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http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&Citations&tp=&arnumber=5986743&contentType=Journals+%26+Magazines&sortType%3Dasc_p_Sequence%26filter%3DAND(p_IS_Number%3A6129833)
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math
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Skip to Main Content
This paper introduces a new structure of radial basis function networks (RBFNs) that can successfully model symbolic interval-valued data. In the proposed structure, to handle symbolic interval data, the Gaussian functions required in the RBFNs are modified to consider interval distance measure, and the synaptic weights of the RBFNs are replaced by linear interval regression weights. In the linear interval regression weights, the lower and upper bounds of the interval-valued data as well as the center and range of the interval-valued data are considered. In addition, in the proposed approach, two stages of learning mechanisms are proposed. In stage 1, an initial structure (i.e., the number of hidden nodes and the adjustable parameters of radial basis functions) of the proposed structure is obtained by the interval competitive agglomeration clustering algorithm. In stage 2, a gradient-descent kind of learning algorithm is applied to fine-tune the parameters of the radial basis function and the coefficients of the linear interval regression weights. Various experiments are conducted, and the average behavior of the root mean square error and the square of the correlation coefficient in the framework of a Monte Carlo experiment are considered as the performance index. The results clearly show the effectiveness of the proposed structure.
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http://simbad.u-strasbg.fr/simbad/sim-ref?bibcode=1996PASP..108..580I
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math
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36 Ophiuchi AB: incompatibility of the orbit and precise radial velocities.
IRWIN A.W., YANG S.L.S. and WALKER G.A.H.
Abstract (from CDS):
The long-period (∼600 yr) binary system 36 Ophiuchi AB consists of two chrompherically active K dwarfs. If we constrain the period using the mass-luminosity relation and the observed parallax, the remaining orbit parameters can be estimated from the 170 years of visual-binary observations. In this paper, we further constrain the orbit by precise measurements of the differential radial velocities (with arbitrary zero points) of both 36 Oph A and B and the difference in radial velocity between 36 Oph B and A. Our best orbit gives a good fit to the visual-binary observations, the difference in velocity, and the mean radial acceleration of A; but the observed acceleration of B is a factor of 164 larger than the value predicted by the orbit. This factor is so large that no reasonable variation in the adopted sum of masses, mass ratio, parallax, or orbit parameters will remove the B acceleration discrepancy. Ths maximum companion mass allowed by the residuals from the visual-binary orbit is of order 8 Jupiter masses for assumed periods between 30 and 100 years so the 36 Oph B acceleration discrepancy would ordinarily make it a candidate for a substellar companion. However, the very high eccentricity (∼0.9) of the binary-star orbit means its closest approach is of order 6 a.u. making it unlikely that any substellar companions would form or survive with the semi-major axis exceeding ∼1.5 a.u. or period exceeding ∼2 years. Thus, 36 Oph B is an important counter-example which serves as a warning that for chromospherically active stars, at least, it is possible to have apparent radial accelerations in the absence of substellar companions.
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https://www.zora.uzh.ch/id/eprint/150725/
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math
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In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined by employing simple tensor-Gauss quadrature. We develop a corresponding perturbation analysis which allows to keep the number of quadrature points small. Numerical experiments have been performed which illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation.
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| 591 | 1 |
http://freetofindtruth.blogspot.com/2016/03/33-96-backlast-against-chris-christie.html
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math
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The Republican Party was once the Whig Party. This could be the last Presidential Election where the party is known by their current name. Notice the sub-headline, keep in mind the country is currently 239-years old.
You have to love that his lowly support among voters dropped from 33% to 27%.
Chris Christie is a Freemason. His endorsement of Trump is all part of the Freemason show. No one likes Chris Christie. He is a fat fuck who harps on about how he was hired by George W. Bush the day before September 11 and was there to give victims hugs on September 11. Other than that, the fat fuck has nothing to say about himself. Think about what a pathetic piece of shit you would have to be to have nothing else to talk about in 15-years of "service".
I want to know how many tax dollars have gone towards Chris Christie's doughnut habit.
9/6/1962 = 9+6+1+9+6+2 = 33
9/6/62 = 9+6+62 = 77
Think about all the '96' headline tributes Donald Trump has received in the past 9 or 10 months. I can't emphasize enough, we are ruled by a network of Masonic assholes.
Christopher = 3+8+9+9+1+2+6+7+8+5+9 = 67/76 (Freemasonry = 67)
Chris = 3+8+9+9+1 = 30/39
James = 1+1+4+5+1 = 12/21
Christie = 3+8+9+9+1+2+9+5 = 46/55
Christopher James Christie = 125/152
Christopher Christie = 113/131
Chris Christie = 76/94
Christopher = 3+8+18+9+19+20+15+16+8+5+18 = 139 (Freemasonry)
Chris = 3+8+18+9+19 = 57
James = 10+1+13+5+19 = 48
Christie = 3+8+18+9+19+20+9+5 = 91
Christopher James Christie = 278
Christopher Christie = 230
Chris Christie = 148
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http://richardholbrook.com/used-technical-mathematics-a-short-summary/
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math
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Used Technical Mathematics – a Short SummaryJanuary 29, 2020 5:07 pm Leave your thoughts
The area of employed mathematics
that is technical|math that is technical that is applied} covers several disciplines such as information systems design, computer engineering, data programs, and artificial intelligence. It’s a specialized discipline by which computer engineers and computer scientists are involved with applying new approaches.
