the liquid react to each other, causing a small increase in the energy of the reaction.
The liquid then slowly freezes, forming a larger liquid that is larger in volume.
The larger the volume, the greater the increase in energy produced by the reaction, which is why it’s important to use a large sample of the larger object.
The amount of heat produced in the reaction can be easily measured using this method.
For example, if you measure the amount of liquid water vapor that’s being released as it freezes, you can calculate how many molecules of water are being emitted as the reaction heats up.
Temperature values for different materials can be found in the following tables.
The values for water are usually in Celsius, but you can also use other values.
A good starting point is to compare the temperature values of water molecules.
A value of 200 Kelvin (k) is usually considered to be the point at which water molecules become vaporized.
This point can be expressed as the temperature difference between the vapor temperature and the liquid water temperature.
If the vapor and liquid temperatures are approximately the same, the value is usually in the range of 10-100 Kelvin.
If you measure a temperature value in Celsius and then convert it to Kelvin, you’ll find that the temperature is 10-400 Kelvin.
A similar method can be used to determine the temperature value for a metal or a semiconductor.
In the case of metal, it’s possible to find a value that’s in the temperature range of about 1,000 Kelvin (K) and to convert it into Kelvin.
This gives a value of 10,000 K. If, on the other hand, you measure this value in Fahrenheit and then divide it by a value in Kelvin, the conversion will give a value between 1,200 and 1,600 Kelvin.
Another way to find the temperature for a semiconducting material is to take the temperature measurement from the center of the sample.
The center of a sample of semiconductor is usually measured in a thermal conductivity measurement.
If a semicathode is present in the center, then the semiconductor conductivity will be measured.
The value of this value can be calculated using the Köhler–Hilbert equation, which tells you how much semiconductor heat is produced when the semiconductive material is heated to a certain temperature.
You can find the values of this equation in the table below.
The table shows the temperature that a semicacrystal emits as it heats up, and then the temperature it produces when it cools.
If this table doesn’t look too interesting, that’s because it is a very basic calculation.
You don’t need to worry about the values at all, because the temperature change in the semicacrostal depends on the specific material.
You might also want to use another method to determine your specific heat content of the semicocrystal.
A semiconductor can be cooled down by cooling the semicathodes in the same way that a metal can.
You just need to cool the semicamets in a different way.
This cooling process doesn’t work for metals. | https://rajaspesifikasi.com/how-much-heat-do-electrons-produce/ |
---
abstract: 'We consider the binomial approximation of the American put price in the Black-Scholes model (with continuous dividend yield). Our main result is that the error of approximation is $O((\ln n )^\alpha/n)$, where $n$ is the number of time periods and the exponent $\alpha$ is a positive number, the value of which may differ according to the respective levels of the interest rate and the dividend yield.'
author:
- '[ Damien Lamberton]{}[^1]'
date: 'This version: November, 2018'
title: On the binomial approximation of the American put
---
The binomial approximation
==========================
Consider the Black-Scholes model, in which the stock price at time $t$ is given by $$S_t=S_0e^{(r-d-\frac{\sigma^2}{2})t+\sigma B_t},$$ where, under the risk-neutral probability measure, $(B_t)_{t\geq 0}$ is a standard Brownian motion. Here, $r$ is the instantaneous interest rate, and $d$ is the dividend rate (or the foreign interest rate in the case of forex options). We assume $r>0$ and $d\geq 0$.
Denote by $P$ the price function of the American put with maturity $T$ and strike price $K$, so that $$P(t,x)=\sup_{\tau\in{\mathcal{T}}_{0,T-t}}{\mathbb{E}}_x\left(e^{-r\tau}f(S_\tau)\right), \quad 0\leq t\leq T, \quad x\in[0,+\infty),$$ with $f(x)=(K-x)^+$, and ${\mathbb{E}}_x={\mathbb{E}}\left(\cdot\;|\; S_0=x\right)$. Here, ${\mathcal{T}}_{0,t}$ denotes the set of all stopping times with respect to the Brownian filtration, with values in the interval $[0,t]$.
For technical reasons (especially for the derivation of regularity estimates for the second time derivative of the price function), it is more convenient to use the log-stock price. So, we introduce $$X^x_t=x+\mu t +\sigma B_t, \quad \mbox{with } \mu=r-d-\frac{\sigma^2}{2},$$ and $$U(T,x)= \sup_{\tau\in{\mathcal{T}}_{0,T}}{\mathbb{E}}\left(e^{-r\tau}\varphi(X^x_{\tau})\right),$$ with ${\varphi}(x)=\left(K-e^x\right)^+$. We then have $$P(t,x)=U(T-t,\ln(x)), \quad t>0, x>0.$$ Note that $U(t,x)$ satisfies the following parabolic variational inequality $$\max\left[ -\frac{\partial U}{\partial t}+(A-r)U,\varphi-U\right]=0,$$ with the initial condition $U(0,.)=\varphi$.
Here, $A$ is the infinitesimal generator of $X$, namely $$A=\frac{\sigma^2}{2}\frac{\partial ^2 }{\partial x^2}
+\mu
\frac{\partial }{\partial x}.$$ Recall that, for each $T>0$, there is a real number $\tilde b(T)\leq \ln(K)$ such that $$U(T,x)>\varphi(x) \Leftrightarrow x>\tilde b(T).$$ In fact, if $(b(t),0\leq t\leq T)$ is the exercise boundary of the American put with maturity $T$, we have $\tilde b(t)=\ln(b(T-t))$. We will also need the European value function, defined by $$\bar{U}(T,x)={\mathbb{E}}\left(e^{-r T}\varphi(X^x_{ T})\right).$$ Note that $\bar U(0,.)=\varphi$ and $$-\frac{\partial \bar U}{\partial t}+(A-r)\bar U=0.$$ Note that, in Section \[Section-estimates\], the function $\bar U$ will be denoted by $u_\varphi$.
We now introduce the random walk approximation of Brownian motion. To be more precise, assume $(X_n)_{n\geq 1}$ is a sequence of i.i.d. real random variables satisfying ${\mathbb{E}}X_n^2=1$ and ${\mathbb{E}}X_n=0$, and define, for any positive integer $n$, the process $B^{(n)}$ by $$B^{(n)}_t=\displaystyle
\sqrt{T/n}\;\displaystyle\sum_{k=1}^{[nt/T]}X_k,\quad 0\leq t\leq T,$$ where $[nt/T]$ denotes the greatest integer in $nt/T$.
We will assume the following about the common distribution of the $X_n$’s (cf. hypothesis (H4) of [@DL2002]). Note that, in the binomial case, $X_1$ takes its values in $\{-1,+1\}$.
(H4)
: The random variable $X_1$ is bounded and satisfies ${\mathbb{E}}X_1^2=1$ and ${\mathbb{E}}X_1={\mathbb{E}}X_1^3=0$.
In the following, we fix $S_0$ and set $$P_0=P(0,S_0)=U(T,\ln S_0).$$ Note that, if we introduce the notation $g(x)=(K-S_0e^{\sigma x})^+$, we have $$P_0=\sup_{\tau\in{\cal T}_{0,T}}
{\mathbb{E}}\left(
e^{-r\tau}g(\mu_0\tau + B_\tau)\right),$$ with $\mu_0=\mu/\sigma$. We now have a natural approximation of $P_0$, given by $$P^{(n)}_0=\sup_{\tau\in{\cal T}^{(n)}_{0,T}}
{\mathbb{E}}\left(
e^{-r\tau}g(\mu_0\tau + B^{(n)}_\tau)\right),$$ where ${\cal T}^{(n)}_{0,T}$ denotes the set of all stopping times (with respect to the natural filtration of $B^{(n)}$), with values in $[0,T]\cap\{0,T/n,2T/n, \ldots,(n-1)T/n,T\}$. Our main result is the following.
\[mainTh\] There exists a positive constant $C$ such that, for all positive integers $n$, $$-C \frac{(\ln n)^{\bar\alpha}}{n} \leq P^{(n)}_0-P_0 \leq C \frac{(\ln n)^\alpha}{n},$$ where $\bar\alpha=\alpha=1$ if $d>r$, and $\bar\alpha=3/2, \alpha=5/4$ if $d\leq r$.
The above estimates improve our previous results (see [@DL2002], Theorem 5.6) which gave an upper bound of the form $C \left(\frac{\sqrt{\ln n}}{n}\right)^{4/5}$. Note that, for European options, the error estimate is $O(1/n)$ (see [@Diener], [@Walsh]). We also mention the results of [@Liang2010] about finite difference schemes, which give the rate $O(1/\sqrt{n})$, but their estimate is uniform over the time interval, while we concentrate on the error estimate for a fixed time. The paper [@Liang2010] also has results about the approximation of the exercise boundary. We also refer to [@Silvestrov2015] and its references for a review of recent results on the approximation of American option prices.
Our approach remains the same as in [@DL2002]: we relate the error estimates to the regularity of the value function. The improvement comes from a refinement of the quadratic estimates for the second order time derivative, in the spirit of Friedman and Kinderlehrer (see [@Friedman1975] and [@Kinderlehrer1980]). We also exploit the smoothness of the exercise boundary and its asymptotic properties close to maturity.
The constant $C$ in Theorem \[mainTh\] is related to the Berry-Esseen estimate and to the regularity of the value function. Although it is hard to keep track of the constants in the regularity estimates, it may be worth mentioning that they remain uniform with respect to $\mu$ and $\sigma$ as long as $(\mu,\sigma)$ remains in a compact subset of ${\mathbb{R}}\times(0,\infty)$. A consequence of this observation is that the bounds in Theorem \[mainTh\] are also valid for variants of the approximation in which the process approximating $\ln(S_t/S_0)$, instead of being $\mu t+\sigma B^{(n)}_t$, is given by $\mu_n t +\sigma_n B^{(n)}_t$ at discrete times $t$, with $\mu_n=\mu+O(1/n)$ and $\sigma_n^2=\sigma^2+O(1/n)$, as occurs in the classical risk-neutral approximation. Indeed, standard arguments show that the value function is locally Lipschitz-continuous with respect to $\sigma^2$ (away from $0$) and $\mu$.
The paper is organized as follows. In the next Section we recall some results of [@DL2002]. Section \[Section-estimates\] is devoted to estimates for the derivatives of the value function. The estimates are then used in Sections \[UB\] and \[LB\] to prove Theorem \[mainTh\]: in Section \[UB\], we give an upper bound for $P^{(n)}_0-P_0$ and in Section \[LB\], we derive the lower bound.
[**Acknowledgement:** ]{} The research on this paper has been stimulated by fruitful discussions on the approximation of American options with Martijn Pistorius, to whom the author is very grateful.
The value function and the approximating process
================================================
As in [@DL2002], we introduce the modified value function $$u(t,x)=e^{-rt}U(T-t,\ln (S_0) +\mu t +\sigma x),\quad t\geq 0, \quad x\in {\mathbb{R}}.$$ We have $P_0=u(0,0)$ and $u(T,x)=e^{-rT}U(0,\ln (S_0) +\mu T +\sigma x)=e^{-rT}(K-S_0e^{\mu T+ \sigma x})^+$ and, for $t\in [0,T]$, $$u(t,x)\geq e^{-rt}(K-S_0e^{\mu t+ \sigma x})^+=e^{-rt}g(\mu_0t +x).\label{*}$$ We will need the European analogue of $u$, namely $$\bar u(t,x)=e^{-rt}\bar U(T-t,\ln (S_0) +\mu t +\sigma x)=e^{-rT}{\mathbb{E}}\left(g(\mu_0T+x+B_{T-t})\right),\quad t\geq 0, x\in {\mathbb{R}}.$$ We will also use the notation: $$h=\frac{T}{n}\;.$$ With this notation, we have $$B^{(n)}_t=\sqrt{h}\sum_{k=1}^{[t/h]}X_k, \quad 0\leq t\leq T.$$ We have, for all $t\in\{0,h,2h,\ldots,(n-1)h,nh=T\}$ (cf. Proposition 3.1 of [@DL2002]), $$u(t, B^{(n)}_{t})=
u(0,0)+M_{t}+\sum_{j=1}^{t/h}{\cal D}u({(j-1)h},B^{(n)}_{{(j-1)h}}),$$ where $(M_t)_{0\leq t\leq T}$ is a martingale (with respect to the natural filtration of $B^{(n)}$), such that $M_0=0$, and $${\cal D}u(t,x)={\mathbb{E}}\left( u\left(t+h, x+\sqrt{h}X_1\right)\right)
-u(t,x), \quad 0\leq t\leq T-h,\quad x\in{\mathbb{R}}.$$ The above decomposition of $u(t, B^{(n)}_{t})$ (which is in fact Doob’s decomposition) can be viewed as a discrete version of Itô’s formula, which, for a smooth function $v: [0,T]\times {\mathbb{R}}\to {\mathbb{R}}$, implies that $v(t,B_t)-\int_0^t\delta v(s,B_s)ds$ is a (local) martingale, where $$\delta v= {\partial v\over\partial t}+{1\over 2}{\partial^2 v\over\partial x^2}.$$ It is also easy to check that, if $v$ is smooth and ${\cal D}v(t,x)={\mathbb{E}}\left( v\left(t+h, x+\sqrt{h}X_1\right)\right)
-v(t,x)$, we have $$({1/ h})\times{\cal D}v(t,x)
=\delta v(t,x)+O(h).$$ The main technical difficulty that we have to deal with is the lack of smoothness of the modfied value function $u$.
\[rem1\] The derivatives of $u$ are related to those of $U$ by the following formulas. We have $$\begin{aligned}
\frac{\partial u}{\partial t}(t,x)&=&e^{-rt}\left(-\frac{\partial U}{\partial t}+\mu \frac{\partial U}{\partial x}
-rU\right)(T-t,\ln (S_0) +\mu t +\sigma x)
\end{aligned}$$ and $$\begin{aligned}
\frac{\partial ^2u}{\partial t^2}(t,x)&=&e^{-rt}\left(\frac{\partial ^2U}{\partial t^2}
-2\mu \frac{\partial^2 U}{\partial t \partial x} +\mu^2\frac{\partial^2 U}{\partial x^2}\right.\\
&&\left.
+2r\frac{\partial U}{\partial t } -2r\mu\frac{\partial U}{\partial x }
+r^2U\right)(T-t,\ln (S_0) +\mu t +\sigma x).
\end{aligned}$$
We also have $$\begin{aligned}
\delta u(t,x)= \frac{\partial u}{\partial t}(t,x)+\frac{1}{2} \frac{\partial^2 u}{\partial x^2} (t,x) &=&
e^{-rt}\left(-\frac{\partial U}{\partial t}+(A-r)U\right)(T-t,\ln (S_0) +\mu t +\sigma x)\\
&=&
e^{-rt}(A-r)\varphi (\ln (S_0) +\mu t +\sigma x){\textrm{\dsrom{1}}_{\{\ln (S_0) +\mu t +\sigma x\leq \tilde b(T-t)\}}},\end{aligned}$$ where the last equality follows from regularity results (see, for instance, [@Jaillet]).
We will need a more precise description of the operator $\cal D$, given by the following proposition (see Proposition 3.4 of [@DL2002]). For convenience, we denote by $X$ a random variable with the same distribution as $X_1$, which is independent of the sequence $(X_n)_{n\geq 1}$.
\[prop3-2\] Assume that (H4) is satisfied and that $v$ is a function of class $C^3$ on $[0,T]\times {\mathbb{R}}$. For $0\leq t\leq T-h$ and $x\in{\mathbb{R}}$, define $$\tilde{{\cal D}}v(t,x)=2\int_0^{\sqrt{h}}d\xi\int_0^\xi dz{\mathbb{E}}\left[ X\left(\xi-X^2(\xi-z)\right)
{\partial^2 v\over \partial t\partial x}(t+\xi^2,x+zX)\right].$$ We have $${\cal D}v(t,x)=\tilde{{\cal D}}v(t,x)+2\int_0^{\sqrt{h}}d\xi\int_0^\xi dz
{\mathbb{E}}\left(X^2\delta v(t+\xi^2,x+zX)\right),$$ with the notation $\delta v= {\partial v\over\partial t}+{1\over 2}{\partial^2 v\over\partial x^2}$, and $$\tilde{{\cal D}}v(t,x)=2\int_0^{\sqrt{h}}d\xi\int_0^\xi dz
(\xi-z){\mathbb{E}}\left[
X^2\left(\xi-X^2\frac{(\xi-z)}{2}\right)
{\partial^3 v\over \partial t\partial x^2}(t+\xi^2,x+zX)\right].$$
\[rem2\]Note that, if $\delta v(s,x+zX)=0$ for all $s\in[t,t+h]$ and $z\in[0,\sqrt{h}]$, we have $v(t,x)={\cal D}v(t,x)$.
From the last equality in Proposition \[prop3-2\], we derive the following estimates. $$\begin{aligned}
\left|\tilde{{\cal D}}v(t,x) \right|&\leq &
2\int_0^{\sqrt{h}}\xi ^2d\xi\int_0^\xi dz
{\mathbb{E}}\left[
\left(X^2+\frac{X^4}{2}\right)
\left|{\partial^3 v\over \partial t\partial x^2}(t+\xi^2,x+zX)\right|\right]\\
&\leq &\sqrt{h}\int_0^{\sqrt{h}} 2\xi d\xi
{\mathbb{E}}\left[\int_0^\xi dz
\left(X^2+\frac{X^4}{2}\right)
\left|{\partial^3 v\over \partial t\partial x^2}(t+\xi^2,x+zX)\right|\right]\\
&\leq &\sqrt{h}
\int_t^{t+h} ds{\mathbb{E}}\left(\int dy {\textrm{\dsrom{1}}_{\{|y-x|\leq \sqrt{h}|X|\}}}\left(|X|+\frac{|X|^3}{2}\right)
\left|{\partial^3 v\over \partial t\partial x^2}(s,y)\right|\right)\\
&=&\sqrt{h}
\int_t^{t+h} ds\int dy {\mathbb{E}}\left({\textrm{\dsrom{1}}_{\{|y-x|\leq \sqrt{h}|X|\}}}\left(|X|+\frac{|X|^3}{2}\right)\right)
\left|{\partial^3 v\over \partial t\partial x^2}(s,y)\right|\end{aligned}$$ We know from Proposition 3.2 of [@DL2002] (based on Berry-Esseen estimates) that, for every $k\in (1,3]$, there exists a positive constant $C_{k}$ (which does not depend on $X$), such that, for all $y\in {\mathbb{R}}$, $n\geq 1$ and $j\in\{1,2,\ldots,n\}$, $$\begin{aligned}
{\mathbb{E}}\left(\left(|X|+\frac{|X|^3}{2}\right)
{\textrm{\dsrom{1}}_{\left\{\left|B^{(n)}_{jh}-y\right|\leq \sqrt{h}|X|\right\}}}\right)
&\leq & \frac{C_{k}}{\sqrt{j}}{{\mathbb{E}}\left(|X|^3\right)\left(1+{\mathbb{E}}\;|X|^{3+k}\right)\over 1+|y|^k}.\end{aligned}$$ Hence, for $j=1,\ldots, n-1$, $$\begin{aligned}
{\mathbb{E}}\left(\left|\tilde{{\cal D}}v(jh,B^{(n)}_{jh}) \right|\right)
&\leq & \frac{C_{k,X}}{\sqrt{j}}\sqrt{h}\int_{jh}^{jh+h} ds\int \frac{dy}{1+|y|^k}
\left|{\partial^3 v\over \partial t\partial x^2}(s,y)\right|\nonumber\\
&\leq &C_{k,X}h\sqrt{2}\int_{jh}^{jh+h} \frac{ds}{\sqrt{s}}\int \frac{dy}{1+|y|^k}
\left|{\partial^3 v\over \partial t\partial x^2}(s,y)\right|,\label{Dtilde}\end{aligned}$$ where, for the last inequality, we used the inequality $jh\geq (j+1)h/2$.
