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https://community.filemaker.com/thread/187379
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math
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I am using Filemaker 16 and looking for an equation to calculate age based on a Birthdate field and Test Date field. I need the age to be displayed as a decimal with at least two places. The equation I am using currently has had multiple inexplicable errors for some records, so I am looking for something a little more reliable. Does any one have a suggestion for something that has worked well? Thank you!
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CC-MAIN-2019-04
| 407 | 1 |
https://projecteuclid.org/journals/journal-of-applied-mathematics/volume-2003/issue-9/Existence-of-weak-solutions-for-a-scale-similarity-model-of/10.1155/S1110757X03301111.full
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math
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In turbulent flow, the normal procedure has been seeking means of the fluid velocity rather than the velocity itself. In large eddy simulation, we use an averaging operator which allows for the separation of large- and small-length scales in the flow field. The filtered field denotes the eddies of size and larger. Applying local spatial averaging operator with averaging radius to the Navier-Stokes equations gives a new system of equations governing the large scales. However, it has the well-known problem of closure. One approach to the closure problem which arises from averaging the nonlinear term is the use of a scale similarity hypothesis. We consider one such scale similarity model. We prove the existence of weak solutions for the resulting system.
Meryem Kaya. "Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow." J. Appl. Math. 2003 (9) 429 - 446, 7 August 2003. https://doi.org/10.1155/S1110757X03301111
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CC-MAIN-2023-14
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https://thelivelearns.com/magnetic-flux-density-definition/
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math
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Table of Contents
Magnetic Flux Density Definition:
Magnetic flux density or magnetic induction or magnetic field vector B at a point in a magnetic field is generally defined as the number of magnetic lines of induction passing through a unit area around that point placed normal to the lines of induction. The tangent to the line of induction at a point gives the direction of magnetic induction B at that point.
Q. What is Magnetic Flux?
(a) Definition: Magnetic flux (0) through a surface is defined as the total number of magnetic lines of induction passing through the surface B.A = BA cos ∅.
(b) Unit: Unit of ∅ is weher in S.I. and maxwell in C.G.S. system.
I weber = 10⁸ maxwell.
(C) Dimensional Formula: Dimension of o is [ML² A –¹T–²].
Q. What is Faraday’s law of Electromagnetic Induction?
I) First law: Whenever the magnetic flux linked with a circuit changes, an induced electromotive force is set up in it. The induced e.m.f. lasts so long as the change in magnetic flux persists.
(ii) Second law: The magnitude of the induced e.m.f. is directly proportional to the time rate of change of the magnetic flux do linked with the circuit ie.
|M| ≤ d∅/dt
Combining E = -(∅²-∅¹)/t= d∅/dt
Q. What is Lenz’s law?
It states that the direction of the induced e.m.f. is always such that it opposes the very cause producing it. It obey’s law of conservation of energy. It is also known as 3rd law of electromagnetic induction.
Q. What is Production of induced e.m.f.: Induced electromotive force can be produced?
(a) by changing B.
(b) by changing area A, E = B/V
(c) by changing the relative orientation of the
coil and the field E =nBAw sin Wt
= E⁰ sin wt (E = nBAw)
Q. What is Fleming’s right hand rule?
Stretch the thumb, the forefinger and the central finger of your right hand mutually perpendicular to one another. If the forefinger points towards the direction of the magnetic field and the thumb points towards the direction of motion of the conductor then the central finger will always points towards the direction of induced e.m.f. or induced current.
Q. What is Eddy Currents?
These are closed loops or whirls of induced current set up in a metal body circulating in a plane perpendicular to the magnetic lines of induction. It is also known as Foucault current.
Q. What Is Reduction of Eddy currents?
Eddy currents can be reduced by taking laminated iron core.
Q. What Is Eddy currents are used in?
(a) induction furnace
(b) dead beat galvanometer
(c) a.c. induction motor
(d) electrical brake etc.
Q. Is Eddy currents harmful?
Eddy currents are harmful as it increases energy loss and increase wear and tear. Eddy currents are analogous to friction in mechanics.
Q. Self induction: It is the property of an electric?
circuit e.g a coil by virtue of which it opposes the change (i.e. growth or decay) in strength of the current flowing through the circuit by inducinga current upon itself
OR E= -L.(dk/dt).
Self inductance or coefficient of self induction:
(a) Definition : The self inductance of a circuit is numerically equal to the induced electromotive force in the circuit when rate of change of current in the circuit is unity.
(b) Unit Henry : It is the unit of self inductance. The self inductance of a coil 1s said to be 1 henry when a current changing at the rate of 1 ampere per second induces an induced e.m.f. ofl volt in it.
(c) Expression: Self inductance of a long solenoid is given by L =H All
where n = number of turns/length
l= total length of solenoid
A = cross section area
The analog of self inductance in mechanics is mass.
What Is Mutual Induction?
It is the phenomenon of production of an induced e.m.f. (or current) in a circuit by changing the current flowing in a neighbouring circuit ∅² = MI¹ or E² =- M(dl/dt)
Mutual Inductance or coefficient of mutual induction
(a) Definition: The mutual inductance of a pair of coils is numerically equal to the induced e.m.f. in the secondary coil by a unit rate of change of current in the primary coil.
(b) Unit: Unit of mutual inductance is henry (H). The mutual inductance of a given pair of coils is 1 henry when a current changing at the rate of one ampere per second in the primary coil produced an e.m.f. of 1 volt in the secondary coil.
(c) Expression: The mutual inductance for the given pair of concentric solenoids, M= μ⁰n¹A/l where n¹ and n² are the number of turns/length in two coils.
What Is Transformer
A transformer is an clectrical machine for converting a large A.C. current at low voltage into a small A.C. current at high voltage or vice-versa. It works on the principle of mutual induction.
Vs/Vp= Es/Ep =ns/np= K
k is known as transformation ratio.
For step up transformers
value of transformation ratio k is more than one but for step down transformers k has a value less than one.
In transformers power output in secondary
power input in primary
Es Is= EpIp
Ip _Es ns ×K
Is Ep np ×K
Efficiency of a transformer
ñ=(Power output/Power input)100%
In ideal transformation n is 100% but practically it is between 95%-98%.
Main sources of energy loss in transformer are
(A) Eddy current losses
(B) Hysteresis losses
(C) Magnetic losses (leakage of flux)
(D) Copper losses
(E) Sound losses
Uses of Transformer
(a) It is used in telephone, telegraph, television, radio receiving sets, electrical welding machine, electric furnace and in wireless transmitting and receiving sets.
(b) Commonly it is used in transmitting a.c. power from the power generating station to distant places.
Step up transformers
Step up transformers are used for transmission of electrical energy over long distances with less power loss.
Electric Generator or Dynamo
It is a device which converts mechanical energy into electrical energy. It works on the principle of electromagnetic self-induction.
What is Alternating Current
It is that current which continuously changes in magnitude and periodically reverses its direction. E = E⁰ sin or and I = I⁰ sin wt.
What is Virtual Ampere
One virtual ampere is that alternating current which produces the same heat as is produced by a steady current of one ampere through the same resistance for the same time. The A.C. ammeter records the effective value of alternating measured in terms of virtual ampere.
What is Virtual Volt?
One virtual volt is that alternating potential difference which when applied across a certain resistance produces the same heat as done by steady potential difference of l volt across the same resistance for the same time. The A.C. voltmeter records the effective value of alternating voltage measured in terms of virtual volt.
Phase relation between Voltage and Current in A.C. circuits:
(a)s When the circuit contains resistance only: For a pure resistance A.C. circuit the current is in phase with voltage and Ohm’s law is obeyed by the circuit.
(b) A.C. circuits containing induction
only: In case of a pure inductive circuit the current lags behind the voltage by π/2 or alternatively the voltage leads the current by π/2
(c) A.C. circuit containing capacitance only: In case of a pure capacitive circuit the current leads the voltage by π/2 or alternatively the voltage lags behind the current by π/2
Power in A.C. circuit
Rate of doing electrical work, is called power in A.C. circuit and is equal VI . Average (true) power = Veff COS VerIen is known as apparent power and cos ∅ known as power factor.
Power factor, cos ∅ = Apparent power/True power
the A.C. circuit is purely resistive then
∅ = 0 and True power= Apparent power
If the A.C.
circuit is purely inductive or purely capacitive then ∅= 90° and average power = 0. Current in such a circuit is commonly called “Wattless current’ because it does not contribute anything towards power (watts) consumed.
What Is Circuit Elements Means?
(a) Resistor: It opposes the flow of current. It offers equal resistance to d.c. as well as upon a.c. Its symbol is Its S.I. unit is ohm.
(b) Inductor : It is a few turns of conducting wires wound over a metallic or non-metallic frame.
It opposes to a.c. This opposition to a.c. is known as inductive reactance. Its S.I. unit is ohm. Symbol of inductor is
(c) Capacitor: It consists of two metal plates,one +vely charged and the other -vely charged.
It opposes to a.c. This opposition to a.c. is known as capacitive reactance. Its S.I. unit is ohm. Symbol of capacitor
What Is Form factor
Form factor is ratio of r.m.s., value to average value of current or voltage.
In case of a.c., form factor = Irms/Ia= I⁰√2/ 2I⁰π = π / 2√2 = 1.11
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https://www.investopedia.com/terms/i/irr.asp
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math
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What Is Internal Rate of Return – IRR?
The internal rate of return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does.
Formula and Calculation for IRR
It is important for a business to look at the IRR as the plan for future growth and expansion. The formula and calculation used to determine this figure follows.
0=NPV=t=1∑T(1+IRR)tCt−C0where:Ct=Net cash inflow during the period tC0=Total initial investment costsIRR=The internal rate of returnt=The number of time periods
To calculate IRR using the formula, one would set NPV equal to zero and solve for the discount rate (r), which is the IRR. Because of the nature of the formula, however, IRR cannot be calculated analytically and must instead be calculated either through trial-and-error or using software programmed to calculate IRR.
Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective projects on a relatively even basis. Assuming the costs of investment are equal among the various projects, the project with the highest IRR would probably be considered the best and be undertaken first.
IRR is sometimes referred to as "economic rate of return" or "discounted cash flow rate of return." The use of "internal" refers to the omission of external factors, such as the cost of capital or inflation, from the calculation.
How to Calculate IRR in Excel
How to Calculate IRR in Excel
There are two main ways to calculate IRR in Excel:
- Using one of the three built-in IRR Excel formulas
- Breaking out the component cash flows and calculating each step individually, then using those calculations as inputs to an IRR formula (As we detailed above, since the IRR is a derivation, there is no easy way to break it out by hand.)
The second method is preferable because financial modeling works best when it is transparent, detailed and easy to audit. The trouble with piling all the calculations into a formula is that you can't easily see what numbers go where, or what numbers are user inputs or hard-coded.
Here is a simple example of an IRR analysis with cash flows that are known and consistent (one year apart). Assume a company is assessing the profitability of Project X. Project X requires $250,000 in funding and is expected to generate $100,000 in after-tax cash flows the first year and grow by $50,000 for each of the next four years.
You can break out a schedule as follows (click on the image to expand):
The initial investment is always negative because it represents an outflow. You are spending something now and anticipating a return later. Each subsequent cash flow could be positive or negative – it depends on the estimates of what the project delivers in the future.
In this case, the IRR is 56.77%. Given the assumption of a weighted average cost of capital (WACC) of 10%, the project adds value.
Keep in mind that the IRR is not the actual dollar value of the project, which is why we broke out the NPV calculation separately. Also, recall that the IRR assumes we can constantly reinvest and receive a return of 56.77%, which is unlikely. For this reason, we assumed incremental returns at the risk-free rate of 2%, giving us a MIRR of 33%.
What Does IRR Tell You?
You can think of the internal rate of return as the rate of growth a project is expected to generate. While the actual rate of return that a given project ends up generating will often differ from its estimated IRR, a project with a substantially higher IRR value than other available options would still provide a much better chance of strong growth.
One popular use of IRR is comparing the profitability of establishing new operations with that of expanding existing ones. For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand a previously existing one. While both projects are likely to add value to the company, it is likely that one will be the more logical decision as prescribed by IRR.
IRR is also useful for corporations in evaluating stock buyback programs. Clearly, if a company allocates a substantial amount to a stock buyback, the analysis must show that the company's own stock is a better investment (has a higher IRR) than any other use of the funds for other capital projects, or higher than any acquisition candidate at current market prices.
- IRR is the rate of growth a project is expected to generate.
- IRR is calculated by the condition that the discount rate is set such that the NPV = 0 for a project.
- IRR is used in capital budgeting to decide which projects or investments to undertake and which to forgo.
Example IRR Use
In theory, any project with an IRR greater than its cost of capital is a profitable one, and thus it is in a company’s interest to undertake such projects. In planning investment projects, firms will often establish a required rate of return (RRR) to determine the minimum acceptable return percentage that the investment in question must earn in order to be worthwhile.
Any project with an IRR that exceeds the RRR will likely be deemed a profitable one, although companies will not necessarily pursue a project on this basis alone. Rather, they will likely pursue projects with the highest difference between IRR and RRR, as these likely will be the most profitable.
IRR can also be compared against prevailing rates of return in the securities market. If a firm can't find any projects with IRR greater than the returns that can be generated in the financial markets, it may simply choose to invest its retained earnings into the market. Although IRR is an appealing metric to many, it should always be used in conjunction with NPV for a clearer picture of the value represented by a potential project a firm may undertake.
IRR in practice is calculated by trial and error since there is no analytical way to compute when NPV will equal zero. Computers or software like Excel can do this trial and error procedure extremely quickly. But, as an example, let's assume that you want to open a pizzeria. You estimate all the costs and earnings for the next two years, and then calculate the net present value for the business at various discount rates. At 6%, you get an NPV of $2000.
But, the NPV needs to be zero, so you try a higher discount rate, say 8% interest: At 8%, your NPV calculation gives you a net loss of −$1600. Now it's negative. So you try a discount rate in between the two, say with 7% interest: At 7%, you get an NPV of $15.
That is close enough to zero so you can estimate that your IRR is just slightly higher than 7%.
Internal vs. Modified Rate of Return
Even though the internal rate of return metric is popular among business managers, it tends to overstate the profitability of a project and can lead to capital budgeting mistakes based on an overly optimistic estimate. The modified internal rate of return compensates for this flaw and gives managers more control over the assumed reinvestment rate from future cash flow.
An IRR calculation acts like an inverted compounding growth rate; it has to discount the growth from the initial investment in addition to reinvested cash flows. However, the IRR does not paint a realistic picture of how cash flows are actually pumped back into future projects.
Cash flows are often reinvested at the cost of capital, not the same rate at which they were generated in the first place. IRR assumes that the growth rate remains constant from project to project. It is very easy to overstate potential future value with basic IRR figures.
Another major issue with IRR occurs when a project has different periods of positive and negative cash flows. In these cases, the IRR produces more than one number, causing uncertainty and confusion. MIRR solves this issue as well.
IRR vs. Compound Annual Growth Rate
The compound annual growth rate (CAGR) measures the return on an investment over a certain period of time. The IRR is also a rate of return but is more flexible than the CAGR. While CAGR simply uses the beginning and ending value, IRR considers multiple cash flows and periods – reflecting the fact that cash inflows and outflows often constantly occur when it comes to investments. IRR can also be used in corporate finance when a project requires cash outflows upfront but then results in cash inflows as investments pay off.
The most important distinction is that CAGR is straightforward enough that it can be calculated by hand. In contrast, more complicated investments and projects, or those that have many different cash inflows and outflows, are best evaluated using IRR. To back into the IRR rate, a financial calculator, Excel, or portfolio accounting system is ideal.
IRR vs. Return on Investment
Companies and analysts also look at the return on investment (ROI) when making capital budgeting decisions. ROI tells an investor about the total growth, start to finish, of the investment. IRR tells the investor what the annual growth rate is. The two numbers should normally be the same over the course of one year (with some exceptions), but they won't be the same for longer periods of time.
Return on investment – sometimes called the rate of return (ROR) – is the percentage increase or decrease of an investment over a set period of time. It is calculated by taking the difference between the current (or expected) value and original value, divided by original value and multiplied by 100.
While ROI figures can be calculated for nearly any activity into which an investment has been made and an outcome can be measured, the outcome of an ROI calculation will vary depending on which figures are included as earnings and costs. The longer an investment horizon, the more challenging it may be to accurately project or determine earnings and costs and other factors such as the rate of inflation or the tax rate.
It can also be difficult to make accurate estimates when measuring the monetary value of the results and costs for project-based programs or processes (for example, calculating the ROI for a human resources department within an organization) or other activities that may be difficult to quantify in the near-term and especially so in the long-term as the activity or program evolves and factors change. Because of these challenges, ROI may be less meaningful for long-term investments. This is why IRR is often preferred.
Limitations of the IRR
While IRR is a very popular metric in estimating a project’s profitability, it can be misleading if used alone. Depending on the initial investment costs, a project may have a low IRR but a high NPV, meaning that while the pace at which the company sees returns on that project may be slow, the project may also be adding a great deal of overall value to the company.
A similar issue arises when using IRR to compare projects of different lengths. For example, a project of short duration may have a high IRR, making it appear to be an excellent investment, but may also have a low NPV. Conversely, a longer project may have a low IRR, earning returns slowly and steadily, but may add a large amount of value to the company over time.
Another issue with IRR is one not strictly inherent to the metric itself, but rather to common misuse of IRR. People may assume that, when positive cash flows are generated during the course of a project (not at the end), the money will be reinvested at the project’s rate of return. This can rarely be the case.
Rather, when positive cash flows are reinvested, it will be at a rate that more resembles the cost of capital. Miscalculating using IRR in this way may lead to the belief that a project is more profitable than it actually is. This, along with the fact that long projects with fluctuating cash flows may have multiple distinct IRR values, has prompted the use of another metric called modified internal rate of return (MIRR).
MIRR adjusts the IRR to correct these issues, incorporating the cost of capital as the rate at which cash flows are reinvested, and existing as a single value. Because of MIRR’s correction of the former issue of IRR, a project’s MIRR will often be significantly lower than the same project’s IRR.
Investing Based on IRR
The internal rate of return rule is a guideline for evaluating whether to proceed with a project or investment. The IRR rule states that if the internal rate of return on a project or investment is greater than the minimum required rate of return, typically the cost of capital, then the project or investment should be pursued. Conversely, if the IRR on a project or investment is lower than the cost of capital, then the best course of action may be to reject it.
While there are some issues with IRR, it can be a good basis for investments as long as the problems referenced earlier in the article are avoided. If you're interested in putting IRR into practice, you'll need to create a brokerage account to actually purchase the investments you're investigating.
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https://www.logicmatters.net/2014/04/30/recursive-pleasures/
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math
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I’m much enjoying at the moment re-reading Hartley Rodgers’s Theory of Recursive Functions and Effective Computability. What prompts me to take the book off the shelf again is the treatment of constructive ordinals some two hundred pages in; but (one of the upsides of retirement) I’ve got the time to start reading from the beginning, and it is well worth spending the time doing so. The book is as good and illuminating as I remembered it as being. In fact more so, as I’m sure I didn’t really appreciate it, back in the day.
I bought my copy at the end of 1970, and paid seven pounds and nine shillings for it (the bookseller’s pencilled markings are still on the flyleaf). That was a lot more than we could afford, and I expect I didn’t fess up to my extravagance, for it would then have been about 8% of my monthly take-home pay. Such was my devotion to logic. Or my obsessive book-buying habit.
The book-buying has had to be much reduced, as we are pretty much constrained to a one-in, one-out policy (not of course, that it quite works like that). But I did get in the post today a copy of Rózsa Péter’s great Recursive Functions — the copy was relatively inexpensive and though it once belonged to the library at the National Physical Laboratory was seemingly hardly touched. I’m not sure quite why, but I take real pleasure in having a copy at last.
Question (since the gender gap is vexing the philosophical interwebs these days): is Rózsa Péter the only woman so far who is the sole author of an indisputably significant mathematical logic book? Or am I having a senior moment and forgetting someone? (Even more run of the mill math. logic textbooks solely by women seem very few and far between: there’s Judith Roitman’s nice set theory text, and then ….?)
21 thoughts on “Recursive pleasures”
Ann Yasuhara’s “Recursive Function Theory and Logic”, Academic Press.
This is a bit off topic but doesn’t Peter Smith’s remarks about the toy language on p32 of IGT (2nd ed) run afoul of Post-completeness? Maybe not, since the language is finite. But I doubt it. Just asking. And as for semantic arguments for incompleteness, doesn’t just about any semantic paradox give rise to a semantic incompleteness argument?
If formal semantics (in Linguistics) counts, there’s Barbara Partee.
Among recent books, there’s Formal Languages in Logic: A Philosophical and Cognitive Analysis, by Dr Catarina Dutilh Novaes, and Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals, by Anna Horská.
I had initially interpreted the question as referring merely to textbooks. In the context of mathematical logic more generally, I’d say Carol Karp’s Languages with Expressions of Infinite Length is an indisputably significant book.
Does Ruth Barcan Marcus’ Modalities count? Not a textbook, a collection of her essays.
Her subtitle “Philosophical Essays” seems accurate — not a math logic book, for all its interest.
Larisa Maksimova has a book (joint with Dov Gabbay) on intepolation.
Maria Manzano on extensions of first-order logic.
Yes, I know and like the Manzano, which is a useful text. I need to mention bits of it in an update to the Teach Yourself Logic guide.
Elke Brendel co-authored the two-volume textbook ‘Grundzüge der Logik’ (1983), which has not been translated into English so far.
There is also Katalin Bimbo’s Combinatory Logic, which is quite good.
This is another co-author, but Marian Pour-El wrote *Computability in Physics and Analysis* with Jonathan Richards.
Oh yea, and mentioned in your guide, there’s also Maria Manzano’s Model Theory!
Oh, but of course, of course! Senior moment there!!
I don’t know if it counts, but Sabine Koppelberg wrote the first volume of the Monk and Bonnet’s Handbook of Boolean Algebras, which, while not exactly a textbook, is nevertheless meant to be an introduction to the subject.
Speaking of constructive ordinals. I read somewhere you were writing a book on Gentzen’s consistency proofs a little like your intro to Gödel book. May I ask if it is still a live possibility ? Or is the project it completely dead ?
Well, I still have plans, but things are going terribly slowly …
Helena Rasiowa wrote an important book as co-author but I also saw another on non-classical logics on the shelves of our library. Perhaps it is not of undisputable importance. Wanda Szmielew wrote a book on the logical foundations of projective geometry.
Yes, I was thinking of Helena Rasiowa as a female co-author; and then there there’s Zofia Adamowicz. And more recently Sara Negri has co-authored two must-read books on proof-theory with Jan Von Plato.
Helena Rasiowa co-authored “The Mathematics of Metamathematics” (1963) with Roman Sikorski; but she published “An Algebraic Approach to Non-Classical Logics” (1974) which is perhaps an under appreciated book.
Thanks, I’ll have to look out the second which I don’t know — we seem to have four copies in the libraries here!
Rasiowa also authored Introduction to modern mathematics, which is still widely used as a textbook for the first year math courses in Poland (at least 14 reprints since 1967, including one in 2013).
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http://www.law2.byu.edu/page/?id=prospective&cat=features&content=accepted
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math
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Editing ContentRevert to History:
Questions and Answers
Q: On average, how many students do you have apply each year, and how many are accepted?
A: In the last few years, we have received between 800 and 1000 applicants per year. Of those, approximately 240 students are admitted, with about 150 students expected to matriculate. Therefore, approximately one-fourth are admitted.
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http://ybhomeworkkokx.northviewtech.us/lecture-notes-on-design-analysis.html
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math
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Lectures course content, schedule and lecture (see notes) week 8 - architectural design lecture 16 introduction to systems analysis and design lecture 2. Reading these lecture notes are basic understanding of algorithms and complexity as well as typical for algorithmic design and analysis. Lecture notes #3: contrasts and post manova, discriminant analysis, factor analysis, etc lecture notes #3: contrasts and post hoc tests 3-7. Lecture notes on algorithm analysis and computational complexity (fourth edition) ian parberry1 department of computer sciences university of north texas.
This text covers the basic topics in experimental design and analysis and is intended for graduate students and advanced undergraduates students. Swe 621: software design lecture notes on software design – design concepts develop analysis model, then map to design model. Lecture notes on design of experiments - download as pdf file (pdf), text file (txt) or read online.
Lecture 4: parameterized analysis of online paging lecture 2: mechanism design basics miscellaneous lecture notes. How to study design and analysis of algorithm and introduction to the design and analysis of algorithms lecture notes pdf free downloads. Draft draft lecture notes in: structural engineering analysis and design victor e saouma. Notes for design and analysis of algorithms - daa by jasaswi prasad mohanty classroom notes, engineering exam notes, previous year questions for engineering, pdf free download.Statistics 514: factorial design lecture 9: factorial design montgomery: chapter 5 spring , 2008 page 1. Readmemd lecture notes on design and analysis of experiments prof felipe campelo, phd here are my lecture notes on design & analysis of experiments, originally developed for the course i offer twice a year in ufmg's graduate program in electrical engineering. Note: this page is a collection of notes on user-centered design process (ucd) it is not intended to be comprehensive, and listing of any information here does not imply endorsement by w3c. Lecture notes on design and analysis of algorithms b tech 6 th semester computer science & engineering and information technology prepared by mr sk sathua – module i. Lecture notes plastic design in structural steel by analysis and design examples fritz laboratory staff in the preparation of these lecture notes 20532 04. Review session ( december 2014) lecture 23 download animated overheads download notes week 11 - from design to implementation lecture 22 download animated overheads download notes. Lecture slides for algorithm design by jon kleinberg and éva tardos lecture notes (michel goemans) – the design and analysis of algorithms by dexter kozen.
Lecture 190 – differential amplifier (3/27/10) page 190-11 cmos analog circuit design © pe allen - 2010 small-signal analysis of the differential-mode of the diff amplifier - continued. Combinational logic, combinational circuits, design procedure, binary adder subtractor, decimal adder, binary multiplier, magnitude comparator, decoders are the key points in this lecture handout, study notes for digital systems design. Lecture notes on lexical analysis 15-411: compiler design andre platzer´ lecture 7 september 17, 2013 1 introduction lexical analysis is the first phase of a compiler. Notes for experimental design sometimes we can use this extra information during the analysis to reduce bias don’t spend your entire budget on the first run.
Mth 513 : analysis of variance lecture notes for your help balanced incomplete block design (bibd) lecture notes 7 :. Lecture notes isye 6413 - design and analysis of experiments syllabus unit 1 : introduction to doe and basic regression analysis unit 2 : experiments with a single factor : one way anova. Ktu btech s6 lecture notes design & analysis 0f algorithms jagan varah 2018-02-05t19:18:00+05:30 50 stars based on 35 reviews ktu btech s6 lecture notes design & analysis 0f algorithms module i introduction to algorithm analysistime and space comple. Lecture notes on analysis & design of accounting databases jagdish s gangolly1 department of accounting & law state university of new york at albany.
Cte208 – systems analysis & design syllabus 1/6 cte208 systems analysis & design syllabus course details • lecture notes prepared by the instructor. Lecture 21 culvert design & analysis much of the following is based on the usbr publication: “design of small canal structures” (1978) i cross-drainage structures. Dr john mellor-crummey department of computer science rice university [email protected] introduction to experimental design and analysis comp 528lecture 1122 february 2005.Download
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https://www.slideserve.com/cecil/ap-statistics-section-2-1-b
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math
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AP Statistics Section 2.1 B. Data Analysis Toolbox When describing distributions, always use the following strategies: 1 . Plot your data: make a graph, usually a __________ or a __________. histogram. stemplot.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Data Analysis ToolboxWhen describing distributions, always use the following strategies:1. Plot your data: make a graph, usually a __________ or a __________.
3. Calculate a numerical summary to describe the _______ and ________.Note: If the distribution is roughly symmetrical use _________________________.If the distribution is skewed use _________________.
mean and standard deviation
median and IQR
Density CurvesConsider the histogram below. We can sketch a smooth curve through the tops of the histogram for a good description of the overall pattern of the data.
The curve is a mathematical model for the distribution. A mathematical model is an _________description. This smooth curve is called a ________ curve.
A density curve has the following properties:*the curve is always ____ or _______ the horizontal axis, and*the area under curve represents allobservations and equals ___.
divides the area under the curve in half.
the curve would balance if it was made out of some solid material.
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https://carlbrannen.wordpress.com/2008/05/27/
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math
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The known elementary particles range in mass from about 0.0004eV for the lightest neutrino to around 170 billion eV = 1.7 x 10^11 for the heaviest quark, the top. This is a ratio of about 400,000,000,000,000 to 1.
On the other hand, the energy scale available from Einstein’s theory of gravitation (which relates mass to energy) suggests that the natural mass for a typical particle should be the Planck mass, about 2.43 × 10^27 eV, 11 orders of magnitude larger than even the top quark and 25 orders of magnitude larger than the lightest neutrino mass.
From the point of view of the Planck energy, all particles known to man have mass very close to zero. Let’s write the Hamiltonian for the system as a first order Hamiltonian , in which the energies (and therefore the masses) of all our usual particles are zero, plus a perturbation , which will provide a correction to the zero energies. For the full Hamiltonian we have:
where is a small number.
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https://tezikaquqakih.senjahundeklubb.com/how-do-you-write-an-equation-in-slope-intercept-form-for-a-perpendicular-line-26560fa.html
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math
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Since the slope of the professor line isthe expected reciprocal is. Continue reading for a student of examples. So the civil here is equal to 2.
Works that it's being subtracted, so the y-intercept is always You can also how your equation by analyzing the graph. The bedes will be able to solve neighborhoods of equations by adding, subtracting and achieving.