Techniques include that which we call procedural essay writing services techniques, that might be applied to areas like economics, mathematics, and technology. Techniques include logic-based, computational, non-procedural, algorithm-based, numerical, and symbolic techniques.
Application includes the applications of these processes. By blending calculations, data, and designs with understanding, computer scientists and engineers have found that they can merge mathematical concepts and techniques to produce applications. By way of example, they could use information visualization strategies click to read more to analyze large quantities of financial data, or they can apply statistical approaches to mimic the dynamics of most complex systems.
In order to explore mathematical engineering applications engineers should run a number of little tasks to test their thoughts contrary to similar layouts. As an applied mathematician you are going to have the ability to help these engineers and will have a excellent understanding of these issues.
Because they need to create units using a reduced price tag mathematical mathematicians tend to favor theoretical modeling. They are far less useful for the most demanding problems, while the layout process cans greatly speed up. Techniques include systems , optimization, stochastic optimization, regression, and polyhedral along with abelian category concept.
Mathematical engineering engineers must be in possession of a strong background in engineering. On account of the https://owl.purdue.edu/owl/subject_specific_writing/writing_in_the_social_sciences/writing_in_psychology_experimental_report_writing/tables_appendices_footnotes_and_endnotes.html field’s importance fields have adopted approaches to better their capacity to review and convey engineering science. For instance, electrical engineering mechanical engineering, and chemical technology have developed resources to aid them assess and design their technology alternatives.
Mathematics also helps to improve the quality of the products that engineers and scientists produce. By allowing engineers to do more with less, it has become possible to produce better results with fewer parts. The success of your projects will depend on the quality of your mathematical techniques.
Categorised in: Uncategorized
This post was written by Scott Brown
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https://www.hindawi.com/journals/jmath/2023/7374882/
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math
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Approximate Solutions for Nash Differential Games
In this paper, we are concerned with an open-loop Nash differential game. The necessary conditions for an open-loop Nash equilibrium solution are obtained, also the existence for the solution of the dynamical system of the differential game is studied. Picard method is used to find an approximate solution, and the uniform convergence is proved. Finally, we constructed figures for the analysis of the differential game. These results can be applied between economic and financial firms as well as industrial firms.
Differential equations have a great importance in our life and many applications in physics and engineering fields . Differential equations help us in describing all the phenomena in which there are rates of change and provide a description of the way this change works, for example, population growth, chemical reactions, launching rockets into space, the spread of diseases, and climate changes. The differential game is a direct application of a differential equation and game theory. The game theory is an important field in mathematics . It has applications in almost all fields of social science, as well as in logic, system science, and computer science. It has an important role in Economics. John Forbes Nash is one of the mathematicians who made fundamental contributions to the game theory. Nash proposed a solution of a noncooperative game including two or more players in which every player is assumed to know the equilibrium strategies of the players. No one can change the strategy or move without the other players knowing that the players have the same strategies. In the game theory, differential games are a group of problems related to the modeling and analysis of conflict (competition) expressed as a dynamical system . It means here a state variable evolves over time according to a differential equation. A state variable is one of the set of variables that are used to describe the mathematical “state” of a dynamical system. The state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. There are many applications of differential game in our life and it is an important case ([4–8]).
In , Hemeda introduced an integral iterative method (IIM) as a modification for PM to solve nonlinear integrodifferential and systems of nonlinear integrodifferential equations.
In , Joseph presented a duopolistic market problem in which two firms sell the same product competitively in a certain time. Each firm has its own market share and the strategy here is one for the two firms, that is, the advertising efforts. Kristina solved the differential game by using the maximum principle with a general inequality constraints theorem. She used a numerical method for finding the solutions. In this work, we used another method and a theorem for finding the necessary conditions for an open-loop Nash equilibrium differential game. We found the approximate solutions using the Picard method, constructed graphs for the solutions, and making comparisons to the two firms simultaneously. We illustrated those comparisons with each graph.
The rest of the paper is organized as the following: In Section 2, the dynamical system of the problem, its payoff functionals, and the necessary conditions for an open-loop Nash equilibrium are presented. The aim of Section 3 is to find an approximate solution using the Picard method. Section 4 is preserved for the discussion of the results. Finally, Section 5 contains a conclusion.
2. Problem Formulation
In this section, first we explain the dynamical system of the problem, the payoff functionals, and the open-loop Nash equilibrium.