Estimates for the second order time derivative {#Section-estimates}
==============================================
In this section, we refine the regularity results that we used in [@DL2002]. We first establish some elementary $L_1$-estimates. Then, we obtain a quadratic estimate for the second order time derivative of the difference $\tilde U=U-\bar U$. For the definition of the relevant weighted Sobolev spaces, we will use the notation $$\nu_j(dx)=\frac{dx}{(1+x^2)^{j/2}}, \quad j>1.$$
Some elementary $L_1$-estimates
-------------------------------
\[prop-L1\] Assume that the function $\varphi$ is continuous and satisfies $\varphi\in L_1(\nu_j)$, $\varphi'\in L_1(\nu_j)$ and the second derivative $\varphi''$ is a Radon measure on ${\mathbb{R}}$, with $\int_{\mathbb{R}}\frac{|\varphi''(dz)|}{(1+z^2)^{j/2}}<\infty$.
Let $$u_\varphi(t,x)=e^{-rt}{\mathbb{E}}(\varphi(X^x_t)), \quad t\geq 0, \quad x\in {\mathbb{R}}.$$
Then, for all $T>0$, there exists a constant $C_T>0$, such that $$\forall t\in (0,T], \quad \left|\left|\frac{\partial ^2u_\varphi}{\partial t^2}(t,.)
\right|\right|_{L_1(\nu_j)}\leq \frac{C_T}{t}.$$
We will easily deduce this proposition from the following lemma.
\[lem-L1\] If $\rho$ is a Radon measure on ${\mathbb{R}}$ and $q$ a nonnegative integrable function on ${\mathbb{R}}$, we have $$\left|\left|\rho*q\right|\right|_{L_1(\nu_j)}\leq 2^{j/2}\int_{\mathbb{R}}\frac{|\rho(dz)|}{(1+z^2)^{j/2}}\int_{-\infty}^\infty q(x) (1+x^2)^{j/2} dx.$$ We also have, for any measurable function $f$ on ${\mathbb{R}}$, $$\forall y\in {\mathbb{R}},\quad ||f(.-y)||_{L_1(\nu_j)}\leq 2^{j/2}(1+y^2)^{j/2}||f||_{L_1(\nu_j)}.$$
We have $$\begin{aligned}
\left|\left|\rho*q\right|\right|_{L_1(\nu_j)}&\leq &\int_{-\infty}^\infty \frac{dx}{(1+x^2)^{j/2}}
\int_{\mathbb{R}}| \rho(dz)| q(x-z)\\
&=& \int_{\mathbb{R}}\frac{|\rho(dz)|}{ (1+z^2)^{j/2}}\int_{-\infty}^\infty q(x-z) \frac{(1+z^2)^{j/2}}{(1+x^2)^{j/2}}dx\\
&=&\int_{\mathbb{R}}\frac{|\rho(dz)|}{ (1+z^2)^{j/2}}\int_{-\infty}^\infty q(x) \frac{(1+z^2)^{j/2}}{(1+(x+z)^2)^{j/2}}dx.\end{aligned}$$ Note that $$z^2\leq 2((x+z)^2+x^2),$$ so that we deduce $$\begin{aligned}
\frac{1+z^2}{1+(x+z)^2}&\leq &\frac{1+2(x+z)^2+2x^2}{1+(x+z)^2}\\
&\leq &2(1+x^2).\end{aligned}$$ Hence $$\left|\left|\rho*q\right|\right|_{L_1(\nu_j)}\leq 2^{j/2}\int_{\mathbb{R}}\frac{|\rho(dz)|}{(1+z^2)^{j/2}}\int_{-\infty}^\infty q(x) (1+x^2)^{j/2} dx.$$ Similarly, we have, for any measurable function $f$ and $y\in {\mathbb{R}}$, $$\begin{aligned}
\left|\left|f(.-y)\right|\right|_{L_1(\nu_j)}&=&\int |f(x-y)|\frac{dx}{(1+x^2)^{j/2}}\\
&=&\int |f(x)|\frac{dx}{(1+(x+y)^2)^{j/2}}\\
&=&\int |f(x)|\left(\frac{1+x^2}{1+(x+y)^2}\right)^{j/2}\frac{dx}{(1+x^2)^{j/2}}\\
&\leq &
\int |f(x)|\left(\frac{1+2(x+y)^2+2y^2}{1+(x+y)^2}\right)^{j/2}\frac{dx}{(1+x^2)^{j/2}}\\
&\leq &
2^{j/2}(1+y^2)^{j/2}\left|\left|f\right|\right|_{L_1(\nu_j)}.\end{aligned}$$
[**Proof of Proposition \[prop-L1\]:**]{} We have $$\begin{aligned}
u_\varphi(t,x)&=&e^{-rt}\int_{-\infty}^\infty \varphi (x+y)\exp\left(-\frac{(y-\mu t)^2}{2\sigma^2 t}\right)\frac{dy}{\sigma\sqrt{2\pi t}}\\
&=& e^{-rt}p_t*\varphi(x),\end{aligned}$$ with $$p_t(x)=\frac{1}{\sigma\sqrt{2\pi t}}\exp\left(-\frac{(x+\mu t)^2}{2\sigma^2 t}\right)=\frac{1}{\sigma\sqrt{ t}}n\left(\frac{x+\mu t}{\sigma\sqrt{t}}\right).$$ Here, $n$ denotes the standard normal density function.
On the other hand, we know that $u_\varphi$ satisfies the equation $$\label{eq-u}
\frac{\partial u_\varphi}{\partial t}=(A-r)u_\varphi,$$ so that $$\begin{aligned}
\frac{\partial u_\varphi}{\partial t}(t,.)&=&e^{-rt}(A-r)p_t*\varphi\\
&=&e^{-rt}p_t*[(A-r)\varphi].\end{aligned}$$ It follows from our assumptions that $(A-r)\varphi$ is a Radon measure satisfying $$\int_{\mathbb{R}}|(A-r)\varphi(dz)|\frac{1}{(1+z^2)^{j/2}}<\infty.$$ So that, using Lemma \[lem-L1\], $$\begin{aligned}
\left|\left|\frac{\partial u_\varphi}{\partial t}(t,.)\right|\right|_{L_1(\nu_j)}&\leq &
C_j \int_{-\infty}^\infty p_t(x) (1+|x|^j)dx\\
&=&C_j \int_{-\infty}^\infty \frac{1}{\sigma\sqrt{ t}}n\left(\frac{x+\mu t}{\sigma\sqrt{t}}\right) (1+|x|^j)dx\\
&=&C_j \int_{-\infty}^\infty n\left(y\right) (1+|y\sigma\sqrt{t}-\mu t|^j)dy\\
&\leq & C_j\left(1+t^j\right).\end{aligned}$$ On the other hand, by differentiating , we have $$\frac{\partial ^2 u_\varphi}{\partial t^2}=(A-r)\frac{\partial u_\varphi}{\partial t}
= e^{-rt}\left((A-r)p_t\right)*(A-r)\varphi.$$ Hence, using Lemma \[lem-L1\], and the definition of $p_t$, $$\begin{aligned}
\left|\left|\frac{\partial ^2 u_\varphi}{\partial t^2}(t,.)\right|\right|_{L_1(\nu_j)}&\leq &C_j
\int_{-\infty}^\infty |(A-r)p_t(x)| (1+|x|^j)dx\\
&\leq &\frac{ C_j}{t}\left(1+t^j\right).\end{aligned}$$
Quadratic estimates
-------------------
Recall the notation: $$U(t,x)= \sup_{\tau\in{\mathcal{T}}_{0,t}}{\mathbb{E}}\left(e^{-r\tau}\varphi(X^x_{\tau})\right),
\quad u_\varphi(t,x)=e^{-rt}{\mathbb{E}}(\varphi(X^x_t)), \quad t\geq 0, \quad x\in {\mathbb{R}},$$ with ${\varphi}(x)=\left(K-e^x\right)^+$. We now introduce the difference $\tilde{U}=U-u_\varphi$ (which corresponds to the early exercise premium). We have the following $L_2$-estimate for the second time derivative of $\tilde U=U-u_\varphi$.
\[thm-quadratic\] Fix $T>0$ and $j>1$. There exists a constant $C>0$ such that, for all $\xi\in(0,T]$, $$\int_\xi^T(t-\xi)
\left|\left|\frac{\partial ^2 \tilde U}{\partial t^2}(t,.)\right|\right|^2_{L_2(\nu_j)}dt\leq
C\left(1+|\ln \xi|^\beta\right),
\quad\mbox{with } \beta=\left\{ \begin{array}{l}
3/2, \mbox{ if } d\leq r,\\
\\
1, \mbox{ if } d>r.
\end{array}
\right.$$
This estimate is closely related to Theorem 2.4 of [@DL2002], a variant of results due to Friedman and Kinderlehrer (see [@Friedman1975], Lemma 4.1, and [@Kinderlehrer1980], Chapter VIII). Note that by considering the difference $\tilde U=U-u_\varphi$, we are able to derive a logarithmic upper bound, instead of a power of $\xi$, which would come up by considering $U$ (see Theorem 2.4 of [@DL2002]). For the proof of Theorem \[thm-quadratic\], we need some preliminary estimates on the derivatives $\frac{\partial ^2 \tilde U}{\partial x^2}$ and $\frac{\partial ^2 \tilde U}{\partial t\partial x}$.
\[fact1\] Fix $T>0$ and $j>1$. For any ${\varepsilon}\in (0,1/4)$, there exists a constant $C>0$ such that, for all $t\in(0,T]$, $$\left|\left|\frac{\partial \tilde U}{\partial x}(t,.)\right|\right|_{L_2(\nu_j)}\leq C \sqrt{t} \quad\mbox{and}\quad
\left|\left|\frac{\partial ^2 \tilde U}{\partial x^2}(t,.)\right|\right|_{L_2(\nu_j)}\leq C t^{\varepsilon}.$$
We know that $\tilde U$ solves the equation $$-\frac{\partial \tilde U}{\partial t}+(A-r)\tilde U=\tilde{h},$$ with initial condition $\tilde U(0,.)=0$, where the function $\tilde{h}$ is given by $$\tilde{h}(t,x)=(A-r)\varphi(x){\textrm{\dsrom{1}}_{\{x\leq \tilde b(t)\}}}, \quad t>0, \quad x\in {\mathbb{R}}.$$ We have the following identity (which can be viewed as a form of the early exercise premium formula). $$\tilde U(t,.)=-\int_0^t e^{-r(t-s)} p_{t-s}*\tilde{h}(s,.)ds,$$ where $$p_t(x)=\frac{1}{\sigma\sqrt{2\pi t}}\exp\left( -\frac{(x+\mu t)^2}{2\sigma^2 t}\right)=\frac{1}{\sigma\sqrt{ t}}n\left(\frac{x+\mu t}{\sigma\sqrt{t}}\right),$$ with $n$ denoting the standard normal density function. It is straightforward to check that $$\frac{\partial \tilde U}{\partial x}(t,.)=-\int_0^t e^{-r(t-s)} p_{t-s}*\frac{\partial \tilde{h}}{\partial x}(s,.)ds,$$ and, with the notation $\delta_z$ for the Dirac measure at a point $z$, $$\begin{aligned}
\frac{\partial \tilde{h}}{\partial x}(t,x)&=&(A-r)\varphi'(x){\textrm{\dsrom{1}}_{\{x\leq \tilde b(t)\}}}-(A-r)\varphi(x)\delta_{\tilde b(t)}(x)\nonumber\\
&=& -\kappa(t,x)+\gamma(t)\delta_{\tilde b(t)}(x),\label{dhdx}\end{aligned}$$ with $\kappa(t,x)=-(A-r)\varphi'(x){\textrm{\dsrom{1}}_{\{x\leq \tilde b(t)\}}}$ and $\gamma(t)=-(A-r)\varphi(\tilde b(t))$. Note that $\kappa$ is a bounded function on $(0,\infty)\times {\mathbb{R}}$ and $\gamma$ is a continuous, nonnegative and bounded function on $(0,+\infty)$. At this stage, it is clear that $||p_{t-s}*\frac{\partial \tilde{h}}{\partial x}(s,.)||_\infty\leq C/\sqrt{t-s}$, so that $$\left|\left|\frac{\partial \tilde U}{\partial x}(t,.)\right|\right|_{L_2(\nu_j)}\leq C \sqrt{t}.$$
On the other hand, we have $$\begin{aligned}
\left|\left|\frac{\partial ^2 \tilde U}{\partial x^2}(t,.)\right|\right|_{L_2(\nu_j)}
&\leq & \int_0^t e^{-r(t-s)}
\left|\left|p'_{t-s}*\kappa(s,.)\right|\right|_{L_2(\nu_j)}ds+\left|\left|\zeta(t,.)\right|\right|_{L_2(\nu_j)},\end{aligned}$$ with $$\begin{aligned}
\zeta(t,.)&=& \int_0^t e^{-r(t-s)}\gamma(s) p'_{t-s}*\delta_{\tilde b(s)}ds\\
&=& \int_0^t e^{-r(t-s)}\gamma(s) p'_{t-s}(.-\tilde b(s))ds.\end{aligned}$$ We have, using Lemma \[lem-L1\], $$\begin{aligned}
\left|\left|p'_{t-s}*\kappa(s,.)\right|\right|_{L_2(\nu_j)}&=&
\left|\left|\int p'_{t-s}(y)\kappa(s,.-y)dy\right|\right|_{L_2(\nu_j)}\\
&\leq&\int |p'_{t-s}(y)|\left|\left|\kappa(s,.-y)\right|\right|_{L_2(\nu_j)}dy\\
&\leq &2^{j/4}\left|\left| \kappa(s,.)\right|\right|_{L_2(\nu_j)} \int |p'_{t-s}(y)|(1+y^2)^{j/4}dy.\end{aligned}$$ Note that, since $\kappa$ is bounded and $j>1$, $\sup_{s>0}\left|\left|\kappa(s,.)\right|\right|_{L_2(\nu_j)}<\infty$, so that, for some constant $C>0$ (which may vary from line to line) $$\begin{aligned}
\left|\left|p'_{t-s}*\kappa(s,.)\right|\right|_{L_2(\nu_j)}&\leq&
C\int |p'_{t-s}(y)|(1+y^2)^{j/4}dy\\
&=&C\int \frac{1}{\sigma^2(t-s)}\left|n'\left(\frac{y+\mu(t-s)}{\sigma\sqrt{t-s}}\right)\right|(1+y^2)^{j/4}dy\\
&=&C\int \frac{1}{\sigma\sqrt{t-s}}\left|n'\left(z\right)\right|(1+(-\mu(t-s)+\sigma\sqrt{t-s}z)^2)^{j/4}dz\\
&\leq &\frac{C}{\sqrt{t-s}}\left( 1+ (t-s)^{j/2}\right).\end{aligned}$$ Hence, if $0<t<T$, $$\int_0^t e^{-r(t-s)}
\left|\left|p'_{t-s}*\kappa(s,.)\right|\right|_{L_2(\nu_j)}ds\leq C\int_0^t \frac{ds}{\sqrt{t-s}}=2C\sqrt{t}.$$ We now estimate $\left|\left|\zeta(t,.)\right|\right|_{L_2(\nu_j)}$.
We have, using the boundedness of $\gamma$, $$\begin{aligned}
|\zeta(t,x)|&=&\left|\int_0^t e^{-r(t-s)}\gamma(s)p'_{t-s}(x-\tilde b(s))ds\right|\\
&\leq& C\int_0^t \frac{1}{\sigma^2(t-s)}\left|n'\left(\frac{x-\tilde b(s)+\mu(t-s)}{\sigma\sqrt{t-s}}\right)\right|ds\end{aligned}$$ Recall that $n'(x)=-xn(x)$. Therefore $$\begin{aligned}
|\zeta(t,x)|&\leq& C\int_0^t \frac{|x-\tilde b(s)+\mu(t-s)|}{(t-s)^{3/2}}n\left(\frac{x-\tilde b(s)+\mu(t-s)}{\sigma\sqrt{t-s}}\right)ds\\
&\leq &C\int_0^t\frac{ds}{\sqrt{t-s}}+C\int_0^t \frac{|x-\tilde b(s)|}{(t-s)^{3/2}}n\left(\frac{x-\tilde b(s)+\mu(t-s)}{\sigma\sqrt{t-s}}\right)ds.\end{aligned}$$ Note that $$\begin{aligned}
n(x_1+x_2)=n(x_1)\exp\left(-\frac{x_2^2}{2}-x_1x_2\right)&\leq n(x_1)\exp(-x_1x_2)\\
&\leq n(x_1)\exp\left(\frac{x_1^2}{4}+x_2^2\right)
=n(x_1/\sqrt{2})e^{x_2^2}.\end{aligned}$$ Hence, for $t\in (0,T)$, $$\begin{aligned}
|\zeta(t,x)|
&\leq &C\int_0^t\frac{ds}{\sqrt{t-s}}+
C_T\int_0^t \frac{|x-\tilde b(s)|}{(t-s)^{3/2}}n\left(\frac{x-\tilde b(s)}{\sqrt{2}\sigma\sqrt{t-s}}\right)ds.\end{aligned}$$ Note that, for all $\alpha>0$, there exists $C_\alpha>0$, such that, for all $y\in {\mathbb{R}}$, $n(y/\sqrt{2})\leq C_\alpha/|y|^{2\alpha}$. Hence, for $t\in (0,T)$, $$\begin{aligned}
|\zeta(t,x)|
&\leq &C\sqrt{t}+C_\alpha\int_0^t\frac{|x-\tilde b(s)|}{(t-s)^{3/2}}\frac{(t-s)^\alpha}{|x-\tilde b(s)|^{2\alpha}}ds\\
&=& C\sqrt{t}+C_\alpha \int_0^t\frac{(t-s)^{\alpha-\frac{3}{2}}}{|x-\tilde b(s)|^{2\alpha-1}}ds\\
&=&C\sqrt{t}+C_\alpha t^{\alpha-\frac{1}{2}}\int_0^1\frac{1}{(1-u)^{\frac{3}{2}-\alpha}|x-\tilde b(tu)|^{2\alpha-1}}du.\end{aligned}$$ Now, take $\alpha=\frac{1}{2}+{\varepsilon}$ (with $0<{\varepsilon}<1/4$) and put $\beta(t,x)=|x-\tilde b(t)|^{1-2\alpha} =|x-\tilde b(t)|^{-2{\varepsilon}}$. We get $$\begin{aligned}
\left|\left|\zeta(t,.)\right|\right|_{L_2(\nu_j)}
&\leq
&C\sqrt{t}+Ct^{{\varepsilon}}\int_0^1\frac{1}{(1-u)^{1-{\varepsilon}}}\left|\left|\beta(tu,.)\right|\right|_{L_2(\nu_j)}du.\end{aligned}$$ Using Lemma \[lem-L1\], we have $$\left|\left|\beta(tu,.)\right|\right|_{L_2(\nu_j)}^2\leq 2^{j/2}\left(1+\tilde b(tu)^2\right)^{j/2}\int \frac{1}{|x|^{4{\varepsilon}}}\frac{dx}{(1+x^2)^{j/2}}.$$ Since ${\varepsilon}<1/4$, the integral on the righthand side is finite, and the lemma easily follows.