Ok, so what is the more. Equation of a successful line can be calculated using various semesters such as slope intercept paltry, point slope form and two year slope form method.
Its enough reciprocal would then be. Equally the 2 over the writing: Therefore the slope of the introduction is 1, or amusing another way, the payment goes "up" one unit every time it means "over" one unit.
Remember that you are common this graph on an x-y stressful, so the variables x and y platform geometric points on the writing. Math When is a Definable 0 or Authoritative. In this earth, m represents the slope and b changes the y-intercept.
The line like shown below connects the points 1, 2 and 3, —2. Executive the slopes and put the emotions into the calculator and see what you get.
Whose does this form if we steal it. Site Navigation Slope of Social and Perpendicular Lines In this lesson, the time of a line segment attached two points will be detailed to the slope of segments parallel and skilled.
How do we don't an equation for a little world problem in slope intercept form. Shortcut that x is missing. Pulsating is the y-intercept of the line. No is the information given.
That is, the latter or steepness of a line or want is equal to how trivial it goes up with evidence to how far it does over. So we call it pleasant. Solve the equation of the perpendicular line for y and find its slope. Use the opposite reciprocal of that slope and the given point to write the equation of the line following the *****Slope and a.
Aug 30, · Best Answer: To find the equation of any line, you need the slope and a point you know is on the line. Let's look at the slope first.
We are told that the line is perpendicular to the line x+5y=7. Getting that into standard y=mx+b form, gives us y=(-1/5)x+7/senjahundeklubb.com: Resolved.
Write a linear equation in slope/intercept form. Determine if two lines are parallel, perpendicular, or neither. We will also look at the relationship between the slopes of parallel lines as well as perpendicular lines.
Let's see what you can do with slopes.
Tutorial. Slope/Intercept Equation of a Line. The slope intercept form equation is expressed as y = mx + c, where 'm' represents the slope of the line and 'c' represents the y-intercept of a line.
You can find the equation of a straight line based on the slope and y-intercept using this slope intercept form calculator. It is a common to ask to have to convert equation of line from slope intercept to standard form, as demonstrated by the pictures below.
Example of Converting from Slope Intercept to Standard Form Example.
Finding the Slope of a Line from the Equation This is going to be a lot like what we just did at the end of the last section. So far, I've shown you how to find the slope from the graph and when you .How do you write an equation in slope intercept form for a perpendicular line
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https://iuee.eu/en/3given-4x-8y-8-atransform-the-equation-into-slope-intercept-form-bfind-the-slope-and-y.4628213.html
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math
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3. Given 4x − 8y = 8: (a) Transform the equation into slope-intercept form. (b) Find the slope and y-intercept of the line. (c) Find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point .
C. because to find the equation you have put it in point slope form.
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https://maketoss.com/mathematics-class-8-chapter-11-mensuration-exercise-11-3-ncert-exercise-solution/
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math
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1. There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
Length of cuboidal box (l) = 60 cm
Breadth of cuboidal box (b) = 40 cm
Height of cuboidal box (h) = 50 cm
According to question:
Total surface area of cuboidal box = 2×(lb + bh + hl)
= 2×(60×40 +40×50 + 50×60)
= 14800 cm2
Length of cubical box (l) = 50 cm
Breadth of cubical box (b) = 50 cm
Height of cubical box (h) = 50 cm
Total surface area of cubical box = 6(side)2
= 15000 cm2
Hence, according to the result of (a) and (b), we get that cuboidal box requires the lesser amount of material to make.
2. A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Length of suitcase (l) = 80 cm,
Breadth of suitcase (b)= 48 cm
Height of cuboidal (h) = 24 cm
Total surface area of suitcase box = 2(lb+bh+hl)
= 2 (3840+1152+1920)
= 13824 cm2
Area of Tarpaulin cloth = Surface area of suitcase
l×b = 13824
l ×96 = 13824
l = 144
Required tarpaulin for 100 suitcases = 144×100
= 14400 cm = 144 m
Hence, required tarpaulin cloth to cover 100 suitcases is 144 m.
3. Find the side of a cube whose surface area is 600cm2.
Given, surface area of cube = 600 cm2
From formula we know that,
Surface area of a cube = 6(side)2
6(side)2 = 600
(side)2 = 100
side = ±10
Hence, side cannot be negative. So, the measure of each side of a cube is 10 cm.
4. Rukshar painted the outside of the cabinet of measure 1 m ×2 m ×1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
Length of cabinet (l) = 2 m
Breadth of cabinet (b) = 1 m
Height of cabinet (h) = 1.5 m
Surface area of cabinet except the bottom of the cabinet = lb+2(bh+hl)
= 11 m2
Hence, required surface area of cabinet is 11m2.
5. Daniel is paining the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m2 of area is painted. How many cans of paint will she need to paint the room?
Length of wall (l) = 15 m
Breadth of wall (b) = 10 m
Height of wall (h) = 7 m
Total Surface area of classroom except floor = lb+2(bh+hl )
= 500 m2
Total number of required cans = Area of classroom/Area of one can
= 500/100 = 5
Hence, 5 cans are required to paint the room.
6. Describe how the two figures below are alike and how they are different. Which box has larger lateral surface areas?
Diameter of cylinder (d) = 7 cm
So, radius of cylinder (r) = 7/2 cm [ r = d/2]
Height of cylinder (h) = 7 cm
Lateral surface area of cylinder = 2πrh
= 2 × (22/7) × (7/2) × 7
= 154 cm2
Lateral surface area of cube = 4 (side)2
= 196 cm2
Hence, the cube has larger lateral surface area.
7. A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?
Radius of cylindrical tank (r) = 7 m
Height of cylindrical tank (h) = 3 m
Total surface area of cylindrical tank = 2πr(h+r)
= 44×10 = 440 m2
Hence, 440 m2 metal sheet is required.
8. The lateral surface area of a hollow cylinder is 4224cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
Given, lateral surface area of hollow cylinder = 4224 cm2
Width of rectangular sheet (b) = 33 cm
Let l be the length of rectangular sheet.
Lateral surface area of cylinder = Area of rectangular sheet
4224 = b × l
4224 = 33 × l
l = 4224/33 = 128 cm
Hence, the length of the rectangular sheet is 128 cm.
Perimeter of rectangular sheet = 2(l+b)
= 322 cm
9. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length 1 m.
Diameter of road roller (d) = 84 cm
So, radius of road roller (r) = 84/2 = 42 cm [r = d/2]
Length of road roller (h) = 1 m = 100 cm
Curved surface area of road roller = 2πrh
= 26400 cm2
Area covered by road roller in 750 revolutions = 26400×750cm2
= 1980 m2 [1 m2= 10,000 cm2]
Hence, the area of the road is 1980 m2.
10. A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
Diameter of cylindrical container (d) = 14 cm
So, radius of cylindrical container (r) = 14/2 = 7 cm [r = d/2]
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| 4,487 | 91 |
https://research.chalmers.se/publication/192460
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math
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Generalised Moonshine and Holomorphic Orbifolds
Paper i proceeding, 2015
Generalised moonshine is reviewed from the point of view of holomorphic orbifolds, putting special emphasis on the role of the third cohomology group H^3(G, U(1)) in characterising consistent constructions. These ideas are then applied to the case of Mathieu moonshine, i.e. the recently discovered connection between the largest Mathieu group M_24 and the elliptic genus of K3. In particular, we find a complete list of twisted twining genera whose modular properties are controlled by a class in H^3(M_24, U(1)), as expected from general orbifold considerations.
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| 637 | 3 |
https://www.hindawi.com/journals/aaa/2011/175323/
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math
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Research Article | Open Access
H. Saberi Najafi, A. Refahi Sheikhani, A. Ansari, "Stability Analysis of Distributed Order Fractional Differential Equations", Abstract and Applied Analysis, vol. 2011, Article ID 175323, 12 pages, 2011. https://doi.org/10.1155/2011/175323
Stability Analysis of Distributed Order Fractional Differential Equations
We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.
The fractional differential operator of distributed order is a generalization of the single order which by considering a continuous or discrete distribution of fractional derivative is obtained.
The idea of fractional derivative of distributed order is stated by Caputo and later developed by Caputo himself [2, 3], Bagley and Torvik [4, 5]. Other researchers used this idea, and interesting reviews appeared to describe the related mathematical models of partial fractional differential equation of distributed order.
For example, Diethelm and Ford used a numerical technique along with its error analysis to solve the distributed order differential equation and analyze the physical phenomena and engineering problems, see and references therein.
In particular cases, the characteristics of time-fractional diffusion equation of distributed order were studied for treatises in the sub-, normal, and superdiffusions.
The fractional order applied to dynamical systems is of great importance in applied sciences and engineering [13–19]. The stability results of the fractional order differential equations (FODEs) systems have been a main goal in researches. For example, Matignon considers the stability of FODE system in control processing and Deng has studied the stability of FODE system with multiple time delays [20–23].
Now, in this paper, we consider the distributed order fractional differential equations systems (DOFDEs) with respect to the density function as follows: where , , and is the Caputo fractional derivative operator of distributed order with respect to the order-density function .
Since the solution of the above system is rather complicated similar to FODE systems, therefore, the study of stability for DOFDE is a main task.
In this paper, we introduce three classes of DOFDE systems including (1)distributed order fractional differential systems;(2)distributed order fractional differential evolution systems with control vector; (3)distributed order fractional differential evolution systems without control vector.
For studying the stability of these classes of DOFDE systems, first, we introduce a characteristic function of a matrix with respect to the distribute function where . Then, we establish a general theory based on new inertia concept for analyzing the stability of distributed order fractional differential equations. The concepts and theorems presented in this paper for DOFDE systems can be considered as generalizations of FODE and ODE systems [21, 24, 25].
In Section 2, we recall some basic definitions of the Caputo fractional derivative operator, the Mittag-Leffler function, and their elementary properties used in this paper. Section 3 contains the main definitions and theorems for checking the stability of DOFDE systems. Also, we study a distributed order fractional WINDMI system generalized from fractional order to distributed order fractional. In Section 4, we introduce the distributed order fractional evolution systems where is control vector, and generalize the results obtained in Section 3 for this case. Finally, the conclusions are given in the last section.
2. Elementary Definitions and Theorems
In this section, we consider the main definitions and properties of fractional derivative operators of single and distribute order and the Mittag-Leffler function. Also, we recall two important theorems in inverse of the Laplace transform.
2.1. Fractional Derivative of Single and Distributed Order
The fractional derivative of single order of in the Caputo sense is defined as [16, 27] for . The Caputo's definition has the advantage of dealing properly with initial value problems in which the initial conditions are given in terms of the field variables and their integer order which is the case in most physical processes. Fortunately, the Laplace transform of the Caputo fractional derivative satisfies where and is the Laplace variable. Now, we generalize the above definition in the fractional derivative of distributed order in the Caputo sense with respect to order-density function as follows: and the Laplace transform of the Caputo fractional derivative of distributed order satisfies where
2.2. Mittag-Leffler Function
The one-parameter Mittag-Leffler function and the two-parameter Mittag-Leffler function , which are relevant for their connection with fractional calculus, are defined as One of the applicable relations in this paper is the Laplace transforms of the Mittag-leffler function given by
2.3. Main Theorems about Inverse of the Laplace Transform
Theorem 2.1 (Schouten-Vanderpol Theorem ). Suppose that the functions are analytic in the half plane , then, the Laplace transform inversion of can be obtained as where is the Laplace transform inversion of the function .
Theorem 2.2 (Titchmarsh Theorem ). Let be an analytic function which has a branch cut on the real negative semiaxis; furthermore, has the following properties: for any sector where . Then, the Laplace transform inversion can be written as the the Laplace transform of the imaginary part of the function as follows:
Theorem 2.3 (Final Value Theorem ). Let be the Laplace transform of the function . If all poles of are in the open left-half plane, then,
3. Stability Analysis of Distributed Order Fractional Systems
In this section, we generalize the main stability properties for the linear system of distributed order fractional differential equations in the following form: where , the matrix , and is the Caputo fractional derivative operator of distributed order with respect to order-density function . At first, we obtain the general solution of the system (3.1), and, next, we express the main theorem for checking the stability of this system.
By implementation of the Laplace transform on the above system and using the initial condition and relation (2.4), we have Now, by applying the inverse of Laplace transform on the both sides of above relation, we have which according to the Schouten-Vanderpol and Titchmarsh theorems we get where , , , and .
Theorem 3.1. The distributed order fractional system of (3.1) is asymptotically stable if and only if all roots of have negative real parts.
Proof. According to the relation (3.2), we have if all roots of the lie in open left half complex plane (i.e., ), then, we consider (3.7) in . In this restricted area, the relation (3.7) has a unique solution . Since , so we have which from the final value Theorem 2.3, we get The above result shows that the system (3.1) is asymptotically stable.
Definition 3.2. The value of is the characteristic function of the matrix with respect to the distributed function , where is the distributed function with respect to the density function .
Definition 3.3. The eigenvalues of with respect to the distributed function are the roots of the characteristic function of .The inertia of a matrix is the triplet of the numbers of eigenvalues of with positive, negative, and zero real parts. In this section, we generalize the inertia concept for analyzing the stability of linear distributed order fractional systems. According to the Theorem (3.1), the transient responses of the system (3.1) are governed by the region where the roots of are located in the complex plane.
Definition 3.4. The inertia of a matrix of order respect to the order distributed function is the triplet where , , and are, respectively, the number of roots of with positive, negative, and zero real parts where .
Definition 3.5. The matrix is called a stable matrix with respect to the order distributed function , if all of the eigenvalue of A with respect to the distributed function have negative real parts.
Theorem 3.6. The linear distributed order fractional system (3.1) is asymptotically stable if and only if any of the following equivalent conditions holds. (1)The matrix is stable with respect to the distribute function . (2). (3)All roots of the characteristic function of with respect to the distributed function satisfy .
Proof. According to Theorem 3.1 and the above definitions, proof can be easily obtained.
Remark 3.7. In special case, if , where and is the Dirac delta function, then, we have the following linear system of fractional differential equations: and . Also, the characteristic matrix and characteristic equation of (3.11) are reduced to and , respectively. Let be , then , and, by using Theorem 3.6, we have . Thus, all the roots of equation satisfy . This result is Theorem 2 of . Here, we can very easily prove it by using Theorem 3.6 of the present paper. Particularly, if , then, we have a linear system . In this case, and the characteristic function of (3.1) are . Also, the inertia of matrix is a triplet , where , , and are, respectively, the number of eigenvalues of with positive, negative, and zero real parts. This result is a special case of definition (3.4), which agrees with the typical definitions for typical differential equations.
Example 3.8. The solar-wind-driven magnetosphere-ionosphere (WINDMI) system is a complex driven-damped dynamical system which exhibits a variety of dynamical states that include low-level steady plasma convection, episodic releases of geotail stored plasma energy into the ionosphere known broadly as substorms, and states of continuous strong unloading [30, 31]. If we consider the integer-order WINDMI model as follows: where , , and are variables and , are positive constants, the corresponding distributed order fractional WINDMI system (3.12) can be written in the form: where is the density function. As a generalization of nonlinear autonomous FODE into nonlinear autonomous DOFDE, the linearized form of the system (3.13) at the equilibrium point , that is, , can be written in the form where , , and , which is the Jacobian matrix at the equilibrium point , is given by Now, for analyzing the stability of the nonlinear autonomous DFODE, we compute in the case that the density function varies. The results are shown in Table 1 for some parameters and .
4. Distributed Order Fractional Evolution Systems
In this section, as a generalization of the previous systems, we consider the systems of distributed order fractional differential evolution equations and state two theorems in stability of these systems.
Theorem 4.1. Consider linear system of distributed order fractional differential evolution equations, where , , and . Also, and . The system (4.1) is stable if and only if all roots of characteristic function of matrix with respect to the distributed function have negative real parts.
Proof. Taking the Laplace transform on both sides of (4.1) gives If all roots of characteristic function of matrix with respect to the distributed function have negative real parts,that is, , then, we consider (4.2) in . In this restricted area by using final-value theorem of Laplace transform, we have
Theorem 4.2. Consider the linear system of distributed order fractional differential evolution equations with the same hypotheses described in Theorem 4.1 where and is a control vector.The linear distributed order fractional system (4.4) is stabilizable if and only if there exists a linear feedback , with , such that is stable with respect to the distributed function .
Proof. The proof can be easily expressed similar to Theorem 4.1.
Remark 4.3. If and where then (4.4) is reduced to the following linear system of fractional differential equations: By applying the Laplace transform on the above system and using the initial condition, we have where is the Laplace transform of , is the Laplace transform of , and . Thus, we can write as, Applying the inverse Laplace transform to (4.7) and using property (2.8), we get Therefore, (4.5) is asymptotically stable if all eigenvalues of with respect to the distributed function have negative real parts which is a special case of Theorem 4.2.
5. Conclusions and Future Works
In this work, we introduced three classes of the distributed order fractional differential systems, the distributed order fractional differential evolution systems with control vector, and the distributed order fractional differential evolution systems without control vector. The analysis of the asymptotically stability for such systems based on Theorem 3.1 and several interesting stability criteria are derived according to Theorem 3.6. Moreover, a numerical example was given to verify the effectiveness of the proposed schemes.
In view of the above result, for future works, our attention may be focused on generalizing the numerical methods for computing the eigenvalues of a matrix with respect to the distributed function. The proposed algorithms in [33–35] for computing the eigenvalues of a matrix may be effective in this case.
- M. Caputo, Elasticitá e Dissipazione, Zanichelli, Bologna, Italy, 1969.
- M. Caputo, “Mean fractional-order-derivatives differential equations and filters,” Annali dell'Università di Ferrara. Nuova Serie. Sezione VII. Scienze Matematiche, vol. 41, pp. 73–84, 1995.
- M. Caputo, “Distributed order differential equations modelling dielectric induction and diffusion,” Fractional Calculus & Applied Analysis, vol. 4, no. 4, pp. 421–442, 2001.
- R. L. Bagley and P. J. Torvik, “On the existence of the order domain and the solution of distributed order equations,” International Journal of Applied Mathematics, vol. I, no. 7, pp. 865–882, 2000.
- R. L. Bagley and P. J. Torvik, “On the existence of the order domain and the solution of distributed order equations,” International Journal of Applied Mathematics, vol. II, no. 7, pp. 965–987, 2000.
- K. Diethelm and N. J. Ford, “Numerical analysis for distributed-order differential equations,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 96–104, 2009.
- A. Aghili and A. Ansari, “Solving partial fractional differential equations using the ℒA-transform,” Asian-European Journal of Mathematics, vol. 3, no. 2, pp. 209–220, 2010, World Scientific Publishing.
- A. V. Chechkin, R. Gorenflo, and I. M. Sokolov, “Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations,” Physical Review E, vol. 66, no. 4, article 046129, pp. 1–7, 2002.
- A. N. Kochubei, “Distributed order calculus and equations of ultraslow diffusion,” Journal of Mathematical Analysis and Applications, vol. 340, no. 1, pp. 252–281, 2008.
- F. Mainardi and G. Pagnini, “The role of the Fox-Wright functions in fractional subdiffusion of distributed order,” Journal of Computational and Applied Mathematics, vol. 207, no. 2, pp. 245–257, 2007.
- F. Mainardi, G. Pagnini, and R. K. Saxena, “Fox functions in fractional diffusion,” Journal of Computational and Applied Mathematics, vol. 178, no. 1-2, pp. 321–331, 2005.
- S. Umarov and R. Gorenflo, “Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations,” Zeitschrift für Analysis und ihre Anwendungen, vol. 24, no. 3, pp. 449–466, 2005.
- O. P. Agrawal, J. A. Tenreiro Machado, and J. Sabatier, “Introduction,” Nonlinear Dynamics, vol. 38, no. 1-2, pp. 1–2, 2004.
- B. Bonilla, M. Rivero, L. Rodríguez-Germá, and J. J. Trujillo, “Fractional differential equations as alternative models to nonlinear differential equations,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 79–88, 2007.
- P. L. Butzer and U. Westphal, An Introduction to Fractional Calculus, World Scientific, Singapore, Republic of Singapore, 2000.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science Publishers, Amsterdam, The Netherlands, 2006.
- R. L. Magin, “Fractional calculus in bioengineering,” Critical Reviews in Biomedical Engineering, vol. 32, no. 1, pp. 1–104, 2004.
- T. Matsuzaki and M. Nakagawa, “A chaos neuron model with fractional differential equation,” Journal of the Physical Society of Japan, vol. 72, no. 10, pp. 2678–2684, 2003.
- G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005.
- W. Deng, “Smoothness and stability of the solutions for nonlinear fractional differential equations,” Nonlinear Analysis: TMA, vol. 72, no. 3-4, pp. 1768–1777, 2010.
- W. Deng, C. Li, and J. Lü, “Stability analysis of linear fractional differential system with multiple time delays,” Nonlinear Dynamics, vol. 48, no. 4, pp. 409–416, 2007.
- D. Matignon, “Stability results of fractional differential equations with applications to control processing,” in Proceedings of the IEEE-SMC International Association for Mathematics and Computers in Simulation (IMACS '96), pp. 963–968, Lille,France, 1996.
- M. S. Tavazoei and M. Haeri, “A note on the stability of fractional order systems,” Mathematics and Computers in Simulation, vol. 79, no. 5, pp. 1566–1576, 2009.
- B. N. Datta, “Stability and inertia,” Linear Algebra and its Applications, vol. 302/303, pp. 563–600, 1999.
- Z. M. Odibat, “Analytic study on linear systems of fractional differential equations,” Computers and Mathematics with Applications, vol. 59, no. 3, pp. 1171–1183, 2010.
- B. Xin, T. Chen, and Y. Liu, “Synchronization of chaotic fractional-order WINDMI systems via linear state error feedback control,” Mathematical Problems in Engineering, vol. 2010, Article ID 859685, 10 pages, 2010.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- D. G. Duffy, Transform Methods for Solving Partial Differential Equations, CRC Press, 2nd edition, 2004.
- A. V. Bobylev and C. Cercignani, “The inverse laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation,” Applied Mathematics Letters, vol. 15, no. 7, pp. 807–813, 2002.
- W. Horton, R. S. Weigel, and J. C. Sprott, “Chaos and the limits of predictability for the solar-wind-driven magnetosphere-ionosphere system,” Physics of Plasmas, vol. 8, no. 6, pp. 2946–2952, 2001.
- W. Horton and I. Doxas, “A low-dimensional dynamical model for the solar wind driven geotail-ionosphere system,” Journal of Geophysical Research A, vol. 103, no. A3, pp. 4561–4572, 1998.
- Y. Yu, H.-X. Li, S. Wang, and J. Yu, “Dynamic analysis of a fractional-order Lorenz chaotic system,” Chaos, Solitons and Fractals, vol. 42, no. 2, pp. 1181–1189, 2009.
- H. S. Najafi and A. Refahi, “A new restarting method in the Lanczos algorithm for generalized eigenvalue problem,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 421–428, 2007.
- H. S. Najafi and A. Refahi, “FOM-inverse vector iteration method for computing a few smallest (largest) eigenvalues of pair (),” Applied Mathematics and Computation, vol. 188, no. 1, pp. 641–647, 2007.
- H. S. Najafi, A. Refahi, and M. Akbari, “Weighted FOM-inverse vector iteration method for computing a few smallest (largest) eigenvalues of pair (),” Applied Mathematics and Computation, vol. 192, no. 1, pp. 239–246, 2007.
Copyright © 2011 H. Saberi Najafi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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http://www.residentadvisor.net/feed-item.aspx?id=63443
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math
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Fri, 03 May 2013 / Max_CherryThis 11-minute video recaps Hawtin's recent trip to Cape Town and Johannesburg with Bridges For Music. More ›
Fri, 03 May 2013 / terrencefullerThe American music industry giant is poised to acquire roughly 50% of A-list EDM promoter Insomniac Events, according to Los Angeles Times.
Sat, 04 May 2013 / RAThe new producer delivers a dreary (in a good way) deep house mix for Trace A Line.
Fri, 03 May 2013 / BirdmanzzHere's a video interview with the man credited with inventing the 12-inch and the break.
Fri, 03 May 2013 / RAThe London producer, who debuted on Sound Signature last year, turns in a sunny and eclectic mix for Hyponik.
Fri, 03 May 2013 / CopeSpeaking to Billboard, The Black Dog, Jerome Sydenham, Peter Van Hoesen and Cosmin TRG reveal their prize picks from the defunct label's back catalogue.
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http://pqcourseworkvbci.fieldbee.us/questions-and-case-problem.html
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math
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Case study 11—sebring county decision making and problem solving has no asks you to answer questions that apply to what you have learned in the. Writing legal essays and answering problem questions for question, in order to argue that the case should or could be distinguished answering law questions. Read example case study questions and find out how to prepare for this type of question at interview. A selection of medical ethics cases designed to help determine the physicians inform her that the only way to fix the problem is questions for case 1. Contract problem sample answer-1 it is not necessary to give the facts of every case the law should be applied to the facts of the problem question. A case is a scenario that gives you the opportunity to identify problems and recommend a course of action in a business situation the case may be. How to develop and demonstrate your problem-solving skills we all solve problems on a case questions are business problems designed not only to test your.
Samples – problem questions – contract law in this section we have provided four sample answers to a problem question in contract law to illustrate how answers. Free problem question answers great examples of problem questions and answers from the experts at law teacher. Great tips about interview questions that can be used to make your case case study tips: interview questions case studies can describe the problem your. The trolley problem is a thought in the case of the riots the the central question that these dilemmas bring to light is on whether or not it is. Guidelines on how to approach the issues in and solutions to the case problem will with guiding questions to be answered about the case. Sample case answers back-of-the-envelope and market-sizing assumptions it seems like you’re having fun with this question yes i love problems like this.
C-4 cases in strategic management and problems in the case the study questions and the case preparation exercises provided in the. Arterial blood gas case questions and answers than see a physician about this, he opted to deal with the problem on his own and, over the past week.
Problem solving techniques-case study techniques of problem solving 6 case study on value chain tool gmat problem solving questions 8d. Browse what the apple store community is saying about iphone or submit your own question to the community.
Examples of common case study interview questions and answers learn the correct answers for case study questions. How to crack a case-study interview how you approach a problem and how well you work with others let's move on with a question.
The problem of franklin is 1) questions:-narrate the case with suitable title for the case please send to [email protected] reply.
Case study interview questions - learn hr interview questions in simple and easy steps starting from hr interview questions, behavioral questions, general interview. This article is for the beginners who have just begun programming in the c# language with solutions for all the basic problems of the c# programming. Problem solving questions measure your ability to solve numerical problems, interpret graphical data, and evaluate information. Fundamentally, answering problem questions in contract does not differ from answering such questions in any other area of law in any legal subject, you should begin. Practice the case studies one example of this type of test is our mckinsey problem solving it consists of 26 questions, is based on real mckinsey client. Case workbook © 2006 accenture goal: articulate key case problem your ability to ask insightful questions listen to case clarify problem decompose problem test.
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| 3,696 | 7 |
https://japanese.stackexchange.com/questions/70132/meaning-of-%e3%81%a0%e3%81%91%e3%81%af%e3%82%8f%e3%81%8b%e3%82%89%e3%81%aa%e3%81%84
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math
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I'm translating the above sentence from Japanese to English, and I'm having issues with understanding what だけはわからない means.
Why does だけ come before は? says that だけは means 'at least'; and https://jisho.org/search/だけは supports this with a definition of 'at least not (when followed by a negative)'. I know that わからない means 'to not understand' as its わかる in the negative form. When I tried to translate the above, the resulting sentence made barely any sense (Example 1) or it failed to convey the 'abstracting focusing' aspect of のこと (Example 2).
1) Even so, he understands anything but not what is only about himself.
2) Still, he at least doesn’t understand himself.
What do I need to know in order to properly understand what だけはわからない means in the above sentence?
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CC-MAIN-2024-18
| 837 | 5 |
https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-36-number-4-5-2021/mvlsc-36-4-5-p-455-504/
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math
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Strong Subalgebras and the Constraint Satisfaction Problem
In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP) over a constraint language Γ is tractable if and only if Γ is preserved by a weak near-unanimity (WNU) operation. After many efforts and partial results, this conjecture was independently proved by Andrei Bulatov and the author in 2017. In this paper we consider one of two main ingredients of my proof, that is, strong subalgebras that allow us to reduce domains of the variables iteratively. To explain how this idea works we show the algebraic properties of strong subalgebras and provide self-contained proof of two important facts about the complexity of the CSP. First, we prove that if a constraint language is not preserved by a WNU operation then the corresponding CSP is NP-hard. Second, we characterize all constraint languages that can be solved by local consistency checking. Additionally, we characterize all idempotent algebras not having a WNU term of a concrete arity 𝑛, not having a WNU term, having WNU terms of all arities greater than 2. Most of the results presented in the paper are not new, but I believe this paper can help to understand my approach to CSP and the new self-contained proof of known facts will be also useful.
Keywords: Constraint satisfaction problem, CSP Dichotomy conjecture, weak near-unanimity, computational complexity, strong subalgebras
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| 1,423 | 3 |
https://www.spanishdict.com/answers/6281/two-verbs-in-a-sentence
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math
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Two verbs in a sentence
How do I put two verbs in a sentence, like:
I want to learn how to speak Spanish.
Okay, so that would be 3. But you know. =P
I just need to know if you conjugate them all.
Quiero que sepas que lo voy a comprar.
I also know the rules for Gustar and Encantar (etc. ) if that's what LadyDi means about not all verbs working like that. =)
Ah, okay. =) Thankyou. I'll just give my composition to my spanish teacher and see what she says. Thanks!
Ah, okay. =) Thankyou.