2.1. The Dynamical System
We consider two firms, Firm 1 and Firm 2. The two firms sell the same product in the market competitively , where is the market share of Firm 1 at time , is the market share of Firm 2 at time . and are the controls which defined as follows: is the advertising efforts of Firm 1 at time , and is the advertising efforts of Firm 2 at time .
In Firm 1, its number of customers increases by its advertising efforts. The advertising efforts of Firm 2 take away the customers of Firm 1. Therefore, the system dynamics can be expressed as the following:with constraints given by
As we are concerned with a differential game with two players, then we have the following definition.
Definition 1. (2-players differential game). In the differential game of two players on the time interval , we have the following:(1)A set of players (2)For each player , there is a vector of controls , where is the set of admissible control values for player (3)A vector of state variables , where is the set of admissible states(4)A strategy set , where the strategy is a decision rule that defines the control as a function of the information available at time
2.2. Payoff Functionals and Open-Loop Nash Equilibrium
We consider the state equation which describes the state of the game and the payoff functionals as the following:
Since the information structure is open-loop, then the equilibrium strategy of player will be .
For obtaining these strategies, we have Hamiltonian’s function for each player .
, where is the costate vector for player .
Definition 2. In the 2-players differential game given by Definition 1 of a duration , we say that player information structure is open-loop; if at time , the only information available to player is the initial state of the game ; hence, his strategy set can be written as .
Definition 3. If and are cost functionals for players , respectively, then an ordered pair control is a Nash equilibrium strategy if for each , we haveFor simplicity, the Nash equilibrium concept means that if one player tries to change his strategy from his own side, he cannot improve his own optimization criterion.
Now, we can define the payoff functionals of the two firms of our problem (1) and (2) as the following:such that , is the interest rate of Firm , is the fractional revenue potential of Firm , and is the advertising cost function of the two firms.
Assuming that ; where is a positive constant andThe Hamiltonian function of player 1 isThe Hamiltonian function of player 2 is
Theorem 1. Let and , be continuously differentiable on i.e., , . If is an open-loop Nash-equilibrium solution and be the corresponding state trajectory, then there exists 2 costate vectors , and 2-Hamiltonian functions such that the following conditions are satisfied:with boundary conditions,where , is an open-loop Nash equilibrium strategy, and is the corresponding equilibrium state trajectory.
The proof of the thereom is proved in .
3. The Approximate Solution by Using the Picard Method
The purpose of this section is to find the existence and convergence of the solution for the problem.
3.1. Existence and Convergence of the Solution
Now, we study the existence of the solution for the problem (10)–(11) (see [12, 13]) and we apply the Picard method for finding an approximate solution and studying the convergence of this solution.
Consider the following system after reducing the necessary conditions of an open-loop Nash differential game as the following:
Assume these assumptions for our problem.(1) are continuous and there are positive constants s.t .(2) satisfies Lipschitz condition with Lipschitz constants such that
We prove the existence of the solution of system (12), then we have to integrate the differential equation in (12), we get
By differentiating the integral equations (14)–(16) with respect to t, we have
Substituting in (14), in (15) and (16), we obtain
Hence, the existence is proved from the equivalence between the system (12) and the integral equations ((14)–(16)). Therefore, there is a solution for our system.
Now, we apply the Picard method to find the solutions of the integral equations (14)–(16). The solution is constructed by the sequences,
can be written as the following:
If , and are convergent, then the infinite series and are convergent, and the solution will be , and , where
If the three series are converged, then the three sequences and will be converged, respectively, to and . For proving the uniform convergence of and , we have to consider the three associated series,
For , we get
Now, we shall get an estimation for , , and
By using the first estimation in (24) and putting , we get
At , we haveand so on
By using the second estimation in (24), we have at
At and so on
By using the third estimation in (24), we get at
At ,and so on
Since such that and , then and are uniformly convergent, and thus the sequences , and are uniformly convergent.
Now, we can apply the Picard method to obtain an approximate solution for our problem.
From Theorem 1, we get the system of the problem as the following:
After reducing these equations, we obtain
By integrating the differential equations in (35), we have the following system:
By applying the Picard method to equations (36)–(38), we have
For , we have
Therefore, the first approximation for and is the following:
Hence, the first approximation of , and is the following:
For , we have
Therefore, the second approximation for and is the following:
Hence, the second approximation of , and is the following:
By putting , and , then we have a comparison between the obtained approximate solutions of the two firms in our problem in the following figures:
Figure 1 indicates the approximated optimal solutions of the state for our problem. In our example and represented, respectively, the market share of Firm 1 and Firm 2 at time t, and from this figure, we found that the market share of Firm 1 is increasing and the market share of Firm 2 is decreasing with the time, and notice that Firm 2 has a greater market share than Firm 1 on the interval .