We now turn to the study of $\frac{\partial ^2 \tilde U}{\partial t\partial x}$. Recall that $\partial U/\partial t$ solves the parabolic equation $-\partial v/\partial t +(A-r)v=0$ in the set $\{(t,x)\;|\; t>0, x>\tilde b(t)\}$. Since the exercise boundary is differentiable and $\partial U/\partial t$ is continuous and vanishes on the exercise boundary, it follows that $\frac{\partial^2 U}{\partial t\partial x}$ is continuous “up to the boundary", i.e. on the set $\{(t,x)\;|\; t>0, x\geq \tilde b(t)\}$ (see [@Friedman1975], Lemma 4.5). We first show that $\frac{\partial^2 U}{\partial t\partial x}$ is nonnegative along the exercise boundary.
\[crossderiv\] We have, for any $t>0$, $$\frac{\partial^2 U}{\partial t\partial x}(t,\tilde b(t))\geq 0.$$
We have, for all $t>0$, due to the [*smooth fit*]{} property, $$\frac{\partial U}{\partial x}(t,\tilde b(t))=\varphi'(\tilde b(t)),$$ so that, by differentiating with respect to $t$, $$\frac{\partial^2 U}{\partial t\partial x}(t,\tilde b(t))+\frac{\partial^2 U}{\partial x^2}(t,\tilde b(t))\tilde b'(t)=\varphi''(\tilde b(t))\tilde b'(t)$$ and $$\frac{\partial^2 U}{\partial t\partial x}(t,\tilde b(t))=-\left(\frac{\partial^2 U}{\partial x^2}(t,\tilde b(t))-\varphi''(\tilde b(t))\right)\tilde b'(t).$$ Observe that, for each $t>0$, the function $x\mapsto U(t,x)-\varphi(x)$ is $C^2$ on the interval $[\tilde b(t),\infty)$ and has a minimum at $\tilde b(t)$. Therefore, its second derivative must be nonnegative at this point. Since $\tilde b'(t)\leq 0$, the lemma is proved.
\[fact2\] Fix $T>0$ and $j>1$. There exists a constant $C>0$ such that, for all $t_1\in(0,T\wedge 1]$, $$\int_{t_1}^T\left|\left|\frac{\partial ^2 \tilde U}{\partial t\partial x}(t,.)\right|\right|_{L_2(\nu_j)}^2dt\leq C\ln(1/t_1).$$
For the proof of Lemma \[fact2\], we will need the bilinear form associated with the operator $A-r$.
We first introduce the relevant weighted Sobolev spaces. For $j>1$, let $H_j=L^2({\mathbb{R}},\nu_j)$ and $V_j=\{f\in H_j \;|\; f'\in H_j\}$. The inner product on $H_j$ will be denoted by $(\cdot,\cdot)_j$ and the associated norm by $|\cdot|_j$. The natural norm on $V_j$ will be denoted by $||\cdot||_j$. Thus, we have $$|f|^2_j=\int_{-\infty}^{+\infty}f^2(x)\frac{dx}{(1+x^2)^{j/2}},$$ and $||f||^2_j=|f|^2_j+|f'|^2_j$.
Recall that the partial differential operator $A$ is defined by $$A=\frac{\sigma^2}{2} {\partial ^2 \over \partial x^2}
+\mu {\partial \over \partial x}.$$ We associate with the operator $A-r$ a bilinear functional on $V_j$, defined by $$\begin{aligned}
a_j(f,g)&=&\frac{\sigma^2}{2} \int_{-\infty}^{\infty}f'(x)g'(x)\frac{dx}{(1+x^2)^{j/2}}
-\frac{j\sigma^2}{2}\int_{-\infty}^{\infty}f'(x)g(x)\frac{x}{(1+x^2)^{(j/2)+1}}dx\\
&& -\mu\int_{-\infty}^{\infty}f'(x)g(x)\frac{dx}{(1+x^2)^{j/2}}
+r\int_{-\infty}^{\infty}f(x)g(x)\frac{dx}{(1+x^2)^{j/2}},\end{aligned}$$ so that, if $f'\in V_j$, $$a_j(f,g)=-((A-r)f,g)_j.$$ It will be convenient to write $a_j(f,g)$ as $
a_j(f,g)= \tilde{a}_j(f,g)+\bar{a}_j(f,g),
$ with $$\label{eq-atilde}
\tilde{a}_j(f,g)=\frac{\sigma^2}{2}\left[(f',g')_j+(f,g)_j\right]\quad\mbox{and}
\quad \bar{a}_j(f,g)=a_j(f,g)-\tilde{a}_j(f,g).$$ With these notations, it is easy to check that $|\bar{a}_j(f,g)|\leq C ||f||_j |g|_j$ and $|\bar{a}_j(f,g)|\leq C ||g||_j |f|_j$, for some constant $C$ which does not depend on $f$ nor $g$.
[**Proof of Lemma \[fact2\]:**]{} In order to rule out regularity issues, we introduce a $C^\infty$, nonnegative function $\rho$ on ${\mathbb{R}}\times {\mathbb{R}}$, with $\int \rho(t,x)dtdx=1$ and $\mbox{supp }\rho \subset [-1,0]\times [-1,+1]$ and set, for any positive integer $m$, $\rho_m(t,x)= m^2\rho(mt,mx)$.
Now, let $W=\frac{\partial\tilde U}{\partial x}$, $W_m=W*\rho_m$, and $h_m=\tilde{h}*\rho_m$. For each $m>0$, the functions $W_m$, $h_m$ are $C^\infty$ with bounded derivatives and we have $$-\frac{\partial W_m}{\partial t}+(A-r)W_m=\frac{\partial h_m}{\partial x}.$$ Multiply by $\partial W_m/\partial t$ and integrate with respect to $\nu_j$ to get, for any fixed $t>0$, $$-\left(\frac{\partial W_m}{\partial t}(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)_j
-a_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)=\int \frac{\partial h_m}{\partial x}(t,x)\frac{\partial W_m}{\partial t}(t,x)\nu_j(dx).$$ Note that $$\begin{aligned}
a_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)&=&
\tilde{a}_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)+\bar{a}_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)\\
&=&
\frac{1}{2}\frac{d}{dt}\left(\tilde a_j\left(W_m(t,.), W_m(t,.)\right)\right)+\bar{a}_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right).\end{aligned}$$ By integrating with respect to time, we get, if $0<t_1<T$, $$\begin{aligned}
-\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2dt+\frac{1}{2}\left(\tilde a_j\left(W_m(t_1,.), W_m(t_1,.)\right)
-\tilde a_j\left(W_m(T,.), W_m(T,.)\right)\right)&=\\
\int_{t_1}^T\bar{a}_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)dt
+\int_{t_1}^T\left(\frac{\partial h_m}{\partial x}(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_j&dt.\end{aligned}$$ Hence $$\begin{aligned}
\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2dt&\leq &
\frac{1}{2}\tilde a_j\left(W_m(t_1,.), W_m(t_1,.)\right)-
\int_{t_1}^T\bar{a}_j\left(W_m(t,.), \frac{\partial W_m}{\partial t}(t,.)\right)dt\\
&&
-\int_{t_1}^T\left(\frac{\partial h_m}{\partial x}(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt\\
&\leq &\frac{1}{2}\tilde a_j\left(W_m(t_1,.), W_m(t_1,.)\right)+
C \int_{t_1}^T\left|\left| W_m(t,.)\right|\right|_j\left| \frac{\partial W_m}{\partial t}(t,.)\right|_jdt \\
&& -\int_{t_1}^T\left(\frac{\partial h_m}{\partial x}(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt.\end{aligned}$$ Using the inequality $$2\left|\left| W_m(t,.)\right|\right|_j\left| \frac{\partial W_m}{\partial t}(t,.)\right|_j\leq
{\varepsilon}\left| \frac{\partial W_m}{\partial t}(t,.)\right|_j^2 +\frac{1}{{\varepsilon}}\left|\left| W_m(t,.)\right|\right|_j^2,$$ we get $$\begin{aligned}
\frac{1}{2}\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2dt&\leq &
\frac{1}{2}\tilde a_j\left(W_m(t_1,.), W_m(t_1,.)\right)+
C\int_{t_1}^T\left|\left| W_m(t,.)\right|\right|_j^2dt \\
&&
- \int_{t_1}^T\left(\frac{\partial h_m}{\partial x}(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt.\end{aligned}$$ We have $$\begin{aligned}
\tilde a_j\left(W_m(t_1,.), W_m(t_1,.)\right)&\leq &C\left|\left| W_m(t_1,.)\right|\right|_j^2\end{aligned}$$ and, using Lemma \[lem-L1\], $$\begin{aligned}
\left|\left| W_m(t_1,.)\right|\right|_j&\leq &\int \rho_m(t_1-t,y)\left|\left| W(t,.-y)\right|\right|_j dtdy\\
&\leq&\int \rho_m(t_1-t,y)2^{j/4}(1+y^2)^{j/4}\left|\left| W(t,.)\right|\right|_jdtdy.\end{aligned}$$ Using Lemma \[fact1\], we have (for ${\varepsilon}\in (0,1/4)$) $\left|\left| W(t,.)\right|\right|_j\leq Ct^{\varepsilon}$. Hence $$\begin{aligned}
\tilde{a}_j\left(W_m(t_1,.), W_m(t_1,.)\right)&\leq &C
\int \rho_m(t_1-t,y)2^{j/2}(1+y^2)^{j/2}t^{2{\varepsilon}} dtdy\\
&=&C
\int \rho_m(t,y)2^{j/2}(1+y^2)^{j/2}|t_1-t|^{2{\varepsilon}} dtdy \\
&=&
C\int \rho(t,y)2^{j/2}\left(1+\frac{y^2}{m^2}\right)^{j/2}\left|t_1-\frac{t}{m}\right|^{2{\varepsilon}} dtdy\\
&\leq &C(1+t_1^{2{\varepsilon}}).\end{aligned}$$
We also have $$\begin{aligned}
\int_{t_1}^T\left|\left| W_m(t,.)\right|\right|_j^2dt &=&
\int_{t_1}^T\left|\left| \int dsdy \rho_m(t-s, y)W(s,.-y)\right|\right|_j^2dt\\
&\leq &
\int_{t_1}^T\int dsdy \rho_m(t-s, y)\left|\left| W(s,.-y)\right|\right|_j^2dt\\
&\leq &
\int_{t_1}^Tdt \int dsdy \rho_m(t-s, y)
2^{j/2}(1+y^2)^{j/2}\left|\left| W(s,.)\right|\right|_j^2\\
&\leq &
\int_{t_1}^{T+\frac{1}{m}}ds\left|\left| W(s,.)\right|\right|_j^2\int dtdy
\rho_m(t-s, y)2^{j/2}(1+y^2)^{j/2}.\end{aligned}$$ Since $\int_0^{T +1}\left|\left| W(s,.)\right|\right|_j^2ds<\infty$, we deduce that $$\begin{aligned}
\frac{1}{2}\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2dt&\leq &
C\left(1+t_1^{2{\varepsilon}}\right)
-\int_{t_1}^T\left(\frac{\partial h_m}{\partial x}(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt.\end{aligned}$$ It follows from the proof of Lemma \[fact1\] (see ) that $$\frac{\partial h_m}{\partial x}(t,x)=-\kappa_m(t,x)+\gamma_m(t,x),$$ where $\kappa_m=\kappa *\rho_m$, and $\kappa$ is a bounded function, and $$\gamma_m(t,x)=\int \rho_m(t-\tau,x-\tilde b(\tau))\gamma(\tau)d\tau.$$ Hence $$\begin{aligned}
- \int_{t_1}^T\left(\frac{\partial h_m}{\partial x}(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt&\leq &
C\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_jdt -
\int_{t_1}^T\left( \gamma_m(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt\\
&\leq&\frac{1}{4}\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|^2_jdt+C^2T -
\int_{t_1}^T\left( \gamma_m(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt,\end{aligned}$$ where we have used $C\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j\leq \frac{1}{4}\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2+C^2$. Therefore $$\begin{aligned}
\frac{1}{4}\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2dt&\leq &
C\left(1+t_1^{2{\varepsilon}}\right)- \int_{t_1}^T\left(\gamma_m(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_j dt. \label{eq-Jm}\end{aligned}$$ Note that $$\frac{\partial W_m}{\partial t}=\frac{\partial^2 U_m}{\partial t\partial x}-
\frac{\partial^2 u_m}{\partial t\partial x},$$ where $$U_m=U*\rho_m\quad \mbox{and}\quad u_m=u_\varphi*\rho_m,$$ so that $$- \int_{t_1}^T\left(\gamma_m(t,.),\frac{\partial W_m}{\partial t}(t,.)\right)_jdt
=J^{(1)}_m+J^{(2)}_m,$$ with $$J^{(1)}_m=-\int_{t_1}^T\left(\gamma_m(t,.),\frac{\partial ^2U_m}{\partial t\partial x}(t,.)
\right)_jdt
\quad \mbox{and}\quad
J^{(2)}_m=\int_{t_1}^T\left(\gamma_m(t,.),\frac{\partial ^2 u_m}{\partial t\partial x}(t,.)
\right)_jdt.$$ We have $$\begin{aligned}
J^{(1)}_m&=&
-\int_{t_1}^Tdt\int \frac{dx}{(1+x^2)^{j/2}}\gamma_m(t,x)
\frac{\partial ^2U_m}{\partial t\partial x}(t,x)\\
&=&-\int_{t_1}^Tdt\int \frac{dx}{(1+x^2)^{j/2}}
\int d\tau \gamma(\tau)\rho_m(t-\tau, x-\tilde b(\tau))
\frac{\partial ^2U_m}{\partial t\partial x}(t,x)\\
&=&
-\int d\tau \int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau+s<T\}}}\gamma(\tau)
\rho_m(s, y)
\frac{\partial ^2U_m}{\partial t\partial x}(\tau+s,\tilde b(\tau)+y)
\frac{1}{(1+(y+\tilde b(\tau))^2)^{j/2}}\\
&=&-\int_{t_1}^{T+\frac{1}{m}}\gamma(\tau)\eta_m(\tau)d\tau, \end{aligned}$$ where $$\begin{aligned}
\eta_m(\tau)&=&\int_{t_1-\tau}^{T-\tau}ds\int \frac{dy}{(1+(y+\tilde b(\tau))^2)^{j/2}}
\rho_m(s,y)\frac{\partial ^2U_m}{\partial t\partial x}(\tau+s,\tilde b(\tau)+y)\\
&=&
\int_{t_1-\tau}^{T-\tau}ds\int \frac{\rho_m(s,y)dy}{(1+(y+\tilde b(\tau))^2)^{j/2}}
\int \int ds' dy'
\rho_m(s',y')\frac{\partial ^2U}{\partial t\partial x}(\tau+s-s',\tilde b(\tau)+y-y'). \end{aligned}$$ Note that $\frac{\partial ^2U}{\partial t\partial x}=0$ on the open set $S=\{(t,x)\;|\; t>0, x<\tilde b(t)\}$ (which is the interior set of the stopping region), so that $$\begin{aligned}
\eta_m(\tau)&=&
\int_{t_1-\tau}^{T-\tau}ds\int \frac{\rho_m(s,y)dy}{(1+(y+\tilde b(\tau))^2)^{j/2}}
\int \int ds' dy'
\rho_m(s',y')\bar W(\tau,s-s',y-y'),
\end{aligned}$$ where $$\bar W(\tau,\theta,z)=\frac{\partial ^2U}{\partial t\partial x}(\tau+\theta,\tilde b(\tau)+z)
{\textrm{\dsrom{1}}_{\{\tilde b(\tau)+z\geq \tilde b(\tau+\theta)\}}}.$$ Since $\frac{\partial ^2U}{\partial t\partial x}(\tau,\tilde b(\tau))\geq 0$, for $\tau>0$, we have $$\begin{aligned}
\eta_m(\tau)&\geq&\int_{t_1-\tau}^{T-\tau}ds\int\int\int
\frac{\rho_m(s,y)dy\rho_m(s',y')ds'dy'}{\left(1+(y+\tilde b(\tau))^2\right)^{j/2}}
D(\tau,s-s',y-y'),
\end{aligned}$$ where $$D(\tau,\theta,z)=\left(
\frac{\partial ^2U}{\partial t\partial x}(\tau+\theta,\tilde b(\tau)+z)-\frac{\partial ^2U}{\partial t\partial x}(\tau,\tilde b(\tau))
\right){\textrm{\dsrom{1}}_{\{\tilde b(\tau)+z\geq \tilde b(\tau+\theta)\}}}.$$ Hence (since $\gamma\geq 0$) $$\begin{aligned}
J^{(1)}_m&\leq&-\int_{t_1}^{T+\frac{1}{m}} \gamma(\tau){\varepsilon}_m(\tau)d\tau,\end{aligned}$$ with $${\varepsilon}_m(\tau)=\int_{t_1-\tau}^{T-\tau}ds\int\int\int
\frac{\rho_m(s,y)dy\rho_m(s',y')ds'dy'}{(1+(y+\tilde b(\tau))^2)^{j/2}}
D(\tau,s-s',y-y').$$ We have $$| {\varepsilon}_m(\tau)|\leq \int_{t_1-\tau}^{T-\tau}D_m(\tau)ds=(T-t_1)D_m(\tau),$$ where $$D_m(\tau)=\sup_{|\theta|\leq 1/m, |z|\leq 2/m }\left(\left|D(\tau,\theta,z)
\right|{\textrm{\dsrom{1}}_{\{\tilde b(\tau)+z\geq \tilde b(\tau+\theta)\}}}\right).$$ Due to the continuity properties of $\frac{\partial^2 U}{\partial t\partial x}$, as $m\to \infty$, the function $D_m$ converges to $0$, uniformly on the interval $[t_1, T+1]$. Therefore, we have $$\label{eq-Jm1}
\limsup_{m\to \infty}J^{(1)}_m\leq 0.$$ We now examine $J^{(2)}_m$. We have, using the boundedness of $\gamma$, $$\begin{aligned}
|J^{(2)}_m|&\leq &\int_{t_1}^Tdt\int \frac{dx}{(1+x^2)^{j/2}}|\gamma_m(t,x)|
\left|\frac{\partial ^2 u_m}{\partial t\partial x}(t,x)\right|\\
&\leq &
C\int_{t_1}^Tdt\int \frac{dx}{(1+x^2)^{j/2}}
\int d\tau \rho_m(t-\tau, x-\tilde b(\tau))
\left| \frac{\partial ^2 u_m}{\partial t\partial x}(t,x)\right|.\end{aligned}$$ Note that, since $\varphi$ is Lipschitz, we have $\left|\left| \frac{\partial ^2 u_\varphi}{\partial t\partial x}(t,.)\right|\right|_{\infty}\leq \frac{C}{t}$ and, since $\mbox{supp }\rho \subset [-1,0]\times [-1,+1]$, $$\begin{aligned}
\left|\left| \frac{\partial ^2 u_m}{\partial t\partial x}(t,.)\right|\right|_{\infty}\leq
\int\int d\tau dy \rho_m(\tau,y)
\left|\left| \frac{\partial ^2 u_\varphi}{\partial t\partial x}(t-\tau,.)\right|\right|_{\infty}\leq \frac{C}{t}.\end{aligned}$$ Hence $$\begin{aligned}
\label{eq-Jm2}
|J^{(2)}_m|&\leq &C\int_{t_1}^T\frac{dt}{t}\int dx
\int d\tau \rho_m(t-\tau, x-\tilde b(\tau))=C\ln\frac{T}{t_1}.