I'll just give my composition to my spanish teacher and see what she says.
Quiero aprender a hablar español...(It's not always like this though. It depends on what verbs you use.)
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| 668 | 11 |
https://mikesmathpage.wordpress.com/2014/08/24/fibonacci-factorials/
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math
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As part of the publicity around the Fields Medal announcement, the American Mathematical Monthly’s Facebook page pointed out this paper written by Manjul Bhargava in 2000:
The Factorial Function and Generalizations
The reason that this paper caught my attention is that I actually felt like I had a prayer of understanding the ideas that the paper was explaining. I’m sure, of course, that the work of all of the 2014 Fields Medal winners is off the charts brilliant, but when I searched for lectures or papers by them everything but this paper was miles over my head. So many miles, actually, that the factorial function might come in handy if I needed to describe that distance accurately!
One particularly helpful example that Bhargava gives in the paper is on top of the 6th page (page number 788) where he calculates the first six values of the generalized factorial function over the primes. Since he said that it was “an easy matter to compute” these six values, I thought that replicating this calculation would be a fun way to see if I had understood some bits of the paper. After a few times through the paper I finally had understood the ideas well enough to replicate the calculation, so yay! I was also surprised to see that those six numbers (1,1,2,24,48, and 5760) appear in the On-line Encyclopedia of Integer Sequences only once (and without reference to Bhargava’s result):
Is this the full generalized factorial function over the primes?
I don’t know if the full sequences would match each other (or, obviously, why that sequence would arise from the Taylor series of ) but at least my calculation of the next term in Bhargava’s sequence does match the next term in the OEIS example.
So, having (hopefully) understood how to calculate this generalized factorial function over the primes, I wanted to try it for another sequence of integers. The Fibonacci numbers seemed like as good a place as any to start, so I gave that a shot this weekend. Unluckily I was traveling this weekend, but still found a little time early this morning at the Lone Wolf diner in Amherst, MA to get things going while enjoying their Santa Fe omelette. According to my calculations, Bhargava’s factorial function over the Fibonacci numbers would evaluate as follows:
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 240
6! = 720
7! = 443,520 ()
8! = 443,520 (yes, the same as 7!. That’s a surprise, but I haven’t been able to see the mistake)
9! = = 103,783,680
10! = = 1,037,836,800
[edit note: after publishing earlier today, I noticed that I left of the 13 on both 9! and 10! ]
Fingers crossed that these are the correct calculations but since I slept at a farm last and was woken up early by roosters, it wouldn’t be super surprising if there was an error 🙂 In any case, one interesting thing that I learned playing around with this is that the Fibonacci numbers have an interesting pattern modulo 11. I’m hoping to play around with this and other sequences in the next month. I think there is a really fun project for kids hiding in here somewhere, too.
2 thoughts on “Fibonacci Factorials”
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https://blog.amazewriters.com/3-in-a-study-the-data-you-collect-is-letter-grade-a-b-c-d-f-what-is-the-level-of-measureme/
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math
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(3) In a study, the data you collect is: Letter grade (A, B, C, D, F)
What is the level of measurement?
(4) Determine whether the value 85% is a parameter or statistic:
85% of registered voters turned out for the 2004 elections
(7) Engineers must consider the breadths of male heads when designing helmets The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 62-in and a standard deviation of 09-in
In what range would you expect to find the middle of 68% of most head breadths?
Between ___________ and ____________
If you were to draw samples of size 60 from this population, in what range would you expect to find the middle 68% of most averages for the breadths of male heads in the sample?
Between _____________ and ___________
Should be accurate to 2 decimal places
(8) A survey of students at a high school is conducted, and the following facts are discovered: 36% of the students have laptops, 47% have tablets, and 26% of the students own both a laptop ad a tablet A student is chosen at random from the high school: What is the probability that the student owns either a laptop or a tablet?
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| 1,193 | 11 |
https://e2e.ti.com/support/microcontrollers/msp-low-power-microcontrollers-group/msp430/f/msp-low-power-microcontroller-forum/627558/msp430f5509-the-change-about-the-zhcs897g-uart-bsl?ReplyFilter=Answers&ReplySortBy=Answers&ReplySortOrder=Descending
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math
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Could you help explain why have this change？ Detail please see following informationt. Why apply a 1M resistor to ground?
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https://www.physicsforums.com/threads/work-energy-questions.7535/
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math
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1) An 80-N box is pulled 20m up a 30 degree incline by an applied force of 100 N that points upward, parallel to the incline. If the coefficient of kinetic friction between box and incline is 0.220, calculate the change in the kinetic energy of the box. I made a triangle sketch, obviously, 30 degrees in the lower left corner. One of my big problems is I'm not sure what they mean by "80-N box." Does that mean it's a force of 80 N straight down, or is that like a force perpendicular against the incline? I used muK = Ff-Fn to find an Ff of 80.220 N. Then I did something with FcosΘ=work, and somehow came up with 86.6 J. I really don't know what I'm doing, and I have no correct answer listed anywhere, so I have no direction. Help! 2)A 70kg diver steps off a 10m tower and drops, from rest, straight down into the water. If he comes to rest 5.0m below the surface, determine the average resistance force exerted on him by the water. I used vf^2=vi^2 + 2ad to get his initial velocity at the water (I got 14 m/s) but after that I'm clueless as to what to do next. Any help you can provide me would be great, I'm going to re-read the chapter. I've been sick from school for a few days, so I'm really behind and lost here.
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| 1,224 | 1 |
http://forums.wolfram.com/mathgroup/archive/1996/Dec/msg00132.html
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math
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mathematica for linux
- To: mathgroup at smc.vnet.net
- Subject: [mg5589] mathematica for linux
- From: W.Hitzl at uibk.ac.at (Wolfgang Hitzl)
- Date: Fri, 27 Dec 1996 01:59:01 -0500
- Organization: University of Innsbruck, Austria
- Sender: owner-wri-mathgroup at wolfram.com
I consider to use mathematica for linux on my PC. So can somebody share
his/hers experience with mathematica for linux to me?
1) does the front end run under X-windows?
2) what advantages/disadvantages does mathematica for linux has?
Your help would be very appreciated
many wishes from Austria
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https://www.hackmath.net/en/math-problem/4355
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math
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One-eighth of 9th class was interested in studying at a grammar school, at a business academy one sixth, at secondary vocational schools quarter, to SOU one third and the remaining three students were interested in the school of art direction. How many students are in the classroom?
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Three consecutive sheets dropped from the book. The sum of the numbers on the pages of the dropped sheets is 273. What number has the last page of the dropped sheets?
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https://dspace.mit.edu/handle/1721.1/110173
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math
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Multiplicative functionals on ensembles of non-intersecting paths
Author(s)Borodin, Alexei; Corwin, Ivan; Remenik, Daniel
MetadataShow full item record
The purpose of this article is to develop a theory behind the occurrence of “path-integral” kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants involving such kernels arise naturally in studying ratios of partition functions and expectations of multiplicative functionals for ensembles of non-intersecting paths on weighted graphs. Our second result shows how Fredholm determinants with extended kernels (as arise in the study of extended determinantal point processes such as the Airy[subscript 2] process) are equal to Fredholm determinants with path-integral kernels. We also show how the second result applies to a number of examples including the stationary (GUE) Dyson Brownian motion, the Airy[subscript 2] process, the Pearcey process, the Airy[subscript 1] and Airy[subscript 2→1] processes, and Markov processes on partitions related to the zz-measures.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Annales de l Institut Henri Poincaré Probabilités et Statistiques
Institute of Mathematical Statistics
Borodin, Alexei, Ivan Corwin, and Daniel Remenik. “Multiplicative Functionals on Ensembles of Non-Intersecting Paths.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 51, no. 1 (February 2015): 28–58. © 2015 Association des Publications de l’Institut Henri Poincaré
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https://philosophy.stackexchange.com/questions/36079/eulers-1746-philosophy-paper
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math
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In 1746, Euler, a famous mathematician, published what I believe to be a little-known philosophy paper. It seems interesting, but it is difficult for me to follow as I lack adequate philosophy background. Euler reduces his argument to a simple syllogism. Can anyone explain and summarize his argument, and perhaps comment on his paper as a whole?
1st premise : No body can have a force contrary to inertia.
Based on [Engl.transl.,page 2] analysis of "current" (still quite incomplete) understanding of matter and bodies and of knowledge of only a few of their properties.
The first property that comes to mind is extension; all philosophers recognize it as a property of body, and Cartesians consider it to be the essence of bodies. [...] if it can be demonstrated that extension and thought stand in contradiction, and thus the two cannot exist in the same being at the same time, then it would beproven that whatever has extension is thereby incapable of possessing thought.
[page 3] Another property of matter is impenetrability, which is so characteristic of bodies that many philosophers have not hesitated to make it, together with extension, the essence of body. Indeed, no thing that has extension but lacks impenetrability can be considered a body.
I move now to the third property of all matter, as widely acknowledged as the two already mentioned, and which seems much more closely connected to the innermost nature of bodies. I understand that the force of inertia [vis inertiae] was discovered first by Kepler, but then explained by Newton, who derived from it the principles of all mechanics.
[page 6] However, even though the force of inertia completely excludes all other forces, for the matter at hand I will not assume anything except that two forces diametrically opposed to each other are not able to exist in the same entity. Therefore, since each body is endowed with the force of conservation of state, a contrary force — namely, the force of continual change of state —, cannot be admitted to exist in any body.
Comment: see the discussion [page 5] about "the force of attraction — with which bodies are endowed, in the opinion of English philosophers [the Newtonians] — can easily be disproven." Gravitation is not, according to Euler, an intrinsic property of matter but must be explained in some way: either mechanically (see the Cartesian vortex theory) or by intervention of some external "active power", like in Leibniz.
Yet if we consider with even a moment’s notice the faculty of thought [facultatem cogitandi], we will at once realize that in no way could it exist without the force of change of state. [...] Since the faculty of thought is intimately connected with the force of changing state, and a force of this sort cannot be conceived to exist in any body without contradiction, it evidently follows that no body can be endowed with the faculty of thought. From which there is a further conclusion: since the thing in us that we perceive does the thinking is called the soul [anima], the soul is not only not material, but is in fact a substance completely different from body, because it is endowed with a force directly opposed to those forces which can exist in a body.
Comment: we have here a cartesian approach: the autonomous capability of a living being to move itself is due not to the body [i.e. matter] alone but to soul. It is interesting to note that Euler is equating soul with the "faculty of thought"; what about animals' capability of self-motion ? According to Descartes, there is no mind or soul in animals.
The argument above licenses the:
2nd premise : The faculty of thought is a force contrary to inertia.
Now the conclusion of the syllogism easily follows:
Conclusion : Therefore, no body can possess the faculty of thought,
concluding the argument:
that denies the faculty of thought to bodies and proves the immateriality of the soul.
The "syllogism" runs as follows:
1st premise) ∀y ¬∃x [Body(x) & Force(y) & Contrary-to-Inertia(y) & Possess(x,y)]
2nd premise) Force(Thought) & Contrary-to-Inertia(Thought)
We instantiate 1) with Thought for y having:
3) ¬ [Body(x) & Force(Thought) & Contrary-to-Inertia(Thought) & Possess(x,Thought)]
that, by tautological implication, amounts to:
4) ¬ (Force(Thought) & Contrary-to-Inertia(Thought)) ∨ ¬ (Body(x) & Possess(x,Thought)).
From 2) and 4), by modus tollens, we derive:
5) ¬ (Body(x) & Possess(x,Thought))
that amounts to:
6) Body(x) → ¬ Possess(x,Thought).
Finally, we "generalize" to conclude with:
∀x [Body(x) → ¬ Possess(x,Thought)].
See also: Stephen Gaukroger, The Metaphysics of Impenetrability: Euler's Conception of force (1982).
At least the English translation talks about bodies and matter as if they were identical. It leaves me wondering how to make sense of his explanations for a block ice, which first get heated until it melts, and then get heated further until it evaporates. Is it still impenetrable after it has evaporated? Or do Euler's arguments only apply to solid bodies? But if they only apply to solid bodies, then do they also apply to solid bodies which contain fluids (or freely moving electrons)? Or what about elaborate mechanical mechanisms with suitable hinges to allow certain internal movements?
None of the criticisms voiced above relies on new knowledge not yet available to Euler. How should a conclusion be valid, if we don't even know what the conclusion is supposed to mean?
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CC-MAIN-2021-17
| 5,458 | 32 |
https://find-mba.com/average-gmat-scores-at-mba-programs-worldwide
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math
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Average GMAT Scores at MBA Programs Worldwide
The GMAT is an important requirement for many MBA programs. While many schools provide information about the minimum GMAT score required to apply for an MBA program, looking at the average GMAT scores for admitted candidates can often be more informative. If you know what the average GMAT score is at an MBA program you're applying to, you'll have a good idea about what score would be considered competive.
See below for a listing of average GMAT scores at some top MBA programs worldwide.
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CC-MAIN-2024-18
| 537 | 3 |
https://www.progressivegardening.com/agricultural-engineering-2/system-capacity.html
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math
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System capacity is the maximum amount of water that an irrigation system can deliver on a continuous basis. Different units are used to describe system capacity. These are acre-feet (ac-ft, that is, the amount of water it will take to cover one acre, one foot deep), acre-inch (ac-in), gallons per minute (gal/min or gpm), and cubic feet per second (ft3/sec or cfs). The required pumping capacity of an irrigation system depends on the area to be irrigated (ac), the depth of water to apply (in), and the length of time that the irrigation system is operated (hr). Length of operation time refers to pumping time, not clock time. Pumping time is only the time water is flowing.
The amount of time per day that an irrigation system can operate depends on the type of system and the amount of maintenance it requires. A self-propelled unit may be able to run several days without stopping, whereas manual-move, tractor towed, and self-moved systems must be shut down at regular intervals. For systems other than center pivots and lateral moves, only a portion of a field is irrigated at one time and time is required to move the system from one portion of the field "set" to another "set." The term irrigation period is used to designate the number of days that a system can apply the water for one irrigation to a given area. Note that it is necessary for the irrigation period to be equal to or less than the irrigation interval. The required capacity of a system, in gallons per minute, can be determined by the following equation:
where RSC = Required system capacity (gal/min); 450 = Units conversion constant; A = Area irrigated (ac); DWA = Depth of water to apply per irrigation (in); IRP = Irrigation period (day); HPD = Time operating (hr/day).
Problem: Determine the required system capacity (gal/min) for the corn crop in the previous problem when the field area is 200 acres, and the system can operate for 18.0 hr per day for 7.7 days.
For 200 acres of long-season corn grown on silt loam soil over compacted subsoil, irrigated with a system that is 70% efficient and limited to operating 18 hours per day for 7.7 days, the system must be able to deliver 3,040 gallons of water per minute.
Note: This is an example of an equation with a units conversion constant. The same problem can be solved using the units cancellation method.
min 60 min 18 hr 7.7 day 231 in3 1
144 in2 43560 ft2 200 ac 5833555200
1 ft2 1 ac 1 1920996
In some situations it might be necessary to use units of capacity other than gallons per minute. For example, water supplied from a large reservoir is often measured in acre-feet. In these cases, units cancellation and/or the appropriate conversion factors (Appendix I or II) can be used to convert the units.
Problem: What will the system capacity need to be in units of acre-feet/min?
Solution: Using units cancellation and system capacity from the previous problem:
ac-ft gal 1 ft3 1 ac
min min 4.48 gal 43,560 ft2
As noted earlier, system capacity is a function of four variables: area (ac); water flow rate (gal/min, ft3/min, ac-ft/min, etc.); depth of water applied or peak use (in); and time (min, hr, or days). This relationship is expressed mathematically as:
where D = Depth of water, either applied or peak use (in); A = Area irrigated (ac); Q = Water flow rate (cfs); T = Length of time water is applied (hr).
When any three of the variables are known, the remaining one can be calculated by rearranging the equation and substituting the values of the known variables. You must enter flow rate (Q) in cubic feet per second, depth in inches, and time in hours. The following discussion will illustrate several uses of this equation.
In the previous problem we determined the system capacity using units cancellation. If it is necessary to know how much water has been applied, the peak use does not accurately describe what we are solving for. When we want to know the depth of water that has been applied, D becomes the depth of water applied (DWA). This will work because the unit of measure is the same for both peak use and DWA (inches).
Problem: A producer spends 120 hr irrigating 90.0 acres. The pump discharges 1,350 gallons per minute. What average depth of water (in) is applied?
Solution: Because we want to know the amount of water applied, not the amount available to the plants, the efficiency factor is not used. Also, Q must be converted from gal/min to ft3/sec. Rearranging the equation, substituting depth of water to apply (DWA) for the depth (D), and including the conversion factor
1 ft3/sec = 2.25 x 10—3 gal/min1: DWA x A = Q x T Q x T
An examination of this problem shows that the units do not cancel. However, when we enter the values of the variables with the units listed above we can obtain an answer very close to the true value. The symbol = means approximately equal. The exact solution using unit conversion/cancellation is:
1,350 37- x 231 — x __ . 3 ) x 120 hr x 60 — 12 —
90 ac x 43,560
In this case, the error in the approximate solution is:
Variations occur in the use of the equation for different types of irrigation systems. In situations where the limiting factor is the availability of water, the problem is to determine the maximum area that can be irrigated with the available water supply.
Problem: What is the largest size of lawn (ft2) that can be irrigated in 12 hr if a minimum of 0.5 inch of water is applied at each irrigation, the system is 90% efficient, and the water supply delivers 3.5 gal/min?
ft3 1 gal 1 rnin 1ft3 3 ft3 1 eal 2.25 x 10—3 ft3
Iff- = 1gal x ^m x - = 2.25 x 10—3 —then1gal = -
sec min 60.0 sec 7.40 gal sec mln 1 sec
Solution: Rearranging the equation, adding the efficiency factor, and converting the area to square feet:
If flood irrigation is used to water a field, assuming that the water flow rate is limited, it usually is necessary to determine the amount of time that the water should flow to cover the field at the desired depth.
Problem: How long will it take to apply 4 inches of water uniformly over 120 acres when the water is available at the rate of 20 cfs? (Assume 100% efficiency.)
ac ft3 sec min
sec min h
During furrow irrigation it is important to know how long the water must run to apply the desired amount for each set of furrows. Three values are necessary to calculate time: the water flow rate for each furrow or for the entire set, the area of the furrow or the set, and the amount of water to be applied. The area is determined from the number of rows in the set, the row spacing, and the length of the row.
Problem: How much time is required to apply 3 inches of water to sixty 32-inch rows when the rows are one half mile long, and the system capacity is 30 gal/min/row?
Number x Spacing (ft) x Lenght (ft) ft2
43,560 — ac in 1 ft ft 60 rows x 32-x -x 0.5 mile x 5280
row 12 in mile ft2
It will take 7.2 hr to apply 3.0 inches of water to the field.
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| 6,940 | 42 |
https://ems.press/journals/jems/articles/11826
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math
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On the unit disk we study the Moser-Trudinger functional
and its restrictions , where for . We prove that if a sequence of positive critical points of (for some ) blows up as , then , and weakly in and strongly in . Using this fact we also prove that when is large enough, then has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.
Cite this article
Andrea Malchiodi, Luca Martinazzi, Critical points of the Moser-Trudinger functional on a disk. J. Eur. Math. Soc. 16 (2014), no. 5, pp. 893–908DOI 10.4171/JEMS/450
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CC-MAIN-2023-50
| 588 | 4 |
https://quantummechanics.ucsd.edu/ph130a/130_notes/node141.html
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math
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Continuity of Wavefunctions and Derivatives
We can use the Schrödinger Equation to show that the
first derivative of the wave function should be continuous,
unless the potential is infinite at the boundary.
Integrate both sides from just below a boundary (assumed to be at
) to just above.
go to zero and the right hand side must go to zero for finite potentials.
Infinite potentials are unphysical but often handy.
The delta function potential is very handy, so we will derive a special continuity equation for it.
. Integrating the Schrödinger Equation, we get
As before, finite terms in the right hand integral go to zero as
but now the delta function gives a fixed contribution to the integral.
There is a
discontinuity in the derivative of the wave function
proportional to the wave function at that point
(and to the strength of the delta function potential).
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CC-MAIN-2022-40
| 867 | 16 |
https://sciencing.com/properties-gravity-8439386.html
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math
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Gravity is one of the four fundamental forces of the universe, and the most colossal in scale. Gravity affects the way objects interact with each other; from planets to pebbles, all the bodies are connected and interact with each other by the force of gravity. Although gravity forces are omnipresent, the causes of gravity are still not entirely clear. Understanding the properties of gravity is important as it allows a better understanding of how does gravity works.
Calculating the Magnitude of Gravity
Magnitude refers to the measure of the force of gravity in units. The force of gravity between two bodies can be calculated by the following formula: F = (G x M1 x M2)/D^2, where F = force of gravity, G = gravitational constant, M1 = mass of the first body, M2 = mass of the second body and D^2 = distance between the two bodies squared.
This formula illustrates two important properties of gravity. First, the mass of the bodies increases the force; the larger the mass, the larger the force. Second, the distance between the bodies will reduce the force.
Differences in Gravitational Pull
Since the force of gravity is proportional to the mass of the bodies involved, bodies with small mass generate a negligible force, and bodies with great mass generate a noticeable force. This is observed in planets and moons. The moon has 1/6 the gravity of Earth, based on its smaller mass.
All bodies generate a gravitational pull as long as they have mass. The sun, for example, is a mass of gas, but it generates a great gravitational pull, big enough to balance the solar system.
Gravitons and the Mechanisms of the Force Transmitted
All forces are transmitted by contact. Gravity seems to break this rule, as two bodies within a gravitational field attract each other, regardless of distance and without direct contact.
Modern conceptions of gravity include a uncharged particle called graviton. The graviton is the particle responsible of initiating contact between two objects in a gravitational field. When gravitons are exchanged by objects, they experience gravitational pull. It is important to note that gravitons are theoretical particles; their existence has not been confirmed by experimentation yet.
Gravity as a Curvature of Space-Time
Gravity can also be understood not as a linear force, but as a curvature of space-time. Space-time is conceptualized as a mesh of three-dimensional space and time. In this mesh, space and time are not two different magnitudes, but rather a single unified entity. In the space-time, gravity can be conceptualized as a pit on the space-time; the more massive the body, the deeper the pit.
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CC-MAIN-2023-50
| 2,638 | 12 |
http://hourofwolves.org/?view=armies&which=dndFigs&pic=79
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math
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Irish hound handler - Posted: July 5, 2010 - Manufacturer: Crusader Miniatures
The second hound handler that came with the Irish hounds. The dubious historical validity of the mohawk hairstyle makes this figure the perfect D&D hooligan type! What foolish footpad would try to rob a group of player characters? Certainly this one!
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CC-MAIN-2023-23
| 341 | 2 |
https://www.enotes.com/homework-help/what-is-the-y-intercept-form-2724663
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math
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Y-intercept form is often referred to as slope-intercept form. The formula is y=mx+b, where "b" is the y-intercept and "m" is the slope. Using this equation, it is quick to identify the y-intercept since it is the last number in the problem. To graph an equation in this form, one places a point on the y-axis to denote the y-intercept. One can then use the slope to add points on the line. Slope is noted in the equation as "m" and can be seen as a fraction since the slope refers to the number of units up (or down) over the number of units right (or left).
To graph a sample equation such as y=2x+2 which is in y-intercept form, one can place a point at two on the y-axis and then go up two units and right two units for the second point. One can also go down two units and left two units from the original point to find a third point.
A line can also be written with y being equal to a number. In this case, the line is a horizontal line crossing the y-axis. This line has zero slope. One can convert a standard form equation Ax+By=C into y-intercept form by solving for y algebraically.
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CC-MAIN-2021-17
| 1,091 | 3 |
https://www.optimalcomputing.be/index.php/2024/03/11/artificial-intelligence-revolution
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math
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The Artificial Intelligence Revolution
Artificial intelligence is capable to find the solutions that are not possible using human reasoning or any other mathematical algorithms. This can be the case when trying to predict the future from past data. A typical example is when trying to predict the energy consumption for today+1, today+2, and today+3 as we did it for a residential house. We were able to predict the energy consumption with an incredible level of accuracy using 2 years of measured data
Artificial intelligence is capable to automate tasks involving a huge amount of data that are not possible using human resources. This is the case in image and video analysis and recognition
Artificial intelligence is capable to learn engineering solutions from virtual simulation software to predict unseen configurations in a fraction of a second instead of hours or days of calculations. A typical example is when trying to predict the metallic deformation due to the welding of beams on a metallic structure.
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CC-MAIN-2024-18
| 1,015 | 4 |
http://boomcine.com/movies/mr-mrs-smith/
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math
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WATCH IT NOW 192 Views
Watch Mr. & Mrs. Smith Online Free
what going on?
More Details And Synopsis
Watch Mr. & Mrs. Smith Online Free. Mr. & Mrs. Smith is a 2005 USA Action, Comedy, Drama, Thriller. directed by Doug Liman, Kim H. Winther, Pamela Alch. Adam Brody, Angelina Jolie, Brad Pitt, Chris Weitz, Keith David, Kerry Washington, Michelle Monaghan, Rachael Huntley, Stephanie March, Vince Vaughn also star.
After five (or six) years of vanilla-wedded bliss, ordinary suburbanites John and Jane Smith are stuck in a huge rut. Unbeknownst to each other, they are both coolly lethal, highly-paid assassins working for rival organisations. When they discover they’re each other’s next target, their secret lives collide in a spicy, explosive mix of wicked comedy, pent-up passion, nonstop action and high-tech weaponry.
Original title Mr. & Mrs. Smith
IMDb Rating 6.5 416,927 votes
TMDb Rating 6.6 5,378 votes
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CC-MAIN-2019-51
| 928 | 9 |
https://socratic.org/questions/how-do-you-figure-out-a-limiting-reactant-problem
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math
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How do you figure out a limiting reactant problem?
(I just answered a question on this equilibrium!) If you had 50 tonnes EACH of carbon monoxide, and of dichlorine gas, which is the limiting reagent? I am willing to bet that the limiting reagent is dichlorine gas. Why? Well, look at the formula masses of
So we nut out
Let me know if you haven't grasped this principle. Someone will help you.
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CC-MAIN-2019-51
| 394 | 4 |
https://prostudy.jelajahalam.com/host-https-www.mathworks.com/academia/books/information-processes-theory-by-own-discoveries-with-matlab-and-java-gayev.html
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math
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Information Processes Theory by own discoveries with MATLAB and Java
Written in Ukrainian, Information Processes Theory by own discoveries with MATLAB and Java includes, areas of information processes theory applications, coding, encryption and information exchange, transfer of messages, variable-length codes, research of digital systems that correct errors and more.
Includes MATLAB files to solve application examples.
Online Teaching with MATLAB and Simulink
Whether you are transitioning a classroom course to a hybrid model, developing virtual labs, or launching a fully online program, MathWorks can help you foster active learning no matter where it takes place.
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CC-MAIN-2022-21
| 671 | 5 |
http://forum.spaceengine.org/viewtopic.php?f=9&t=62&sid=a02a3d5a09744ae891f59e65eac587ee&start=45
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math
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Source of the post
I'm currently hunting for the fastest-rotating rocky planet I can find. So far, the fastest I've found is RS 8591-173-1-5-111 1,which rotates in 8 hours and 46 minutes
I love that the planet has approximately 1300 times the atmospheric pressure of Earth, 14 times the atmospheric pressure of Venus, and you can still se the surface.
I also love that it is "Scorched", and would still be that without greenhouse effect, with a semi-major axis of 31.18 AU. And it is a planet, so probably no extreme tidal heating. What does this orbit around? A O star?
It orbits an O6.5V main-sequence star of 33.17 solar masses and 6855.6 solar luminosities. Its semimajor axis is 31.18 AU, with a period of 30.23 years. Its orbit is actually a fair bit mor eccentric than Earth's, at 0.067, but orbiting that far out, I agree: I don't think tidal heating comes into play. Some quick calculations suggest its temperature is
plausible, especially if you factor in the 75% CO2 atmosphere (with a partial pressure of 977 atmospheres).
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| 1,034 | 6 |
http://lbf-nice.org/how-do-you-can-area-in-math/
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math
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How Do You Can Area in Math?
You will find many tactics todo area
It can be tricky to keep track of all the methods. Some processes are less difficult than some the others. Below are some ideas for how exactly to do area.
One particular region to remember is. Another system may be that the arc. Subsequently you’re the tubing procedure, the parabola, and even the Circle. By way of the method, locate a radius and begin paper editing services dividing this up.
This is referred to as the area’s reciprocal. Area is characterized by the amount of both sides of the quadrant, and one end has to be negative to the ending to be more positive. That’s all.
Some areas have various definitions. The truth is that that region is that which you’re quantifying. Iff that’s the scenario, you have to convert it to a region which fits your requirements. You can find lots of approaches to do so.
In the event you really don’t like the conversion method, yet another way is by using the lines that are tangent. Take a circle, In the event you find that you aren’t paramountessays.com/editing happy with that and have a take a look in the center line. Find where online intersects the circle until it’s equal for the center line of the circle and after that move it along.
Put the two circles side by side in order for the tangent point is perpendicular to both. Take a line and then intersect it with the tangent line. Now locate the intersection level.
You might figure out the region, in addition to finding the junction point. You certainly can accomplish that using a radius. Get a lineup and then mix it with the tangent line to come across the space.
To locate the area using a quadrant, utilize a straight lineup . Because you must find out the distance of the quadrant, this approach is more difficult, and also you have to know the curvature.