In Figure 2, we show that the approximated optimal controls to the problem. In the problem, the controls and represented, respectively, the advertising efforts of Firm 1 and Firm 2 at time t, and from this figure, we noticed that the advertising efforts of Firm 1 is decreasing and the advertising efforts of Firm 2 increases until it reaches a certain time and then begins to decrease again. We found that Firm 1 has a greater advertising effort than Firm 2 on the interval .
In Figure 3, we explore the approximated solutions of the advertising cost function to the problem. In the problem, and represented respectively the advertising cost function of Firm 1 and Firm 2 at time t, and from this figure we noticed that the advertising cost function of Firm 1 is decreasing and the advertising cost function of Firm 2 is marginally increasing. We found that Firm 1 has a greater advertising cost function than Firm 2 on the interval .
In Figure 4, we present the approximated optimal solutions of the costate variables to the problem. The costate here represents the marginal value of the market share. In other words, the adjoint for this problem is the rate of change in the payoff for small changes in the market share. From this figure we see that in Firm 1, increases while decreases in Firm 2 on the time interval .
In this study, we discussed the competing between two firms in the market.(1)Firm 2 is existing in the market and there is no competitor to it, and its market share is . Firm 1 entered the market to compete this firm, and its market share is .(2)Firm 1 started to make an advertising campaign by getting a loan. It earned profits and increased its sales.(3)Firm 2 had no advertisements, while the number of customers of the new firm increased and so, its market share increased; therefore, the new firm controlled the market.(4)Firm 2 started to lose and its sales decreased. It got a loan for doing advertisements because of its loss.(5)The cost of Firm 1 was too much and after increasing its sales, the cost started to decrease and also the advertisements started to increase from the negative value. This means that debts decrease with time. After a specific time, the advertisements of the old firm started to increase and this increase is almost slight, so the cost seems constant.(6)Finally, we used an iterative method (Picard method) for finding the solution and proved the convergence of the solution. On the other hand, Kristina used a numerical algorithm for the solution (Forward-Backward sweep algorithm), but she did not determine the solution .
In this paper, we concerned with an open-loop Nash differential game. We proved that there is a solution for the problem, we studied the existence for the solution of the dynamical system of the differential game, and we used the Picard method for finding an approximate solution. Also, we studied the convergence for the Picard method to make sure that the approximate solution is uniformly convergent. Finally, we added the figures to compare between the behavior of the two firms in the problem with respect to market share, the advertising efforts, the advertising cost function, and the costate variables. We proved the convergence at , so we chose the interval [0, 0.5]. If we reach to , the solution will be divergent.
No new data were collected or generated for this article.
Conflicts of Interest
All authors declare that they have no conflicts of interest in this paper.
A. A. Megahed proposed the idea of the manuscript and put the headline, H. F. A. Madkour wrote the manuscript text, A. A. Megahed, and H. F. A. Madkour studied all the analysis in the manuscript. Finally, A. A. Hemeda reviewed the manuscript.
Y. Sibuya and P.-F. Hsieh, Basic Theory Differential Equations, Springer-Verlag New York, Inc, New York, NY, USA, 1999.
G. Owen, Game Theory, Academic Press, Cambridge, Massachusetts, United States, 1982.
A. Friedman, Differential Games, John Wiley & Sons, Hoboken, New Jersey, United States, 1971.
A. A. Megahed, “The Stackelberg differential game for counter-terrorism,” Quality and Quantity: International Journal of Methodology, vol. 53, no. 1, 2018.View at: Google Scholar
A. E. M. A. Megahed, “The development of a differential game related to terrorism: min-Max differential game,” Journal of the Egyptian Mathematical Society, vol. 25, no. 3, pp. 308–312, 2017.View at: Publisher Site | Google Scholar
A. E. M. A. Megahed, “A differential game related to terrorism: min-max zero-sum two persons differential game,” Neural Computing & Applications, vol. 30, no. 3, pp. 865–870, 2016.View at: Publisher Site | Google Scholar
M. Dehghan Banadaki and H. Navidi, “Numerical solution of open-loop Nash differential games based on the legendre tau method,” Games, vol. 11, no. 3, p. 28, 2020.View at: Publisher Site | Google Scholar
B. W. Wie, “A differential game model of Nash equilibrium on a congested traffic network,” Networks, vol. 23, no. 6, pp. 557–565, 1993.View at: Publisher Site | Google Scholar
A. A. Hemeda, “Afriendly iterative technique for solving nonlinear integro-differential and systems of nonlinear integro-differential equations,” International Journal of Computational Methods, vol. 15, no. 03, Article ID 1850016, 2018.View at: Publisher Site | Google Scholar
K. Joseph, “Open-Loop Nash And Stachelberg Equilibrium For Non-cooperative Differential Games with Pure State Constraints, Uiversity of Kwazulu-Natal, College of Agriculture, Engineering and Science School of Mathematics, Statistics and Computer Science,” Tech. Rep., 2017, Master thesis.View at: Google Scholar
M. A. E. H. Kassem, A. E. M. A. Megahed, and H. K. Arafat, “A Study on Nash-Collative Differential Game of N-Players for Counterterrorism,” Journal of Function Spaces, vol. 2021, Article ID 7513406, 8 pages, 2021.View at: Publisher Site | Google Scholar