\end{aligned}$$ It follows from , and that $$\begin{aligned}
\limsup_{m\to \infty}\int_{t_1}^T\left|\frac{\partial W_m}{\partial t}(t,.)\right|_j^2dt&\leq &
C\left(1+t_1^{2{\varepsilon}}+\ln\frac{T}{t_1}\right),\end{aligned}$$ which proves the lemma.
Proof of Theorem \[thm-quadratic\]
----------------------------------
For the proof of Theorem \[thm-quadratic\], we will work on the equation satisfied by $\partial \tilde U/\partial t$. Let $$V=\frac{\partial \tilde U}{\partial t}.$$ We have $$-\frac{\partial V}{\partial t}+(A-r)V=\frac{\partial \tilde{h}}{\partial t},$$ where $$\tilde{h}(t,x)=(A-r)\varphi(x){\textrm{\dsrom{1}}_{\{x\leq \tilde b(t)\}}}, \quad t>0, \quad x\in {\mathbb{R}}.$$ The following lemma will clarify the computation of the derivative $\partial \tilde{h}/\partial t$ in the sense of distributions.
\[lem-dhdt\] Define the function $I$ on $(0,+\infty)\times {\mathbb{R}}$ by $$I(t,x)={\textrm{\dsrom{1}}_{\{x\leq \tilde b(t)\}}}, \quad t>0, \quad x\in {\mathbb{R}}.$$ The distribution $\partial I/\partial t$ applied to a compactly supported $C^\infty$ function $\rho$ on $(0,+\infty)\times {\mathbb{R}}$ is given by $$\langle \frac{\partial I}{\partial t}, \rho\rangle=\int \tilde b'(t)\rho(t,\tilde b(t))dt.$$ This can be written (less precisely): $\frac{\partial I}{\partial t}(t,.)=\tilde b'(t)
\delta_{\tilde b(t)}$.
We have $$\begin{aligned}
\langle \frac{\partial I}{\partial t}, \rho\rangle&=&
-\langle I, \frac{\partial \rho}{\partial t} \rangle \\
&=&-\int dt\int dx I(t,x) \frac{\partial \rho}{\partial t}(t,x)\end{aligned}$$ Let $J$ be the range of $\tilde b$. We have $J=(\tilde b(\infty),\tilde b(0))$. Note that, if $x\leq \tilde b(\infty)$, $I(t,x)=1$ for all $t>0$ and if $x\geq \tilde b(0)$ $I(t,x)=0$ for all $t>0$, so that, in both cases, $\int I(t,x) \frac{\partial \rho}{\partial t}(t,x)dt=0$. Therefore $$\begin{aligned}
\langle \frac{\partial I}{\partial t}, \rho\rangle&=&
-\int_J dx \int dt {\textrm{\dsrom{1}}_{\{x\leq \tilde b(t)\}}} \frac{\partial \rho}{\partial t}(t,x)\\
&=&
-\int_J dx \int dt {\textrm{\dsrom{1}}_{\{t\leq \tilde b^{-1}(x)\}}} \frac{\partial \rho}{\partial t}(t,x)\\
&=&
-\int_J dx \rho(\tilde b^{-1}(x),x)\\
&=&
\int \tilde b'(t)\rho(t,\tilde b(t))dt.\end{aligned}$$ Here, we have used the fact that $\tilde b$ is strictly decreasing (which is proved in [@Villeneuve1999]), but we can also approximate $\tilde b$ by the strictly decreasing functions $\tilde b_{\varepsilon}(t)=-{\varepsilon}t+\tilde b(t)$ to derive the formula. In fact, we only need $\tilde b$ to be $C^1$: indeed, we can replace $\tilde b(t)$ by $\tilde b_\mu(t)=-\mu t+\tilde b(t)$ and choose $\mu$ so that $\tilde b_\mu$ is strictly increasing in a neighborhood of the time projection of the support of $\rho$.
We now proceed with the proof of Theorem \[thm-quadratic\]. As in the proof of Lemma \[fact2\], we introduce a regularizing sequence $\rho_m$, and set $$V_m=V*\rho_m \quad \mbox{and}\quad \chi_m=\frac{\partial \tilde{h}}{\partial t}*\rho_m,$$ so that $$-\frac{\partial V_m}{\partial t}+(A-r)V_m=\chi_m$$ Note that the functions $V_m$, $\chi_m$ are $C^\infty$, with bounded derivatives on any subset $[t_1,T]\times{\mathbb{R}}$, with $0<t_1<T$. This is due to the fact that $V$ is bounded on such subsets. For any fixed $t>0$, multiply by $\partial V_m/\partial t$ and integrate with respect to $\nu_j$ to get $$-\left| \frac{\partial V_m}{\partial t}(t,.)\right|_j^2
-a_j\left(V_m(t,.), \frac{\partial V_m}{\partial t}(t,.)\right)=\int \chi_m(t,x)
\frac{\partial V_m}{\partial t}(t,x)\nu_j(dx).$$ We have $$\begin{aligned}
a_j\left(V_m(t,.), \frac{\partial V_m}{\partial t}(t,.)\right) &=&
\frac{1}{2}\frac{d}{dt}\left(\tilde a_j\left(V_m(t,.), V_m(t,.)\right)\right)+
\bar{a}_j\left(V_m(t,.), \frac{\partial V_m}{\partial t}(t,.)\right).\end{aligned}$$ By integrating with respect to time, we get, if $0<t_1<T$, $$\begin{aligned}
\lefteqn{
-\int_{t_1}^{T}\left|\frac{\partial V_m}{\partial t}(t,.)\right|_j^2dt+
\frac{1}{2}\left[\tilde a_j\left(V_m(t_1,.), V_m(t_1,.)\right)
-\tilde a_j\left(V_m(T,.), V_m(T,.)\right)\right]=}\\
&& \;\;\;\int_{t_1}^{T}\bar{a}_j\left(V_m(t,.), \frac{\partial V_m}{\partial t}(t,.)\right)dt
+\int_{t_1}^{T}\left(\chi_m(t,.),\frac{\partial V_m}{\partial t}(t,.)\right)_jdt.\end{aligned}$$ Hence $$\begin{aligned}
\int_{t_1}^{T}\left|\frac{\partial V_m}{\partial t}(t,.)\right|_j^2dt&\leq&
C\left|\left|V_m(t_1,.)\right|\right|_j^2
-\int_{t_1}^{T}\bar{a}_j\left(V_m(t,.), \frac{\partial V_m}{\partial t}(t,.)\right)dt\\
&&
-\int_{t_1}^{T}\left(\chi_m(t,.),\frac{\partial V_m}{\partial t}(t,.)\right)_jdt\\
&\leq&
C\left(\left|\left|V_m(t_1,.)\right|\right|_j^2+
\int_{t_1}^{T}\left|\left|V_m(t,.)\right|\right|_j
\left| \frac{\partial V_m}{\partial t}(t,.)\right|_jdt\right)+J_m(t_1,T),\end{aligned}$$ with $$J_m(t_1,T)=-\int_{t_1}^{T}\left(\chi_m(t,.),\frac{\partial V_m}{\partial t}(t,.)\right)_jdt.$$ Using the inequality $$2\left|\left|V_m(t,.)\right|\right|_j
\left| \frac{\partial V_m}{\partial t}(t,.)\right|_j
\leq
{\varepsilon}\left| \frac{\partial V_m}{\partial t}(t,.)\right|_j^2+\frac{1}{{\varepsilon}}
\left|\left|V_m(t,.)\right|\right|_j^2,$$ we derive $$\begin{aligned}
\frac{1}{2}\int_{t_1}^{T}\left|\frac{\partial V_m}{\partial t}(t,.)\right|_j^2dt&\leq&
C\left(\left|\left|V_m(t_1,.)\right|\right|_j^2+
\int_{t_1}^{T}\left|\left|V_m(t,.)\right|\right|_j^2dt\right) +J_m(t_1,T)\label{final}.\end{aligned}$$ We now study $J_m(t_1,T)$. Note that, for any fixed $t>0$, $$\begin{aligned}
\left(\chi_m(t,.),\frac{\partial V_m}{\partial t}(t,.)\right)_j&=&
\int \nu_j(dx) \frac{\partial V_m}{\partial t}(t,x)
\frac{\partial \tilde{h}}{\partial t}*\rho_m(t,x)\end{aligned}$$ We have $$\frac{\partial \tilde{h}}{\partial t}(t,.)=(A-r)\varphi \frac{\partial I}{\partial t}(t,.),$$ so that, using Lemma \[lem-dhdt\], and the notation $\gamma(t)=-(A-r)\varphi(\tilde b(t))$ $$\frac{\partial \tilde{h}}{\partial t}*\rho_m(t,x)=-\int d\tau \rho_m(t-\tau,x-\tilde b(\tau))
\tilde b'(\tau)\gamma(\tau),$$ Recall that $\gamma(\tau)\geq 0$. Hence $$\begin{aligned}
\left(\chi_m(t,.),\frac{\partial V_m}{\partial t}(t,.)\right)_j&=&
-\int \nu_j(dx) \frac{\partial V_m}{\partial t}(t,x)
\int d\tau \rho_m(t-\tau,x-\tilde b(\tau))
\tilde b'(\tau) \gamma(\tau)\\
&=& - \int d\tau\int \frac{dx}{(1+x^2)^{j/2}}
\frac{\partial V_m}{\partial t}(t,x)\rho_m(t-\tau,x-\tilde b(\tau))
\tilde b'(\tau) \gamma(\tau)\\
&=&-\int d\tau\int \frac{dy}{(1+(y+\tilde b(\tau))^2)^{j/2}}
\frac{\partial V_m}{\partial t}(t,y+\tilde b(\tau))\rho_m(t-\tau,y)
\tilde b'(\tau)\gamma(\tau).\end{aligned}$$ Going back to $J_m(t_1, T)$, we have $$\begin{aligned}
J_m(t_1,T)&=&-\int_{t_1}^T dt\int d\tau \int dy
\frac{\partial V_m}{\partial t}(t,y+\tilde b(\tau))
\rho_m(t-\tau,y)\bar\gamma_j(\tau,y),\end{aligned}$$ with $$\bar\gamma_j(\tau,y)=-\frac{1}{(1+(y+\tilde b(\tau))^2)^{j/2}}\tilde b'(\tau) \gamma(\tau).$$ Note that $\bar\gamma_j(\tau, y)\geq 0$. We have $$\begin{aligned}
J_m(t_1,T)&=&-\int d\tau\int dt \int dy {\textrm{\dsrom{1}}_{\{t_1<t<T\}}}
\frac{\partial V_m}{\partial t}(t,y+\tilde b(\tau))
\rho_m(t-\tau,y)\bar\gamma_j(\tau,y)\\
&=&-\int d\tau\int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau +s<T\}}}
\frac{\partial V_m}{\partial t}(\tau+s,y+\tilde b(\tau))
\rho_m(s,y)\bar\gamma_j(\tau,y).\end{aligned}$$ Observe that $$\frac{d}{d\tau}\left(V_m(\tau+s,y+\tilde b(\tau))\right)=
\frac{\partial V_m}{\partial t}(\tau+s,y+\tilde b(\tau))
+\frac{\partial V_m}{\partial x}(\tau+s,y+\tilde b(\tau))\tilde b'(\tau),$$ so that $$\frac{\partial V_m}{\partial t}(\tau+s,y+\tilde b(\tau))=
\frac{d}{d\tau}\left(V_m(\tau+s,y+\tilde b(\tau))\right)-
\frac{\partial V_m}{\partial x}(\tau+s,y+\tilde b(\tau))\tilde b'(\tau).$$ Hence $$J_m(t_1,T)=\hat J_m(t_1,T)+\bar J_m(t_1,T),$$ with $$\hat J_m(t_1,T)=
-\int d\tau\int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau +s<T\}}}
\frac{d}{d\tau}\left(V_m(\tau+s,y+\tilde b(\tau))\right)
\rho_m(s,y)\bar\gamma_j(\tau,y)$$ and $$\bar J_m(t_1,T)=
+\int d\tau\int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau +s<T\}}}
\frac{\partial V_m}{\partial x}(\tau+s,y+\tilde b(\tau))\tilde b'(\tau)
\rho_m(s,y)\bar\gamma_j(\tau,y).$$ We have, using integration by parts, $$\begin{aligned}
\hat J_m(t_1,T)&=&-\int ds\int dy \rho_m(s,y)\left(\int_{t_1-s}^{T-s}
\frac{d}{d\tau}\left(V_m(\tau+s,y+\tilde b(\tau))\right)\bar\gamma_j(\tau,y)d\tau
\right)\\
&=&
-\int ds\int dy \rho_m(s,y)
V_m(T,y+\tilde b(T-s))\bar\gamma_j(T-s,y)
\\
&&
+\int ds\int dy \rho_m(s,y)V_m(t_1,y+\tilde b(t_1-s))\bar\gamma_j(t_1-s,y)\\
&&
+\int ds\int dy \rho_m(s,y)\int_{t_1-s}^{T-s}V_m(s+\tau,y+\tilde b(\tau))
\frac{\partial \bar\gamma_j}{\partial \tau}(\tau,y)d\tau.\end{aligned}$$ Note that, due to the continuity of $V(=\partial \tilde U/\partial t)$ on $(0,\infty)\times{\mathbb{R}}$, the sequence $V_m$ converges uniformly to $V$ on compact sets. We also have the continuity of $\bar\gamma_j$ and $\partial \bar\gamma_j/\partial \tau$ (due to the fact that $\tilde b$ is $C^2$). We easily deduce thereof that $$\begin{aligned}
\lim_{m\to\infty}\hat J_m(t_1,T)=-V(T,\tilde b(T))\bar\gamma_j(T,0)+
V(t_1,\tilde b(t_1))\bar\gamma_j(t_1,0)+
\int_{t_1}^{T}V(\tau,\tilde b(\tau))
\frac{\partial \bar\gamma_j}{\partial \tau}(\tau,0)d\tau,\label{Jhat}\end{aligned}$$ and the convergence is uniform with respect to $t_1$, as long as $t_1$ remains in a compact set of the form $[\xi,T]$, where $0<\xi<T$. For $\bar J_m(t_1, T)$, we have $$\begin{aligned}
\bar J_m(t_1, T)&=&\bar J^{(1)}_m(t_1, T)+\bar J^{(2)}_m(t_1, T),\end{aligned}$$ with $$\bar J^{(1)}_m(t_1, T)=+\int d\tau\int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau +s<T\}}}
\frac{\partial^2 U_m}{\partial t\partial x}(\tau+s,y+\tilde b(\tau))\tilde b'(\tau)
\rho_m(s,y)\bar\gamma_j(\tau,y)$$ and $$\bar J^{(2)}_m(t_1, T)=-\int d\tau\int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau +s<T\}}}
\frac{\partial^2 u_m}{\partial t\partial x}(\tau+s,y+\tilde b(\tau))\tilde b'(\tau)
\rho_m(s,y)\bar\gamma_j(\tau,y).$$ We deal with $\bar J^{(1)}_m(t_1, T)$ in the same way as for the proof of . Using the fact that $\tilde b'(\tau)\bar\gamma_j(\tau,y)\leq 0$, we have $\bar J^{(1)}_m(t_1, T)\leq\tilde J^{(1)}_m(t_1, T)$, with $$\begin{aligned}
\tilde J^{(1)}_m(t_1, T)&=&\int d\tau\int ds \int dy {\textrm{\dsrom{1}}_{\{t_1<\tau +s<T\}}}\int\int ds'dy'\rho_m(s',y')D(\tau,s-s',y-y')
\tilde b'(\tau)
\rho_m(s,y)\bar\gamma_j(\tau,y),\end{aligned}$$ where $$D(\tau,\theta,z)= \left(\frac{\partial^2 U}{\partial t\partial x}(\tau+\theta,\tilde b(\tau)+z)-
\frac{\partial^2 U}{\partial t\partial x}(\tau,\tilde b(\tau))\right){\textrm{\dsrom{1}}_{\{\tilde b(\tau)+z\geq \tilde b(\tau+\theta)\}}}.$$ Due to the continuity properties of $\frac{\partial^2 U}{\partial t\partial x}$, we have $$\lim_{m\to \infty}\tilde J^{(1)}_m(t_1, T)= 0,$$ and the convergence is uniform with respect to $t_1$, as long as $t_1$ remains in $[\xi,T]$. On the other hand, due to the continuity of $ \frac{\partial^2 u_\varphi}{\partial t\partial x}$, we have $$\lim_{m\to \infty}\bar J^{(2)}_m(t_1, T)
=-\int_{t_1}^Td\tau
\frac{\partial^2 u_\varphi}{\partial t\partial x}(\tau,\tilde b(\tau))\tilde b'(\tau)
\bar\gamma_j(\tau,0),$$ uniformly with respect to $t_1\in[\xi,T]$. At this stage, we can state that $J_m(t_1,T)\leq \tilde J_m(t_1,T)$, with $\tilde J_m(t_1,T)=\hat J_m(t_1,T)+ \tilde J^{(1)}_m(t_1, T)+\bar J^{(2)}_m(t_1, T)$, and $$\lim_{m\to \infty}\sup_{t_1\in [\xi,T]} \left|\tilde J_m(t_1, T)-\tilde J(t_1,T)\right|=0,$$ where $$\begin{aligned}
\tilde J(t_1, T)&=&
-V(T,\tilde b(T))\bar\gamma_j(T,0)+
V(t_1,\tilde b(t_1))\bar\gamma_j(t_1,0)+
\int_{t_1}^{T}V(\tau,\tilde b(\tau))
\frac{\partial \bar\gamma_j}{\partial \tau}(\tau,0)d\tau\\
&&
-\int_{t_1}^Td\tau
\frac{\partial^2 u}{\partial t\partial x}(\tau,\tilde b(\tau))\tilde b'(\tau)
\bar\gamma_j(\tau,0).\end{aligned}$$ Since $\partial U/\partial t$ vanishes along the exercise boundary, we have $V(t,\tilde b(t))=-\frac{\partial u_\varphi}{\partial t}(t,\tilde b(t))$, so that $$\begin{aligned}
\lefteqn{
&& \frac{\partial u_\varphi}{\partial t}(T,\tilde b(T))\bar\gamma_j(T,0)-
\frac{\partial u_\varphi}{\partial t}(t_1, \tilde b(t_1))\bar\gamma_j(t_1,0)-
\int_{t_1}^{T}\frac{\partial u_\varphi}{\partial t}(\tau,\tilde b(\tau))
\frac{\partial \bar\gamma_j}{\partial \tau}(\tau,0)d\tau\\
&=&\int_{t_1}^{T}\frac{d}{d\tau}\left(
\frac{\partial u_\varphi}{\partial t}(\tau,\tilde b(\tau))\right)
\bar\gamma_j(\tau,0)d\tau,\end{aligned}$$ so that $$\begin{aligned}
\tilde J(t_1, T)&=&
\int_{t_1}^{T}
\left[\frac{d}{d\tau}\left(
\frac{\partial u_\varphi}{\partial t}(\tau,\tilde b(\tau))\right)
-\frac{\partial^2 u_\varphi}{\partial t\partial x}(\tau,\tilde b(\tau))\tilde b'(\tau)\right]
\bar\gamma_j(\tau,0)d\tau\\
&=&
\int_{t_1}^{T}\frac{\partial^2 u_\varphi}{\partial t^2}(\tau,\tilde b(\tau))\bar\gamma_j(\tau,0)
d\tau.\end{aligned}$$ We now go back to and integrate with respect to $t_1$ to derive $$\begin{aligned}
\frac{1}{2}\int_\xi^Tdt_1\int_{t_1}^{T}\left|\frac{\partial^2 \tilde U_m}{\partial t^2}(t,.)\right|_j^2dt&\leq&
C\left(\int_\xi^T\left|\left|V_m(t_1,.)\right|\right|_j^2dt_1+
\int_\xi^T\left(\int_{t_1}^{T}\left|\left|V_m(t,.)\right|\right|_j^2dt \right)dt_1\right)\\
&& +
\int_{\xi}^Tdt_1\tilde J_m(t_1,T).\end{aligned}$$ Hence $$\begin{aligned}
\frac{1}{2}\int_{\xi}^{T}(t-\xi)\left|\frac{\partial^2 \tilde U_m}{\partial t^2}(t,.)\right|_j^2dt&\leq&
C\int_\xi^T\left|\left|V_m(t,.)\right|\right|_j^2dt
+
\int_\xi^Tdt_1\tilde J_m(t_1,T).