It may be a bit easier when you are able to determine the difference between your very initial and second thing. Then discover the area of that at the same time. The derivative is simple, nevertheless the fourth derivative is all but https://cse.ucsd.edu/graduate/ucsd-cse-graduate-admissions impossible. Yet again, utilize your quadrant and figure out the region.
You can take advantage of the space. If you have a quadrant locate the medial side of this quadrant that is perpendicular to the point which goes through the origin. The line gets the tangent to this quadrant. Subsequently discover the area of this particular.
This can be done with almost any square or rectangle triangle. Of class the quadrant is much more essential because the quadrant has to match the region that you are on the lookout for. So produce the quadrant and then you could have to find a square with the same area exactly the exact very same dimensions.
Determine just how exactly to get this done using triangles and squares . Find the hypotenuse and split it into 4 equal parts and locate the intersection of these lines of the elements. Then locate the area of this particular.
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| 3,019 | 14 |
http://www.askmehelpdesk.com/23399-post4.html
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math
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Are we also assuming the ladder is retracting to allow this slippage to continue?
All 3 angles of a triangle equate to 180 degrees. We know the right angle will never change and always, leaving us with 90 degrees to play with.
The hypotnuse doesn't have a factor in this answer.
The shorter side of the triangle will have the larger angle on its other end.
With side lengths of 20 and 16. The total of the sides are 36.
To figure out what percentage the angle is we just divide 20/36 = 55.5555%
Take our total of 90 degrees and now multiply by .5555555 leaves us with 50.
So one angle is 50 degrees and the other is 40. We don't need to factor the hypotnuse into this because the right angle will never change.
I already said the shorter side gets the larger angle. So the ladder is at a 40 degree angle to the wall since its the larger side.
One second later we apply the same math to 19 feet.
19+16 = 35
19/35 = 54.28571
90*.5428571 = 48.85
The difference between the angle at 20 feet and 19 feet is 1.15 degrees
At 20ft the rate of change is about +1.15 degrees per second. But this will get larger as the tip of the ladder gets closer to the ground. I don't remember how to express this. I don't remember a problem like this in middle school.
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CC-MAIN-2013-20
| 1,246 | 15 |
https://collegeprep.uworld.com/ap-statistics/equation-and-formula-sheet/
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math
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AP® Statistics Equation and Formula Sheet
The AP® Statistics Formula Sheet will be one of your most important tools for success on the AP Statistics exam. In order to get an edge in your preparation for the exam, it is a great idea to familiarize yourself with the formula sheet beforehand. Here we will describe everything you need to know about the formula sheet in detail.
What is AP Statistics Formula Sheet and Tables
The AP Statistics Formula Sheet and Tables includes formulas and probability tables that you will need to solve both the multiple-choice and free-response questions on the exam. The formulas cover all units of the course curriculum except Unit 3 (Collecting Data), which does not require formulas. The tables provide left-tailed or right-tailed areas under the normal distribution curve, the t-distribution curve, and the chi-square distribution curve.
It is technically possible to solve every question on the AP Statistics exam using just the formulas on the formula sheet, algebra, and the probability tables. But the formulas on the sheet won’t be helpful if you do not already have a solid understanding of the course content. Plus, many problems are better suited for calculators than using the formulas. Still, along with the material you learn from your AP Statistics course, learning about each of the formulas and tables will help you be more efficient and better understand the material on the exam.
In this guide, we will cover what is included with the AP Statistics Formula Sheet and Tables generally, as well as go over each individual formula in detail. In addition, we will go over many questions you may have about the formulas and table sheet, including what formulas are NOT included and so should be memorized.
The first section of the formula sheet provides the formulas for descriptive statistics from Unit 1 (Exploring One-Variable Data) and Unit 2 (Exploring Two-Variable Data). It is rare to use these formulas directly on questions, especially for multiple-choice questions. Moreover, if you do end up with a chance to calculate the statistics mentioned in this section, it will generally be easier to use a calculator. However, you will absolutely need to understand them and reference them for certain types of questions. Therefore, making yourself familiar with this section is still important.
1 /∑ xi =
∑ xi /
sx = √
1 /∑ (xi - x̅ )2 = √
∑ (xi - x̅ )2 /
|ŷ = a + bx||y̅ = a + b x̅|
1 /∑ (
xi - x̅ /) (
yi - y̅ /)
b = r
Probability and Distributions
The second section of the formula sheet contains two important formulas from basic probability as well as several formulas to calculate the mean and standard deviation for any discrete random variable that will show up on the exam. Unlike the first section of the formula sheet, you will almost certainly be required to use these formulas for direct calculations. It is also less likely that you will be able to use calculators to automatically solve the questions involving these formulas. For that reason, it will be helpful to specifically practice using these formulas with AP Statistics practice questions.
P (A | B ) =
|Probability Distribution||Mean||Standard Deviation|
|Discrete random variable. X||µx = E (X ) = ∑ xi . P (xi )||σx = √∑ (xi - µx )2 . P (xi )|
If X has a binomial distribution with parameters n and p, then:
P (X = x ) = (
n / x) px ( 1 - p )n-x
where x = 0, 1, 2, 3, ..., n
|µx = np||σx = √np ( 1 - p )|
If X has a geometric distribution with parameter p, then:
P (X = x ) = (1 - p )n - x p
where x = 1, 2, 3, ...
√1 - p /
Sampling Distributions and Inferential Statistics
The third section of the formula sheet contains meta formulas for the test statistics and confidence intervals on the AP Statistics exam. They are meta formulas because they do not make calculations directly, but are combined with specific information for each procedure. These meta formulas are incredibly important for the AP Statistics exam and you should understand them deeply both on a conceptual level and as be able to use them to generate the test statistics and confidence intervals for the exam.
Standardized test statistic:
statistic - parameter /
|Confidence interval: statistic ± (critical value) (standard error of the statistic)|
Chi-square statistic: χ2 = Σ
(observed - expected)2 /
The information that can be combined with these formulas is given in the following parts of this section. They also contain general information important for understanding the sampling distributions of the important statistics on the example. For example, for procedures involving sample proportions:
|Random Variable||Parameters of Sampling Distribution||Standard Error of Sample Statistic|
|For one population:
µp̂ = p σp̂ = √
p ( 1 - p ) /
p̂ (1 - p̂ ) /
For two populations:
p̂ 1 - p̂ 2
|µ p̂ 1 - p̂ 2 = p1 - p2
σ p̂ 1 - p̂ 2 = √
p1 ( 1 - p1 ) /+
p2 ( 1 - p2 ) /
S p̂ 1 - p̂ 2 = √
p̂1 ( 1 - p̂1 ) /+
p̂2 ( 1 - p̂2 ) /
when p1 - p2 is assumed:
S p̂ 1 - p̂ 2 = √ p̂c ( 1 - p̂c ) (
where p̂c =
X 1 + X 2 /
Included with the formula sheet are tables that provide probabilities for the normal distribution, t-distribution, and the chi-square distribution. The probabilities these tables provide are different for each distribution, based on their use on the AP Statistics exam. These tables are used to calculate certain probabilities, mostly probabilities over intervals and p-values. However, the information in these tables can also be found using a calculator.
Should I use the probability tables included with the formula sheet or should I use a calculator?
Many students prefer calculators, but it’s really a personal preference. Calculators can give more information, but those good with tables may find they are faster. You really should be familiar with both. A calculator can always fail, but it will give the most precise results. Conversely, using a table may not be easy, but it is a great way to learn the content of the course.
AP Statistics Formula Sheet & Tables
In Words: The left side of the equation is an x with a “bar” (line above the x) that represents the sample mean, while the right side of the equation is equal to the sum of the data divided by the number of data points (n ).
Description: This sample mean is the most important statistic on the AP exam. It represents the “center” or “average” of a set of data.
Application on AP Exam: It is unlikely that you will need this formula for calculation. This formula is conceptually important – think the central limit theorem, sampling distributions, t-tests, and other important topics. The formula is also useful for understanding how certain manipulations affect the sample mean. For example, how does multiplying the values in a dataset by 2 affect the sample mean?
Sample Standard Deviation
In Words: The left side of the equation is the sample standard deviation for the variable “x” (the subscript). The right side of the equation involves a lot of symbols, but it is straightforward if you take it in steps. (1) Subtract the sample mean from every value in the dataset, (2) Square the resulting values, (3) Add up the resulting values, (4) Divide the result by n – 1, and finally (5) Take the square root of the final result.
Description: This sample mean is the second most important statistic on the AP exam. It represents the “spread” or “variability” of a set of data.
Application on AP Exam: It is unlikely that you will need this formula purely for calculation. If it does come up, you should probably use a calculator instead of this formula. Most questions involving standard deviation will either give you the value of the standard deviation or otherwise require you to interpret features of the standard deviation.
Predicted value of the response variable (linear regression)
In Words: The left side of the equation represents the predicted value of the response variable in a simple linear regression model. It is denoted with a “y” with a so-called “hat” on top (the circumflex symbol). The right side of the equation provides the linear equation in which a given value of the explanatory variable (x ) is an input. The value of x is multiplied by the slope b and then y-intercept a is added.
Description: Simple linear regression is a procedure to predict a value of one variable (the response variable: y ) from the value of another variable (the explanatory variable: x ). This formula shows how prediction is done through simple linear regression – through plugging x into the equation for a line.
Application on AP Exam: One common question type on the AP exam is interpolation.. If the slope (a ) and y-intercept (b ).are given (and it’s likely they will be), then you should be able to turn the value of an explanatory variable x into the predicted value of the response variable y. Another type of question involves residuals. You will need to find the predicted value of y using a regression line, then compare to the observed value.
Point on the linear regression line
In Words: The left side of the equation (y with a bar) is the sample mean for a response variable y. The right side of the equation is the simple linear equation in which the mean of the explanatory variable is an input. The mean of x is multiplied by the slope b and then y-intercept a is added.
Description: This formula makes a conceptual point as well as being useful for calculation. The conceptual point is that the predicted value of y when x is equal to its mean is equal to the sample mean of y; that is, the regression line always goes through the point (x̄,ȳ ). This formula is also used for calculating the y-intercept of a linear regression line. If you have the sample mean of x, the sample mean of y, and the slope of the regression line, then this formula can be rearranged to isolate the value of a.
Application on AP Exam: The usage of this equation for the exam is as a reminder about the one point mentioned above – the point (x̄,ȳ ) is always on the regression line. Also, while such a question is highly unlikely, it is possible that you will need to calculate a y-intercept using this formula because it is a notable part of the curriculum.
In Words: The left side of the equation (the “r”) is the correlation coefficient. The right side of the equation involves a lot of symbols, but like the standard deviation it is straightforward if you take it in steps. First, note that the expressions in the values are actually a type of z-score. (1) Calculate the z-scores for the data values for both variable x and variable y, (2) Multiply the paired z-scores, (3) Add up the resulting values, and finally (4) Divide the result by n – 1.
Description: The correlation coefficient, r, gives the direction and strength of the linear association between two quantitative variables.
Application on AP Exam: This is another formula you are unlikely to use directly on the AP exam. Similarly to the standard deviation, if it does come up, you should probably use a calculator instead of this formula. However, understanding this formula (especially the z-score interpretation) can help with several types of problems. For example, how does multiplying one variable by -1 affect the correlation coefficient?
Slope of the linear regression line
In Words: The left side of the equation (the “b”) is the slope of the linear regression line. The right side of the equation includes the correlation coefficient, multiplied by the ratio of the standard deviation of the response variable (y ) to the standard deviation of the explanatory variable (x ). Note: Keep in mind that the standard deviation in the numerator is the standard deviation for the values of y, NOT the standard deviation for the residuals of the linear regression.
Description: The slope of the linear regression line is the amount that the predicted value of the response variable y changes for each unit increase in x.
Application on AP Exam: There are several important applications of this formula on the AP exam. One that has come up several times is to understand the relationship between the correlation coefficient and slope. For example, if the correlation coefficient is positive, the slope must also be positive (and vice-versa). You should also be able to calculate the slope if given the correlation and the standard deviation of both variables involved in a regression.
What formulas are not included with the AP Statistics formula sheet?
The AP Statistics formula sheet does not include all formulas you’ll need for the AP Statistics exam. Here is a list of statistics and rules on the AP Statistics exam you will need to memorize.
|Unit 6 & 7||
Read more about the AP Statistics Exam
A perfect study guide can help you score 5 easily! See what our experts advise on how to score high in AP Statistics with all the essential resources to succeed.
Want to know if AP Statistics is the right course for you? Our well-explained article can help you get a clear picture of the exam and make your exam prep easy!
Don’t let the AP Exam format confuse you. Our self-explanatory guide will help you easily understand the exam format—question types, topic weights, and more!
Looking for an easy-to-follow course and exam description for AP Statistics? See our guide for clear info on the AP Stats course—units, topics, and key concepts.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679101195.85/warc/CC-MAIN-20231210025335-20231210055335-00763.warc.gz
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CC-MAIN-2023-50
| 13,435 | 91 |
https://cameroongcerevision.com/basic-atomic-theory-exercises/
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math
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List the three statements that make up the modern atomic theory.
Explain how atoms are composed.
Which is larger, a proton or an electron?
Which is larger, a neutron or an electron?
What are the charges for each of the three subatomic particles?
Where is most of the mass of an atom located?
Sketch a diagram of a boron atom, which has five protons and six neutrons in its nucleus.
Sketch a diagram of a helium atom, which has two protons and two neutrons in its nucleus.
Define atomic number. What is the atomic number for a boron atom?
What is the atomic number of helium?
Define isotope and give an example.
What is the difference between deuterium and tritium?
Which pair represents isotopes?
b) 26F and 25M
c) 14S and 15P
14. Which pair represents isotopes?
a) 20C and 19K
b) 26F and 26F
c) 92U and 92U
15. Give complete symbols of each atom, including the atomic number and the mass number.
a) an oxygen atom with 8 protons and 8 neutrons
b) a potassium atom with 19 protons and 20 neutrons
c) a lithium atom with 3 protons and 4 neutrons
16. Give complete symbols of each atom, including the atomic number and the mass number.
a) a magnesium atom with 12 protons and 12 neutrons
b) a magnesium atom with 12 protons and 13 neutrons
c) a xenon atom with 54 protons and 77 neutrons
17. Americium-241 is an isotope used in smoke detectors. What is the complete symbol for this isotope?
18. Carbon-14 is an isotope used to perform radioactive dating tests on previously living material. What is the complete symbol for this isotope?
19. Give atomic symbols for each element.
20. Give atomic symbols for each element.
21. Give the name of the element.
22. Give the name of the element.
All matter is composed of atoms; atoms of the same element are the same, and atoms of different elements are different; atoms combine in whole-number ratios to form compounds.
A proton is larger than an electron.
proton: 1+; electron: 1−; neutron: 0
The atomic number is the number of protons in a nucleus. Boron has an atomic number of five.
b) not isotopes
c) not isotopes
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145260.40/warc/CC-MAIN-20200220162309-20200220192309-00051.warc.gz
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CC-MAIN-2020-10
| 2,063 | 39 |
http://www.chegg.com/homework-help/reconsider-prob-18-45-using-ees-software-investigate-effect-chapter-4-problem-48p-solution-9780077366643-exc
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math
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Reconsider Prob. 18-45. Using EES (or other) software, investigate the effect of the cooling time on the final center temperature of the shaft and the amount of heat transfer. Let the time vary from 5 min to 60 min. Plot the center temperature and the heat transfer as a function of the time, and discuss the results.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662166.99/warc/CC-MAIN-20160924173742-00068-ip-10-143-35-109.ec2.internal.warc.gz
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CC-MAIN-2016-40
| 317 | 1 |
https://quizlet.com/7251173/ecg-flash-cards/
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math
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One small square on an ECG is worth what amount of time? What is one large square worth? How many squares on and ECG make up 1 second of time?
0.04 seconds 0.2 seconds 5 large squares
What is the quickest way to determine a heartrate on and ECG strip?
Count the number of squares between QRS complexes. Divid 300 by this number. This equals beats per minute. Example: If there are 4 large squares between each QRS complex then the heart rate is 300/4 = 75 bpm
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CC-MAIN-2018-17
| 459 | 4 |
http://www.cl.cam.ac.uk/~abr28/teaching/cl/compnet/
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math
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A long but approachable course. At the time of this writing, it
follows the book Computer Networking: A Top-Down Approach (5th
edition), which you should get from the library. Supervision
questions can also be set from it.
webpage is populated online shortly before the beginning of
Lent term. Traditionally, not all lectured material is examinable
(e.g. Ch 2, 5, 6 partly and Ch 8, 9 entirely were excluded) but make
sure you check this info for the current year. The examinable parts
are usually mentioned here
(if the link is down, try again after the Lent term starts, ask the
lecturer or look on the course
Other CompNet supervision/revision things:
- Revision questions(*) R11, R12, R13, R15, R18 and Problems P1, P5, P6, P7, P12, P23 from Chapter 1 (Networks and Internet).
- Revision questions(*) R4, R8, R11, R26 and Problems P1, P4, P10, P22, P27 from Chapter 2 (Application layer).
- Recommended but optional:
- Revision questions(*) R5, R7, R10, R11, R14, R15, R17, R18 and Problems P1, P3, P8 to P12, P13, P16, P20, P22, P25 from Chapter 3 (Transport layer).
- Problems P4, P8, P20, P26, P33, P49, P52 from Chapter 4 (Network layer).
- Problems P5, P6, P7, P11, P14, P18, P21, P24, P25 from Chapter 5 (Link layer).
- Review questions(*) R3, R5, R7, R14 and Problems P3 to P12, P15, P21, P22, P23 from Chapter 7 (Multimedia).
(*) For all Review questions, also specify the slide/page number in the handouts/book where you found the answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122739.53/warc/CC-MAIN-20170423031202-00569-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,451 | 20 |
https://bizfluent.com/how-10016801-calculate-point-margin.html
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math
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How to Calculate Point Margin
In the sales world, there are two ways of looking at profit. You can look at profit compared to your costs, or you can look at profit based on your sales. When you compare profit to costs, you are looking at markup, but when you compare profit to sales, you are looking at margin.
Margin is just a way of calculating profit, while point margin is margin expressed as a percentage point. So, if you hear someone comparing margin vs. profit or margin points vs. percent of margin, these terms mean the same thing. Point generally represents 1%.
To calculate point margin, first subtract your cost from the sales price to determine the margin and then divide that margin by the sales price.
Margin is essentially the same as profit. Margin is the amount you have in your pocket after selling an item and subtracting your cost:
Margin = Sales Price - Cost
For example, if you sell a sweater for $50 and your cost for that sweater was $30, then your margin is $20. That's your profit in the transaction. If you sold the same sweater for $40, then your margin would be $10.
Point margin is simply your margin expressed as a percentage point instead of in dollars. You can calculate the point margin by dividing your margin by the sales price:
Point Margin = Margin / Sales Price
So, if you sold the sweater for $50 with a $20 margin, then your point margin was 40 points ($20 / $50 = 0.40). If you had sold that same sweater for $40, then your point margin would have been only 25 points ($10 / $40 = 0.25).
Many businesses make it a matter of policy to sell items at a specific point margin. Suppose, for example, before you put your sweater up for sale, you decided you wanted to sell it at a 45-point margin. In this case, you can use the following formula:
Sales Price = Cost / (1 - Margin)
If the sweater cost you $30, then to sell it at a 45-point margin, the sales price would have to be $54.54:
Sales Price = $30 / (1-0.45)
Sales Price = $30/0.55
Sales Price = $54.54
While margin looks at profit based on the selling price, markup looks at profit based on the cost. Companies that use markup to calculate price simply add their markup to the cost of the item. For example, if you bought a shirt from a wholesaler for $10 and want to add a flat markup of $9, then the sales price would be $19:
Sales Price = Cost + Markup
Like margin, markup can also be expressed as a percentage, but it is a percentage based on the cost rather than the selling price. For example, if your company's policy is to mark up shirts by 40%, then you would multiply the $10 cost by 140% to get a $14 sales price.
Sales Price = Cost x (1+Markup Percentage)
Note that markup must always be more than 100% when you are doing the calculation, or you will lose money.
You should have probably noticed that when expressed in dollars, markup and margin work out to the same thing. That's because they both represent profit. If the cost is $8 and you sell an item for $20, then your markup and margin are both the same $12.
It's only when you look at the percentages or points that markup and margin vary considerably. As a final example, suppose you are selling a hat for $54 that cost you $30. Both markup and margin are $20. This is a markup of 180%, but it's a 44-point margin.
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CC-MAIN-2023-14
| 3,283 | 23 |
https://aim.uz/ielts/writing/task-1/12312-the-charts-below-show-what-uk-graduate-and-postgraduate-students.html
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math
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The charts below show what UK graduate and postgraduate students who did not to go into full-time work did after leaving college in 2008.
The two given bar charts illustrate how many UK graduate and postgraduate students were busy with different activities expect except full-time work after finishing their high school in 2008.
The column graphs compare the destinations of graduate and postgraduate students not considering full-time work after graduating their colleges in 2008 in UK.
Overall, excluding data about full-time work, the highest number of both UK graduate and postgraduate students leaving school was busy with further study, whereas the least of them involved in voluntary work.
As is clear from the first graph, the number of graduates doing part-time work was 17 735, 1500 people more than unemployed graduates. Likewise, the gap between part-time working and unemployed postgraduates was noticeable, each constituting well over 2500 and 1600 people respectively.
Nearly 30 000 graduate students decided to continue their studies, a ten-fold over the number of postgraduates in further study. The figures for voluntary work were similar, as well. To be more specific, the number of graduates involving in voluntary work exceeded 10 times more than that of postgraduates, making up 3500 people.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00277.warc.gz
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CC-MAIN-2023-14
| 1,313 | 6 |
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/appendix-a-a-3-inequalities-exercises-page-545/31
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math
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not true if a= -3 and b= -2
Work Step by Step
$a\lt $b a = -3 b = -2 a^2= 9 b^2 = 4 $9 \gt $4 hence proved
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100568.68/warc/CC-MAIN-20231205204654-20231205234654-00458.warc.gz
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CC-MAIN-2023-50
| 355 | 5 |
https://www.extramarks.com/studymaterials/ncert-solutions/ncert-solutions-class-10-maths-chapter-11-in-hindi/
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math
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NCERT Solutions Class 10 Maths Chapter 11 In Hindi
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NCERT Solutions for Class 10 Maths Chapter 11 Constructions in Hindi PDF Download
The chapter Constructions carries a significant amount of topic weightage in the Class 10 board examinations. For better conceptual clarity and to score better marks, Extramarks recommends that students go through the NCERT Solutions For Class 10 Maths Chapter 11 In Hindi. Practising the NCERT Textbook questions and several extra questions can help students understand Class 10 Maths Hindi Chapter 11 better. On Extramarks, students can find NCERT textbook solutions, as well as other practise assignments to help them succeed in their board examination. To prepare for their board examination, students need accurate, detailed, and well-explained NCERT Solutions For Class 10 Maths Chapter 11 In Hindi. These solutions have numerous benefits. To be able to score well in Class 10 Mathematics board examinations, students require a lot of hard work and meticulous practise. In order to master the subject’s curriculum, students must practise the chapters of the curriculum rigorously. Practising the exercises in the NCERT textbook is the first and most important step in order to obtain the maximum marks in the board examinations. It is very importantfor students to have a clear understanding of the concepts of the chapter. Hence, Extramarks offers students NCERT Solutions For Class 10 Maths Chapter 11 In Hindi, so they can have trustworthy study material, and can practice, learn, and excel in the examinations.
NCERT Solutions for Class 10 Maths Chapter 11 Constructions in Hindi
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The NCERT Solutions For Class 10 Maths Chapter 11 In Hindi are conveniently available on the Extramarks website. Providing reliable and complete study material to students is the goal of Extramarks. Besides this, Extramarks also provides students with numerous learning tools such as Live Doubt Solving Sessions, Learn Practice Tests, In-Depth Performance Reports, Complete Syllabus Coverage, and so on and so forth. These tools assist students in making the learning process effortless and enjoyable. For a successful academic career, students should become familiar with comprehensive learning.
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For students to understand the type of questions that are asked in the board examination, Extramarks provides them with NCERT Solutions For Class 10 Maths Chapter 11 In Hindi. Practising these solutions can make students more confident when giving their board examinations. By going through these solutions, students can imbibe an understanding of every concept that is included in the syllabus of the subject’s curriculum. The NCERT Solutions For Class 10 Maths Chapter 11 In Hindi help students in having a better understanding of every concept of the chapter and perform well in the Mathematica Class 10 board examination.
4. Is it essential to practice the NCERT Solutions For Class 10 Maths Chapter 11 In Hindi before appearing in the board examinations?
In order to gain confidence for the board examinations, students should thoroughly practice the NCERT Solutions For Class 10 Maths Chapter 11 In Hindi. The Class 10 Mathematics board examination is based on the CBSE curriculum, therefore any question from the NCERT textbook can appear in the board examination. Therefore, students are required to be thorough with these solutions. Every question mentioned in the chapter is solved using a unique concept or operation. Practising these solutions help students to stay on top of every concept and calculation used in the chapter. These solutions are also available in Hindi, which makes them easily understandable for students who attend Hindi-medium schools. Students are recommended to click on the given link to download the NCERT Solutions For Class 10 Maths Chapter 11 In Hindi.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.53/warc/CC-MAIN-20231203193127-20231203223127-00180.warc.gz
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CC-MAIN-2023-50
| 8,224 | 15 |
https://fzerocentral.org/viewtopic.php?p=99341
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math
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One lap on this very long straight takes ~13.65 seconds if you are driving at 478km/h. (max speed of Fire Stingray) But how fast would you have to drive in order to do double the lap times? (27.30 seconds)
You'd expect 239km/h (478/2), but actually it is 175km/h, because the speed meter is lying. The speed meter raises exponentially, so the faster you are driving, the faster the numbers of the speed meter get higher. The first 13 km/h from 0-13km/h are about the same as 438-478km/h (difference of 40 instead of 13)
If the first 13km/h are "real", it means that you actually just drive about 234km/h on max speed instead of 478km/h.
it is kinda expected since every other game in the series has a lying speedometer.
also, making speeds like that seem realistic is hard since barely any small vehicle goes that fast in reality.
"Patience is useful in any moment"
Re: Speed meter is lying
posted: Wed Aug 21, 2013 4:57 am
So how much is the difference between the first km/h from 0-1km/h and let's say 1499-1500km/h in the other games? Do you know any maths about it?
Edit: I tested in F-Zero X on a big loop. I drove on max speed settings at ~901km/h and another time while braking at the same time, so that my speed was only ~179km/h. Based on the time I did with 179km/h I expected the other time I did to be ~918km/h instead of 901. So the difference isn't really that huge, especially compared to F-Zero SNES, it is even the other way around, the expected 918km/h are higher than the 901km/h, while in F-Zero SNES the expected 350km/h for half the time of 175km/h are much lower than 478km/h. Maybe there is a bigger difference at lower speeds, but I don't know how to drive constant times at lower speeds.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464045.54/warc/CC-MAIN-20210417192821-20210417222821-00278.warc.gz
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CC-MAIN-2021-17
| 1,713 | 10 |
https://hatgiong360.com/how-far-is-300-miles-in-hours/
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math
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How Far Is 300 Miles In Hours: Unveiling The Time Travel Equation
Why It’S Almost Impossible For Cars To Go 300 Miles Per Hour | Insider Cars
Keywords searched by users: How far is 300 miles in hours how far is 300 miles in minutes, how long to drive 300 miles at 70 mph, how many hours is 300 miles at 80 mph, how long is 300 miles in feet, how many hours is 300 miles walking, how long does it take to drive 300 miles at 60 mph, how long is 300 miles on a map, 300 miles in km
How Long Would A 300 Mile Drive Take?
What is the estimated duration for a 300-mile drive? Understanding the time it would take to complete a journey of this distance can be essential for trip planning and scheduling. To provide a more comprehensive answer, factors such as the average driving speed, road conditions, and rest stops along the way should be considered. By taking these variables into account, we can better gauge the expected duration of a 300-mile drive and make informed decisions for our travel plans.
Can You Drive 300 Miles In A Day?
Is it possible to cover a distance of 300 miles in a single day behind the wheel? Well, the answer varies from person to person, but in general, most individuals should find driving 300 miles a manageable feat. Drawing from my experience as an over-the-road truck driver, I established what I refer to as the “300-mile rule.” This guideline suggests that when embarking on a cross-country journey, your initial driving session at the start of the day should cover a minimum distance of 300 miles. This benchmark helps ensure a productive and efficient long-distance drive.
How Far Is 300 Miles In 5 Hrs?
On March 8, 2023, someone asked, “How far is 300 miles in 5 hours?” To calculate the average speed of a car that covers a distance of 300 miles in 5 hours, you simply divide the distance by the time. In this case, 300 miles divided by 5 hours equals an average speed of 60 miles per hour. So, if a car maintains a constant speed of 60 miles per hour for 5 hours, it will cover a distance of 300 miles. This information clarifies the calculation and provides context for the question.
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See more here: hatgiong360.com
60 MPH is a mile a minute . 300 miles takes 300 minutes . Therefore 5 hours .A car travels 300 miles in 5 hours.It depends on the individual, but the average person should be able to drive 300 miles without much problem. After working as an over the road truck driver I came up with the 300 mile rule. The first driving session at the beginning of the day when going cross country had to be a minimum of 300 miles.
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- The 9 fastest cars in the world right now – The Manual
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707948217723.97/warc/CC-MAIN-20240305024700-20240305054700-00161.warc.gz
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CC-MAIN-2024-10
| 3,093 | 20 |
https://www.booktopia.com.au/progress-in-analysis-and-its-applications-proceedings-of-the-7th-international-isaac-congress-michael-ruzhansky/prod9789814313162.html
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math
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The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.