A. M. A. El-Sayed, E. E. Eladdad, and H. F. A. Madkour, “On some equivalent problems of stochastic differential equations of fractional order,” J. of Fractional calculus and applications, vol. 6, no. 2, pp. 115–122, 2015.View at: Google Scholar
A. M. A. El-Sayed, E. E. Eladdad, and H. F. A. Madkour, “On the Cauchy problem of a delay stochastic differential equation of arbitrary (fractional) orders,” Fractional Differential Calculus, vol. 5, no. 2, pp. 163–170, 2015.View at: Publisher Site | Google Scholar
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| 16,259 | 82 |
https://www.clickoncare.com/basic-mathematical-economics
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math
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Use of mathematical tools in economics helps in systematic understanding of relationships and derivation of certain results which would be more complex through verbal logic. The mathematical approach can be considered as a quick mode of transportation from a set of postulates to a set of conclusion. The purpose of this book is to give an introduction to basic tools of mathematics for use in economic theory and econometrics. The author believes that this book serves as elementary study materials for the students of economics as it is presumed that the readers are acquainted with basic calculus, matrix algebra and economic theory.This book can be used as reference material for the student of M.S. Agricultural Economics.
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https://math.answers.com/Q/What_is_multiplying_a_negative_number_the_same_as
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math
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The same as a positive one. If you are multiplying a positive number by a negative, the answer will be negative. If you are multiplying a negative number by a negative, the answer will be positive.
The rules for dividing negative numbers is the same as multiplying them. A negative number multiplied/divided by a negative number is positive and a negative number multiplied/divided by a positive number is negative.
Positive A simple rule to remember this is when multiplying two numbers with the same sign, the result is ALWAYS positive. When multiplying two numbers with different signs, the results is ALWAYS negative.
a positive number
The result of multiplying a positive number by a negative number is a negative number.
Multiplying a positive and negative number will give a negative result. The result is a negative number.
multiplying and dividing a negative number will "flip" the sign of the other number. So multiplying two negative numbers will produce a positive number. Multiplying one positive and one negative number will produce a negative. And of course two positive numbers yield a positive.
Using the same principles as multiplying a negative whole number by a positive whole number, where the result would be a negative, the product of a (positive) fraction and a negative whole number would equal the product of the two, with the minus sign included. For example, 1/2 x -4 = -2. The same rule can be applied the other way around, multiplying a negative fraction by a positive number would produce the same result.
it is the same as multiplying by 0.4
Yes. Multiplying a negative number by a very large positive number will equal a large negative number. If you have the function y = -x, then as x approaches infinity, y will approach negative infinity at the same rate.
Multiplying a positive number by a negative number gives a negative number. For example, 4 x (-2) = -8.
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
(-5)2 = 25. This is because multiplying two negative numbers together always leads to a positive number. Think about it like taking a negative amount of negative numbers, which switches them over to positive numbers. -52 = -25, because you are not multiplying negative 5 by negative 5, you are multiplying 5 by 5, and then multiplying that value by negative 1.
When you multiply both sides by a negative number the inequality must be flipped over. You do not do that when multiplying by a positive number.
Multiplying anything non-zero by a negative number changes the sign. A positive number multiplied by a negative number becomes negative. A negative number multiplied by a negative number becomes positive.
When multiplying integers, multiplying by the same sign will always produce a positive integer. Such as a negative times a negative equals a positive. If the signs are different then the product will be a negative.
The answer 25. Multiplying two negative numbers results in a positive answer. Adding a negative number to that result is the same as subtracting a positive.
Multiplying something by a negative number makes it change signs. A positive number multiplied by a negative is negative therefore a negative * a negative is positive.
Yes it does
It depends on what you are doing to the two identical numbers. If you are multiplying them, it becomes a negative. If you are dividing them, it becomes a negative. If you are adding them, it will always be zero (e.g., 2+ -2 = 0, etc.). There are two ways to subtract. If you are subtracting a positive from a negative, the number remains negative. If you are subtracting a negative from a positive, or a negative from a negative, the negative becomes a positive and you just add from there.
no, dividing a number is halving it, multiplying iy by 2 is doubling it
If you are multiplying negative numbers, an odd number of factors will have a negative product. An even number of factors will have a positive product.
The same as multiplying any other function by a negative number - after multiplying, positive numbers will become negative numbers, and vice versa.