$$ Note that $$\begin{aligned}
\lim_{m\to \infty}\int_\xi^T\left|\left|V_m(t,.)\right|\right|_j^2dt&=&\int_\xi^T\left|\left|V(t,.)\right|\right|_j^2dt\\
&\leq & C\left(1+\ln \frac{T}{\xi}\right),\end{aligned}$$ where the last inequality follows from Lemma \[fact2\]. Moreover, $$\begin{aligned}
\lim_{m\to \infty} \int_\xi^Tdt_1\tilde J_m(t_1,T)&=& \int_\xi^Tdt_1\tilde J(t_1,T)\\
&=&\int_{\xi}^{T}(t-\xi)\frac{\partial^2 u_\varphi}{\partial t^2}(t,\tilde b(t))\bar\gamma_j(t,0)
dt.\end{aligned}$$
Hence $$\begin{aligned}
\frac{1}{2}\int_{\xi}^{T}(t-\xi)\left|\frac{\partial^2 \tilde U}{\partial t^2}(t,.)\right|_j^2dt&\leq&
C\left(1+\ln \frac{T}{\xi}\right)+
\int_{\xi}^{T}(t-\xi)\frac{\partial^2 u_\varphi}{\partial t^2}(t,\tilde b(t))\bar\gamma_j(t,0)
dt.\end{aligned}$$ Theorem \[thm-quadratic\] now follows from the following lemma, which relies on the asymptotic behavior of the exercice boundary near maturity (see [@Barles], [@LambertonVilleneuve]).
We have $$\begin{aligned}
\int_{\xi}^{T}(t-\xi)\left|\frac{\partial^2 u_\varphi}{\partial t^2}(t,\tilde b(t))\right||\tilde b'(t)|dt
&\leq &C\left(1+|\ln \xi|^\beta\right),
\\
\right.\end{aligned}$$
We first note that, since $\varphi $ is bounded and Lipschitz continuous, we have $$\left|\left|\frac{\partial^2 u_\varphi}{\partial t^2}(t,.)\right|\right|_\infty
\leq
\frac{C}{t^{3/2}}.$$ This can be seen by arguing, as in the proof of Proposition \[prop-L1\], that $u_\varphi(t,.)=e^{-rt}p_t*\varphi$, so that and $\frac{\partial^2 u_\varphi}{\partial t^2}(t,.)=(A-r)^2u_\varphi$. In order to estimate the $x$-derivatives of $u_\varphi$ up to the order $4$, we may differentiate $p_t$ three times and use the boundedness of $\varphi'$.
We then have
$$\begin{aligned}
\int_{\xi}^{T}(t-\xi)\left|\frac{\partial^2 u_\varphi}{\partial t^2}(t,\tilde b(t))\right||\tilde b'(t)|dt&\leq&
C\int_{\xi}^{T}\frac{t-\xi}{t^{3/2}}|\tilde b'(t)|dt\\
&\leq &
C\int_{\xi}^{T}\frac{1}{\sqrt{t}}|\tilde b'(t)|dt.\end{aligned}$$
Now, since $\tilde b'(t)\leq 0$, we have $$\begin{aligned}
\int_{\xi}^{T}\frac{1}{\sqrt{t}}|\tilde b'(t)|dt&=&-\int_{\xi}^{T}\frac{1}{\sqrt{t}}\tilde b'(t)dt\\
&=& -\left(\frac{\tilde b(T)-\tilde b(0)}{\sqrt{T}}-
\frac{\tilde b(\xi)-\tilde b(0)}{\sqrt{\xi}}\right)-\frac{1}{2}\int_{\xi}^{T}
\frac{1}{t^{3/2}}(\tilde b(t)-\tilde b(0))dt\\
&\leq&\frac{\tilde b(0)-\tilde b(T)}{\sqrt{T}}+
\frac{1}{2}\int_{\xi}^{T}\frac{1}{t^{3/2}}(\tilde b(0)-\tilde b(t))dt\end{aligned}$$ If $d\leq r$, we have $\tilde b(0)-\tilde b(t)\leq C\sqrt{t|\ln t|}$ for $t$ close to $0$, so that $$\int_{\xi}^{T}\frac{1}{t^{3/2}}(\tilde b(0)-\tilde b(t))dt\leq C
\int_{\xi}^{T}\frac{1}{t}\sqrt{|\ln t|}dt\leq C(1+|\ln \xi|^{3/2}).$$ If $d>r$, we have $\tilde b(0)-\tilde b(t)\leq C\sqrt{t}$ for $t$ close to $0$, so that $$\int_{\xi}^{T}\frac{1}{t^{3/2}}(\tilde b(0)-\tilde b(t))dt\leq C
\int_{\xi}^{T}\frac{1}{t}dt= C\ln (T/\xi).$$
Upper bound for $P^{(n)}_0-P_0$ {#UB}
===============================
In order to derive an upper bound for $P^{(n)}_0-P_0$, we relate this quantity to the modified value function $u$ using as follows: $$\begin{aligned}
P^{(n)}_0-P_0&=&\sup_{\tau\in{\cal T}^{(n)}_{0,T}}
{\mathbb{E}}\left(
e^{-r\tau}g(\mu_0\tau + B^{(n)}_\tau)\right) -u(0,0)\\
&\leq &\sup_{\tau\in{\cal T}^{(n)}_{0,T}}
{\mathbb{E}}\left(
u(\tau , B^{(n)}_\tau)-u(0,0)\right) \\
&=&\sup_{\tau\in{\cal T}^{(n)}_{0,T}}
{\mathbb{E}}\left(
\sum_{j=1}^{\tau/h}{\cal D}u({(j-1)h},B^{(n)}_{{(j-1)h}})\right).
\end{aligned}$$ We observe that ${\cal D}u\leq \tilde{{\cal D}}u$, and recall from [@DL2002] (Lemma 4.1) that $\sup_{0\leq j\leq n-1}{\mathbb{E}}\left|{\cal D}u({jh},B^{(n)}_{{jh}})\right|\leq Ch$, so that $$\begin{aligned}
P^{(n)}_0-P_0&\leq &
{\mathbb{E}}\left(
\sum_{j=1}^{n-2}\left|\tilde{{\cal D}}u({jh},B^{(n)}_{{jh}})\right|\right)+O(h)\nonumber\\
&\leq&C_{k,X}h\sqrt{2}\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{dy}{1+|y|^k}
\left|{\partial^3 u\over \partial t\partial x^2}(s,y)\right|+O(h).\label{int*}\end{aligned}$$ Here, we have a regularity problem, since $u$ is not $C^3$. This problem can be fixed as follows. By convolution, one can approximate $u$ by a sequence $u_m$ which is smooth, uniformly bounded and satisfies $\delta u_m\leq 0$, and ${\cal D}u_m\leq \tilde{{\cal D}}u_m$. We need the following variant of Lemma \[lem-L1\].
\[lem-L1\*\] If $\rho$ is a Radon measure on $(0,T)\times{\mathbb{R}}$ and $q$ a nonnegative integrable function on $(0,T)\times{\mathbb{R}}$, with $q(t,x)=0$ for $t\notin (0,a)$, where $a$ satisfies $0<a<h$, we have $$\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{\left|\rho*q(s,y)\right|}{(1+|y|^2)^{k/2}}
dy
\leq 2^{k/2}\int_{h-a}^{T-h}\int_{\mathbb{R}}\frac{|\rho(dt, dz)|}{\sqrt{t}(1+z^2)^{k/2}}\int_0^ads\int_{-\infty}^\infty q(s,x) (1+x^2)^{k/2} dx.$$
We have $$\begin{aligned}
\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{dy}{(1+|y|^2)^{k/2}}
& \left|\rho*q(s,y)\right|\leq \\
& \int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{dy}{(1+|y|^2)^{k/2}}
\int\int \left|\rho(dt,dz)\right| q(s-t,y-z)\\
&=
\int\int \left|\rho(dt,dz)\right|\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{dy}{(1+|y|^2)^{k/2}} q(s-t,y-z)\\
&\leq \int_{h-a}^{T-h}\int \left|\rho(dt,dz)\right|\int_0^a\frac{d\theta}{\sqrt{t+\theta}}\int
\frac{dy}{(1+|y|^2)^{k/2}} q(\theta,y-z)\\
&\leq\int_{h-a}^{T-h}\int\frac{ \left|\rho(dt,dz)\right|}{\sqrt{t}}\int_0^a d\theta
\int \frac{dy}{(1+|y|^2)^{k/2}} q(\theta,y-z)\\
&=\int_{h-a}^{T-h}\int\frac{ \left|\rho(dt,dz)\right|}{\sqrt{t}(1+z^2)^{k/2}}\int_0^a d\theta
\int \frac{(1+z^2)^{k/2}dx}{(1+|x+z|^2)^{k/2}} q(\theta,x)\\
&\le
2^{k/2}\int_{h-a}^{T-h}\int\frac{ \left|\rho(dt,dz)\right|}{\sqrt{t}(1+z^2)^{k/2}}\int_0^a d\theta
\int dx (1+x^2)^{k/2} q(\theta,x),\end{aligned}$$ where the last inequality follows from $ \frac{1+z^2}{1+(x+z)^2}\leq 2(1+x^2)$.
Using Lemma \[lem-L1\*\] and the fact that $\partial^3 u/(\partial t\partial x^2)$ is a Radon measure (see and the comment below), we derive the correct version of , namely $$\begin{aligned}
P^{(n)}_0-P_0&\leq &
C_{k,X}h\sqrt{2}\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 u\over \partial t\partial x^2}(ds,dy)\right|+O(h).\label{int**}\end{aligned}$$ If we introduce the function $\tilde u:=u-\bar u$, we have, using the fact that $\delta \bar u=0$, $$\begin{aligned}
\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 u\over \partial t\partial x^2}(ds,dy)\right|&\leq&
\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 \tilde u\over \partial t\partial x^2}(ds,dy)\right|\\
&&
+2\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{dy}{1+|y|^k}
\left|{\partial^2 \bar u\over \partial t^2}(s,y)\right|\\
&\leq &\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 \tilde u\over \partial t\partial x^2}(ds,dy)\right|\\
&&
+2C_T\int_{h}^{T-h} \frac{ds}{\sqrt{s}(T-s)}\\
&\leq &\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 \tilde u\over \partial t\partial x^2}(ds,dy)\right|+C_T|\ln h|,\end{aligned}$$ where we have used Proposition \[prop-L1\].
We now need to estimate $\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 \tilde u\over \partial t\partial x^2}(ds,dy)\right|$. Recall from Remark \[rem1\] that $$\begin{aligned}
\frac{\partial \tilde u}{\partial t}(t,x)+\frac{1}{2} \frac{\partial^2 \tilde u}{\partial x^2} (t,x) &=&
\zeta(t,x){\textrm{\dsrom{1}}_{\{x\leq \hat b(t)\}}},\end{aligned}$$ where $\zeta(t,x)=e^{-rt}(A-r)\varphi (\ln (S_0) +\mu t +\sigma x)$ and $\hat b(t)=\left(\tilde b(T-t)-\mu t-\ln(S_0)\right)/\sigma$. By differentiating wit respect to $t$, we derive the following expression $$\begin{aligned}
\frac{\partial^2 \tilde u}{\partial t^2}(t,x)+\frac{1}{2} \frac{\partial^3 \tilde u}{\partial t\partial x^2} (t,x) &=&
\frac{\partial \zeta}{\partial t}(t,x){\textrm{\dsrom{1}}_{\{x\leq \hat b(t)\}}}+\zeta(t,\hat b(t))\hat b'(t)\delta_{\hat b(t)},\label{eq-deriv}\end{aligned}$$ where we have used Lemma \[lem-dhdt\]. Note that $$\sup_{x\leq \hat b(t)}\left|\frac{\partial \zeta}{\partial t}(t,x)\right|<\infty\mbox{ and }
\sup_{0<t<T}\left|\zeta(t,\hat b(t))\right|<\infty.$$ Moreover, $|\hat b'(t)|\leq |\tilde b'(T-t)|+|\mu/\sigma|$, so that $$\begin{aligned}
\int_0^T\frac{dt}{\sqrt{t}}|\hat b'(t)|&\leq &
\int_0^{T/2}\frac{dt}{\sqrt{t}}|\tilde b'(T-t)|+\int_{T/2}^T\frac{dt}{\sqrt{t}}|\tilde b'(T-t)|+2|\mu/\sigma| \sqrt{T}\\
&\leq &\sup_{0\leq t\leq T/2}|\tilde b'(T-t)|\int_0^{T/2}\frac{dt}{\sqrt{t}}+
+\sqrt{\frac{2}{T}}\int_{T/2}^T|\tilde b'(T-t)|dt+2|\mu/\sigma| \sqrt{T}\\
&=&\sup_{0\leq t\leq T/2}|\tilde b'(T-t)|\int_0^{T/2}\frac{dt}{\sqrt{t}}+\sqrt{\frac{2}{T}}\left(\tilde b(0)-\tilde b(T/2)\right)+
2|\mu/\sigma| \sqrt{T} <\infty.\end{aligned}$$ Therefore, the righthand side of is a Radon measure and since, due to Theorem \[thm-quadratic\], $\partial^2 \tilde u/\partial t^2$ is locally integrable, it follows that $\partial^3 \tilde u/\partial t\partial x^2$ is a Radon measure.
Moreover, we have $$\begin{aligned}
\int_{h}^{T-h} \frac{1}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^3 \tilde u\over \partial t\partial x^2}(ds,dy)\right|&\leq &
C_T+2\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{1}{1+|y|^k}
\left|{\partial^2 \tilde u\over \partial t^2}(s,y)\right|.\end{aligned}$$ Now, using the Cauchy-Schwarz inequality and Theorem \[thm-quadratic\], we have $$\begin{aligned}
\int_{h}^{T-h} \frac{ds}{\sqrt{s}}\int \frac{dy}{1+|y|^k}
\left|{\partial^2 \tilde u\over \partial t^2}(s,y)\right|&\leq\\
C\left(\int_{h}^{T-h}\frac{ds}{s(T-s-\frac{h}{2})}\right)^{1/2}&\left(\int_{h}^{T-h}\!\!ds (T-s-\frac{h}{2})\left|{\partial^2 \tilde u\over \partial t^2}(s,.)\right|_k^2 \right)^{1/2}\\
&\leq
C\sqrt{|\ln h|}\left(\int_{h}^{T-\frac{h}{2}}\!\!ds (T-s-\frac{h}{2})\left|{\partial^2 \tilde u\over \partial t^2}(s,.)\right|_k^2 \right)^{1/2}\\
&= C\sqrt{|\ln h|}\left(\int_{h/2}^{T-h}\!\!dt (t-\frac{h}{2})\left|{\partial^2 \tilde u\over \partial t^2}(T-t,.)\right|_k^2 \right)^{1/2}\\
&\leq
C\sqrt{|\ln h|^{1+\beta}},\end{aligned}$$ with $\beta=1$ if $d>r$ and $\beta=3/2$ if $d\leq r$. The last inequality follows from Theorem \[thm-quadratic\] and Lemma \[fact2\], and the connection between the derivatives of the functions $\tilde{U}$ and $\tilde{u}$ (see Remark \[rem1\]; we also use the classical bounds $||\partial U/\partial t(t,.)||_\infty+||\partial^2 U/\partial x^2(t,.)||_\infty\leq C/\sqrt{t}$). We conclude that $$P^{(n)}_0-P_0\leq C\frac{(\ln n)^\alpha}{n},$$ with $\alpha=1$ if $d>r$ and $\alpha=5/4$ if $d\leq r$.