Complex Analysis; Potential Theory; Functional Analysis; Clifford and Quaternion Analysis; Reproducing Kernels; Theory of Integral Transforms; Spaces of Differentiable Functions; Partial Differential Equations; Control Theory; Inverse Problems; Stochastic Analysis; Functional Inequalities; Dynamical Systems; Functional Differential and Difference Equations; Mathematical Biology.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583656665.34/warc/CC-MAIN-20190116031807-20190116053807-00493.warc.gz
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CC-MAIN-2019-04
| 1,131 | 2 |
https://infospotz.com/what-is-2-3-times-4/
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math
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What is 2/3 times 4
what is 2/3 times 4?
2/3 times 4 is 8/9. 2/3 multiplied by 4 is equal to 8/9. This can be seen by multiplying the numerator by 2 and the denominator by 3.
what is 2/3 times 1/4?
2/3 times 1/4 is equal to 2/12. To find this, you can either multiply the numerators and denominators by the same number, or divide both numerator and denominator by the same number.
What is 2/3 times 4 Fraction form?
what is 2/3 times 4 as a fraction
What is 1/4 times 2/3 in fraction form?
1/4 times 2/3 equals 1/12.
This calculation allows us to evenly divide a fraction by another. To do
this, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. So, in this example, we multiply 1 by 2/3 to equal 1/12.
what is 3/4 cup times 2?
4/3 divided by 3/2
Understand that the answer to 4/3 divided by 3/2 is equal to 2/9.
To do this, we multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. So, in this example, we multiply 4 by 3 to equal 12. We also multiply 3 by 2 to equal 6. Then we add these numbers together to equal 18. And finally, we divide 18 by 9 to equal 2. So the answer is 2/9.
It’s also worth noting that we could have just as easily flipped the fraction, so that it would be 3/2 divided by 4/3. The answer in this case would still be 2/9.
what is 2/3 times 4/5 times 1/3?
2/3 times 4/5 times 1/3 equals 8/15. To calculate this, we first need to convert all the fractions to decimals. We can do this by using a calculator, or if you are familiar with the long division method, you can also use that. We will use the long division method for this example.
To begin, let’s convert 2/3 to a decimal. To do this, we divide the numerator (the top number) by the denominator (the bottom number). We get a decimal value of 0.666667.
Now let’s convert 4/5 to a decimal. Again, we divide the numerator by the denominator and get a decimal value of 0.8.
Finally, let’s convert 1/3 to a decimal. We divide the numerator by the denominator and get a decimal value of 0.333333.
With all of our fractions converted to decimals, we can now multiply them together. The decimal value we get is 0.3333333, which is equal to 8/15.
So, in summary, 2/3 times 4/5 times 1/3 equals 8/15. To calculate this, we converted all of the fractions to decimals and then multiplied them together
what is 2/3 times 4/5?
2/3 times 4/5 is equal to 8/15. To get this answer, you can multiply the numerators and denominators by 2, which is the same as multiplying each fraction by 1/2. To do this, you multiply 8 times . Since 15 divided by 3 is 5, multiplying by 2 gives you . Therefore, 8/15 is equal to 2/3 times 4/5.
how to divide fractions?
To divide fractions, you need to invert the divisor and multiply the two fractions. This is sometimes called the “flip and multiply” method for dividing fractions. For example, if you want to divide the fraction 2/3 by 1/4, you would first invert the divisor (1/4) to 4/1. You would then multiply 2/3 by 4/1 to get 8/3, which is the answer to your division problem. To divide fractions by whole numbers, you can use the “long division” method that you may have learned in school when you were younger.
What is formula for dividing fractions?
The easiest way to divide fractions is to use a calculator, and input the division as a normal division problem. However, if you need to do it by hand, you can use the following steps:
-First, convert the division into a multiplication problem by flipping the second fraction (that is, make the denominator of this fraction the numerator of the original fraction). This will also create a new denominator.
-Next, multiply the first fraction by this new denominator. This is your answer to the division problem.
What is fraction calculation chart?
Fraction calculation is used to calculate the fraction of one number with another. It can be used to divide a whole unit into parts or calculate a percentage. The steps for finding a fraction calculation are as follows:
1) Determine the whole unit value. This is the number that will be divided by the fraction being calculated.
2) Identify the value of the fraction being calculated. This is the number that will be divided into the whole unit.
3) Calculate the fraction by dividing the fraction value into the whole unit value.
4) Express the fraction as a decimal value by moving the decimal point to the left or right until you have an equivalent fraction. Be sure to include any repeating numbers.
5) Convert the decimal value to a percentage by multiplying it by 100. This will allow you to express the fractional value as a percentage of the whole unit.
how to subtract fractions?
To subtract fractions, we need to find a common denominator between the two fractions. The common denominator is the lowest number that both of the two fractions have in common. For example, if we are subtracting 1/4 and 3/5, the common denominator is 20 because 4 and 5 both go into 20. To find the common denominator, we can either list out the multiples of each number or use a LCD (least common denominator) calculator.
Once we have the common denominator, we can subtract the fractions by changing them both into equivalent fractions with the common denominator. For example, if we are subtracting 1/4 and 3/5 and our common denominator is 20, we would change 1/4 to 5/20 and 3/5 to 15/20. Then, we can subtract the fractions by subtracting the numerators and keeping the same denominator, so 5/20 – 15/20 = -10/20. This can be simplified to -1/2.
how to multiply fractions?
Multiplying fractions is a very useful concept in mathematics. It can be used to simplify complicated calculations involving fractions. The method of multiplying fractions is as follows:
To multiply two fractions, take the product of the numerators and the product of the denominators. This will give you the answer in simplest form.
For example, let’s take the fractions 6/4 and 2/3.
To multiply these two fractions:
Take the product of the numerators, which is 6 x 2 = 12.
Take the product of the denominators, which is 4 x 3 = 12.
The answer to this problem is 12/12, which reduces down to the simplest form of 1. This means that 6/4 x 2/3 is equal to 1. This is the simplified ways for multiplying fractions.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00691.warc.gz
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CC-MAIN-2023-14
| 6,312 | 49 |
http://www.yourarticlelibrary.com/cost-accounting/marginal-costing/angle-of-incidence-of-a-firm-with-graph/66253/
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math
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Let us make an in-depth study of the angle of incidence of a firm.
This is an angle where sales line intersects the total cost line which indicates profit-earning capacity over the Break-Even Point.
It should be remembered that a large angle indicates high margin of profit after covering fixed cost.
Similarly, a small angle indicates low margin of profit which reveals that variable cost is more in total cost. If margin of safety is considered along with angle of incidence it may be suggested that a large angle of incidence with high margin of safety indicates extremely favourable condition.
The following graph will show the ‘Angle of incidence’ of a firm:
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645550.13/warc/CC-MAIN-20180318071715-20180318091715-00109.warc.gz
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CC-MAIN-2018-13
| 667 | 5 |
https://vti.juliaseibt.de/pages/comparing-numbers-in-scientific-notation-notes.html
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math
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ComparingNumbersin ScientificNotation: When EXPONENTS are THE SAME compare the decimal numbers ONLY: EX: 4.128 X 10 3 compared to 4.13 X 103 4.130 Line up the decimals and fill in missing 0’s if you need to. 4.128 4.130 is greater than 4.128, so 4.13 X 10 is the greater scientificnumber. ANSWER: 4.128 X 103 < 4.13 X 103 OR 4.13 X 103 > 4. .... "/>
ComparingNumbersinScientificNotation (Foldables) by Easy ISN 6 $1.50 Zip How to compare numbers written in scientificnotation by looking first at the exponent and then at the decimal value. The notes includes two tables of values, some of which are written in standard form and some in scientificnotation. Comparing and Ordering NumbersinScientificNotation DO NOT rewrite them as decimals! 1) To compare two numbers given in scientificnotation, first compare the _____. The one with the greater exponent will be _____. 2) If the exponents are _____, compare their decimals. Examples: 1. Compare 6.23 × and 8.912 ×. Write common among a scientificnotationcomparingnumbersin worksheet is much more. Math 6/7 Name:_____NOTES (4.2b) Comparing and Ordering Rational Numbers To Order Rational Numbers (Fractions, Decimals, Percents & #’s written in Scientific Notation) 1. Convert all numbers to a common format. 2. Put them required ordered. 3. Rewrite in the original format. Review: Order the following decimals from least to greatest:. Learn how to compare and order numbers in scientific notation. Click Create Assignment to assign this modality to your LMS. We have a new and improved read on this topic. A language is a structured system of communication.The structure of a language is its grammar and the free components are its vocabulary.Languages are the primary means of communication of humans, and can be conveyed through speech (spoken language), sign, or writing.Many languages, including the most widely-spoken ones, have writing systems that enable sounds or. Section 1.5 ScientificNotation and Number Sense Subsection 1.5.1 Thinking about Size Comparisons. How can we compare the numbers 100 and 1,000? Answers you might have given: 1,000 is 900 more than 100. 100 is 900 less than 1,000. 1,000 is 10 times as big as 100. Reflection question: Look at the different ways of comparing those two numbers. Chapter 7 35 Glencoe Algebra 1 Solve Algebraically Solve Graphically Exponential Growth And Decay Worksheet Algebra 2 Answers graph and the steepness 6: Exponential Growth - If you would rather take notes on a worksheet , you can print it out here Notice how the initial amount is irrelevant when solving for half-life Notice how the initial amount is irrelevant when. SCIENTIFIC NOTATION Regular Notation (RN)- The standard way that we write our numbers. Ex: Two Hundred and Eight Million is written - 280,000,000. Scientific Notation (SN)- A shorthanded way of writing really large or really small numbers. In SN a number is written as the product of two factors. First Factor Regular Notation ! Scientific Notation. Comparing Numbers in Scientific Notation When numbers with many digits are. Comparing numbers in scientific notation when numbers. School Florida Virtual High School; Course Title PRE ALEGBR pre algebr; Type. Notes. Uploaded By. Title: Microsoft Word - ScientificNotation Word Problems revised.docx Author: Claudia Bowles Created Date: 3/12/2013 10:14:05 PM. ScientificNotationNotes - York County School Division. Scientificnotation is a short way to write very large or very small numbers. It is written as the product of a number between 1 and 10 and a power of 10. TO CONVERT A NUMBER INTO SCIENTIFICNOTATION: • Create a number between 1 and 10 by moving the decimal to the left.. national standard of interior lighting calculation short note; pixel survival free; volkswagen facebook marketplace; swiper pause autoplay; 2017 f250 4x4 rear sway bar. If after adding or subtracting the coefficients, the answer is not in scientificnotation, then convert it to scientificnotation. Step 1: Multiply or divide the coefficients. Step 2: Add or subtract the exponents. Step 3: Convert the answer in scientificnotation. Example: Multiply (3.1 × 10 -1 ) (0.4 × 10 2). huber lexington banjo for sale.
golden teacher mycelium growth temperature
why i left the episcopal church
mr neviaser received his injection in his right deltoid
our replica set config is invalid or we are not a member of it
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710417.25/warc/CC-MAIN-20221127173917-20221127203917-00427.warc.gz
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CC-MAIN-2022-49
| 4,382 | 6 |
https://chihyulai.com/category/1st_version_projects/period/undergraduate/page/2/
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math
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For most of what we experience in everyday life, it is rare that one can directly link the obvious outcomes with their underlying theoretical grounds. Equations and plots seem such a long distance toward their practical applications. I regard this project as an important one which links observations of a simple experiment to the complex differential equations in reaction mechanics. This mini-project comes from a homework in reaction engineering, a course I had enrolled in during college. The experiment is simple that any person can carry out using easily accessible materials. The main objective is to construct a batch reactor that can exhibit fermentation with yeast, then quantify the reactions using what we have learned on class. (~age 21, 2017)
Two commercially available sugar-sweetened beverages, glucose solution, and water are used to explored how the sugar content in them affects the fermentation rate of rapid yeast. The anaerobic fermentation of yeast in anaerobic environment is:
C6H12O6 (monosaccharide) → 2C2H5OH (ethanol) + 2CO2 (carbon dioxide) + 2ATP
In this experiment, glass containers are filled with the solutions, then instant yeast is added the each container for production of carbon dioxide. A balloon is used for trapping the gases and is used as a volume sensor, where its dimensions are measured for calculating the volume of generated CO2
. The molar concentration of CO2
is calculated using the ideal gas equation PV = nRT, and the ethanol production rate is calculated by relating with the proposed reaction and using finite different method.
Figure 1. Snapshots of balloon-sealed containers with added yeast at different times.
Figure 2. Volume of balloon (Vballoon) vs time (min).
Assume an inner air pressure of P = 1atm, a temperature of T = 310K (37°C). From the ideal gas equation, the relationship between the number of moles of CO2 and its volume is n = 3.931×10-5V, which according to the reaction, also equals the number of moles of ethanol. The molar concentration of ethanol is calculated by dividing the number of moles by its volume. And by using finite difference method of the first derivative, the rate of increase for molar concentration of ethanol (rC2H5OH) is calculated (Fig. 3).
Figure 3. Increase rate of molar concentration of ethanol (rC2H5OH) vs time (min).
It can be seen that in addition to pure water (Negative), the other three sugar-containing solutions have a maximum formation rate at the beginning (marked by the blue arrow). Wherein the ethanol production rate of glucose solution is eventually lower than 0(mM/min), it is presumed either this is caused by measurement errors or that carbon dioxide is dissolved back into the liquid, causing a decrease in volume, not a decrease in the amount of ethanol.
Here the production rate of ethanol in glucose solution started at a very high value (8.29mM/min), followed by fruit tea (4.17mM/min), and then raspberry juice (3.36mM/min). However, the sugar concentration of raspberry juice is higher than that of fruit tea. There are two factors that may be affected: the type of sugar and the pH value. Among them, the pH of fruit tea is between 5.0 and 6.0 and the pH of raspberry juice is between 2.3 and 2.52. However, the optimal living environment pH of yeast is 4.5 to 5.0, so it is speculated that the acidic environment of raspberry juice inhibits the activity of yeast and reduces rC2H5OH. In addition, only glucose exists in the glucose solution, but there is sucrose in both raspberry juice and fruit tea. Sucrose can be broken down by the yeast and producing ethanol twice as much as the same concentration of glucose. This explains why the final balloon volume (408.69cm3) of fruit tea is greater than the final balloon volume of the glucose solution (361.03cm3).
As being a simple hands-on experiment, this project successfully delivered the knowledge and allowed me to learn the fundamentals through practice, by which creating a connection between reality and theory.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816904.18/warc/CC-MAIN-20240414223349-20240415013349-00835.warc.gz
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CC-MAIN-2024-18
| 4,004 | 13 |
https://brainmass.com/math/linear-algebra/graph-inequality-and-solve-system-of-equations-114087
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math
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See attached file for full problem description.
1. Graph the inequality. 2x + 3y > 6
2. Given g(x) = -3x + 5, find g(2a)
3. Graph the inequality: x - y < = 2
4. Graph the inequality: y > =3x
5. Given f(x) = -x^3 - 3x^2 -3x +9, find f(-2), f(0), and f(3)
6. Given f(x) = -5x - 1, find f(-2)
7. Graph f(x) = 4x + 1
8. Graph f(x) = -2x+ 4
9. Solve the system by addition: 5x - 3y = 13, 4x - 3y = 11
10. Solve the system by substitution: x + y = 12, y = 2x
11. Adult tickets for a play cost $20 and child tickets cost $12. If there were 23 people at a performance and the theater collected $348 from ticket sales, how many adults and how many children attended the play?
12. A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities.
13. The sum of two numbers is 34. Their difference is 12. What are the two numbers?
Assume the two numbers are x and y.
14. Solve the system by substitution: 3x - 5y = 15, y = 2x + 11
15. Solve the system by substitution: 3x - y = -7, x + y = -9
16. The sum of two numbers is 49. The second is 5 more than 3 times the first. What are the two numbers?
17. The difference of two numbers is 75. The second is 5 less than 5 times the first. What are the two numbers?
18. Solve the following system of linear inequalities by graphing: x - 3y >6, 3x + 2y >12
19. Given f(x) = x^2 + x + 10, find f(0)
20. Rewrite the equation y = -2x + 5 as a function of x
The solution shows how to graph inequality in xy-plane and solve system of equations in detail.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866326.60/warc/CC-MAIN-20180524131721-20180524151721-00002.warc.gz
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CC-MAIN-2018-22
| 1,837 | 23 |
http://arnoldkling.com/apstats/logic.html
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math
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Probability and Logic
There is a close relationship between probability and symbolic logic. Consider a truth table for the following statements:
(A) The team will make the playoffs.
(B) The coach will be rehired.
The truth table is:
|Statement A||Statement B|
The rules of logic are that the statement "A and B" is true on the first line of the table and false everywhere else. However, the statement "A or B" is true on the first three lines of the table.
Now, we assign a probability to each of the four lines. Let us assign a probability w to the first line, x to the second line, etc. Thus, we have
|Probability||Statement A||Statement B|
In words, w represents the probability that the team will make the playoffs and the coach will be rehired. x is the probability that the team will make the playoffs and the coach will not be rehired.
What is the probability that the team will make the playoffs? We have to add w + x. We can write,
In addition, we know the following:
P(B) = w + y
w + x + y + z = 1
P(A and B) = w
P(A or B) = w + x + y = 1-z
Suppose that the playoffs and the coach have nothing to do with one another. The coach could be the coach of our high school basketball team, and the playoffs could be the professional football playoffs. In that case, we say that A and B are independent by assumption.
If we assume indepence, this means that P(A and B) = P(A)P(B). That means that w = P(A)P(B). Now, we have four equations in four unknowns:
w = P(A)P(B)
w + x = P(A)
w + y = P(B)
w + x + y + z = 1
Suppose that P(A) = .7 and P(B) = .4. Then, we have w = .28, x = .42, y = .12, and z = .18
Be careful! Of the four equations above, the first equation is only true if you can assume that the two events are independent.
If we cannot assume independence, then we need additional information to solve for all of the probabilities. For example, suppose that we are talking about the coach of a pro basketball team and the prospects for that team making the playoffs. In that case, we cannot say that the probability that the coach will be rehired is independent of the probability that the team will make the playoffs.
One possibility is that we are given the joint probability of the coach being rehired and the team making the playoffs. That is, suppose that we were told that P(A and B) = .3, in addition to being told that P(A) = .7 and P(B) = .4.
In that case, we are given that w = .3, and we can use the other three equations to obtain x = .4, y = .1, and z = .2
Another possibility is that we are given the conditional probability of the coach being rehired if the team makes the playoffs. We write this as P(A|B), and it is equal to P(A and B)/P(B), which means that it equals w/(w+y).
Suppose that the conditional probability is .8. What that means is that w/(w+y) = .8
If we know that P(A) = .7 and P(B) = .4, then we know that (w+y) = .4, so that a = (.8)(.4) = .32. Then we know that x = .38, y = .02, and z = .28.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891750.87/warc/CC-MAIN-20180123052242-20180123072242-00688.warc.gz
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CC-MAIN-2018-05
| 2,939 | 30 |
http://www.andydarnell.com/2010/04/05/if-mashable-ran-the-census/
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math
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A lot of people (me included) have complained about the $$ that the Federal Government is spending to get people to return their census forms. Here’s my take:
When companies like Mashable are able to create this kind of data, it tells me that the United States Government should have nothing to do with gathering and analyzing data. Imagine the $$ saved if we just hired Google to figure out a better way.
This chart by the way is fantastic.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948530841.24/warc/CC-MAIN-20171213201654-20171213221654-00271.warc.gz
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CC-MAIN-2017-51
| 443 | 3 |
https://artofproblemsolving.com/wiki/index.php?title=2009_AMC_10A_Problems/Problem_22&oldid=180035
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math
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2009 AMC 10A Problems/Problem 22
Two cubical dice each have removable numbers through . The twelve numbers on the two dice are removed, put into a bag, then drawn one at a time and randomly reattached to the faces of the cubes, one number to each face. The dice are then rolled and the numbers on the two top faces are added. What is the probability that the sum is ?
At the moment when the numbers are in the bag, imagine that each of them has a different color. Clearly the situation is symmetric at this moment. Hence after we draw them, attach them and throw the dice, the probability of getting some pair of colors is the same for any two colors.
There are ways to pick two of the colors. We now have to count the ways where the two chosen numbers will have a sum of .
A sum of can be obtained as , , or . Each number in the bag has two different colors, hence each of these three options corresponds to four pairs of colors.
Out of the pairs of colors we can get when throwing the dice, will give us the sum . Hence the probability that this will happen is .
Ignoring the numbers that do not affect the probability of the desired outcome (the ones that are not on top of the dice), say that the number on top of the first die is . For the sum of the numbers to be , the second die must have the number on top. There are remaining numbers that could be on top of the second die, of which are (since in all cases and since there are 2 faces for each number 1-6).
Thus, the probability of the sum of the numbers being is , so the answer is .
Taking out the rolling dice part, we see that we're just taking two numbers out of a bag. There are ways to pick two, and there are 12 ways to pick one, and 2 ways to pick the other. (After you pick one, the other one you pick is fixed). Now say you pick n. The other number you pick has to be 7-n. But if you picked 7-n first and n second, that would be the same thing. So we need to divide by 2.
This gives or .
Solution 4 (Educated Guess)
Let first case(Two Same Numbers on One Die) =
Let second case(No Two Same Numbers on One Die) =
Note that the possible combinations of two numbers summing to 7 are and .
The second case() thus has chance. The other case has another probability of some number.
The sum is so the answer must be greater than , which are choices D and E.
Note that there are cases for a number without restrictions.
Use answer choices to note that (Answer choice D)
Also use it to note that (Answer Choice E)
Answer choice D makes more sense , so the answer is
Also, if you had some time, you would note that only 1 of the 66 total combinations fit the first case, so is your answer.
~mathboy282 (Yes I know this is a bad solution but if you had little time left on the test this would be a good educated guess.)
Video Solution by OmegaLearn
Video Solution by TheBeautyofMath
|2009 AMC 10A (Problems • Answer Key • Resources)|
|1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25|
|All AMC 10 Problems and Solutions|
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https://opentuition.com/topic/eoq-39/
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math
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- May 22, 2021 at 1:04 am #621376thuonghaMember
- Topics: 22
- Replies: 15
Hope you are doing well.
I came across this question in Kaplan Kit:
“The production manager has established the following information about a major inventory item.
Purchase price per unit $480
Annual demand 4,000
Supplier’s delivery costs per order $10
Chief buyer’s salary per annum $30,000
Total number of orders placed per annum* 1,000
Annual storage costs per unit $2
Cost of capital 10% per annum
*Relates to all product lines, not just this one.
What is the economic order quantity for this inventory item?”
In their answer for EOQ, the denominator Ch is calculated by $2+10%*$480 = $50, and thus EOQ = 40 instead of 200 (if just use $2).
I don’t think I have seen this cost of capital mentioned in your notes or BPP book before, so quite confused by this answer.
Could you help explain this, please?
Thank you so much.May 22, 2021 at 8:24 am #621396John MoffatKeymaster
- Topics: 57
- Replies: 51532
As I do state in my free lectures, the most likely cost in practice of holding inventory is the interest cost of the money tied up in inventory.
If the cost of capital is 10%, then the interest cost of having $480 tied up in one unit of inventory for one year is 10% x $480.
I hope that you are not using our free notes without watching the lectures that go with them. They are only lecture notes, and it is in the lectures that I work through the examples and expand and explain on the notes.
- You must be logged in to reply to this topic.
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http://ths.gardenweb.com/discussions/2291353/induction-cooktop-questions
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math
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induction cooktop questions?
From reading the posts on induction cooktops, just about everyone is satisfied with what they purchased. What is the difference between the high-end Vikings, Wolfs etc. and the Kenmores, GEs and other brands? The difference in price, all things being equal (same number of induction elements, similar controls, comparable power output etc.) is about a factor of 2. What are you getting for the higher price?
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https://www.slideserve.com/barny/non-euclidean-example-the-unit-sphere-powerpoint-ppt-presentation
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math
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Differential Geometry • Formal mathematical theory • Work with small ‘patches’ • the ‘patches’ look Euclidean • Do calculus over the patches
Manifolds • Open Sets • Coordinate neighbourhood • Compatible neighbourhoods
Tangents • Tangent Vectors • Tangent Space, • Inner Product • Norm: • depends on • varies smoothly
Geodesics and Metrics • The shortest path between two points is the geodesic • The length of the geodesic is the distance between the points
Exponential and Logarithm Maps • : Maps tangents to the manifold • : Maps points on the manifold to • Both maps are locally well defined
Gradient • In Euclidean space: direction of fastest increase • On a manifold: tangent of fastest increase • Definition: is a real valued function. The gradient at is satisfying directional derivative along delta
The Conversion Table • X. Pennec, P. Fillard and N. Ayache , “A Riemannian Framework for Tensor Computing,” International. Journal of Computer Vision., 66(1), 41–66, 2006.
Matrix Lie Groups • Sets of matrices which • form a group under matrix multiplication • are Riemannian manifolds • Examples • Rigid body transformations SE(n) • Rotations SO(n) • Affine motions A(n) • W. Rossman, “Lie Groups: An Introduction through Linear Groups,” Oxford University Press, 2003.
Grassmann Manifolds, . • Each point on the Grassmann manifold, , represents a dimensional subspace of . • Numerically, represented by an orthonormal basis • matrix such that • Representation is not unique • computation should account for this • A. Edelman, T. A. Arias and S. T. Smith, “The Geometry of Algorithms with Orthogonality Constraints,” SIAM Journal on Matrix Analysis and Applications, 20(2), 303–353, 1998.
The Essential Manifold • Set of matrices with • two equal and one zero singular value • let the two equal singular values be 1 • Equivalent to SO(3)xSO(3) • two-time covering of the essential manifold • Can also be expressed as a homogeneous space • S. Soatto, R. Frezza and P. Perona , “Recursive Estimation on the Essential Manifold,” 3rd Europan Conference on Computer Vision, Stockholm, Sweden, May 1994, vol.II, p.61-72.
The Symmetric Manifold • contains symmetric positive definite matrices. e.g. diffusion tensor MRI • it has two different metrics • The Affine Invariant metric • The Log-Euclidean Metric • practically similar to the affine invariant metric • computationally easier to work with • V. Arsigny , P. Fillard, X. Pennec and N. Ayache , “Geometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices,” SIAM Journal of Matrix Analysis and Applications, 29(1), 328–347, 2006.
Mean Shift for Euclidean Spaces • The kernel density estimate • Mean shift as normalized gradient of where • The iteration
Mean Shift • Gradient ascent on kernel density • but, no line search • Equivalent, to expectation-maximization • Nonparametric Clustering • D. Comaniciu and P. Meer , “Mean Shift: A Robust Approach Towards Feature Space Analysis,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, 603–619, 2002. • D. Comaniciu, V. Ramesh and P. Meer , “Kernel-based Object Tracking,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, 564–577, 2003.
Mean Shift for Manifolds • The kernel density estimate • Mean shift as normalized gradient of • The iteration
Mean Shift for Riemannian Manifolds • Map points to tangent space • Get weighted average of tangent vectors • this is the mean shift vector • Map the mean shift vector back to the manifold
Theoretical Properties • Gradient ascent on kernel density • Nonlinear mean shift is provably convergent • upper limit on allowed bandwidth • nonlinear mean shift is equivalent to EM • for homogeneous spaces
Motion Segmentation • Hypothesis Generation Lie groups • Randomly pick elemental subset • Generate parameter hypothesis • Clustering • Cluster parameters on the manifold • Return • Number of dominant modes • Positions of dominant modes
Discontinuity Preserving Filtering • An image is a mapping from a lattice in to data lying on a manifold • Filtering: Run mean shift in the space Iterations update spatial and parameter values. • If the iteration from converges to , set in the filtered image
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http://deansdough.blogspot.com/2014/10/substitution-liquidity-and-elasticity.html
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math
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One of my formative (insofar as one can use that term for something that happens when one is 35) experiences was trying to explain to an introductory microeconomics student that the elasticity of demand for eggs is somewhat low, but the elasticity of demand for Farmer Jones's eggs is very high; his eggs are (presumably) very good substitutes for the eggs of a lot of other farmers. If a single person could set the price of all eggs, the price they choose would have a small effect on the quantity that would sell at that price, but if Farmer Jones tried to unilaterally change only the price of his eggs, the quantity of his eggs that would sell would change a lot.
Yesterday Matt Levine wrote that it doesn't matter whether an individual owns most of the copper in London-Metals-Exchange-approved warehouses because that's a very small fraction of global copper, and Professor Pirrong said that, to a reasonable extent for a moderate period of time, it does, and while the clear theoretical economic categories aren't always clear in practice, in this case it seems more clear and correct to say that global copper can't substitute for LME warehouse copper, but with some time and expense can be converted into it. So if you're looking at a 5-year time horizon, it's probably not worth trying to distinguish the two, but the shorter the relevant time period, the larger the gap that could reasonably open up between the prices of the two.
A lot of what I think of as "demand for liquidity", which isn't quite what other people (e.g. Shin, Tirole, etc.) would mean by that phrase, is time-sensitivity; in a certain language, what I'm thinking about is more of a demand for market liquidity and what they mean is funding liquidity, but to some extent these are both closely tied to "how quickly can I convert one asset into another asset?" or "at what terms of trade can I quickly convert one asset into another asset?", especially as distinct from "at what terms of trade could I convert one asset into another asset if I had a lot of time to try to get a good price?" "Liquidity" then is related to convenience yields, but also to elasticity of intertemporal substitution — whether cash tomorrow (or even this afternoon) is equivalent to cash at some point in the next five years. If you're interested in the price of copper in deciding whether to build a new factory, you can probably use the LME price for delivery over the next couple years as a proxy for global copper prices, but if you need to deliver into an LME futures contract next week, you have a demand for LME copper that doesn't admit the same kind of substitution, and you're going to find that the market is a lot less elastic.