This happens because a negative number is dominant over a positive one, so the number will multiply just as if you were multiplying even numbers, but at the end, just put a negative symbol. Also, if you multiply two negatives, they cancel themselves out, and the answer just becomes positive, but that only goes when multiplying an even amount of negative numbers together. For all of these, do the equation the same way, but at the end you may have to just add or take away a negative or positive symbol.
dividing by one third is the same as multiplying by three
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| 4,679 | 25 |
https://documents.uefa.com/r/UEFA-Guidelines/UEFA-European-Championship-Final-Tournament-2024-Legal-Information/Maximum-Working-Hours
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math
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Maximum working hours per week must not exceed:
maximum 60 hours per week; and
a maximum average of 48 hours per week in each 24-week period.
This means that over a period of 24 weeks, maximum 1152 working hours may be planned while considering the maximum average working time per period. For example, if staff works 60 hours (6x10) in a certain week, this needs to be compensated by a work week of 36 hours (within the 24-week period) to comply with the maximum average of 48 hours.
If an employee qualifies as night worker (see below), the maximum working hours per week must not exceed 48 hours.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817382.50/warc/CC-MAIN-20240419074959-20240419104959-00597.warc.gz
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CC-MAIN-2024-18
| 599 | 5 |
https://books.google.com.jm/books?id=zAoAAAAAYAAJ&lr=
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math
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An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms
J. Munroe, 1843 - Algebra - 284 pages
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approximate values arithmetical becomes body called coefficient consequently contained continued product Corollary corresponding decimal denominator denote derivative difference Divide dividend division Elimination equal roots EXAMPLES exponent Extract factor figure Find Find the greatest Find the square Find the sum follows fourth fraction Free function given equation gives greater greatest common divisor Hence imaginary increased integral known last term less letter limit logarithm means method monomials multiplied negative number of real number of terms obtained places polynomial positive preceding Problem progression proportion putting quotient ratio real roots reduced remainder result reverse row of signs Solution Solve the equation square root substitution subtracted successive Theorem third true unity unknown quantity variable whence zero
Page 48 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 192 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 268 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.
Page 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 186 - I = the last term, r = the common difference, n = the number of terms, S = the sum of all 'the terms.
Page 55 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Page 32 - The 2d line of col. 1 is the 1st line multiplied by 7 in order to render its first term divisible by the first term of the new divisor ; the remainder of the division is the 4th line of col.
Page 127 - Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend. III. Double the root already found and place it on the left for a divisor.
Page 232 - Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.
Page 47 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference. Ratio of Sum of two first Terms to that of two last. Moreover, in finding...
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CC-MAIN-2023-14
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http://www.ocoins.es/products/fa393b662011865.html
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math
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Circular Cylinder Rectangular Prism Volume Conversion CalculatorImages of Swiss vertical Cylindrical Tank oil Volume
Octanes Tank Volume Calculator makes it really easy to work out the volume of your storage tank.All you need to do is follow the 4 steps below 1.Click one of the 3 tabs across the top which represents your tank 2.Select your measurement units 3.Enter your tanks length,width etc 4.Click Calculate.Tank Volume CalculatorA = r 2 where r is the radius which is equal to d/2.Therefore V (tank) = r2h.The filled volume of a vertical cylinder tank is just a shorter cylinder with the same radius,r,and diameter,d,but height is now the fill height or f.Therefore V (fill) = r2f.Tanks - slideshare.netDec 23,2008·In this case 5,500 = 0.9916V60 Volume at 60 0 F = 5,546.6 gallons Shrinkage = 5,546.6 - 5,500 = 46.6 gallons Volume of liquid in vertical cylindrical tanks Measure the depth of the liquid and either the diameter or supplant the results of accurate tank strapping,which take circumference of the tank,then the volume in many other factors into
Vertical Cylindrical Shaped Tank Contents Calculator Volume of Liquid in Tank.The volume of the liquid contents held in the tank are displayed here in your preferred volumetric units.% Full Tank.This shows the percentage of tank capacity that is filled.
Your email address will not be published. Required fields are marked with *
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056711.62/warc/CC-MAIN-20210919035453-20210919065453-00461.warc.gz
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CC-MAIN-2021-39
| 1,395 | 4 |
https://ep.jhu.edu/courses/525708-iterative-methods-in-communications-systems/
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math
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Generalization of the iterative decoding techniques invented for turbo codes has led to the theory of factor graphs as a general model for receiver processing. This course will develop the general theory of factor graphs and explore several of its important applications. Illustrations of the descriptive power of this theory include the development of high performance decoding algorithms for classical and modern forward error correction codes (trellis codes, parallel concatenated codes, serially concatenated codes, low-density parity check codes). Additional applications include coded modulation systems in which the error correction coding and modulation are deeply intertwined as well as a new understanding of equalization techniques from the factor graph perspective.
Background in linear algebra, such as EN.625.609 Matrix Theory; in probability, such as EN.525.614 Probability and Stochastic Processes for Engineers; and in digital communications, such as EN.525.616 Communication Systems Engineering. Familiarity with MATLAB or similar programming capability.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100229.44/warc/CC-MAIN-20231130161920-20231130191920-00270.warc.gz
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CC-MAIN-2023-50
| 1,072 | 2 |
http://easicorp.com/easicorp-com_004.htm
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math
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"Recipe Calculator" is a simple to use Recipe portion converter.