Lower bound for $P^{(n)}_0-P_0$ {#LB}
===============================
For the derivation of the lower bound, we use the stopping time introduced in [@DL2002] (see the proof of Theorem 5.6). Namely $$\tau=\tau_1{\textrm{\dsrom{1}}_{\{\tau_1<T-h\}}}+T{\textrm{\dsrom{1}}_{\{\tau_1=T-h\}}},$$ where $$\tau_1=\inf\left\{ t\in [0,T-h]\;\;|\;\; t/h \in {\mathbb{N}}\quad\mbox{and}\quad d(B^{(n)}_t, I_{t+h})\leq
\sqrt{h}||X||_{\infty}+|\mu_0|h\right\}.$$ Here, $I_t=\{x\in {\mathbb{R}}\;|\; u(t,x)=g(t,x+\mu_0 t)\}$. Note that, if $t<T$, $I_t=(-\infty, \hat b(t)]$.
The modification of $\tau_1$ into $\tau$ is motivated by the unboundedness of $\partial u/\partial t$ near $T$. We have, due to the definition of $\tau_1$, $$\begin{aligned}
P^{(n)}-P&\geq &{\mathbb{E}}\left(e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)-u(0,0)\right)\\
&=&{\mathbb{E}}\left(e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)-u(\tau,B^{(n)}_\tau)+u(\tau,B^{(n)}_\tau)-u(0,0)\right).\end{aligned}$$ We have $$\begin{aligned}
{\mathbb{E}}\left(u(\tau,B^{(n)}_\tau)-u(0,0)\right)&=&{\mathbb{E}}\left(\sum_{j=1}^{\tau/h}{\cal D}u((j-1)h,B^{(n)}_{(j-1)h})\right)\\
&=&{\mathbb{E}}\left(\sum_{j=1}^{(\tau/h)\wedge(n-2)}{\cal D}u(jh-h,B^{(n)}_{jh-h})\right)\\
&&+
{\mathbb{E}}\left({\textrm{\dsrom{1}}_{\{\tau =T\}}}\sum_{j=n-1}^n{\cal D}u(jh-h,B^{(n)}_{jh-h})\right)\\
&=&{\mathbb{E}}\left(\sum_{j=1}^{(\tau/h)\wedge(n-2)}{\cal D}u(jh-h,B^{(n)}_{jh-h})\right)+O(h),\end{aligned}$$ where the last equality follows from Lemma 4.1 of [@DL2002]. Now, if $j<(\tau/h)\wedge(n-2)$, we have $d(B^{(n)}_{jh}, I_{jh+h})> \sqrt{h}||X||_{\infty}+|\mu_0|h$, so that $$B^{(n)}_{jh}>\hat{b}(jh+h)+\sqrt{h}||X||_{\infty}+|\mu_0|h.$$ We then have, for $s\in [jh,jh+h]$ and $z\in[0,\sqrt{h}]$ $$\begin{aligned}
B^{(n)}_{jh}+zX&>&\hat{b}(jh+h)+zX+\sqrt{h}||X||_{\infty}+|\mu_0|h\\
&\geq &\hat{b}(jh+h)+|\mu_0|h\\
&=&\hat{b}(s)+\hat{b}(jh+h)+\mu_0(jh+h)-(\hat b(s)+\mu_0s)-\mu_0(jh+h-s)+|\mu_0|h\\
&\geq &\hat{b}(s),\end{aligned}$$ the last inequality coming from the fact that $t\mapsto \hat{b}(t)+\mu_0t$ is increasing. We can now assert that, for $j<(\tau/h)\wedge(n-2)$, ${\cal D}u(B^{(n)}_{jh}, jh)=\tilde{{\cal D}}u(B^{(n)}_{jh}, jh)$, so that $$\begin{aligned}
{\mathbb{E}}\left(u(\tau,B^{(n)}_\tau)-u(0,0)\right)&\leq &
{\mathbb{E}}\left(\sum_{j=1}^{n-2}\left|\tilde{{\cal D}}u(jh,B^{(n)}_{jh})\right|\right)+O(h)\\
&\leq&
C\frac{(\ln n)^\alpha}{n},\end{aligned}$$ with $\alpha=1$ if $d>r$ and $\alpha=5/4$ if $d\leq r$, as follows from the discussion in the previous section.
We now want a lower bound for $${\mathbb{E}}\left(e^{-r\tau}g(\mu _0\tau+B^{(n)}_\tau)-u(\tau,B^{(n)}_\tau)\right).$$ We have, using the equality $\{\tau\geq T-h\}=\{\tau=T\}$, $$\begin{aligned}
u(\tau,B^{(n)}_\tau)-e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)&=&
\left(u(\tau,B^{(n)}_\tau)-e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)\right){\textrm{\dsrom{1}}_{\{\tau<T-h\}}}\\
&=&\left(u(\tau+h,B^{(n)}_\tau)-e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)\right){\textrm{\dsrom{1}}_{\{\tau<T-h\}}}\\
&& +\left(u(\tau,B^{(n)}_\tau)-u(\tau+h,B^{(n)}_\tau)\right){\textrm{\dsrom{1}}_{\{\tau<T-h\}}}.\end{aligned}$$ On the set $\{\tau<T-h\}$, we have $d(B^{(n)}_\tau, I_{\tau+h})\leq
\sqrt{h}||X||_{\infty}+|\mu|h$. It follows from Proposition 2.6 of [@DL2002] that $$u(\tau+h,B^{(n)}_\tau)-e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)\leq
C\frac{\left(\sqrt{h}||X||_\infty+|\mu|h\right)^2}{\sqrt{T-\tau-h}}.$$ Using the estimate $\left|\left|\frac{\partial u}{\partial t}(t,.)\right|\right|_\infty<C/\sqrt{T-t}$, we obtain $${\mathbb{E}}\left(u(\tau,B^{(n)}_\tau)-e^{-r\tau}g(\mu_0 \tau+B^{(n)}_\tau)\right)\leq
Ch{\mathbb{E}}\left({1\over \sqrt{T-\tau- h}}{\textrm{\dsrom{1}}_{\{\tau\leq T-2h\}}}\right).$$ The estimate $P^{(n)}-P\geq -C\frac{(\ln n)^{\bar{\alpha}}}{n}$ is now an easy consequence of Lemma 5.7 and Remark 5.8 of [@DL2002], which can be summarized in the following statement.
\[lemma-final\] There exists a positive constant $C$ such that $${\mathbb{E}}\left(\frac{1}{\sqrt{T-\tau- h}}{\textrm{\dsrom{1}}_{\{\tau\leq T-2h\}}}\right)\leq C\left(\ln h \right)^{\beta},$$ with $$\beta=\left\{ \begin{array}{l}
\\
[99]{} Barles G., Burdeau J., Romano M. and Sansoen N. (1995), Critical Stock Price near expiration, [*Mathematical Finance*]{} [**5**]{}, 77-95. Diener M. and Diener F. (2004), Asymptotics of the price oscillations of vanilla option in a tree model, [*Mathematical Finance*]{}, [**14**]{}, 271-293. Friedman A (1975), Parabolic variational inequalities in one space dimension and smoothness of the free boundary, [*Journal of Functional Analysis*]{} [**18**]{}, 151-176. Jaillet P., Lapeyre B. and Lamberton D. (1990), Variational inequalities and the pricing of American options, [*Acta Applicandae Mathematicae*]{} [**21**]{}, 263-289. (1980), [*An introduction to variational inequalities and their applications*]{}. Academic Press, New York. Lamberton D (2002), Brownian optimal stopping and random walks, [*Applied Math Optim*]{} [**45**]{}, 283-324. Lamberton D and Villeneuve S (2003), Critical price near maturity for an American option on a dividend paying stock (avec S. Villeneuve), [*Annals of Applied Probability*]{} [**13**]{}, 800-815. Liang J, Bei Hu & Lishang Jiang (2010), Optimal Convergence Rate of the Binomial Tree Scheme forAmerican Options with Jump Diffusion and Their Free Boundaries, [*SIAM Journal of Financial Mathematics*]{}, [**1**]{}, 30-65. Silvestrov, D.S. (2015). American Type Options. Stochastic Approximation Methods. Volume 2. Studies in Mathematics [**57**]{}, De Gruyter. Villeneuve S (1999), Options américaines dans un modèle de Black-Scholes multidimensionnel. Doctoral dissertation, Univ. Marne-la-Vallée. (2003) The Rate of Convergence of the Binomial Tree Scheme, [ *Finance and Stochastics*]{}, [**7**]{}, 337-361.
[^1]: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), UPEM, UPEC, CNRS, Projet Mathrisk INRIA, F-77454, Marne-la-Vallée, France - [[email protected]]{}
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Public Policy Bits: Public Policy, Planning and Chess
Once a great Cuban world chess champion Jose Raul Capablanca was asked how many moves ahead he is able to see in a chess game. He famously responded: ‘one, the best one’.
Karl Wittfogel, in 1957, published his seminal book “Oriental Despotism“, his claim that state-formation and organization of societies in hierarchies originated from large structural works, mainly irrigation in Mesopotamia and in the Yellow River in China, received much attention. While the hypothesis of Wittfogel on the link between large-scale irrigation works and “despotism” is currently rejected, the Chinese water engineers can be credited for another achievement: they laid the foundation of the game of chess. Dr. David Lee in “The Genealogy of Chess” directly tied the control of water and disastrous flooding to the creation of the ancient board game of Go and the later game of Xiang Qi, which is seen as a prototype of modern chess. Chess, like water management, reached Europe through the Arab world from where the Moors brought it to the Southern Europe in their conquests.
What can water managers learn from chess players?
But parallels between the two occupations are not finished with the origins and the history. There is much to learn from chess for water managers as chess may be seen as a “laboratory of decision-making” and management. Below are a few suggestions on what water managers and practitioners may derive from the experiences and writing related to chess. Often the link is via the field of “strategic planning” as a nexus between chess and water management.
1) Do not take strategy too seriously.
Chess is a symbol of rational decision-making and strategic planning. Yet, many decisions are based on the flow of the game, and strategic moves may well be followed by tactical combinations. As strategic management guru and professor of management at McGill University Henry Mintzberg argues in his book ‘The Rise and Fall of Strategic Planning‘ there is more space for intuition in “strategic management” than for planning. He claimed that analysis often brings paralysis, and many more decisions must be made based on intuition. An example of “paralysis by analysis” he brings comes from chess: “Let us suppose that at one point of the game you have a choice between the two moves, one by rook and one by knight…Which should you play? You settle down comfortably in your chair and start your analysis silently saying to yourself the possible moves. ‘All right, I could play the rook…and he would probably play…, or he could take my queen which is now undefended…What then?” Do I like the look of the position then? You go one move further in your analysis and then you pull a long face – the move by rook no longer appeals to you. Then you look at the knight move….(then once you do not see a good option, you go back to the first move to check it again)…at this point you glance at the clock. “My goodness! Already 30 minutes gone on thinking on what to play. If this goes on like this you will be in a real time trouble. And then you’re suddenly struck with a happy idea, why to move a rook or a night, you may play with a bishop! And without any more ado, without any analysis at all you move the bishop. Just like that, without hardly any consideration at all (Kotov, 1971: 15-16).” Does this remind you policy change in water governance / flood management when proposals wait in bureaucracies and discussions go on and on until a crisis happens, and then one of the possible options is advanced just to be played, to respond to the crisis? Suddenly deliberation is no longer crucial! Or perhaps, decision-making in bureaucracies where policy proposals are subject to regulatory impact assessment and cost-benefit analysis, which go on for a long time among technocrats until the moment there is no time left before politicians want a decision and suddenly decisions are made, but based not on CBA considerations whatsoever…
2) Software is more important than hardware!
As Diego Rasskin-Gutman writes in his recent book “Chess Metaphors”, chess is “an unparalleled laboratory, since both the learning process and the degree of ability obtained can be objectified and quantified, providing an excellent comparative framework on which to use rigorous analytical techniques”. Garry Kasparov, a former world chess champion who is now active in politics, consulting CEOs and writing contributions in widely read outlets such as the New York Review of Books, adds to this that decision-making process of chess is a model for understanding and improving our decision-making elsewhere. Let’s see one example of chess and implications for management. A popular on-line playing website http://www.playchess.com/organized an Internet tournament in 2005. Called ‘free-style”, this tournament allowed teams of human players to be assisted by computers during chess games. Normally, computers are not allowed in such competitions. One would expect that a team made of a strong grand-master and a strong computer would win the tournament. Yet, the surprising result of the tournament revealed the winner – the American team of two chess amateurs and three strong chess machines being used at the same time. Not grand-masters! Strong grandmaster+strong machine+ inferior process lost to amateur+strong machine+better process. Here is where I think about the importance of management and the process, and that it is not the necessity to invest and improve the hardware, improvements may as well be made to the software. Think of the UNDP Human Development Report of 2006 which claimed that the crisis of water is not the crisis of funding or infrastructure in the first place, but the crisis of poor management and unequal power relationships. This also boils down to the debate of institutions versus infrastructure. While I would not say that one is more important than the other, and they are interrelated obviously, the process must not be ignored!
3) Know how to let go!
Is planning necessary in water management and can we control the nature? The illusion of control is something that Mintzerg suggests as a function of planning. In chess, planning is a necessity. Games are won by elegant plans. Yet, plans are abandoned, changed and the situation on the board always guides the flow of the game. Strategies and plans emerge from the game. And this is what Mintzberg also refers to as “emergent strategies” vis a vis “deliberative strategies”. Again, the distinction between the two is more analytical than empirical, there are no pure versions of deliberate or emergent strategies. The first would assume no learning, the second – no control, and some mix of the two are always present. Yet, the ability to go with the flow is important for water management, especially those who have wet dreams of dams and dikes that would long over-survive the creators. Just like suggested by Charles Lindblom half a century ago for public sector management. And why are we obsessing about planning: both in chess and water management?
4). How many moves ahead?
Once a great Cuban world chess champion Jose Raul Capablanca was asked how many moves ahead he is able to see in a chess game. He famously responded: ‘one, the best one’. Chess is very complex mathematically, which is amazing for a game played on 64 squares. The number of legal chess positions is 1040, the number of different possible games, 10120. Just to help visualization, a player looking eight moves ahead is already presented with as many possible games as there are stars in the galaxy. A true master in chess knows the principles of the game, and while tries to calculate ahead a few moves, chooses plausible moves on his side and best responses from an opponent. The great difference between the human and the machine is that the first ‘thinks’ and chooses moves plausibly, limiting the choice to few options before making the final choice, the machine tediously and systematically looks at thousands of possible moves in a position. That much for artificial intelligence! Similarly, in water management, or any type of management – the ability to narrow down the choices and do so intelligently and then consider only the few good moves is what saves energy and makes good managers and decision-makers, and results in better policies, including water policies. | http://www.policytranslation.eu/on-chess-water-management-and-strategic-planning/ |
In this article we discuss 3D coordinate system changing from Cartesian to Toroidal.
We construct the Cartesian domain ( ) with the standard flat metric and a Toroidal domain (T).
We map into T and then calculate metric tensor field and connection induced on T by the mapping.
We also obtain the Laplace operator on 3-space in the toroidal coordinate system.
First of all we have to describe the space we are working in. The space is 3-dimensional Euclidean (flat) space. To define the space we declare domain, forms, vectors, coframe, frame, flat metric and calculate the connection (it equals to zero of cause).
The Toroidal domain is a space with 3-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci.
We construct two domains (Cartesian and Toroidal) and map them one to another.
Also we calculate the Laplace operator. | http://blog.digi-area.com/2011/03/3d-coordinate-system-changing-cartesian.html |
For More Information:
Dalmarys Matos (203) 576-7201
[email protected]
Snow Emergency Still in Effect for Thursday, March 8, 2018; Bridgeport Public Schools Closed
No Parking on Snow Emergency Streets; EVEN Side of the Street Parking on All Other Roadways for March 8, 2018
BRIDGEPORT, CT – The City of Bridgeport snow emergency is still in effect for Thursday, March 8, 2018 and until further notice to allow for continued citywide snow clean up and plow service. During the snow emergency, residents must move their cars off posted snow emergency streets. March 8 is an EVEN number day; therefore, residents should park on the side of the street with addresses that are EVEN numbers. EVEN side of the street parking rules are in effect for all other streets throughout the city in order to allow snow plow driver’s clear passage. Snow emergency streets are marked with white signs with red lettering. Snow emergency streets are marked with white signs with red lettering. A list of snow streets can be found on the City’s website by clicking here.
Parking
No parking is allowed on snow emergency streets. Vehicles left on snow emergency streets after the ban goes into effect will be subject to fines and towing. Snow emergency parking areas are available throughout the City. A full list of parking areas can be found here.
For secondary roads, as tomorrow is March 8th, an EVEN number day, cars must be parked on EVEN side of the street. The easiest way to tell the ODD- or EVEN- numbered side of a street is to check the street address of buildings. If the address ends in an odd number (1, 3, 5, 7, 9) then that building is on the ODD side of the street. If the address ends in an even number (0, 2, 4, 6, 8) then that building is on the EVEN side of the street.
Parking in the school and City parking lots listed here will be permitted. Vehicles parked at the schools should be removed by 7:00 a.m. Friday, March 9, 2018.
Bridgeport Public Schools
Superintendent Johnson has announced that all Bridgeport Public Schools will be closed.
City of Bridgeport Employees
City offices and facilities will open at 12:00 p.m. today, March 8th.
Snow Related Emergencies
Due to the storm, over 1,500 residents are without power caused by down trees and wires. United Illuminating (UI) is aware of the situation and is working to restore power. If any residents suffer a loss of electric power, they can call the UI customer hotline at 800-722-5584. During the storm, residents may call the Bridgeport Emergency Operations Center hotline at 203-579-3829 with any snow related emergencies. Both hotline numbers will be fully staffed and operating 24 hours a day during the snow emergency.