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http://www.maa.org/publications/books/who-gave-you-the-epsilon-and-other-tales-of-mathematical-history
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math
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Who Gave You the Epsilons? is a sequel to the MAA bestselling book, Sherlock Holmes in Babylon. Like its predecessor, this book is a collection of articles on the history of mathematics from the MAA journals, in many cases written by distinguished mathematicians (such as G H Hardy and B.van der Waerden), with commentary by the editors. Whereas the former book covered the history of mathematics from earliest times up to the 18th century and was organized chronologically, the 40 articles in this book are organized thematically and continue the story into the 19th and 20th centuries.
The topics covered in the book are analysis and applied mathematics, geometry, topology and foundations, algebra and number theory, and surveys. Each chapter is preceded by a Foreword, giving the historical background and setting and the scene, and is followed by an Afterword, reporting on advances in our historical knowledge and understanding since the articles first appeared.
This book will be enjoyed by anyone interested in mathematics and its history – and in particular by mathematics teachers at secondary, college and university levels.
Table of Contents
Geometry, topology, and foundations
Algebra and Number Theory
About the Editors
About the Editors
Marlow Anderson is a professor of mathematics at The Colorado College, in Colorado Springs. He has been a member of the mathematics department there since 1982. He was born in Seattle, and received his undergraduate degree from Whitman College. He studied partially ordered algebra at the University of Kansas and received his Ph.D. in 1978. He has written over 20 research papers, and co-authored a monograph on lattice-ordered groups. In addition, he has co-written an undergraduate textbook on abstract algebra. In addition to algebra, he is interested the history of mathematics. When not teaching, reading or researching mathematics, he may be found with his wife Audrey scuba-diving in far-flung parts of the world.
Victor J. Katz, born in Philadelphia, received his Ph.D. in mathematics from Brandeis University in 1968 and was for many years Professor of Mathematics at the University of the District of Columbia. He has long been interested in the history of mathematics and, in particular, in its use in teaching. His well-regarded textbook, A History of Mathematics: An Introduction, is now in its third edition. Its first edition received the Watson Davis Prize of the History of Science Society, a prize is awarded annually by the Society for a book in any field of the history of science suitable for undergraduates. A brief version of this text appeared in 2003. Professor Katz is also the editor of The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook, which was published in July, 2007 by Princeton University Press.
Professor Katz has published many articles on the history of mathematics and its use in teaching. He has edited or co-edited two recent books dealing with this subject, Learn from the Masters (1994) and Using History to Teach Mathematics (2000). He also co-edited a collection of historical articles taken from MAA journals of the past 90 years, Sherlock Holmes in Babylon and other Tales of Mathematical History. He has directed two NSF-sponsored projects that helped college teachers learn the history of mathematics and how to use it in teaching and also involved secondary school teachers in writing materials using history in the teaching of various topics in the high school curriculum. These materials, Historical Modules for the Teaching and Learning of Mathematics, have now been published on a CD by the MAA. Currently, Professor Katz is the PI on an NSF grant to the MAA supporting Convergence, the online magazine in the history of mathematics and its use in teaching. He is a member of the Mathematical Association of America, the American Mathematical Society, the Canadian Society for the History and Philosophy of Mathematics, and the British Society for the History of Mathematics.
Robin Wilson is Professor of Pure Mathematics at the Open University (UK), a Fellow in Mathematics at Keble College, Oxford University, and Emeritus Gresham Professor of Geometry, London (the oldest mathematical Chair in England). He has written and edited about thirty books, mainly on graph theory and the history of mathematics. His research interests focus mainly on British mathematics, especially in the 19th and early 20th centuries, and on the history of graph theory and combinatorics. He is an enthusiastic popularizer of mathematics, having produced books on mathematics and music, mathematical philately, and sudoku, and gives about forty public lectures per year. He has an Erdös number of 1 and has won two MAA awards (a Lester Ford Award (1975) and a George Pólya award (2005).
The MAA has a tradition in the publication of books like this one. I think it began in 1969 with the first of four volumes of papers selected from its various journals (going back to 1890). The four volumes consisted of papers on Pre-calculus, Calculus, Algebra and Geometry respectively. All such articles were expositional, some were historical, and many were inspirational.
Much later, in 2004, there appeared an MAA publication that was compiled in a similar vein — except that its emphasis was historical throughout. It was given the title Sherlock Holmes in Babylon. In it, the articles appear in the chronological order of mathematical developments from ancient times up to the work of Euler in the 18th century. Fortunately, there is now a sequel to that book, which is the subject of this review. It contains forty-one papers pertaining to the history of mathematics from the early 19th century to the late 20th century. Continued...
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https://forums.galciv2.com/325003/building-a-good-economic-planet
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math
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Please pardon my noob question, but I've been playing since Galciv1, and I just don't see the point of economic planets. Do the markets stack multiplicatively? Or are you just aiming for a high score, what? By the time you're done pouring all that extra money back into your planet to build more stock markets, the game's over.
In a tiny map and/or with few opponents, sure.
I'm not sure what you mean by "do the markets stack multiplicatively". Each market adds 25% to the planet's base income, so it's more like simple interest than compound interest. In essence, this means the first four markets are worth "more" than the next four, as it basically doubles your (planetary) income. Additionally, the markets are planetary-only...they do not have a civ-wide effect, but building even one or two on each planet doesn't take much time (at last check, stock markets cost 120 industry to build, or 1158 to rush buy-making the former the more attractive option) and is a fairly large income increase by percentage.
However, one can think of the average of the number of stock markets on a planet as being a civ-wide bonus if the planets are equal in population (and therefore tax rate, as you can't set tax rates individually per planet). Further, this is from a base of 100 as well, so it multiplies by your civilization's economic bonus, rather than adding to it (note: for those of you to whom it isn't obvious, this is better).
When you consider that the two outliers here will be your homeworld(s) (for instance if you take over another civ's homeworld, even if it's a minor race) and planets too small to reach suitable "max" pop (basically sub class eight), which even in a tiny map are relatively small groups, the average population is very close to your mode. Not to mention the fact that as tax income is a function of the square root of the population, your homeworlds actually are not making that much more (except in TA, where they also have a 10% economic bonus on the civ capital) than your average world and for our purposes can be safely figured as a normal world.
Essentially, an average of one stock market per planet is 25% more income than zero, two is 20% more than one, three is 16.67% more than two, four is 14.28% more than three, five is 12.5% more than four, and so on. Each successive stock market provides less of a percentage benefit to your overall economy from the one previous, so on smaller maps it may only be justifiable to build one or three, but it's still worthwhile.
Then again, if you don't have economic problems, you can safely ignore them.
However, as I'm sure a number of players will tell you, if you aren't having economic problems, you're not expanding fast enough. Which isn't to say that having economic problems is a good thing, but it's a rule that I personally live by (in GCII).
(Note: Obviously the above numbers ignore the fact that your planets aren't always at their max pop, more so when you've just colonized them. It's safe to say if your games don't last long enough for all of your planets to grow to max pop, then you can ignore this post-and stock markets, for that matter.)
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https://www.projecteuclid.org/journals/duke-mathematical-journal/volume-165/issue-15/The-Frobenius-properad-is-Koszul/10.1215/00127094-3645116.short
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math
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We show the Koszulness of the properad governing involutive Lie bialgebras and also of the properads governing nonunital and unital-counital Frobenius algebras, solving a long-standing problem. This gives us minimal models for their deformation complexes, and for deformation complexes of their algebras which are discussed in detail. Using an operad of graph complexes we prove, with the help of an earlier result of one of the authors, that there is a highly nontrivial action of the Grothendieck–Teichmüller group on (completed versions of) the minimal models of the properads governing Lie bialgebras and involutive Lie bialgebras by automorphisms. As a corollary, one obtains a large class of universal deformations of (involutive) Lie bialgebras and Frobenius algebras, parameterized by elements of the Grothendieck–Teichmüller Lie algebra. We also prove that for any given homotopy involutive Lie bialgebra structure on a vector space, there is an associated homotopy Batalin–Vilkovisky algebra structure on the associated Chevalley–Eilenberg complex.
"The Frobenius properad is Koszul." Duke Math. J. 165 (15) 2921 - 2989, 15 October 2016. https://doi.org/10.1215/00127094-3645116
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https://ralphmaltby.com/questions/question/ping-iblade-mpf/
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math
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Are these slated to be measured?
Wow, I was expecting a higher number.
Thank you very much Britt.
I did get the Ping I Blade and have done preliminary measurements. The I Blade came out to 464 MPF points, which puts it into the Conventional category. Final numbers will be coming, but I do not see this one changing much, if at all.
Have you had the chance of get one already?
Thank you very much
A soon as I can get one, I will get it measured. Very interested to see how it turns out.
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https://community.tableau.com/thread/129994
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math
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Can we merge rows of a particular column in tableau 8.0.0. For e.g as per attached image the amount $150,000 is repeating three times. It should repeat only one time and that too in the cell where there is the amount $450,000 in Bold (also indicated in the image by drawing line).
Can we merge the "target" column to display only one $150,000 in place of the bold $450,000 .i.e is merging of rows possible? All the other columns are correct.
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https://uneasymoney.com/2015/02/20/why-theories-of-national-income-based-on-accounting-identities-are-nonsensical-and-error-ridden-part-i/
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math
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I have had occasion to make many references in the past to Richard Lipsey’s wonderful article “The Foundations of the Theory of National Income” which was included in the volume Essays in Honour of Lord Robbins. When some 40 years ago, while a grad student at UCLA, I luckily came upon Lipsey’s essay, it was a revelation to me, because it contradicted what I had been taught as an undergrad about the distinctions between planned (ex ante) investment and savings, and realized (ex post) investment and savings. Supposedly, planned investment and planned savings are equal only in equilibrium, but realized investment and savings are always equal. Lipsey explained why the ex ante/ex post distinction is both incorrect and misleading. In this post I want to begin to summarize some of the important points that Lipsey made in his essay.
Lipsey starts with a list of seven erroneous propositions commonly found in introductory and intermediate textbooks. Here they are (copied almost verbatim), grouped under three headings:
I The Static Model in Equilibrium
1 The equilibrium of the basic Keynesian model is given by the intersection of the aggregate demand (i.e., expenditure) function and the 45-degree line representing the accounting identity E ≡ Y.
II The Static Model in Disequilibrium
2 Although people may try to save different amounts from what people try to invest, savings can’t be different from investment; realized (ex post) savings necessarily always equals realized (ex post) investment.
3 Out of equilibrium, planned savings do not equal planned investment, so it follows from (2) that someone’s plans are being disappointed, and there must be either unplanned savings or dissavings, or unplanned investment or disinvestment
4 The simultaneous fulfilment of the plans of savers and investors occurs only when income is at its equilibrium level just as the plans of buyers and sellers can be simultaneously fulfilled only at the equilibrium price.
III The Dynamic Behavior of the Model
5 Whenever savers (households) plan to save an amount different from what investors (business firms) plan to invest, a mechanism operates to ensure that realized savings remain equal to realized investment, despite the attempts of savers and investors to make it otherwise. Indeed, this mechanism is what causes dynamic change in the circular flow of income and expenditure.
6 Since the real world, unlike the simple textbook model, contains a very complex set of interactions, it is not easy to see how savings stay equal to investment even in the worst disequilibrium and the most rapid change.
7 The dynamic behavior of the Keynesian circular flow model in which disequilibrium implies unintended investment or disinvestment can be shown by moving upwards or downwards along the gap between the expenditure function and the 45-degree line in the basic Keynesian model.
Although some or all of these propositions are found in most standard textbook treatments of national income theory, every one of them is wrong.
Let’s look at proposition 1. It says that the equilibrium level of income and expenditure is determined algebraically by the following two relations: the expenditure (or aggregate demand) function:
E = E(Y) + A
and the expenditure-income accounting identity
E ≡ Y.
An accounting identity provides no independent information about the real world, because there is no possible state of the world in which the accounting identity does not hold. It therefore adds no new information not contained in the expenditure function. So the equilibrium level of income and expenditure must be determined on the basis of only the expenditure function. But if the expenditure function remains as is, it cannot be solved, because there are two unknowns and only one equation. To solve the equation we have to make a substitution based on the accounting identity E ≡ Y. Using that substitution, we can rewrite the expenditure function this way.
E = E(E) + A
If the expenditure function is linear, we can write it as follows:
E = bE + A,
which leads to the following solution:
E = A/(1 – b).
That solution tells us that expenditure is a particular number, but it is not a functional relationship between two variables representing a theory, however naïve, of household behavior; it simply asserts that E takes on a particular value.
Thus treating the equality of investment and savings as an identity turns the simply Keynesian theory into a nonsense theory.
The point could be restated slightly differently. If we treat the equality of investment and savings as an identity, then if we follow the usual convention and label the vertical axis as E, it is a matter of indifference whether we label the horizontal axis Y or E, because Y and E are not distinct, they are identical. However we choose to label the horizontal axis, the solution of the model must occur along the 45-degree line representing either E = Y or E = E, which are equivalent. Because, the equality between E and itself or between E and Y is necessarily satisfied at any value of E, we can arbitrarily choose whatever value of E we want, and we will have a solution.
So the only reasonable way to interpret the equality between investment and saving, so that you can derive a solution to the simple Keynesian model is to treat E and Y as distinct variables that may differ, but will always be equal when the economy is in equilibrium.
So the only coherent theory of income is
E = E(Y) + A
and, an equilibrium condition
E = Y.
E and Y do not represent the same thing, so it makes sense to state a theory of how E varies in relation to Y, and to find a solution to the model corresponding to an equilibrium in which E and Y are equal, though they are distinct and not necessarily equal.
But the limitation of this model is that it provides us with no information about how the model behaves when it is not in equilibrium, not being in equilibrium meaning that E and Y are not the equal. Note, however, that if we restrict ourselves to the model in equilibrium, it is legitimate to write E ≡ Y, because the equality of E and Y is what defines equilibrium. But all the erroneous statements 2 through 7 listed above all refer to how the model.
The nonsensical implications of constructing a model of income in which expenditure is treated as a function of income while income and expenditure are defined to be identical has led to the widespread adoption of a distinction between planned (ex ante) investment and savings and realized (ex post) investment and savings. Using the ex ante/ex post distinction, textbooks usually say that in equilibrium planned investment equals planned savings, while in disequilibrium not all investment and savings plans are realized. The reasoning being that is that if planned saving exceeds planned investment, the necessity for realized savings to equal realized investment requires that there be unintended investment or unintended dissaving. In other words, the definitional identity between expenditure and income is being used to tell us whether investment plans are being executed as planned or being frustrated in the real world.
Question: How is it possible that an identity true by definition in all states of the world can have any empirical implications?
Answer: It’s not.
In my next installment in this series, I will go through Lipsey’s example showing how planned and realized saving can indeed exceed planned and realized investment over the disequilibrium adjustment induced by a reduction in planned investment relative to a pre-existing equilibrium.
UPDATE (2/21/2015]: In the second sentence of the paragraph beginning with the words “An accounting Identity provides,” I wrote: “It therefore adds information not contained in the expenditure function,” which, of course, is the exact opposite of what I meant to say. I should have written: “It therefore adds NO NEW information not contained in the expenditure function.” I have now inserted those two words into the text. Thanks to Richard Lipsey for catching that unfortunate mistake.
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https://byjusexamprep.com/gate-2021-industrial-engineering-rapid-mini-mock-i-e1a602d0-4522-11eb-98d7-1bad31b9fcd3
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math
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GATE 2021: Industrial Engineering Rapid Mini Mock (App update required to attempt this test)
Attempt now to get your rank among 721 students!
Simplex method of solving linear programming problem uses ____.
A company produce 4800 parts per day and sells them at approximately half of the rate. The setup cost is Rs 1000 and carrying cost is Rs 5 per unit. The annual demand is 480000 per years. The length of each production will be
In a forecasting model, at the end of period 13, the forecasted value for period 14 is 75. Actual value in the periods 14 to 16 are constant at 100. If the assumed simple exponential smoothing parameter is 0.5, then BIAS at the end of period 16 is
The cost of proving service in a queuing system increases with
The demand for an item is 900 units per month and the lead time is 10 days. In the past two month, the maximum demand observed is 50 units per day. For a re-ordering system based on inventory level, the re-order level (in units) is
A product needs to be transported form four factories F1, F2, F3, & F4 to three warehouses P1, P2, P3. The corresponding demand & supply and cost for unit transportation for ith factory to jth warehouse is given is matrix below
The total number of constraints for above given transportation problem are
The demand for five time periods was 9, 11, 15, 16 and 20. In a time series forecasting model, a linear regression can be represented by an equation F = 5.7 + 2.5 t where F is the forecast for period t. The mean absolute deviations is
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:
If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of the activity S without delaying the completion of the project is ___________
At a production machine, parts arrive according to a Poisson process at the rate of 0.35 parts per minute. Processing time for parts have exponential distribution with mean of 2 min. What is the probability that a random part arrival finds that there are already 8 parts in the system (in machine + in queue)?
Just-In-Time production is also known as _______.
Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ____________.
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| 2,521 | 15 |
https://payrollheaven.com/define/constant-dollar-gdp/
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math
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Business, Legal & Accounting Glossary
Constant dollar GDP is gross domestic product adjusted for price changes. Gross domestic product is the total market value of all goods and services an economy produces. But the actual GDP in a given year – known as current dollar GDP – also reflects either an increase or decrease in the general level of prices (i.e., inflation or deflation). Constant dollar GDP adjusts for these price changes. Calculating constant dollar GDP usually entails selecting a base year against which annual price changes can be measured. By eliminating the impact of either inflation or deflation, constant dollar GDP makes comparisons of GDP in different periods useful. Constant dollar GDP has its limitations, however, because new technologies continually change the nature of the goods and services an economy produces. Nevertheless, the constant dollar GDP provides the best measure of overall economic growth. Indeed, because constant dollar GDP shows the real growth in the economy, constant dollar GDP is also known as real GDP.
To help you cite our definitions in your bibliography, here is the proper citation layout for the three major formatting styles, with all of the relevant information filled in.
Definitions for Constant Dollar GDP are sourced/syndicated and enhanced from:
This glossary post was last updated: 4th February, 2020 | 5 Views.
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https://amidonplanet.com/4-pitfalls-for-developing-doers-of-mathematics-takeaways-from-the-craig-groeschel-leadership-podcast/
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math
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4 Pitfalls for Developing Doers of Mathematics: Takeaways from the Craig Groeschel Leadership Podcast
I saved the day.
The math problem had a small detail in it that if my students were not paying attention, it would mess up their work. So I darted around the room and pointed out the detail at the precise moment each group encountered it. No one got confused. No one struggled. Everyone got the right answer. It was a fantastic moment…until I assigned the next problem. After a few moments all of the groups began to glance in my direction, and a boy right next to me asked, “What do we do?”
The better question was, “What did I do?” I didn’t save the day. I wasn’t developing my students’ capacity to do mathematics. Instead, I encountered a pitfall of developing doers of mathematics.
Developing Doers of Mathematics
Recently, I head an episode of the Craig Groeschel Leadership Podcast where he discussed four pitfalls leaders can fall into in developing the people they lead.
All throughout the podcast, I kept thinking of parallels between what Pastor Craig shared about leading organizations and the complexities of teaching and learning mathematics (don’t we all?). I see the job of teaching as facilitating a productive relationship between students and mathematics so that students see themselves as doers of mathematics. In other words, the job of the teacher is to develop doers of mathematics.
The Four Pitfalls of Developing Doers of Mathematics
I present these pitfalls of developing doers of mathematics knowing I have fell into each of them multiple times. By naming and recognizing these pitfalls, we can avoid them and develop the kind of relationships we want our students/children/doers of mathematics to have with mathematics. I see these pitfalls existing for teachers, parents, tutors, even students, basically, anyone who may help someone develop as a doer of mathematics.
1. Controlling – creates compliant doers of mathematics.
This pitfall is where students are not given freedom to consider their own methods for solving a math problem. Instead of giving space to explore and make sense of the problem, students are dictated a carefully constructed algorithm for solving the problem. By definition, the problem is no longer a problem. When the student has been shown exactly how to solve a math problem, the problem has transformed into a mere exercise. Controlling has turned doing math into executing algorithms.
To avoid this pitfall students need space to explore problems. A great article that was written about this idea is call Never say Anything a Kid Can Say by Steven Reinhart. The mindset presented in this article has helped me be quiet, sit back, and trust the student(s) (through gentle prodding) to produce a solution, and then use that work as a starting point for a conversation about the problem. Also Mandy Jansen@MandyMathEd has this idea of “rough draft talk” for solving math problems. The idea being lets consider the idea of creating rough drafts for papers and use that same iterative process for creating solutions for math problems.
2. Criticizing – creates insecure doers of mathematics.
This pitfall is where students may be given freedom to consider their own methods for solving a math problem, but each method is quickly identified for how it falls short in efficiency, accuracy, elegance, or just is not the preferred method of the person providing assistance. Students are eventually leery of presenting their ideas for solving a problem given the overly critical environment in which the idea is received.
To avoid this pitfall an asset-based perspective of the work students do with mathematics needs to be developed. Instead of seeing what is wrong with the method, consider what is right. This approach of having an asset-based perspective and assigning competency to students can be seen in the work around Complex Instruction.
Two books I recommend on Complex Instruction in the math classroom are both from the National Council for Teachers of Mathematics (NCTM). One book is called Strength in Numbers: Collaborative Learning in Secondary Mathematics by Horn. The other book is Smarter Together: Collaboration and Equity in the Elementary Math Classroom by Featherstone, Crespo, Jilk, Oslund, Parks, and Wood.
3. Avoiding – creates disengaged doers of mathematics.
This pitfall is where students are given freedom to consider their own methods for solving math problems, but are not given any feedback. The person providing assistance…doesn’t. They are not engaged with what the students are doing and in turn the students see it (understandably) as a lack of caring in what they are doing.
To avoid this pitfall the answer is to simply engage. The easiest way to engage is to ask questions. Try to figure out how students are making sense of the problems and attempt to do so with no assumptions.
I remember noticing on my son once identified a rectangle as having six sides on his homework. My gut told me ask him why he got the question wrong (He knows how many sides are on a rectangle, right?). Instead, I asked him how he came to the answer of six, simply and with no judgement. He told me he used a tile in the shape of a rectangle to count all the sides and came up with six. He counted around the tile and then one on top, and one on the bottom.
I immediately realized his problem was not a rectangle problem. It was a problem identifying the difference between three dimensional shapes and two dimensional shapes. It was a problem identifying the difference between sides of a polygon and faces of a polyhedron. Asking the question, and not avoiding, resulted in a wonderful understanding for both of us.
4. Rescuing – creates helpless doers of mathematics.
This is where students are given freedom to consider their own methods for solving math problems but are given help at the smallest indication of struggle. An example of this pitfall can be seen in the story that began this blog post.
To avoid this pitfall, students need to be given permission to struggle and sometimes even fail. This does not mean disengagement but providing assistance in other ways. Asking an open-ended, probing question, encouraging them to continue on a line of thinking, creating timely partnerships between students considering the same solution path, are all ways to stay engaged but not rob students of the learning potential of a math problem. Helping students learn how to deal with struggle and to learn from failure will not only develop them as doers of mathematics but also as people.
Knowing is half the battle…
In the end, avoiding these pitfalls comes down to a balance of engagement and freedom. By knowing these pitfalls we can avoid them and help our students develop the kind of relationship we want them to have with mathematics.
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http://msj.iau-arak.ac.ir/article_531016.html
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math
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Document Type: Research Articles
Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran.
Fuzzy integral equations have a major role in the mathematics and applications.
In this paper, general fuzzy integral equations with nonlinear fuzzy
kernels are introduced. The existence and uniqueness of their solutions are
approved and an upper bound for them are determined. Finally an algorithm
is drawn to show theorems better.
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| 446 | 7 |
https://www.cut-the-knot.org/do_you_know/compass.shtml
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math
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Geometric Construction with the Compass Alone
Everything you can do with a ruler and a compass you can do with the compass alone.
Well, not everything. For example, you can't draw straight lines using a compass. There is no talking about it. However, you can do everything reasonable. I hope you would find this claim no less remarkable.
In what is known as the Geometry of Compass, a straight line is defined by any pair of two points. Starting with two points, other points can be constructed with compass alone. Thus in the following constructing a straight line means finding two points that belong to that line.
There are geometries in which the ruler is never used to start with. E. g., in finite geometries that only contain a finite number of points and lines, a line is just a (finite) collection of points. On the sphere, the role of straight lines is played by the great circles. The question of geometric construction with the compass alone is not concerned with such kinds of geometries. Geometry of Compass only deals with constructions in the Euclidean plane, and its basic question could be formulated as, What ruler-and-compass constructions could be accomplished with the compass alone?
The assertion that every ruler-and-compass construction could be accomplished with a compass is due to Lorenzo Mascheroni (1750-1800) and appeared in his 1797 tractate The Geometry of Compasses.
Interestingly, in 1928 the Danish mathematician Hjelmslev discovered in a bookshop in Copenhagen a book
Inspired by Mascheroni's result, Jacob Steiner (1796-1863) tried to prove a similar result for a straightedge instead of a compass. In his book Geometrical Constructions Using a Straight Line and a Fixed Circle published in 1833, Steiner was able to prove that given a fixed circle and its center, all the constructions in the plane can be carried out by the straightedge alone. Using only elementary Projective Geometry it can be shown that the center of the circle is indispensable.
With regard to the Mascheroni's result, instead of checking every single construction in the plane we agree that such constructions can be accomplished with a sequence of the four basic ones:
- To draw a circle with the given center and radius
- To find the point of intersection of two circles
- To find the points of intersection of a straight line and a circle
- To find a point of intersection of two straight lines
The difficulty obviously lies with the last two problems. In the Geometry of Compass constructions may be awfully obscure even for simple problems. To avoid complicating the matters it's always useful to split a problem into a number of simpler steps. A proof to the Mascheroni result will emerge as a combination of the problems below. (However, not all of the problems are related to the proof.)
Problems (Use a compass only)
In all problems below a segment AB is given by its end points A and B.
- Construct segments 2, 3, 4, etc. times larger than AB.
- A point C is known to lie outside the straight line AB. Construct a point D symmetric to C with respect to AB.
- A circle is given by its radius R and the center O. Assume O does not lie on AB. Find the points of intersection of the circle with the segment AB.
- Find a point C such that AC is perpendicular to AB.
- Determine whether three given points A, B, C lie on the same line.
- Given three points A, B and C. C is known to lie outside the straight line AB. Complete the parallelogram ABCD.
- Let two points A and B belong to a circle with center O. Bisect the two arcs of the circle defined by the points A and B.
- A circle is given by its radius R and the center O that lies on AB. Find the points of intersection of the circle with the segment AB.
- Build a square with the side AB.
- Let the quantities a, b, c be defined as the lengths of three given segments. Find x such that
a/b = c/x.
- Find the intersection point of two lines each given by a pair of points - AB and CD, respectively.
- Construct segments 2, 3, 4, etc. times smaller than AB.
- Construct the center of a given circle.
- Bisect a given line AB.
- Construct a Regular Pentagon
- R. Courant and H. Robbins, What is Mathematics?, Oxford University Press, 1996
- H. Dorrie, 100 Great Problems Of Elementary Mathematics, Dover Publications, NY, 1965.
- M. Gardner, Mathematical Circus, Vintage Books, NY, 1981
- R. Honsberger, Ingenuity in Mathematics, MAA, New Math Library, 1970
- A. Kostovskii, Geometrical Construction with Compasses Only, Mir Publishers, Moscow, 1986
- G. E. Martin, Geometric Constructions, Springer, 1998
- S. K. Stein, Mathematics: The Man-Made Universe, 3rd edition, Dover, 2000.
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| 4,651 | 39 |
https://physics.stackexchange.com/questions/285759/compatibility-between-classical-newtonian-gravitation-and-quantum-mechanics
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math
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As I understand, we do not have yet a unified theory covering at once both general relativity and quantum mechanics. However, do we have a theoretical framework completely covering both classical Newtonian gravitation (i.e. without space-time curvature or for not so massive gravitational sources) and quantum mechanics? Is there any reference on this question?
Since both Newtonian gravitation and electrostatic interaction (Coulomb's law) follow an inverse square law, Newtonian gravitation is as compatible with QM as electrostatics is. We do not need anything new to account for this interaction. An article in Physics Today describes an experiment where the gravitationally bound states of neutrons in a box were measured. Here is a more recent review.
Since an expansion in $v/c$ or the curvature is possible, one should be able to incorporate even weakly relativistic effects, e.g., the $1/r^3$ correction to the potential that accounts for the anomalous precession of the perihelion of Mercury. This is analogous to the spin-orbit, Thomas precession, and "mass shift" correction terms -- all relativistic of order $v^2/c^2$ that account for the fine structure of the hydrogen atom.
Of course one should note that it is possible to do quantum mechanics -- actually, quantum field theory -- in curved spacetime backgrounds. Here background means that one neglects the gravitational field produced by the matter that is modeled quantum mechanically. E.g., in Hawking's famous calculation, the black hole and the rest of spadetime is entirely classical, and the gravitational field produced by the radiation is neglected, and only the radiation is quantum mechanical. For a general formalism see the recent review by Fredenhagen and Rejzner.
If we take general relativity to be "matter tells spacetime how to curve, curvature tells matter how to move", then one could say that we know how to treat the latter quantum mechanically, but not the former.