Simply tap on one of the fields to enter data. Tap on the New Amount field to calculate the new amount.
When you tap on a field for data entry, the Title of that field will turn green.
"Original Serving Size"
This is the number of servings that the recipe is designed for.
"Desired Serving Size"
This is the desired number you want to serve.
This is the amount of the recipe ingredient. Such as: 1 1/2 cups would be 1 1/2. When you change any of the other inputs, this button changes to "Calc".
This buttons toggles the fraction buttons to display eighths. The last button enters "/16" when pressed. To enter 3/16, simply enter 3 and the "/16" button.
"Recipe Calculator" calculates answers to the nearest fraction found on it's standard fraction buttons (1/4-3/4). It can calulate to 1/8 or 1/16 if you enter a value with 1/8,3/8,1/16 etc in the amount field.
"Recipe Calculator" will place the minus ( "-" ) symbol next to an answer if the answer is 10 percent less then the nearest fraction. This means that the answer is slightly less then the displayed answer.
"Recipe Calculator" will place the plus "+" symbol next to an answer if the answer is 10 percent more then the nearest fraction. This means the the answer is slightly more then the displayed answer.
Currently For Android Phones
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816351.97/warc/CC-MAIN-20180225090753-20180225110753-00263.warc.gz
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CC-MAIN-2018-09
| 1,358 | 13 |
https://www.wyzant.com/resources/answers/topics/chain-rule
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math
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10 Answered Questions for the topic Chain Rule
Compute f'(x) in three different ways
f(x)=(2x^2-5)^21.) multiplying out and then differentiating2.) Using the product rule3.) Using the chain ruleShow that the results coincide
Extending Differentiation (Confused...)
VOLUME : A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 cm and (b) 60... more
Given that y=1/2x-1 + 1/(2x-1)^2, find the exact value of dy/dx when x=2
How do I solve d/dx e^(2x)(x^2 + 5^x)?
I believe I am supposed to use the chain rule? I am still new to the concept so please, step by step how would I solve this?
Chain Rule Calculus 3
Using chain rule to find formula
Let f(x,y,z) = ex+ysinz, and let x= g(s,t), y=h(s,t), z=k(s,t) and m(s,t)=f(g(s,t),h(s,t),k(s,t)). Find a formula for mst using the chain rule and verify that your answer is symmetric in s and t.
Using chain rule and product/quotient rule, find derivative of sin(3x^2)/x when x=(squareroot of pi)
sin(3x^2)x^-1 this is how far I got. when do I sub in √pi ? what do I do next?
I'm having trouble approaching this problem. The problem says: differentiate with respect to t: y=bcost+t^2sint.
The chain rule has been giving me problems. Maybe some tips on carrying the chain rule through?
let h(x)=f(g(x)). Find: (a) h'1 (b) h'(2) (c) h'(3)
Need help let h(x)=f(g(x)). Find: (a) h'1 (b) h'(2) (c) h'(3)
Use the chain rule using all steps possible
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141732696.67/warc/CC-MAIN-20201203190021-20201203220021-00489.warc.gz
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CC-MAIN-2020-50
| 1,507 | 18 |
https://www.theproblemsite.com/reference/mathematics/algebra/polynomials/coefficients-and-roots
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math
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Coefficients and RootsReference > Mathematics > Algebra > Polynomials
Often the words "zeroes" and "roots" will be used interchangeably. However, they are not the same thing, and it is good to understand the difference.
A zero is a value for which a polynomial is equal to zero.
A root is a value for which a polynomial equation is true.
Why are these terms used interchangeably sometimes? Because if you set a polynomial equal to zero, you have a polynomial equation, and that equation's roots are the same as the polynomial's zeroes.
For example, the polynomial x - 10 has one zero: x = 10. And the polynomial equation x - 10 = 0 has one root: x = 10.
In this section we're going to deal strictly with polynomial equations in which a polynomial is set equal to zero. We're going to begin by looking at some quadratic equations, and explore the relationship between the coefficients and the roots. From there, we will expand the concept to higher degree polynomials.
Let's consider the quadratic equation x2 - 7x + 12 = 0. The roots of this equation (which you can find by factoring) are 3 and 4. Isn't it interesting that the roots multiply to 12 (which is the constant term in the equation) and add to 7 (which is the opposite of the coefficient of x)! We should wonder if that's always the case. Let's try another example: x2 + 14x + 48 = 0. In this case, the roots are -6 and -8. Sure enough, they add to the opposite of 14, and multiply to 48.