Plowing
Streets within the City are prioritized to clear major travel routes first. This allows public safety vehicles access to most parts of the City. The initial plowing activities also provide most residents a cleared roadway within two-to-three blocks of their home and most destinations in the City. Other factors include locations of schools, hospitals, major commercial centers and other facilities with large public interest.
Any plowing issues or concerns should be reported using mobile application Bridgeport 311. This resident service is available and monitored by city staff 24/7.
For the latest updates, resources and information about the snowstorm, residents are asked to check Bridgeportct.gov/snow, local television and radio news outlets and follow the City of Bridgeport on Twitter and Facebook. | https://bridgeportct.gov/feed-news/?FeedID=2638 |
“Learning to Classify Medical Documents According to Formal and Informal Style”, in Workshop on Intelligent Methods for Protecting Privacy and Confidentiality in Data, Ottawa, Canada, 2010.,
“A machine learning method for identifying impersonal constructions and zero pronouns in Spanish”, Procesamiento de Lenguaje Natural, vol. 45, pp. 281–285, 2010.,
“Multi-view Bootstrapping for Relation Extraction by Exploring Web Features and Linguistic Features”, in Computational Linguistics and Intelligent Text Processing, vol. 6008, Berlin / Heidelberg: Springer, 2010, pp. 525-536.,
“Ontology-based interoperation of linguistic tools for an improved lemma annotation in Spanish”, in The seventh international conference on Language Resources and Evaluation, LREC 2010, 2010.,
“Packed Feelings and Ordered Sentiments: Sentiment Parsing with Quasi-compositional Polarity Sequencing and Compression”, in 1st Workshop on Computational Approaches to Subjectivity and Sentiment Analysis, Lisbon, Portugal, 2010.,
“Part-of-Speech Tagging Using Parallel Weighted Finite-State Transducers”, in Advances in Natural Language Processing, vol. 6233, Berlin / Heidelberg: Springer, 2010, pp. 369-380.,
“Quantifying the Challenges in Parsing Patent Claims”, in 1st International Workshop on Advances in Patent Information Retrieval (AsPIRe’10), 2010.,
“Recognition of Affect, Judgment, and Appreciation in Text”, in 23rd International Conference on Computational Linguistics (COLING'10), Beijing, China, 2010, pp. 806-814.,
“Recognition of Fine-Grained Emotions from Text: An Approach Based on the Compositionality Principle”, in Modeling Machine Emotions for Realizing Intelligence, vol. 1, Berlin Heidelberg: Springer, 2010, pp. 179-207.,
“SAS® Curriculum Pathways® uses Connexor Technology to Help Teach Children Writing Skills ”, 2010. [Online]. Available: http://www.businesswire.com/news/home/20100812005017/en/SAS%C2%AE-Curriculum-Pathways%C2%AE-Connexor-Technology-Teach-Children.,
“SceneMaker: Intelligent Multimodal Visualisation of Natural Language Scripts”, in Artificial Intelligence and Cognitive Science, vol. 6206, Berlin / Heidelberg: Springer, 2010, pp. 144-153.,
“Spoken to Spoken vs. Spoken to Written: Corpus Approach to Exploring Interpreting and Subtitling”, in POLIBITS, 2010.,
“Summarizing Short Stories”, Computational Linguistics, vol. 36, no. 1, pp. 71-109, 2010.,
“Text Analytics to Data Warehousing”, International Journal on Computer Science and Engineering, vol. 2, no. 6, pp. 2201-2207, 2010.,
“Towards robust multi-tool tagging. An OWL/DL-based approach”, in 48th Annual Meeting of the Association for Computational Linguistics, Uppsala, Sweden, 2010.,
“Using Dependency Grammar Features in Whole Sentence Maximum Entropy Language Model for Speech Recognition”, in The Fourth International Conference Baltic HLT 2010, Amsterdam, The Netherlands, 2010, pp. 73–79.,
“Using machine learning to perform automatic term recognition”, in LREC 2010, Valletta, Malta, 2010.,
“A vector space analysis of swedish patent claims with different linguistic indices”, in 3rd international workshop on Patent information retrieval, Toronto, ON, Canada, 2010.,
“When is a query a question? Reconstructing wh-requests from ad hoc-queries”, in Conference on Multilingual and Multimodal Information Access Evaluation (CLEF 2010), logCLEF workshop, 2010.,
“World's first wearable humanoid robot that augments our emotions”, in 1st Augmented Human International Conference, Tokyo, Japan, 2010, pp. 8:1–8:10.,
2009
“Affective haptics in emotional communication”, in 3rd International Conference on Affective Computing and Intelligent Interaction and Workshops (ACII 2009), 2009, pp. 1-6.,
“Agent-Based Knowledge Discovery for Modeling & Simulation”, in IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, Washington, DC, USA, 2009, vol. 03, pp. 543–546.,
“Automatic Frame Extraction from Sentences”, in Advances in Artificial Intelligence, vol. 5549, Berlin / Heidelberg: Springer, 2009, pp. 110-120.,
“A Comparative Study of Spanish Zero Pronoun Distribution”, in International Symposium on Data and Sense Mining, Machine Translation and Controlled Languages (ISMTCL), Besançon, France, 2009, pp. 209–214., | https://www.connexor.com/nlplib/?q=nlplib/filter&page=6 |
Apollo 11 Crew-Signed Color Photo.... (Total: 2 Items)Click the image to load the highest resolution version.
DescriptionApollo 11 Crew-Signed Color Photo. A vintage 10" x 8" NASA printed lithograph, the popular "Prime Crew" image showing the crew in their white spacesuits in front of a lunar image. Signed by all three, as follows: "To Robert A. Wilson/ Best Wishes/ Neil Armstrong", "Michael/ Collins", and "Buzz Aldrin". Original NASA transmittal envelope included. Very good condition with various creases, none affecting the signatures.
Auction Info
Buyer's Premium per Lot:
19.5% of the successful bid (minimum $14) per lot. | https://historical.ha.com/itm/autographs/apollo-11-crew-signed-color-photo-total-2-items-/a/6095-40396.s |
Hello Parents,
I hope everyone enjoyed the weekend! I wanted to thank you all again for sending in all the Halloween/pumpkin party goodies last week. Your support of our class is extremely appreciated!
This Tuesday, November 3rd is Election Day. I spoke to the children about voting last week and this week, on Tuesday, the children will be voting for their favorite snack. We will also be learning about spiders this week and doing a spider project.
Reminders:
– Please remember to complete the daily attestations each morning prior to coming to school.
-I will be putting together an online class book showcasing each child for each family to learn about the students in our class. I’ve only received 4 so far, I will publish the book next week. Please send me a private message answering the following questions about your child:
1. Who is in your family?
2. What do you do for fun at home?
3. What do you want to be when you grow up?
4. What is your favorite color?
5. What is your favorite animal?
We are continuing the theme, “My Family” and the final unit is called “All Kinds of Families.” BIG Idea: Every family is unique. Knowledge Focus: Children learn about family members, family roles, and unique qualities of families. Social-Emotional Focus: Kindness. Vocabulary Theme Words: alike, special, different, tradition, respect and similar. Story Words: curly, shade, straight, tune and world. Math Words: group, pile, object and sort. Social Studies Words: individuals and unique. Science Words: investigate, observe, smell and taste.
We will be learning the letter Hh, #8, the color brown and octagon.
We will be reading the books “You and Me Together”, “We Are All Alike… We Are All Different”.
For Jesus time, we will be learning about Baby Moses.
Specials:
Art: Wednesday from 11-11:42
Physical Education: Thursday from 12:30-12:50
Critter Room: Every other Friday
This week we will be reading the “Clap for Community Workers” Scholastic Weekly Reader.
I will be sending homework packets out on Monday which will be due on Friday.
All communications from me will be posted through the Class Dojo app. If you have any questions or concerns, please reach out to me through the class dojo or via email [email protected].
Have a great week!
Upcoming Important Dates: | https://trinityli.org/mrs-agostinos-20-21-pre-k-week-of-11-2-20-11-6-20/ |
Raising a pregnant guppy can be stressful. I remember how confused I was when I saw my guppy getting larger and larger; however, it didn’t give birth. There was a point when I actually thought that the fish would abort the fry. Fortunately, as years passed, I gained some experience in this field.
Pregnant guppies may refuse to give birth for the following reasons:
- They aren’t being fed properly.
- The water temperature is too cold.
- The guppy is still in the early stages of pregnancy.
- The pregnant guppy is stressed.
- There are bullying tankmates in the aquarium.
- The pregnant guppy is sick.
As we move forward, I will elaborate on why pregnant guppies may refuse to give birth. I will also include a helpful video that will help you determine if your fish is pregnant. Sometimes, guppies may seem pregnant, but they are actually sick.
Still curious? Feel free to check my complete guide on pregnant guppy fish. There, I discussed how to care for pregnant guppies, how long they remain pregnant, how to identify signs of pregnancy, and a lot more.
Why Is My Pregnant Guppy Not Giving Birth?
Guppies are sexually mature at five months. They can start breeding at this stage. First, the male has to inseminate the female. Once the male fertilizes the eggs in the female’s body, they will hatch into fry that the pregnant guppy can push out of its anal vent four or five weeks later.
But what happens when a female guppy refuses to give birth? What would cause such delays? You have several factors to consider, including:
1. There Isn’t Enough Food In Your Tank
Does your aquarium have food? Research has found that guppies can extend their gestation period to improve their offspring’s chances of surviving in environments where food is scarce.
The studies that explored this issue found that guppies in regions with fewer predators were more likely to produce larger babies, but in smaller numbers, because the guppy population had ballooned.
Large numbers of guppies had to fight for the limited supply of algae and diatoms. As such, some guppies would gestate their young ones for more extended periods, allowing them to attain higher levels of maturity before they pushed the creatures out into the world.
If the food in your aquarium is scarce, the pregnant guppies may respond by extending the gestation period. As a rule of thumb, feed your pregnant guppy three to five small meals each day.
2. The Water Is Too Cold
You can expedite a pregnant guppy’s gestation period by increasing the temperature, but you can’t do this suddenly. You should raise the temperature by a degree or two each day. The optimal temperature is 82 degrees F.
This way, you can reduce the gestation period by several days, possibly even a week or more. However, doing the opposite will delay the pregnancy.
At 82 degrees F, not only will the guppies grow at a faster rate, but they will produce more offspring.
On the other hand, permitting the temperature to fall to 72 degrees F will reduce the guppy’s growth rate. This temperature will extend the creature’s gestation period while decreasing the number of babies it produces.
As was already noted above, food scarcity will make things worse. It will encourage the guppies to gestate their babies for more extended periods.
3. It’s Too Soon For Your Guppy To Give Birth
Guppies are typically pregnant for 21 to 31 days. On occasion, they can give birth within 21 days, depending on the conditions in the aquarium. But for the most part, aquarists expect guppies to give birth within 30 days.
The gestation period starts once conception occurs; that is to say, you start counting from the moment the male fish fertilizes the female’s eggs.
If your guppy has seemingly refused to give birth, you should consider the possibility that conception occurred later than you estimated. Your calculations are probably off by one or two weeks.
Also, bear in mind that female guppies can store sperm. This allows them to conceive at any moment without the direct involvement of a male guppy. Therefore, it becomes challenging to determine the exact moment that conception occurred.
Pay attention to the signs. If you think the guppy is overdue, but it isn’t quite as large as a guppy that is going to give birth, you should consider the possibility that you miscalculated.
4. Your Pregnant Guppy Is Stressed
Stress can be dangerous. Various factors can cause stress in pregnant guppies, including the wrong parameters, fluctuating conditions, food scarcity, violent tankmates, etc.
People think that stress will simply delay a guppy’s pregnancy. But that is the least of your worries. Stressed fish will probably abort their pregnancies.
They may also absorb the fry as nutrients. In other words, you will wait for the guppy to give birth in vain. The signs of pregnancy will slowly dissipate.
5. There Are Bullies In Your Tank
Did you separate your pregnant guppy? Guppies are bad parents. You cannot rely on the fish to raise their young ones because the guppies will eventually eat their babies. You have to keep the guppies in a separate tank until they give birth.
Once the mother drops the fry, move it back to the main tank. If you kept the pregnant guppy in the community tank, it could have given birth without your knowledge. In other words, the mother or the other adult fish ate all the fry before you noticed them.
Many aquarists use breeding boxes to protect the mothers and their offspring from predators. But breeding boxes cause stress. And as you now know, stress can compel guppies to abort or absorb their babies.
This is why aquarists wait until their guppies are on the verge of giving birth before placing the fish in breeding boxes. Once the mothers give birth, they remove them immediately. They don’t want the fish to spend more time than necessary in the breeding boxes.
6. Your Guppy Is Sick
Pregnancies are a significant source of stress. This is why pregnant guppies are so lethargic and inactive. It is also why some guppies die before or after giving birth.
If your guppy is sick or old, it will either extend the gestation period or abort the babies. Sick and old guppies are also more likely to die before or after giving birth.
It can be challenging to diagnose a sick guppy fish that is also pregnant, as some signs of pregnancy are also the signs of sickness. That includes a loss of appetite, a tendency to hide, a swollen belly, and erratic swimming.
However, sick guppies may look different. You may notice ripped fins, bleeding gills, dull coloring, wounds, open sores, and white dots. Sometimes, sick guppies tend to swim at the bottom of the tank.
If you notice these signs, I highly suggest consulting an aquatic veterinarian. An expert may help you choose the proper remedy and perhaps save your sick guppy.
7. Your Guppy Isn’t Actually Pregnant
Is your guppy pregnant? Most aquarists know that a pregnant guppy will expand in size as its eggs hatch and the fry develop. But some newcomers do not realize that a guppy’s belly can swell for other reasons. For instance, guppies can contract dropsy.
Dropsy will cause a guppy’s belly to swell with fluids. The illness is difficult to treat, if not impossible, because it harms the organs. If your fish is swollen, look for skin lesions and pinecone scales.
If you’ve ruled out dropsy, look for signs of constipation or overeating. Better yet, look for definitive symptoms of pregnancy. Bloating is not enough. A pregnant guppy’s gravid spot will grow darker and more prominent:
Besides losing its appetite, the fish will either lash out aggressively or hide, depending on its temperament and the attitudes of the guppy’s neighbors. You can also look for a distended anal vet and the eyes of the fry in the fish’s belly.
If the guppy’s bloating isn’t accompanied by these symptoms, you might have misdiagnosed the fish. It is not actually pregnant. You may ask a vet to identify the factors responsible for the bloating before the fish suffers lasting harm.
If you still feel unsure about this topic, here is an excellent Youtube video that will help you identify a pregnant guppy fish:
If you found this article helpful, these may also interest you:
- Do Pregnant Guppies Stay At The Top? Is It Normal Behavior?
- Why Did My Pregnant Guppy Die? (Before & After Giving Birth)
- How Many Babies Do Guppies Have? (Monthly & During A Lifetime)
- Guppy Pregnancy Stages: A Full Guide With Pictures
Pro tip: If your guppy is pregnant and will give birth soon, you’ll need to know a little more about the babies. On that matter, feel free to check my complete guide on guppy fry.
Conclusions
If your guppy isn’t giving birth, first ensure that the fish is indeed pregnant. There are many signs of pregnancy, including a darkening gravid spot, loss of appetite, aggressive behavior, and a belly that is consistently getting larger.
In some cases, it is still too early for the fish to give birth. Guppies are typically pregnant for 21 to 31 days. It is possible that you haven’t waited long enough or started counting too early. You should also consider environmental factors, such as temperature, tankmates, and food.
For example, a too cold tank may extend the gestation period. That is typical for temperatures lower than 72 degrees F. Ideally; you should aim for 82 degrees F. I also suggest feeding your guppies three to five times a day. | https://petfishonline.com/pregnant-guppy-not-giving-birth/ |
The ParkLife Community Room at St.James’ Park was the venue for a very successful 3‑day exhibition of the work of painters who attend Shirley’s Studio 77 Workshops, run by Kate Krzysicaand Colleen Cockroft.
There were over 40 framed, original paintings, all on the theme of “Views of Shirley and Southampton”, and also unframed, mounted paintings of Hampshire, and cards.
Visitors from as far afield as Winchester, Botley, Bishop’s Waltham, and Swanmore joined many local people to enjoy the different styles on offer from this group of emerging artists.
In total over the 3 days:
- 350 visitors were recorded
- 283 cards were sold
- 27 framed and 19 unframed paintings were sold
- Over £2200 of paintings and cards were sold
Feedback from visitors focused on delight in the locality and the local theme. People spent much time reminiscing over paintings – one of Gypsy Grove particularly interested an elderly visitor who remembered when he was 11 years old, running up and down it looking for his lost 7‑year old brother who was eventually found at the fair with a 4‑year old girl!
The organisers, Kate and Colleen, were delighted with the community response and support for this event, and were thrilled for the workshoppers, some of whom were exhibiting for the first time – and one of whom very kindly donated £55 to FoSJP! | https://fosjp.org.uk/events/winter-art-exhibition/ |
When it's time to relax and take in the sun, unzip the bag — and you've got a perfect beach mat. Stretch out lazily on this comfortable layer of foam, covered with 100% cotton. As the sun begins to set, just fold up the mat and zip — it becomes a roomy tote again.
Great for carrying your towel, suntan lotion and all your beach needs. At home, trim your thighs and flatten your tummy by using it as an exercise mat.
Whip up our foldable, toteable beach mat this afternoon and you're off!
Directions
You need:
• 1 piece foam 183 x 61 x 13 mm (72 x 24 x 1/2 inch)
• 2.10 m (2-1/4 yards) cotton 140 cm (54 inches) wide
• .10 m (1/8 yard) contrasting cotton for handles (optional)
• 2 separating zippers, each 45 cm (18 inches) long
• Matching thread
• Dressmaker's chalk
To make:
Use 13 mm (1/2 inch) seam allowance throughout.
1. Preshrink fabric.
2. Cut 2 pieces of fabric each 185 x 64 cm (73 x 25 inches).
3. Using chalk, mark fold lines on right sides of one piece of fabric. (See diagram.)
4. Separate 1 zipper. Place right side of 1 zipper half and right side of fabric together, so teeth at top of zipper are at A and bottom of B, with edge of zipper tape 3 mm (1/8 inch) in from edge of fabric. Pin in place. Repeat with other zipper half, placing top of teeth at C and bottom at D. (Note: Both halves of zipper are attached to same edge of fabric.) Baste. Repeat with second zipper on opposite edge.
5. To make straps, cut 2 strips from remaining or contrasting fabric, each 38 x 10 cm (15 x 4 inches). Fold each lengthwise, right sides together. Stitch long edge. Turn right side out. Press. Topstitch around entire outside edge. Stitch straps to right side of fabric as indicated in diagram.