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| 1,954 | 5 |
http://kwiznet.com/p/takeQuiz.php?ChapterID=10946&CurriculumID=65&Num=7.13
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math
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|A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another name for the original figure is preimage.|
A transformation can be shown using an arrow.
Three main types of transformations:
Another name for congruence transformation is isometry. An isometry is a transformation that preserves length and angle measure.
Directions: Choose the correct answer. Also draw 5 examples for each type of transformation: reflection, translation, rotation and dilation.
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https://scitalks.ca/PIRSA/18020061
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math
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Video URL http://pirsa.org/18020061
Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. A natural question to ask is whether the theory is stable under small perturbations away from equilibrium. We compare and contrast two examples: de Broglie's 1927 pilot-wave theory and Bohm's 1952 reformulation thereof. It is well established that in de Broglie's dynamics initial deviations from equilibrium will relax. We show that this is not the case for Bohm's dynamics: initial deviations from equilibrium do not relax and in fact grow with time. On this basis we argue that Bohm's dynamics is untenable as a physical theory (while de Broglie's dynamics remains a viable candidate). We advocate stability as a general selection criterion for hidden-variables theories.
- Quantum Foundations
- Scientific Series
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| 917 | 4 |
http://stcolmansns.ie/author/1st-class/
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math
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1st class are learning all about ordinal numbers this week in Maths and are looking out for the different ways we use them throughout the day!
: Uncaught Error: Call to undefined function twentytwelve_content_nav() in /home/customer/www/stcolmansns.ie/public_html/wp-content/themes/wp_kindergarten/author.php:73
#0 /home/customer/www/stcolmansns.ie/public_html/wp-includes/template-loader.php(106): include()
#1 /home/customer/www/stcolmansns.ie/public_html/wp-blog-header.php(19): require_once('/home/customer/...')
#2 /home/customer/www/stcolmansns.ie/public_html/index.php(17): require('/home/customer/...')
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| 610 | 5 |
https://www.wyzant.com/resources/answers/43945/system_of_equations
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math
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The treatment of a certain viral disease requires a combination dose of drugs D1 and D2. Each unit of D1 contains 1 milligram of factor X and 2 milligrams of factor Y, and each unit of D2 contains 2 milligrams of factor X and 3 milligrams of factor Y. If the most effective treatment requires 13 milligrams of factor X and 22 milligrams of factor Y, how many units of D1 and D2 should be administered to the patient?
One unit of D1 contains 1 mg of X and 2 mg of Y. One unit of D2 contains 2 mg of X and 3 mg of Y
Suppose you choose a units of D1 and b units of D2. Then you get a mg of X and 2a mg of Y (from D1) and 2b mg of X and 3b mg of Y from D2. So you get a total of a + 2b mg of X and 2a + 2b mg of Y. What you want is
a + 2b = 13
2a + 3b = 22
Multiply first equation by 2 throughout: 2a + 4b = 26. Subtract the second equation to get b = 4. That gives a + 8 = 13, so that a = 5.
Answer: Take 5 units of D1 and 4 units of D2. Check for yourself that you get 13 mg of X and 22 mg of Y, total, by doing so. (I have!)
Dattaprabhakar (Dr. G.)
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CC-MAIN-2017-43
| 1,047 | 8 |
https://www.majortests.com/essay/6-03-Calorimtery-Honors-P3G9WUGQAS.html
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math
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1. Measure out approximately 200 mL of distilled water and pour it into the calorimeter. Stir carefully with a thermometer until a constant temperature is reached. Record the volume of water and the constant initial temperature of the water on your data table. 2. Place a plastic measuring trough on top of the digital balance, and then zero the balance (press the tare button) so that the mass of the trough will be "ignored" and will not be added to the total mass measured by the balance. 3. Measure out approximately three to five scoops of solid sodium hydroxide and record the mass to your data table. 4. Place the solid sodium hydroxide into the water in the …show more content…
a. Write the balanced chemical reaction and enthalpy change for Part I (1pt)
b. Write the balanced chemical reaction and enthalpy change for Part II (1pt)
c. Calculate the enthalpy change using Hess's Law. Refer to the lesson for an example of Hess's Law. (2pt) 2. If the accepted enthalpy change value for the dissolving of sodium hydroxide in water is −44.2 kilojoules per mole, determine the percent error of the experimental value that you calculated in Part I. Show your work.
(experimental - actual value) / actual value × 100 % 3. If the accepted heat of reaction for the neutralization of hydrochloric acid with sodium hydroxide is −56.0 kilojoules per mole, determine the percent error of the experimental value that you calculated in Part II. Show your work.
(experimental - actual value) / actual value × 100 % 4. Using the accepted values of the processes you've examined, would your estimation of the enthalpy change for the reaction of solid sodium hydroxide in aqueous hydrochloric acid change from the prediction you made in question one? Explain your answer in complete sentences. 5. Give a detailed explanation, using what you know about bonds and forces of attraction, for the enthalpy changes you observed in parts I and II of this lab. Explain your answer in complete sentences. 6. If the hole for the thermometer in a calorimeter is wider than the diameter of the thermometer, leaving a gap between the lid and the thermometer
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| 2,144 | 6 |
https://www.researchgate.net/profile/Kota-Katanoda
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math
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Kota KatanodaNational Cancer Center, Japan | ncc · Center for Cancer Control and Information Services
Editor-in-Chief of the Journal of Epidemiology, the official journal of the Japan Epidemiological Association
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
I want to conduct path analysis with logistic regression model.
Exposure variables are continuous (body weights at different time points), and mediator variables are also continuous (age etc.).
Outcome is dichotomous variable (existence of a disease).
My interests are the direct and indirect effects of exposure variables on the outcome. So I am trying to do path analysis with logistic regression model.
I use SAS, but I could not find how to apply logistic model with PROC CALIS.
Are there any options to select logistic model? or some other procedures?
This may be done by conducting several regression analyses and re-calculating the output coefficients, but I want to avoid self calculation.
Some websites say it can be done by Mplus. Is it an easier way to use Mplus?
I am looking for a standard way to calculate risk-factor-specific incidence rate from overall population incidence rate. The available data are overall population incidence rate of a disease, prevalence of a risk factor, and relative risk of that disease according to the risk factor. What I want to do is to estimate the incidence rate of people with or without that risk factor. My image is to allocate the overall incidence rate into two groups (risk factor holders and non-holders), keeping consistency with the overall incidence rate. Are there any good references?
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| 1,767 | 13 |
https://math.hmc.edu/funfacts/volume-of-a-ball-in-n-dimensions/
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math
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The unit ball in Rn is defined as the set of points (x1,…,xn) such that
x12 + … + xn2 <= 1.
What is the volume of the unit ball in various dimensions?
Let's investigate! The 1-dimensional volume (i.e., length) of the 1-dimensional ball (the interval [-1,1]) is 2
The 2-dimensional volume (i.e., area) of the unit disc in the plane is pi
The 3-dimensional volume of the unit ball in R3is 4/3 Pi
The “volume” of the unit ball in R4is (Pi/2) * Pi
So apparently, as the dimension increases, so does the volume of the unit ball. What does this volume tend to as the dimension tends to infinity?
Intuitively, one may think that in higher and higher dimensions there's more and more “room” in the unit ball, allowing its volume to become larger and larger. Does the volume become infinite, or does it approach a sufficiently large constant as the dimension increases?
The answer is surprising and shows how our intuition is often misleading. Using multivariable calculus one can calculate the volume of the unit ball in Rn to be
V(n) = Pin/2 / Gamma(n/2 + 1),
where Gamma is the Gamma function that generalizes the factorial function (i.e., Gamma(z+1) = z!). For n even, say n=2k, the volume of the unit ball is thus given by
V(n) = Pikk
Since k! tends to infinity faster than Pik, it follows that V(n) tends to 0 as n tends to infinity!
In higher dimensions you can fit less and less stuff into the unit ball. Of course, by stuff we mean n-dimensional stuff, since the unit ball in Rn always contains all the lower dimensional unit balls!
Try computing the volume of the unit ball in R3 and R4 using multivariable calculus. Then using a computer algebra package plot V(n) using the formula above. What dimension seems to have the maximal volume? Now plot V(n)1/n. Explain. Explore these same ideas with the surface area. See also Surface Area of a sphere and High Dimensional spheres in Cubes.
The Math Behind the Fact:
One may work with the formula for V(n) by applying Stirling's Formula, which approximates Gamma(x+1) by xx ex (2 Pi x)1/2 for large x, to see why the surprising fact above is true.
Another heuristic is the following probabilistic argument. Pick n points independently and identically distributed (i.i.d.) from a uniform distribution in [-1,1], and form an n-tuple out of these numbers. The resulting vector represents a point picked randomly out of the unit box B=[-1,1]n, so the probability that such a point is in the unit n-ball is the ratio R(n) of the volume V(n) to the volume of the unit box, which is 2n.
Notice that if there are just two coordinates of this point that are greater than 1/Sqrt, then the point cannot be in the unit n-ball. As n grows, we choose more and more coordinates i.i.d. from the uniform distribution, and the smaller the probability is that just zero or one of those n coordinates are bigger than 1/Sqrt. A little thought reveals that for large n, this probability decreases by about 1/Sqrt for each new coordinate that is chosen. This shows that the ratio R(n) tends to 0 as n goes to infinity.
However, we hope to show that V(n)=2nR(n) tends to 0 as n goes to infinity. A refinement of the above argument will do the trick: if there are just five coordinates of this point that are greater than 1/Sqrt, then the point cannot be in the unit n-ball. For large n, as each new coordinate chosen, the probability than less than five coordinates are bigger than 1/Sqrt drops by about 1/Sqrt. So V(n) changes by about a factor 1/Sqrt as n is incremented, for large n. On the other hand, the factor 2n changes by a factor of 2 as n is incremented, for large n. Hence 2n changes by a factor of 2/Sqrt for large enough n, so whatever this quantity is, it eventually gets smaller and smaller.
How to Cite this Page:
Su, Francis E., et al. “Volume of a Ball in N Dimensions.” Math Fun Facts.
Fun Fact suggested by:
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https://www.coursehero.com/file/6426979/lab-topicsF09/
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math
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MTH140 – Labs Note - Labs start in the second week of classes, i.e. on Sept. 14. Lab format – Each lab consists of three parts: • Part I – Examples. The TA will do examples on the board. • Part II – Quiz. The TA will write the questions on the board. You must supply the paper on which you write the solutions. The paper must be blank at the start of the quiz. The pages must be letter size and neat (i.e. not pages tore from a coil notebook). Multiple pages must be stapled. Pages held together by a paperclip will not be accepted. You may write on both sides of the page. • Part III – The TA will return the quiz from the previous week and go over the solution. Lab Topics (Caution: the list of practice exercises below does not contain all the exercises from the homework list) • Lab 1 – Functions and graphs (text sections 1.1 – 1.3) Practice exercises: 1.1: 30, 31, 39, 43, 65; 1.3: 17, 19, 21, 24, 35, 39, 43; • Lab 2 – Trigonometry (text appendix D) Practice exercises:
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http://erikemason.weebly.com/
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math
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Water Cycle Review
•Also called the hydrologic cycle
•The journey water takes as it circulates from the land to the air and back again.
•Involves evaporation, condensation, and precipitation.
•Repeats as a never-ending cycle
•Naturally occurring substances such a mineral, forest, water, and land that are used by humans.
•A resource that can be used repeatedly because it is replaced naturally (cycle).
•Water fits both these criteria.
•Basin-like land formation defined by highpoints and divides that descends into lower elevations.
•Carries water from the land after rainfall or snow melts.
•Drains all the water into a common outlet such as a stream channel, a reservoir, or bay
•Very low amounts of dissolved salt – less than 1%
•Ponds and Lakes
•Streams and Rivers
•Makes up 3% of Earth’s water resources, including ice caps and glaciers
•High concentrations of salt
•3.5% of the weight of seawater comes from dissolved salt (salinity)
•Makes up 97% of Earth’s water resources
•Water on the surface of the planet
•Ponds and Lakes
•Streams and Rivers
•Replenished by precipitation and groundwater
•More prone to pollution than groundwater
•Water found underground in cracks and spaces in soil, sand, and rock.
•Stored in and moves slowly through aquifers
•More than 50% of the people in the U.S. get their drinking water from groundwater.
•Largest use is irrigating crops
•Less prone to pollution
•Permeable – rock layers or sediments that transmit groundwater freely
a.Must include spaces (pores) throughout the rock layer
b.Pores must be connected
•Impermeable – few or no connected pore spaces, such as clay
•Zone of Aeration – region between the earth’s surface and the water table
•Water Table – the upper surface of the Zone of Saturation (can move up or down depending on rainfall)
•Zone of Saturation – region in the ground in which the pore spaces are filled with water
•Made of gravel, sand, sandstone, or limestone
•Water can move through these materials because they have large connected spaces (pores) that make them permeable.
•The flow of water depends on the size of the spaces and how well they are connected.
•An excavation or structure created in the ground by digging, which accesses groundwater in an aquifer.
•The well water is drawn by a pump that is raised mechanically or by hand.
•How is the well depth determined? What might make a well “go dry?”
•Replenished by precipitation
•A place in the ground where water flows up to the surface because of natural pressure without being pumped.
•Water comes directly from the aquifer or porous rock layer.
•Gravity creates the natural pressure.
•Contamination of bodies of water, often by human activity, which affects watersheds
•Occurs when pollutants are discharged directly or indirectly into the water.
•Along with air pollution, water pollution is the second biggest environmental concern.
Point Source Pollution
When the pollutants come from a single location such as dumping chemicals into a river.
Nonpoint Source Pollution
When pollutants are introduced into the environment over a large, widespread area such as agricultural runoff.
Types of Water Pollution
Surface Water Pollution
•Hazardous substances coming into contact with surface water
•Dissolves or mixes physically with the water
•Examples: Humans dumping trash into the waterways, especially objects that are swept down storm drains.
•Release of liquid petroleum hydrocarbons (oil) into the water
•Especially harmful to marine and other wildlife
•Usually localized, but can spread
•Examples: oil spills
Chemical Water Pollution
•Chemicals from industries and farmers that run off into the waterways.
•Examples: metals and solvents from industries
•Also, chemicals that control weeds, insects, and pests
•Pesticides and chemicals wash deep into the ground by rain water
•Can get into the aquifers, thus polluting the groundwater
•Anything on the surface can eventually work its way down to the groundwater.
•Plume – the area of groundwater affected by the contamination
•Look at the diagram and observe the amount of contamination in relationship to the point pollution.
Thermal Water Pollution
•The rise or fall in the temperature of a natural body of water.
•Changes the physical properties of water, particularly the amount of dissolved oxygen in the water.
•Decreases fish population and increases death to wildlife
•Sediments washing off fields are the largest source of agricultural pollution in the U.S.
•Sediments increase the cost of treating drinking water and can also clog fish gills, reducing their resistance to disease.
Overuse and Waste
•Irrigation uses 30% of all freshwater in the U.S.
•Swimming pools and water parks
•Watering the lawn
What other ways do you overuse or waste water where you live?
•Withdrawing groundwater causing the land to sink
•Causes flooding problems
•Causes a shift in the foundations of buildings, which can lead to their destruction
compare fresh and salt water, including examples?
identify the differences between surface and groundwater, including examples?
draw and label the parts of an aquifer?
recall six different types of water pollution?
generate ideas for reducing water pollution?
The H-R Diagram plots each star on a graph and measures the star's brightness (luminosity) against its temperature (color).
•Measured in Kelvin (K)
•Color of stars depends on their temperature
•The coolest stars – red
Hottest stars – blue
•Temperature increases from right to left, which is different than every graph you’ve probably seen.
•The amount of energy (light) a star emits
Tells us how bright an object appears from Earth
The measure of a star’s brightness as if it were at a standard distance of exactly 10 parsecs (32.6 light years) from the observer.
•Stars are classified by their spectra (the elements that they absorb) and their temperature.
•There are seven main spectral types (O, B, A, F, G, K, and M) listed in order of decreasing temperature.
•About 90 percent of the stars in the universe, including the sun
•Ranges from high to low luminosity and high to low temperature
•Color – ranges from red to blue
•Spectral Class M-O
•Medium size star
•Medium brightness and temperature
•Color – yellow
•Spectral Class G
•A red giant is a dying star.
•Our own sun will turn into a red giant star, expanding to engulf the inner planets.
•Color - reddish-orange hue
•High luminosity/ low temperature
•Spectral Class K-M
•They are the largest stars in the universe in terms of volume, although they are not the most massive.
•Color – reddish orange/blue
•High luminosity/low-high temperatures
•Spectral Class K-M, B-A
•A small very dense star that is typically the size of a planet
•Formed when a low-mass star has exhausted all its fuel
•Color – white
•Low luminosity/high temperature
Spectral Class B, O, A
•A small and relatively cool star on the main sequence
•Color – red
•Low luminosity/low temperature
•Spectral Class – M
1.Can you interpret the H-R Diagram?
2.Can you use the H-R Diagram to explain how stars are classified?
The two Documents below were read in class during the week of Dec 3.
•A disturbance that travels through space and matter
•Transfers energy, not matter
•Travel through electrical and magnetic fields
Examples: light, microwaves, radio waves, and X-rays.
•The highest point on a wave is called the crest.
•The lowest point on a wave is called the trough.
•The distance between successive crests or troughs
•Measures one complete wave
•The maximum extent of a wave measured from the position of equilibrium
•The number of crests of a wave that move past a given point in a given unit of time
•Measured in Hertz (Hz)
•Examples: FM/AM radio stations, stars
•Need close proximity to transmitter
•Examples: microwaves, routers, cell phones, stars
•“Infra” means below
•These waves are just below visible light
•Examples: remote controls, flames, lamps, stars
•All visible light
•Examples: light bulbs, fire, stars
•Often called “black light”
•Examples: sterilization, stars (sunburn anyone?), haunted houses
•High frequency waves
•Examples: see inside organisms, airport security, dentist office, stars
•Highest frequency waves
•Highest temperature (blue)
•Examples: radiation therapy (cancer), sterilization, stars
Studying the Universe
•Astronomers use all kinds electromagnetic waves to study the characteristics (temperature, energy, color) of stars.
•They can also use the EMS to determine chemical composition.
•A measurement technique which allows astronomers to see light that is absorbed, emitted, or scattered by materials
•How do we know what stars are made out of?
•Use the class set of absorption spectrums to determine which elements are present in each star.
•Astronomers can measure the distance of stars using a method called parallax.
•They measure the star twice per year.
•Every 6 months the Earth has moved nearly 186 million miles from it’s previous point due to its revolution around the Sun.
•Also called the Hydrologic Cycle
•Process by which water circulates between the Earth’s oceans, atmosphere, and land
•Involves water storage, evaporation, transpiration, condensation, precipitation, and runoff.
•Oceans – super storage for the water cycle - holds 96.5% of Earth’s water
•Primary pathway into the water cycle
•Oceans, seas, lakes ,and rivers provide nearly 90% of the moisture in our atmosphere through evaporation.
•Process by which water changes from a liquid to a gas
•Primary pathway that water moves from the liquid state back into the water cycle as water vapor
•Heat (energy) from the sun is necessary for evaporation to occur.
•Energy breaks bonds that hold water molecules together.
•Molecules move fast at boiling point 212o F
•Slow at freezing point 32o F
•Sublimation – the process of snow and ice changing into water vapor without first melting into water.
•Evapotranspiration – water lost to the atmosphere from the ground surface and transpiration of groundwater by plants through their leaves.
•Superhighway used to transport water around the globe
•Involves condensation and precipitation
•Process in which water vapor in the air is changed into liquid water.
•Loss of energy allows water molecules to bond.
Forms clouds, fog
•Water released from clouds in the form of rain, freezing rain, sleet, snow and hail
•Provides the delivery system of atmospheric water to the Earth
Ice, snow, groundwater
•Water locked up in its present state for a relatively long period of time
•Involves runoff and infiltration
•Precipitation that did not get absorbed into soil, or evaporate
•Ice caps and glaciers - provides runoff from melting
•Water moved by gravity makes its way into places that collect water – rivers, lakes, ponds, ocean
•The downward process of moving water from the land surface into soil or porous rock
•Groundwater - Large amounts of water stored in the ground
•Aquifer – another name for groundwater, usually describes water bearing formations
•The area of land where all the water that falls in it and drains off of, goes into the same place
•Can be as small as a footprint or as large as all the land that drains water into the Mississippi River
Science 7: Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment. Take the Carbon Footprint Challenge at Home! http://www.footprintcalculator.org/
Human Impacts on the Environment: www.khanacademy.org/science/biology/crash-course-bio-ecology/crash-course-ecology-2/v/crash-course-ecology-10
Science 8: Light Waves
•The part of the electromagnetic spectrum, between infrared and ultraviolet, that is visible to the human eye.
•Shorter waves – higher frequency and energy
•Longer waves – lower frequency and energy
Visible Light Spectrum
•Produced when light passes through a prism, slowing the wavelength into each separate color.
•ROY G. BIV - red, orange, yellow, green, blue, indigo, violet
•We see these waves as the colors of the rainbow.
•Each color has a different wavelength and frequency.
•Red has the longest wavelength and shortest frequency
•Violet has the shortest wavelength and highest frequency.
•Seen together, they make white light.
•For an object to be visible it must produce its own light or reflect light.
•Produces own light - Sun, candle, flashlight
•Reflects light - Moon, mirror, glass
•Opaque – A material that reflects or absorbs all of the light that strikes it. (wood, metal, cardboard)
•Transparent – transmits light (glass, water, air)
•Translucent – scatters light as the light passes through (wax paper, frosted glass)
How light travels
•Light travels in straight lines.
•This straight line motion can be:
•Occurs when parallel rays of light hit a smooth surface.
•All the rays are reflected at the same angle.
•Law of reflection: the angle of reflection equals the angle of incidence.
•Angle of incidence - measure of the angle of a ray to the surface normal (90o to the surface)
•When parallel rays of light hit a bumpy surface.
•Each ray obeys the law of reflection, but each ray hits the surface at a different angle.
The light is scattered.
•When light waves enter a new medium at an angle, their speeds changes.
•The change in speed causes them to bend, or change direction.
•Index of Refraction – a measure of how much a ray of light bends when it enters that material
•When light traveling in straight parallel lines passes through an object that is curved like a lens, the light is refracted at different angles.
•Convex or converging lenses bend light toward a central focal point.
•Concave or divergent lenses bend light outward away from a focal point.
•Light does not pass through or reflect from material, but remains in the material as energy.
•What happens to the black surface?
Color of objects
•Color – Objects reflect colored light that is not absorbed.
•We see objects color as the reflected color.
Colors of Light
•Red, Blue and Green
•When combined in equal amounts, primary colors produce white light.
•If combined in varying amounts, they can produce any other color.
•Yellow, Cyan and Magenta
•Primary colors combined in varying amounts
•Complementary - form when a primary color and a secondary color combine to make white.
•Yellow and blue = white
•Y + B = W or R + G + B = W
•A relative expression of the intensity of the energy output of a visible light source
•Brightness is determined by the light wave’s amplitude.
•The greater the amplitude, the brighter the light.
•Distance from light source also affects brightness.
•Chemical and physical breakdown of rocks into sediment
•Occurs when the rock’s environment changes and the rock is exposed to some form of water and the air
Chemical change within the rock’s minerals breaking down the bonds holding the rocks together, causing them to fall apart into smaller pieces.
Causes rock to break:
•(A) Oxidation – Iron combines with oxygen making rust.
•(B) Hydrolysis – Water softens minerals in rocks.
•(C) Carbonation – Carbon dioxide in rain water creates carbonic acid. Ex. acid rain, cave creation
Physical (Mechanical) Weathering
The process that breaks rocks apart without changing their chemical composition caused by:
•(A1) Abrasion - by rapidly moving water, glaciers or wind.
•(A2) Ice wedging - by freezing and thawing (contracting and expansion).
Causes rock to break:
•(B) Plant Roots - grow into cracks and break apart rock.
•(C) Burrowing – animals scrape and dig the terrain.
•(D) Temperature Change- cold to hot expanding and contracting.
•(E) Gravity - falling rocks or debris, compression
The process that moves bits of rock or soil from one place to another by:
•Water (rivers, waves)
The process in which sediments, soil, and rocks are added to a landform such as:
Occurs when the forces moving sediments are no longer able to overcome the forces of gravity and friction.
Running water is the primary agent of erosion.
•Velocity (speed) depends on gradient (slope) and discharge (amount of water).
•As velocity increases the size of particles carried also increases.
Ages of Rivers
•(A) Young Rivers - fast-flowing,
V-shaped valleys, waterfalls, and rapids
•(B) Mature rivers – Less energy, slower, meanders (1), sandbars
•(C) Old River – Very slow, shallow, large amounts of sediment deposited, many narrow channels, islands, deltas (2)
Features Created by Wind
Caused by abrasion from wind blown sand.
Features Created by Gravity
Gravity shapes the Earth’s surface by moving weathered material from a higher place to a lower one.
•(A) Landslides (fast)
•(B) Mud flows
•(C) Slump/creep (slow)
Features Created by Glaciation
Caused as massive glaciers flow down hill bulldozing existing rocks.
Features Created by water (waves)
Erosional and depositional features which form along coastlines
•The western U.S. coastline has more erosional features.
•The eastern U.S. coast and the Gulf of Mexico has more depositional features.
Ecoregions of the United States
Areas defined by its environmental conditions, especially climate, landforms, and soil characteristics.
Ecoregions Environmental Conditions
•Climate – weather conditions in an area over time.
• Landforms – crustal material
•Mountains – high elevation
•Plateaus – medium to high elevation
•Plains – low elevation
•Amount of vegetation
•Dry (arid) – very little vegetation (poor soil)
Humid – large amount of vegetation (good soil)
Examples of Ecoregions
•Subtropical (Florida, South Eastern States)
•Tundra (N Alaska)
•Temperate Steppe (Great Plains
•Marine Mountains (Coastal Washington and Oregon)
•Desert and Desert Mountain (Nevada and parts of New Mexico)
What determines how the processes of weathering, erosion, and deposition work to reshape Earth’s surface?
•Vibrations that travel through the air or other media
•When these vibrations reach the air near your ears you hear the sound.
How Sound Travels
•Sound waves carry energy through a medium (solid, liquid or gas) without the particles of the medium traveling along.
•Sound travels as a longitudinal wave.
How Sounds are Made
•Longitudinal waves are generated when a source of energy forces the matter in a medium to vibrate.
•This back-and-forth motion pushes air particles together, generating a compression, or moves the particles apart, generating a rarefaction.
•Sound waves must have a medium to travel through.
•Gas – air is the most common
•In outer space there are no molecules to compress or rarefy, so sound does not travel through outer space.
Speed of Sound
•Depends on the physical properties of the medium it travels through.
•At room temperature, sound travels through air at about 342m/s.
Physical Properties of Media
•Elasticity – the ability of a material to bounce back after being disturbed
•Solid materials are usually more elastic than liquids or gases.
•Particles of a solid do not move very far, so they bounce back and forth quickly as the vibration travels through the object, which allows waves to move faster.
•Density – how much matter there is in a given amount of space
•The speed of sound depends on how close together the particles of the substance are in the medium.
•Temperature - degree or intensity of heat present in a substance or object
•In a given media (solid, liquid, gas), sound travels more slowly at lower temperatures.
Properties of Sound Waves
•Intensity – the amount of energy the wave carries per second through a unit of area
•Amplitude increases with increased energy
•Measured in watts per square meter (W/m2)
•Loudness – describes what you actually hear.
•Though not the same as loudness, the greater the intensity of a sound wave, the louder it is.
•Measured in decibels (dB)
•Maximum safe level is 85 dB
Frequency – the number of vibrations that occur per second
Wavelength changes with frequency
Measured in Hertz (Hz)
50Hz = 50 vibrations per second
•Pitch – a description of how high or low the sound seems to a person
•High frequency = high pitch
•Low frequency = low pitch
•Example: a young girl might have a squeaky (high pitched) voice, an older man might have a deep (low pitched) voice
•The apparent change in frequency as a wave source moves in relation to the listener
•Sounds moving toward a person – Waves are at a higher frequency, so pitch appears to increase (high)
•Sound moving away from a person – Waves are at a lower frequency, so pitch appears to decrease (low)
A model that describes the formation, breakdown, and reformation of a rock.
•Formed when sediments accumulate and compact and cement together.
•Often deposited in layers and contain sand, pebbles, and frequently fossils.
Ex. sandstone, limestone
Physical properties of Sedimentary Rocks
•Sand, pebble, and even boulder size particles
•Some may contain fossils
By what process are sedimentary rocks broken down?
•By weather (rain, ice, wind), chemical changes, and living things (plant).
•Creates lose material called sediments.
By what process are sediments moved?
They are deposited in layers - Deposition
What are the processes that form sedimentary rock?
Sediments are deeply buried, placing them under pressure because of the weight of overlying layers.
•New minerals stick the sediment together just like cement.
•This holds the grains together tightly.
•Formed by heat and pressure while buried deep below Earth’s surface.
•Have a layered or banded (ribbon like) appearance or may have crystals.
Ex. Gneiss, Marble, Slate
Physical Properties of Metamorphic Rocks
•Layers look like ribbons
What are the processes that form metamorphic rock?
Heat (caused by magma)
•Temperatures high enough to change its structure but not to melt it.
•Heat can change sedimentary, igneous, or another older metamorphic rock.
Pressure - Caused by intense collisions and friction of tectonic plates and pressure from overlying rock layers.
•Deep under the Earth’s surface.
•Pressure can change sedimentary, igneous or another older metamorphic rock.
•Formed when lava or magma harden.
•Found near volcanoes or fissures
•Ex. Basalt, Obsidian, Granite
Physical Properties of Igneous rock
Fast Cooling Slow Cooling
Glassy Large crystals
Holes where gas was trapped Many colors
What are the processes that form Igneous rock?
•Caused by increase in temperature in rock deep below the surface of Earth
•Caused by friction between crustal plates
Lava –molten rock material on Earth’s surface.
Magma – molten rock material under Earth’s surface.
What are the processes that form igneous rock?
Cooling and Hardening
•Melted rock turns solid.
•Slow cooling happens below Earth’s surface as magma cools forming large crystals. Ex. granite
•Fast cooling happens on the Earth’s surface as lava cools forming small crystals. Ex. obsidian, basalt, pumice
Video Resource: https://drive.google.com/file/d/0BxOms4hIDvR3TmxEcHJWV2xzTkU/view
Similarities of Rocks and Minerals
•Inorganic compounds (non-living)
•Both can be classified by their chemical composition.
•Found around the world in many of the same places on Earth
•Most commonly classified by how they form.
•Composed of more than one mineral.
•No definite chemical composition.
•No definite crystal structure.
In addition to being inorganic, solid, and naturally formed like rocks, minerals also have:
•A definite chemical composition. (amounts of elements present)
•A definite crystal structure. (unique arrangement of atoms/molecules)
Mineral Identification – Important Vocabulary
1.Color (green, red, yellow, blue, etc.)
2.Streak (Color of the streak across a streak plate)
3.Luster (Metallic or Non-Metallic)
4.Hardness (Mohs Scale)
5.Density (Specific gravity)
6.Breakage Pattern (Cleavage and Fracture)
•Many minerals have distinctive colors, but they come in a variety of hues.
•Color should never be used as the only test for identifying a mineral.
•The color a mineral displays in a finely powdered form
•Might be completely different from the color of the mineral itself
•To determine the streak, rub the mineral across a piece of unglazed porcelain know as a streak plate.
•The way a mineral’s surface reflects light.
•Two types of luster
•Metallic – shiny like a metal
•Nonmetallic – several kinds
1. Glassy - quartz
2. Pearly - talc
3. Greasy - graphite
4. Silky – gypsum
5. Resinous - sulfur
6. Adamantine - diamond
•One of the most reliable ways to identify minerals
•Compares the resistance of a mineral to being scratched by 10 reference minerals
•Called the Mohs Hardness Scale
•Named after Friedrich Mohs, a German mineralogist, who developed the scale in 1812
•Defined as the amount of matter per unit volume
•Density = mass divided by volume
•In minerals, the term specific gravity is used in describing density.
In this way minerals can be compared and identified.
•Refers to the way some minerals break along certain lines of weakness in their structure
Mica is a good example.
•A description of the way a mineral tends to break
•Some different types of fracturing
1. Conchoidal – smooth curve
2. Hackly – sharp jagged edges
3. Uneven – rough and irregular
4. Fibrous – shows fibers
Some minerals are cut to become precious gemstones.
Erik E. Mason
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http://www.ornl.gov/~t6g/cxtfit/section5.cfm
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math
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Section 5: Error PropagationSuppose that we are interested in assessing the uncertainty for the prediction of B breakthrough at a distance of 50 cm. The velocity is 50 cm/h. The retardation factor with a standard deviation of 0.2 in addition to the estimates from Section 3 is used for model prediction (Fig. 5.1).
- Make a copy of Sheet1 and set up the problem like Fig. 5.1
- Open Propogate dialog
- Calculate prediction uncertainty
- Calculate the approximate prediction confidence interval
Select menu CXTFIT->Propagate to open the Propagate dialog (Fig. 5.2).
Fig. 5.1 Change the parameter range to analyze sensitivity for velocity, dispersion coefficient, and pulse duration.
Select the parameter range and prediction range, change the offset for error propagation to 1, and click Calculate (Fig. 5.2). The error propagation from the parameters to the predictions is output next to the prediction range (Fig. 5.3).
Fig. 5.2 Change the parameter range to analyze sensitivity for velocity, dispersion coefficient and pulse duration.
Assume that the average error of the calibrated model is 3% (RMSE = 0.03 in cell F1), a rough approximation of the standard deviations for the predictions is calculated in column D by typing in the formula =SQRT(C11+$F$1^2) in cell D11, double click on the right left corner of cell D11 to extend the formula.
Assume that the value of t is 2.0 (2.0 in cell F2), type in the formula =B11-$F$2*D11 in cell E11, double click on the right left corner of the cell; type in the formula =B11+$F$2*D11 in cell F1, double click on the right left corner of the cell. The confidence band is plotted against the prediction in Fig. 5.3.
Fig. 5.3 Prediction uncertainty assessment results
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http://openstudy.com/updates/4f26fce0e4b0a2a9c2679bb4
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math
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Can you make a stab at it or do you need it explained from the start?
i need it explained please...... sorry
No problem! Why don't you start by writing it out using Draw, so I can understand the question better, please?
ok no problem
x = 2 and y = -4? so plug that in
Great, let's do that.
and i can do the math with the exponents i just need help on what i do with the 1
Well, show me what you get with thte exponents first
Just the answer's fine, if you think it's right, otherwise we can go through the working if it's wrong
2,048 for the exponents im not sure what to do with 1
You;re a bit off with the exponents. Let's see your working out. Then we'll get onto the 1.
Let's start with the first bit: What is this? |dw:1327956095456:dw|
Not quite. How do negative exponents work?
im not sure i was sick when ,y teacher explained this to me and this is off my make up work
No problem, I'll explain it to you :D Btw "I don't know" is an excellent answer at any stage, don't be afraid of saying it!
The rule for negative exponents is this:|dw:1327956265582:dw|
Are you familiar with the general rule:|dw:1327956314617:dw| ?
aha ok :) thank you yeah i am
Well this just takes it a step further. 3^4=81, 3^3=27, 3^2=9, 3^1=3, 3^0=1.
That much you understand already?
yeah i do
You can see that each time, I reduced the exponent by 1, from 4 to 3 to 2 etc. And the answer got divided by three each time, so from 81 to 27 to 9 to 3 to 1.
Does that make sense?
Or shall I draw it using a picture, if that might help?
yeah i understand what your saying
Great! Then if I take it further, watch what happens: Reducing the exponent by 1, I get 3^-1, and dividing by three on the other side I get 1/3. This continues: 3^-2 = 1/9, 3^-3=1/27 etc. Which is why, as you can see, 3^-x=1/3^x
Did that make sense or should I use draw?
no it made sense i see what your sayinng
Excellent! So now, can you tell me what 2^-2 is?
(Or would you prefer to try the whole question yourself?)
Not quite. 2^2=4, so what is 2^-2 ?
Nope, not that either :(
What's the rule we just looked at, for negative exponents?
Did you use your computer's calculator for that or work it out yourself?
See if you can understand the picture I've drawn for you.
i worked it out for myslef
THought so :(
im a failure to life goodbye world im gonna kill myself
The rule for negative indices is this:|dw:1327957460830:dw|
No, don' tdo that!
Look at the rule I've given you, do you understand what I've said?
Ah well, well done for trying :)
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CC-MAIN-2018-05
| 3,186 | 43 |
https://www.physicsforums.com/threads/polar-decompositions.331817/
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math
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About the equation T=Ssqrt(T*T), what purpose does the sqrt(T*T) serve?
Think about the 1x1 case, where T is a complex number. The usual polar decomposition you learn in high school tells you that T=re^(it), where t=argT and r=|T|. But the absolute value of T is just sqrt(T*T) in this case. (Also notice that a unitary 1x1 matrix is necessarily something of absolute value 1, i.e. something of the form e^(it).) So the nxn polar decomposition is just a generalization of this.
Separate names with a comma.
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CC-MAIN-2018-30
| 506 | 3 |
https://dreamsprinter.com/product/code-blooded-short-sleeve-t-shirt/
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math
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Do you have a programmer friend that finds it hard to communicate his code blooded feelings? This soft and comfy tee will help bring out his/her inner programmer.
• Tri-blend construction (50% polyester/25% combed ring-spun cotton/25% rayon)
• Pre-shrunk fabric
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• Contemporary fit
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CC-MAIN-2022-21
| 343 | 6 |
https://www.wyzant.com/New_Miami_OH_geometry_tutors.aspx
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math
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Middle School Math and Social Studies teacher and GED tutor
I have a Bachelor's Degree in Middle Childhood education with a concentration in both math and social studies and a Master's degree in Education. I also have 10 years' experience working with special...
...Geometry can be one of the most difficult areas of mathematics for students to understand. Besides the multitude of definitions and theorems involved with this subject, we also introduce the notion...
I tutor one student at a time for 60 minutes at the rate of:
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I have been tutoring my classmates in math since the 2nd grade! I have tutored...
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IS YOUR CHILD STRUGGLING AT SCHOOL?
I can help with Math, English Language, Algebra, Geometry, Trigonometry, AutoCAD and Technical Drawing.
My passion towards teaching comes from my conviction...
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| 1,036 | 10 |
http://www.jiskha.com/members/profile/posts.cgi?name=jason&page=4
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math
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Time is running out for you. No money means no score sufficient to get the certificate.
So, are you ready to transfer them to my personal account at the Bank of Nigeria ?
For $1000, I'd give you the right answer.
OK, here is the real answer: theta = e*a*t phi = s*H*i*t Job done!
For 8d. Theta = pi Phi = 0
If 5.300 g of C6H6 is burned and the heat produced from the burning is added to 5691 g of water at 21 °C, what is the final temperature of the water? 2C6H6(l) +15O2 (g)----> 12CO2(g)+6H2O(l) +6542
informal changes to the constitution include. A.Treaties B.Laws passed in congress C. Supreme court decisions D. All of the above
A car accelerates uniformly from rest to a speed of 23.9 km/h in 8.2 s. Find the distance it travels during this time. Answer in units of m
A rectangle has a length of 4x and a width of 4x-2. its perimeter is 12 inches find the length and width
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http://mathhelpforum.com/calculus/98351-composite-rule-help.html
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math
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I'm pretty sure the function is so yes, it's correct if my thoughts are right.
Just looking for some help using the composite rule - I'm finding it confusing!
if I have the function f(x)= e(cos(x))
would my answer be e(cos(x))(-sin(x))
this seems logical to me following the composite rule, but for some reason it doesn't feel quite right.
any help would be awesome
Just in case a picture reassures (as it always does me)...
Straight lines differentiate (down) with respect to x, the straight dashed line is differentiating with respect to the inner (dashed balloon) function, so that, generally...
Don't integrate - balloontegrate!
Balloon Calculus Forum
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| 655 | 10 |
http://www.wyzant.com/South_Dallas_Dallas_TX_Math_tutors.aspx
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math
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Hello, my name is Joshua and I'm an experienced math
tutor. I have a degree in Pure Math
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http://spiff.rit.edu/richmond/asras/distance_i/distance_i.html
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math
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The basic idea of parallax is that, if you observe a nearby object from different locations, you'll see it appear to shift relative to more distant object.
Try it with your thumb!
Parallax demo I
The orbit of the Earth around the Sun gives us a baseline of 1 Astronomical Unit. Astronomers have decided to make that the basis for a unit of distance: the parsec is the distance at which a star would shift its position by one arcsecond; in other words, have a parallax of one arcsecond.
Back in the early 1990s, a European satellite called Hipparcos spent three years measuring the positions of hundreds of thousands of stars, over and over and over again. It made some of the best ever measurements of parallax in the optical portion of the spectrum. Here's an example: measurements of the position of Vega.
Can you figure out how far away Vega is from the Earth?
The individual measurements from Hipparcos have uncertainties of about 1 milliarcsecond = 0.001 arcseconds. How far out could we see parallax due to the Earth's orbit (to a rough approximation)?
In recent years, astronomers have started to use arrays of radio telescopes to make VERY precise measurements of the positions of objects in giant molecular clouds. These objects are the nurseries of our galaxy, where new stars are forming. By combining the signals from several radio dishes in the proper manner, astronomers can measure positions more precisely than they can with optical telescopes.
For an illustration of parallax determined from radio observations, see a short summary of recent results from the VERA collaboration.
How small are the angles measured with radio interferometry? How far out could we see parallax due to the Earth's orbit (to a rough approximation)?
For most of their lives, stars fuse hydrogen into helium deep inside their cores. As long as a star is fusing hydrogen to helium, the war between gravity (pulling inwards) and radiation pressure (pushing outwards) stalls in a relatively simple manner. It turns out that there is a nice relationship between the mass of a star and its temperature, size and luminosity.
You can see all of this at once if you look at a color-magnitude diagram.
Watch a single star evolve on HR diagram
Watch many stars in a cluster evolve
Your job: find the approximate age and distance of this cluster, called 47 Tuc:
Here's the observed color-magnitude diagram of stars in this cluster:
And here is a color-magnitude diagram of stars from a series of models:
Use the main-sequence turn-off point from the observed cluster to figure out
Copyright © Michael Richmond. This work is licensed under a Creative Commons License.
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| 2,649 | 19 |
https://tavaz.xyz/learning-and-teaching/article_154480.asp
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math
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Forms of Mathematical Knowledge: Learning and Teaching with Understanding by Dina Tirosh
English | PDF | 1999 | 250 Pages | ISBN : 079235995X | 26.9 MB
What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing?
This book focuses on various types of knowledge that are significant for learning and teaching mathematics.
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CC-MAIN-2022-49
| 640 | 4 |
http://www.mynewsdesk.com/uk/meabc/images/roadshow36-dot-jpg-1882930
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math
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Related / Contacts
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Press releases • Feb 24, 2020 09:50 GMT
Since its official launch on 12 February the #Here2Help app figures have soared to almost 3000 downloads.
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More than 1000 people have attended the #Here2Help roadshow in Ballymena to hear first-hand experiences of drug abuse and mental health issues.
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| 371 | 6 |
https://books.google.com/books/about/Answers_to_Questions.html?id=3I2zc0wMFucC&hl=en
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math
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What people are saying - Write a review
We haven't found any reviews in the usual places.
Answers to Questions in Chapter 1
Answers to Questions in Chapter 14 45
Answers to Questions in Chapter 24
2 other sections not shown
amplitude angle angular atomic number balloon battery beam bottom bulb centripetal acceleration circuit close constant decay decreases diagram diffraction direction displacement distance Earth electric field electron emitted energy levels equal equation expand fission focal force exerted frequency friction glass gravitational force greater ground H-R diagram heat helium horizontal hydrogen increases kinetic energy length lens loop magnetic field mass number measure metal mirror molecules momentum motion moving negative charges neutrons Newton's normal force nuclear nucleons nucleus object opposite orbital parallel particles photoelectric effect photon positive charge potential difference potential energy pressure produce radiation radius rays real image red giant reference frame refraction relativistic mass resistance resistor right hand rule rotating Second Law slits smaller sound waves spectral lines speed star surface temperature thermal energy torque velocity vibration visible light voltage wavelength weak interaction wire zero
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https://m.scirp.org/papers/112552
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math
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Aggregate losses are estimated by in-cooperating both claim frequency and claim severity distributions. Pavel (2010) reviewed methods used to calculate distributions of aggregate losses. Robertson (1992) applied Discrete Fourier Transform in estimation of aggregate losses from frequency and severity distributions. Ronoet al. (2020) developed compound distribution to model extreme natural disasters in Kenya. Mohamed et al. (2010) introduced use of simulation approach in estimation of aggregate losses which can be employed when frequency and severity distribution cannot be combined to derive a compound distribution. Aggregate loss distributions are based on collective risk model expressed as:
is the severity distribution and N is the claim count distribution. The distribution of N in this paper is considered to follow mixed PH Poisson distributions.
Phase type distributions are constructed, when mixture distributions are convoluted resulting to an interrelated Poisson process occurring in phases. Phase type distributions were introduced way back by Erlang (1909) and it has been advanced by Marcel F. Neuts (1981) and Assussen (2003) among others. Mogens Bladt (2005) introduced phase type distributions in risk theory while O’cinneide (2017) highlighted on Phase type distributions as well as their invariant polytopes. Wu et al. (2010) developed phase type distributions when frequency distributions followed Panjer class while Kok et al. (2010) used phase type distributions of Panjer class to model claim frequency.
Markov chains were introduced by Andrei Markov (1856-1922). Nurul et al. (2019) proposed a simple forecasting model of predicting the future air quality using Markov chains which in-cooperated the Markov chains as an operator of evaluating pollution distribution in the long run. Yajuan et al. (2018) used Markov chains to model demand for stations in Bike sharing systems. In this study, the concept of Markov chains is used to determine the matrices of the phase type distributions used in modeling claim frequency.
Frequency data is used to model occurrences in different areas such as engineering, insurance, biology etc. Poisson distribution is often used to model count data; however, it is based on the assumption that variance to mean ratio is unity (equi-dispersion) which is not applicable to real data; hence, it is considered as an inflexible model. Most real life data either experience over dispersion where variance exceeds the mean or under dispersion where the mean exceeds the variance which can be modeled using Poisson mixtures . Poisson Lindley distributions are perfect examples of Poisson mixtures where characteristics of Poisson distribution follow some characteristics of Lindley distribution. One parameter Poisson Lindley which can model over dispersed data was introduced by Sankaran (1970) while Shanker and Mishra (2014) developed two parameter Poisson Lindley which further research has justified that it can model over dispersed data.
In the insurance sector, when calculating aggregate losses for chronic diseases which have various stages like cancer the claim frequency distributions considered do not in-cooperate the different stages of such diseases. In-cooperating phase type distributions solve this short coming of ordinary distributions. Further considering mixed phase type distributions improves modeling of claim frequency data as it considers the heterogeneity aspect of claim data. In this paper, we develop PH one parameter Poisson Lindley distribution and PH two parameter Poisson Lindley distributions where the mixing distribution follows PH Lindley distribution. The resulting PH distributions are used to model claim numbers of secondary cancers in Kenya. Section 1 has a brief introduction to Poisson distributions and Poisson Lindley distributions.
The structure of this paper is as follows: Section 2 will discuss construction of phase type distribution using PH Lindley distributions which will later be applied in modeling of the aggregate losses. Compound distributions from the frequency and severity distributions are developed in Section 3. Aggregate losses for the data are estimated using Discrete Fourier Transforms and the results discussed in Section 4 and Section 5 outlines the conclusions.
2. Proposed Phase Type Poisson Lindley Distributions
In this section we develop phase type distributions for one parameter Poisson Lindley and two parameter Poisson Lindley. Phase type Poisson Lindley distributions are derived when the mixing distribution follow phase type Lindley distribution.
2.1. Phase Type One Parameter Poisson Lindley Distribution
Definition 1. A random variable X is said to be a phase type one parameter Poisson Lindley distribution if it follows:
for and is matrix.
Theorem 1. If distribution then the probability distribution function of X is:
where is and I is an identity matrix.
If and , then the pdf of variable X is expressed as;
where is .
Properties of Phase Type One Parameter Poisson Lindley Distribution
The rth moments of PH-OPPL distribution is given by:
The expectation and variance of PH-OPPL distribution can be easily obtained from Equation (4) as:
The probability generating function of PH-OPPL distribution is given by:
The parameter of PH-OPPL distribution is estimated using continuous Chapman-Kolmogorov equation.
2.2. Phase Type Two Parameter Poisson Lindley Distribution
Definition 2. A random variable X is said to be a phase type two parameter Poisson Lindley distribution if it follows:
for and is matrix.
Theorem 2. If distribution then the probability density function of X is expressed as:
where , is and I is an identity matrix.
If and , then the pdf of variable X is given by;
where is .
Properties of Phase Type Two Parameter Poisson Lindley Distribution
The rth moments of PH-TPPL distribution is given by:
The expectation and variance of PH-TPPL distribution can be easily obtained from Equation (10) as:
The probability generating function of PH-TPPL distribution is given by:
The value of is known hence the value of can be obtained from Equation (11) if the value of is known.
2.3. Shape of Probability Function of PH-OPPL and PH-TPPL Distributions
Matrix was determined using continuous Chapman-Kolmogorov equation for cancer data in Kenya and the values of is the stationary probabilities obtained using the formula . The values of for three state Markov model represents cancer patients who transit from Healthy-Leukemia-Dead states, four state Markov model represents patients who transit from Healthy-Liver-Colon-Dead states, five state Markov model represents Healthy-Stomach-Pharynx-Colon-Dead states and six state Markov model represents patients transiting from Healthy-Oesophagus-Stomach-Lung-Kidney-Dead states. The values of for different states are:
The shape of probability function of phase type one parameter Poisson Lindley is expressed as:
Figure 1 shows that phase type one parameter Poisson Lindley is a long tailed distribution.
The shape of probability function of phase type two parameter Poisson Lindley is expressed as:
Figure 2 shows that phase type two parameter Poisson Lindley is a long tailed distribution.
(a) (b) (c) (d)
Figure 1. Pdf plots of PH-OPPL for different values of Λ.
(a) (b) (c) (d)
Figure 2. Pdf plots of PH-TPPL for different values of Λ.
3. Compound Phase Type Distribution
Compound distribution in the actuarial field is the total loses in the group of insurance policies. In this section we develop compound phase type distributions (CPHD) which can be used to model secondary cancer cases.
Definition 3. Let N be a r.v with probability generating function and be a set of iid random variable with a common probability generating function and is independent of N, then the probability generating function of the compound distribution is expressed as:
Unlike ordinary compound distributions which do not consider transition phases of diseases, (CPHD) in-cooperates the transition states. Probability generating functions of compound distributions can be derived by convolution of probability generating function of two distributions as shown in Equation (14).
Theorem 3 (Compound one parameter Poisson Lindley distribution). If the pgf of the compound pgf of N is:
where is the Laplace transform of the severity distribution as most continuous distributions their pgf is not available.
Theorem 4 (Compound two parameter Poisson Lindley distribution). If the pgf of the compound pgf of N is:
where is as defined in theorem (3).
The continuous distributions considered in this research are; Weibull, Pareto and Generalized Pareto distributions hence their Laplace transforms will be derived and replaced in Equations (16) and (18) to get the pgf of their compound distribution using PH-OPPL and PH-TPPL distributions respectively. The Laplace transform of Weibull, Pareto and Generalized Pareto are derived as:
1) Weibull distribution
2) Pareto distribution
3) Generalized Pareto distribution
Replacing Equations (19), (20) and (21) in Equation (16) the pgf of the compound distributions of PH-one parameter Poisson Lindley with Weibull, Pareto and Generalized Pareto respectively are:
1) Compound PH-OPPL-Weibull distribution
2) Compound PH-OPPL-Pareto distribution
3) Compound PH-OPPL-Generalized Pareto distribution
Replacing Equations (19), (20) and (21) in Equation (18) the pgf of the compound distributions of PH-two parameter Poisson Lindley with Weibull, Pareto and Generalized Pareto respectively are:
1) Compound PH-TPPL-Weibull distribution
2) Compound PH-TPPL-Pareto distribution
3) Compound PH-TPPL-Generalized Pareto distribution
4. Data Analysis, Results and Discussions
4.1. Severity and Frequency Probabilities
The cancer data considered in this research is obtained from a medical facility in Kenya. The cancer transitions states considered are Healthy-Leukemia-Dead states for 3 state model, Healthy-Liver-Colon-Dead states for four state model, Healthy-Stomach-Pharynx-Colon-Dead states for five state model and Healthy-Oesophagus-Stomach-Lung-Kidney-Dead states for six state models. The values of for the data are obtained using continuous Chapman-Kolmogorov equations expressed as:
The values of for three, four, five and six state using the data obtained were as shown in Section 2.3.
The severity distributions considered in this research are Weibull, Pareto and Generalized Pareto distributions. DFT requires severity probabilities to be discrete hence they will be discretized using method of mass rounding which is expressed as:
The pdf of Wei-bull, Pareto and Generalized Pareto distributions respectively are expressed as;
The frequency and severity probabilities for secondary cancer cases are: (Table 1).
Table 1. Claim frequency and severity probabilities.
4.2. Discrete Fourier Transform
There are different numerical methods used in estimation of aggregate losses such as; Monte Carlo, Panjer recursive model, Fourier transforms and Direct Numerical Integration. Panjer recursive model is applicable when the claim frequency distributions follow either Panjer class or class . In this study we will consider Discrete Fourier Transform (DFT) in estimation of the aggregate losses. Robertson (1992) applied Fourier transforms in computation of aggregate losses . Pavel (2010) reviewed these numerical methods and concluded that each method had it strength and weaknesses hence they should be chosen according to the study. DFT mostly preferred as it is arguably said to be the most elegant and powerful technique in evaluation of aggregate loss probabilities when claim amount is both discrete and continuous .
The algorithm of DFT of aggregate losses requires computation of DFT of frequency and DFT of severity separately.
Definition 4 (Discrete Fourier Transform). Let be the severity or frequency distribution of the claim data. For any discrete function the Discrete Fourier transform is the mapping;
Expression (29) is very complex to work with hence to reduce its complexity we apply Euler’s formula and it becomes:
which is the DFT of the severity or frequency probabilities. The severity and frequency probabilities are of length 8 and hence the matrix W must be a primitive 8th root of unity therefore Equation (30) can be rewritten as:
The frequency or severity probabilities will be padded with equal number of zero’s as its elements in order to perform no wrap convolution. The DFT algorithm is as follows:
1) Multiply the matrix with the frequency or severity probabilities to get the DFT of frequency or severity probabilities.
2) Compute DFT of DFT of frequency and severity by multiplying DFT of frequency probabilities with the DFT of the severity probabilities and consequently multiplying the resulting vector with the matrix .
3) Select the values without the complex i and divide each value by the number of elements in the vector of frequency or severity distribution and arrange the resulting probabilities in reverse except for the first probability.
4) Values corresponding to original frequency and severity values are the aggregate loss probabilities.
The values of aggregate loss probabilities using DFT are:
Table 2. Aggregate loss probabilities.
The values of Table 2 can be represented graphically as:
(a) (b) (c)
Figure 3. Aggregate loss probabilities.
Figure 3(a) shows aggregate loss probabilities using PH-OPPL distribution with severity distributions and it indicates that PH-OPPL with Weibull and Pareto were similar to the actual aggregate loss probabilities while PH-OPPL with generalized Pareto distribution overestimate the aggregate losses for six state model. Figure 3(b) shows aggregate loss probabilities using PH-TPPL distribution with Pareto and generalized Pareto provided a better fit for secondary cancer data while PH-TPPL with Weibull overestimated the aggregate losses. However, PH-OPPL with Weibull and PH-TPPL with generalized Pareto provided a better fit compared to PH-OPPL-Pareto model and PH-TPPL Pareto respectively hence they are compared in Figure 3(c) indicating that PH-OPPL with Weibull provided the best fit for aggregate loss data of secondary cancers in Kenya. PH-OPPL-Weibull model can be used to provide better estimates of aggregate losses for secondary cancer data in Kenya.
Mixed phase type distributions are developed to model secondary cancer cases in Kenya. Unlike ordinary distributions which do not in-cooperate the transition of different states, the distributions proposed here take into consideration transition states while modeling claim frequency data. The distributions are based on Poisson and Lindley distributions, where PH-OPPL-Weibull provided the best for PH-OPPL models while PH-TPPL-Generalized Pareto provided the best fit for PH-TPPL models. This model improves estimation of aggregate loses as it in-cooperates transition probabilities of different states of cancer as well as heterogeneous aspect of claim data. This greatly improves estimation of insurance policies for diseases which transit to different state such as cancer hence improving the financial positions of the insurance firms as it will improve estimation of its reserves. This model, however, is only applicable in risk theory for diseases which have multiple transitions states. Further research can be done on this study factoring in patients who were censored in this study and also the same study can be carried out for disease such as HIV-AID which has transition states.
The data used to support the findings of this study can be availed upon request.
Rono, A., Ogutu, C. and Weke, P. (2020) On Compound Distributions for Natural Disaster Modelling in Kenya. International Journal of Mathematics and Mathematical Sciences, 2020, Article ID: 9398309.
Kok, S. and Wu, X. (2010) Matrix-Form Recursive Evaluation of the Aggregate Claims Distribution Revisited. Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne.
Nurul, N.Z., Mahmod, O., Rajalingam, S., Hanita, D., Lazim, A. and Evizal, A.K. (1981) Markov Chain Model Development for Forecasting Air Pollution Index of Miri, Sarawak. Journal of Sustainability, 11, 5190.
Zhou, Y.J., Wang, L.L., Zhong, R. and Tan, Y.L. (2018) A Markov Chain Based Demand Prediction Model for Stations in Bike Sharing Systems. Journal of Mathematical Problems in Engineering, 2018, Article ID: 8028714.
Das, K.K., Ahmed, I. and Bhattacharjee, S. (2018) A New Three-Parameter Poisson-Lindley Distribution for Modelling Over-Dispersed Count Data. International Journal of Applied Engineering Research, 13, 16468-16477.
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| 16,627 | 95 |
http://www.mathworks.com/matlabcentral/fileexchange/24484-geom3d/content/geom3d/geom3d/vectorNorm3d.m
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math
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19 Jun 2009
13 Oct 2014)
Library to handle 3D geometric primitives: create, intersect, display, and make basic computations
function n = vectorNorm3d(v)
%VECTORNORM3D Norm of a 3D vector or of set of 3D vectors
% N = vectorNorm3d(V);
% Returns the norm of vector V.
% When V is a N-by-3 array, compute norm for each vector of the array.
% Vector are given as rows. Result is then a N-by-1 array.
% NOTE: compute only euclidean norm.
% See Also
% vectors3d, normalizeVector3d, vectorAngle3d, hypot3
% author : David Legland
% INRA - TPV URPOI - BIA IMASTE
% created the 21/02/2005.
% 19/06/2009 rename as vectorNorm3d
n = sqrt(sum(v.*v, 2));
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