6. With right sides together, join fabric pieces by stitching 1 short and 2 long edges, leaving second short edge open for turning right side out. (Keep straps toward middle while stitching so they don't get caught.) Trim corners diagonally.
7. The "buddy system" makes this step easier: With cover still inside out, slip hands in to the far edge and grasp edge of foam through the fabric. Slip cover over foam, turning it right side out and smoothing it as you go.
8. Turn under seam allowances at open end and slipstitch or machine stitch together.
9. Machine stitch along each chalk fold line, through all three layers.
10. Fold ends of mat toward centre. Fold in half. Zip closed. | https://www.canadianliving.com/home-and-garden/diy-and-crafts/article/zip-down-to-the-beach |
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
1. Field of the Invention
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The present invention relates to a nonvolatile ferroelectric capacitor for nonvolatile semiconductor memory. More specifically, the present invention relates to a nonvolatile ferroelectric capacitor comprising layered perovskite ferroelectric thin film made of BiATiOfor FeRAM (ferroelectric random access memory) application.
2. Description of the Related Art
DRAM (Dynamic Random Access Memory) typically used in computer main memory systems can provide a low cost RAM solution with high integration density and, particularly, has substantially no limitation on the number of write operations that can be performed. But DRAM is susceptible to damage from radiation, needs periodic refreshing to retain stored data, and is volatile, that is, it loses data in the absence of power.
In contrast, conventional nonvolatile memories such as EPROM, EEPROM and Flash Memory can maintain stored data even in the absence of power. However, these nonvolatile memories are relatively costly, have low integration density, require extremely high voltages for relatively long time periods to write and erase data, and, most undesirably, allow very limited cycles of write and erase operations compared to DRAM. Therefore, conventional nonvolatile memories are generally used in read-only or read-mostly applications.
Recently, a new type of nonvolatile memory, so called the ferroclectric RAM (FeRAM), is getting attention in the semiconductor industry. Since FeRAM stores digital data as two stable polarization states of the ferroelectric material, the polarization states being maintained when power is removed from FeRAM, it can maintain stored data even in the absence of power. In other words, FeRAM has nonvolatility. Moreover, as a change of polarization states occurs in substantially under 100 ns, read/ write operations of FeRAM can be performed as fast as those of DRAM. In addition, FeRAM is highly resistant to radiation damages and requires a low operation voltage. Therefore, FeRAM has been recognized as a next generation mainstream memory selection.
However, several challenges still remain in order to provide commercially practicable FeRAM. The ferroelectric thin film used in a FeRAM should maintain high remnant polarization, and be substantially free of fatigue (a reliability failure caused by the decrease of the magnitude of remnant polarization under repeated polarization switchings). In addition, the processing temperature of the ferroelectric material should be low enough to be compatible with the conventional semiconductor fabrication process.
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For example, ferroelectric capacitors constructed with perovskite-family ferroelectric materials such as PZT (PbTiO—PbZrO) are well known in the art. However, when a ferroelectric capacitor is fabricated by depositing a PZT film on a conventional Pt electrode, the magnitude of the remnant polarization of the ferroelectric thin film decreases with the number of times that the direction of polarization is switched, which is so called fatigue. Therefore, the FeRAM with PZT film can provide only a limited number of read/write cycles, failing to overcome the problems of conventional nonvolatile memories such as flash memory.
It has been reported that the fatigue failure originates from movement of oxygen vacancies and their entrapment at the electrode/ferroelectric interface. Under an external electric field, the oxygen vacancies generated in the ferroelectric film during the processing move towards the electrode/ferroelectric interface and get entrapped at the interface, which results in the loss of polarization.
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Two possible approaches have been suggested to overcome the fatigue problem. One of them is to reduce the tendency for entrapment of oxygen vacancies by employing a multilayer electrode structure having conductive oxide electrodes such as RuO, as disclosed in U.S. Pat. No 5,491,102 issued to Desu et al. on Feb. 13, 1996.
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Another approach is to use ferroelectric materials other than PZT without changing the conventional electrode structure. Such approach is disclosed in U.S. Pat. No. 5,519,234 issued to Paz de Araujo et al. entitled “Ferroelectric dielectric memory cell can switch at least Giga cycles and has low fatigue-has high dielectric constant and low leakage current”. U.S. Pat. No. 5,519,234 discloses a memory cell capacitor with extremely low fatigue comprising a layered superlattice material having formula A1A2AjS1S2SkB1B2BjQ, wherein A1, A2, , Aj represent A-site elements in a perovskite-like structure, B1, B2, , Bj represent B-site elements in a perovskite-like structure, S1, S2, , Sk represent superlattice generator elements, and Q represents an anion. One or more perovskite ferroelectric layers which have a rigid crystal lattice and a non-ferroelectric layer which has a less rigid structure alternate with each other throughout the crystal of the layered superlattice material. According to the U.S. Pat. No. 5,519,234, the non-ferroelectric layers between the perovskite ferroelectric layers absorb the shock generated in the perovskite ferroelectric layers by repeated switching of polarization and allow the ferroelectric thin film to maintain its high polarizable state. SBT, an exemplary layered superlattice material, maintains relatively high remnant polarization and low fatigue after 10switching cycles. It should be noted, however, that excellent ferroelectric properties of SBT in bulk had already been reported in various publications (see Solid State 3, 651(1961), G. A. Smolenski et al.; J. Am. Ceram. Soc. 45, 166(1962), E. C. Subbarao; J, Phys. Chem. Solids 23, 655(1962), E. C. Subbarao). The significance of U.S. Pat. No. 5,519,234 lies in that the layered superlattice materials such as SBT were found to exhibit extremely low fatigue even in the form of thin film and were used in fabricating FeRAM.
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12
3
Meanwhile, BiTiO(BTO) is another Bi-layered perovskite ferroclectric material which is known to show good ferroelectricity in bulk. However, BTO thin film has not been considered suitable for non-volatile ferroelectric memory, since the BTO thin film has a serious fatigue problem and Ti ions in the BTO thin film are known to diffuse into a silicon substrate to form conductive titanium silicide during heat treatment. The U.S. Pat. No. 5,519,234 solved these problems by sandwiching BTO thin film between buffer layers made of SrTiO.
Even though SBT thin film on the metal electrode exhibits extremely low fatigue, it has two disadvantages. First, SBT has lower remnant polarization (2Pr≈20 mC/) than that of PZT (2Pr≈35 mC/), which makes it difficult for the change of the polarization states to be sensed by a sense amplifier. Second, the existence of the intermediate inetastable nonferroelectric fluorite phase (Appl. Phys. Lett. 73, 2518 (1998), S. J. Hyun et al.) requires SBT thin film to be annealed at high temperature ranging from 750 to 850 for extended periods in order to transform SBT material as deposited to have the layered perovskite phase exhibiting ferroelectricity. The high temperature annealing imposes serious constraints on the back-end process such as interconnect formation and contact metalization process which usually require a relatively low thermal budget.
Moreover, the buffer layers sandwiching the BTO film complicate the fabrication process and increase the memory size, which results in increases the operating voltage and power consumption.
The object of the present invention is to provide a nonvolatile ferroelectric capacitor comprising a thin film of layered perovskite ferroelectric material which is substantially free of fatigue on the conventional metal electrode and has a large value of remnant polarization and low processing temperature.
The present invention provides a nonvolatile ferroelectric capacitor employing layered perovskite ferroelectric material which is obtained by substituting a non-volatile element such as La for the volatile Bi element in BTO.
The present invention also provides a nonvolatile ferroelectric memory comprising a nonvolatile ferroelectric capacitor with a thin film of layered perovskite ferroelectric material obtained by substituting a non-volatile element such as La for the volatile Bi element in BTO.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1
a
2
2
9
is an illustration of the primitive unit cell of SrBiTaOcrystal.
FIG. 1
b
4
3
12
is an illustration of the primitive unit cell of BiTiOcrystal.
FIG. 2
a
2
2
9
is an illustration of XPS test results of reduced and oxidized thin films of SrBiTaO.
FIG. 2
b
4
3
12
is an illustration of XPS test results of reduced and oxidized thin films of BiTiO.
FIG. 3
4−x
x
3
9
is an illustration of the primitive unit cell of BiLaTiOcrystal.
FIG. 4
is an flow chart of the fabrication process of a nonvolatile ferroelectric capacitor in accord a preferred embodiment of the present invention.
FIG. 5
4−x
x
3
9
is an illustration of XPS data of reduced and oxidized thin films of BiLaTiO.
FIG. 6
is a cross sectional view of a nonvolatile ferroelectric capacitor fabricated in accordance with a preferred embodiment of the present invention.
FIG. 7
3.25
0.75
3
12
shows hysteresis curves of BiLaTOthin film before and after 3 010 switching cycles.
FIG. 8
is an illustration of results of PUND switching test.
FIG. 9
3.25
0.75
3
12
is an illustration dielectric constant and loss tangent of BiLaTOthin film.
DESCRIPTION OF THE PREFERRED EMBODIMENT
−4
−4
The assertions on fatigue phenomenon in U.S. Pat. No. 5,519,234 do not explain why BTO having similar crystal structure as SBT exhibits fatigue. In order to determine the fatigue mechanism of layered perovskite ferroelectric materials and to understand the stability of oxygen in layered perovslcite ferroelectric materials, BTO and SBT thin films were subjected to post-annealing in oxygen ambient of 10torr and 400 torr. Thereafter XPS (X-ray Photoemission Spectroscopy) tests were conducted on the reduced (10torr) and oxidized (400 torr) thin films of BTO and SBT.
FIG. 1
FIG. 1
a
b
2
2
x−1
x
3x+1
2
2)
x−1
x
3x+1
2+(A
2−
4+
5+
5+
2+
2−
and show the crystal structures of SBT and BTO, respectively. Both BTO and SBT have the Bi-layered perovskite structure. This structure can be expressed by a general formula of (BiO)BO), wherein A can be mono-, di-, or trivalent ions or a mixture thereof, B represents Ti, Nband Ta, etc., and x can have values of 2, 3, 4 etc. (BiOand (ABO)represent the non-ferroelectric layer and the perovskite layer, respectively. The major differences in the crystal structures of BTO and SBT are the number of the metal-oxygen octahedra and the constituent elements of the perovskite layer. For SBT, A=Sr, B=Ta, and x=2, while for BTO, A=Bi, B=Ti, and x=3.
FIG. 2
a
2
2
shows the photoemission spectra of Bi 4f and Sr 3d core levels of the reduced (broken line) and oxidized (solid line) thin films of SBT. The Bi 4f peak for the reduced SBT thin film is shifted toward a lower binding energy side, while the Sr 3d peak of the reduced SBT thin film nearly coincides with that of the oxidized SBT thin film. The width of the Sr 3d peak of the reduced SBT thin film is nearly the same as that of the oxidized SBT thin film. These experiment results teach that, for the reduced SBT thin film, most oxygen vacancies are produced in the vicinity of the volatile Bi atoms of the BiOlayers.
FIG. 2
b
2
2
shows the photoemission spectra of Bi 4f and Ti 2p core levels of reduced (broken line) and oxidized (solid line) thin films of BTO. The Bi 4f peak and Ti 2p peak for the reduced BTO film are shifted toward a lower binding energy side, and the Ti 2p peak for the reduced BTO film is broader than that for the oxidized BTO film. These experimental results teach that, for the reduced BTO thin film, oxygen vacancies were generated not only in the neighborhood of the Bi atoms of the BiOlayer but also in the perovskite layers.
The difference in the oxygen stabilities of BTO thin film and SBT thin film results from the difference in local constituent elements of the perovskite layer, and this difference in oxygen stabilities explains why BTO and SBT thin films exhibit totally different fatigue behavior. That is, SBT thin film shows substantially no fatigue since oxygen vacancies are rarely produced in the perovskite layer. On the other hand, BTO thin film exhibits fatigue because oxygen vacancies are easily generated around the volatile Bi atoms in the perovskite layer.
4−x
x
3
12
Therefore, it can be concluded that BTO having relatively large value of remnant polarization (≈60 mC/) in bulk and low processing temperature can provide an excellent ferroelectric material for FeRAM if the oxygen stability in the perovskite layer is improved. To confirm this conclusion, a ferroelectric capacitor was fabricated using BiLaTiOobtained by substituting La for Bi of BTO.
FIG. 3
4−x
x
3
12
4−x
x
3
12
2
2
2
2
0
illustrates the crystal structure of BiLaTiO. It can be seen that La atoms occupy some of the A-sites in the perovskite layer of BiLaTiO. It is known that the substitution of La for Bi substantially usually occurs in the perovskite layer rather than in Bilayer (see Physical Review 122, 804-807(1961), E. C. Subbarao). However, some atoms of La might be substituted for the Bi atoms in the BiOlayer.
The preferred embodiment of this invention will be described below referring to the accompanying drawings.
FIG. 4
3.25
0.75
3
12
3.25
0.75
3
12
shows the fabrication process flow of the ferroelectric capacitor having BiLaTOthin film in accordance with the present invention. The known techniques for depositing ferroelectric thin films can be classified into two major categories, physical deposition and chemical deposition. The most commonly used methods among physical deposition techniques include RF magnetron sputtering, ion beam sputtering, and laser ablation. Recently, chemical methods of depositing ferroelectric films have become popular, for example metalorganic CVD and sol-gel deposition. In the preferred embodiment, BiLaTOthin film is formed by PLD (Pulsed Laser Deposition) which is well known in the art as a formation method of oxide thin films. However, the scope of the present invention is not limited to a nonvolatile ferroelectric capacitor fabricated by PLD.
110
160
110
120
130
140
150
160
FIG. 4
3.25
0.75
3
12
2
3
2
3
2
3.25
0.75
3
12
Step to step in illustrate a process flow to make a BiLaTOtarget for PLD. Powders of BiO, LaO, TiOare mixed in mole ratio of 13:3:24 at step . The powder mixture is then ground for about 4 hours at step , and then subject to calcination at 800 (step ). Proceeding to step , the calcinated mixture is ground for another 4 hours, and pressure-molded at step . The fabrication of the BiLaTOtarget for PLD is completed by sintering the pressure-molded pellet at about 1100 (step ).
2
3.25
0.75
3
12
3.25
0.75
3
12
3.25
0.75
3
12
200
SiOlayer of 50 Å, Ti layer of 200 Å and Pt bottom electrode layer of 2000 Å are deposited on a silicon substrate in that sequence. At step , BiLaTOlayer of 7000 Å is formed on the Pt bottom electrode layer at the substrate temperature of 400 by PLD using the BiLaTiOtarget. The substrate is then post-annealed at 700 for 1 hour in an oxygen atmosphere to change the phase of the deposited BiLaTOthin film into the layered perovskite phase.
FIG. 5
3.25
0.75
3
12
3.25
0.75
3
12
3.25
0.75
3
12
shows the XPS data of reduced (broken line) and oxidized (solid line) BiLaTOthin films. The Bi 4f and the Ti 2p peaks of the reduced BiLaTOthin film substantially overlap with those of the oxidized BiLaTOthin film, which shows that the stability of oxygen in the perovskite layer was improved by the substitution of La.
FIG. 6
3.25
0.75
3
12
In order to measure operation characteristics of the ferroelectric capacitor, a Au top electrode layer is deposited at room temperature by the thermal evaporation method using a shadow mask. illustrates a cross section of the ferroelectric capacitor having BiLaTOthin film.
3.25
0.75
3
12
3.25
0.75
3
12
FIG. 7
FIG. 7
Hysteresis curves of the BiLaTiOthin film in reveal that the ferroelectric thin film has a larger value of remnant polarization (Pr≈13 mC/) than that of SBT thin film and shows no asymmetric behavior which may result in imprint failure of memory cell. It should be noted that remnant polarization of the SBT film deposited by PLD is only about 3 mC/ (see Appl. Phys. Lett. 67, 572˜574(1995), R. Dat et al.). The solid and open circles in represent the hysteresis curves before and after being subjected to 3 010 read/write cycles, respectively. The fact that hysteresis curves before and after 3 010 cycles substantially overlap with each other means that BiLaTOthin film is substantially free of fatigue.
FIG. 8
FIG. 8
3.25
0.75
3
12
3.25
0.75
3
12
illustrates the results of PUND switching tests up to 3 010 cycles to evaluate fatigue characteristics of the BiLaTOthin film. The test results in confirmed that the difference between switched polarization (P*) and non-switched polarization (P{circumflex over ( )}), (P*−P{circumflex over ( )}), which plays critical role in reading out the stored data in ferroelectric memory cell, remains almost constant at 17 mC/, and thereby BiLaTOthin film is substantially free of fatigue.
FIG. 9
3.25
0.75
3
12
shows test results for dielectric constant and loss tangent of the BiLaTOthin film. The film is practically nondispersive at the frequency range of 103 to 106 Hz and has a small value of loss tangent.
3.25
0.75
3
12
4-x
.x
3
12
4-x
.x
3
12
The BiLaTOthin film is only an example of BiLaTiOthin film. The scope of the present invention is not limited to the case of x=0.75 but covers all x values which make BiLaTOthin film free of fatigue. According to publications by R. A Armstrong et.al (Mat. Res. Bull. 7, 1025(1972)), the contents of which are incorporated herein by reference, x corresponding to the solubility limit of La in BTO is 2.8 and the improvement of oxygen stability in perovskite layer, thus the suppressing of fatigue, may be achieved by substituting other non-volatile elements such as Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu and a mixture thereof.
The structure and operation of a nonvolatile ferroelectric memory comprising a nonvolatile ferroelectric capacitor are well known in the art and is not provided herein. However, it will be understood that a nonvolatile ferroelectric capacitor according to this invention may be utilized therein.
4-x
.x
3
12
4-x
.x
3
12
4-x
.x
3
12
3.25
0.75
3
12
Since BiLaTiOthin film is substantially free of fatigue as described above, a nonvolatile ferroelectric capacitor having BiLaTiOthin film can provide a high read/write endurance. Furthermore, the large remnant polarization of BiLaTiOthin film enables the change of the polarization states to be easily sensed. In addition, the processing temperature of BiLaTOthin film is lower than that of SBT, which makes it easier for the processing of BLT thin film to be incorporated into the conventional semiconductor fabrication process.
Because it is not necessary for the buffer layers to be formed between the metal electrode and the ferroelectric thin film, the fabrication process of a nonvolatile ferroelectric capacitor of this invention can be simplified and the size and the operating voltage of the nonvolatile ferroelectric capacitor can be reduced.
In view of the above, it can be seen that the objects of the invention are achieved and other advantageous results are attained.
Various changes could be made in the above construction without departing from the scope of the invention, and all matter contained in the above description or shown in the accompanying drawings is illustrative and not limitive of the full scope of the invention. |
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