But let's not be hasty to draw a conclusion; let's try this equation: 2x2 - x - 15 = 0. This one has roots x = -5/2 and x = 3. These add to 1/2 and multiply to 15/2. This doesn't quite match what we saw before. However, if we take the coefficient of x and divide it by the coefficient of x2, we get -1/2, and if we divide the constant term by the coefficient of x2, we get -15/2. and these two numbers match our pattern.
It turns out that this is a rule that is always true: the sum of the roots of a quadratic is the opposite of the coefficient of x divided by the leading coefficient, and the product of the roots is always the constant term divided by the leading coefficient.
To put it another way: In the quadratic equation ax2 + bx + c = 0, the roots add to -b/a, and they multiply to c/a.
Example: Find a quadratic which has 5 and 7 as its roots.
Solution: 5 + 7 = 12, and 5 x 7 = 35, so a quadratic equation could be x2 - 12x + 35 = 0
Note that in this question, I asked you to find A quadratic, not to find THE quadratic. This is because there are multiple quadratic equations that match the requirements. Consider what happens if you multiply each term by 2: 2x2 - 24x + 70 = 0. Does it have the same roots? Yes it does! So it's good to remember that we can have multiple solutions. Generally we give the quadratic in which all the terms are relatively prime (in the case of my second answer, all the coefficients are divisible by 2, so they're not relatively prime).
Example: Find b if one of the roots of 2x2 + bx + 12 = 0 is 3.
Solution: The product of the roots is 12/2 = 6. Since one of the roots is 3, the other must be 2. The sum of the roots is therefore 5, and thus -b/2 = 5, or b = -10.
Example: The roots of x2 - 7x + c = 0 are two integers which differ by 3. Find c.
Solution: The sum of the roots is 7. If the roots are m and n, then m + n = 7 and m - n = 3, which leads to m = 5, n = 2. Thus, since c is the product of the roots, c = 10.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510462.75/warc/CC-MAIN-20230928230810-20230929020810-00108.warc.gz
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CC-MAIN-2023-40
| 3,411 | 18 |
http://mathhelpforum.com/geometry/155022-cog-belt-problem-print.html
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math
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There are 2 cogs, connected together by 1 belt. Find the length of the belt.
The large cog has a radius of 11cm. The small cog has a radius of 4cm. The distance between the centre of the 2 cogs is 25cm.
(Diagram not drawn to scale)
I'm stuck because I cannot solve the angle AOB or YPZ, and I cannot solve the length of AY or BZ. Once I get those, then I can get solve the answer.
Can anyone tell me how to get the angle or length?
Does the angle AOB = angle YPZ?
I got for angle AOB and for the reflex angle of YPZ because I assumed they were equal, but it doesn't seem right.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218194600.27/warc/CC-MAIN-20170322212954-00360-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 577 | 7 |
https://www.physicsforums.com/threads/memorizing-mathematical-definitions.737876/
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math
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Hi Usually when learning math, understanding the theorems and ideas helps tremendously to remember math. I get that... I got through calculus, linear algebra and complex analysis easily. The problem for me started with three branches in mathematics: Real analysis, measure theory and abstract algebra. The theorems are no problem. However, remembering the definitions is really hard: Rings, fields, sigma-rings, algebras, sigma-algebras, integral domains, outer measure, Lebesgue measure, metric space, norm space... The list goes on... Not only are there many definitions; They are often very similar to each other. So, remembering the differences can be an art in itself. I have to retake exams because I could not remember the definitions. What were the exact definitions of pointwise and uniform continuity? I remembered only vaguely and had to try to deduce parts of the definitions.. How can I remember the definitions more easily? I keep forgetting them..
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647545.84/warc/CC-MAIN-20180320224824-20180321004824-00068.warc.gz
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CC-MAIN-2018-13
| 962 | 1 |
https://edurev.in/course/quiz/attempt/9734_Test-Belt-Constructions/e1e0a563-6ffc-422d-a07d-5e5f10f6bca2
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math
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The layer of a belt is generally called as
Velocity ratio for chain drive is lesser than that for belts.
Explanation: Velocity ratio for chain drives is about 15:1 while for belts it is around 7:1.
Fabric rubber belts are not widely used as they can’t be operated at high speeds.
Explanation: These belts can be operated at 300m/s.
Power transmitting capacity of V belts is more than that of flat belt.
Explanation: Coefficient of friction is 2.92times of flat belts in V belts for identical materials.
The optimum velocity of the belt for maximum transmission is given by √P/6m.
Explanation: It is given by √P/3m.
Creep is the slight absolute motion of the belt as it passes over the pulley.
Explanation: It is a relative and not absolute motion.
In horizontal belt, the loose side is generally kept on the bottom.
Explanation: Loose side is kept on the top so that arc of contact increases and hence efficiency of the drive increases.
Vertical drives are preferred over horizontal.
Explanation: In vertical drive, gravitational force on the belt causes slip which reduces the efficiency.
The law of belting states that the centreline of the belt when it approaches a pulley must not lie in the midplane of the pulley.
Explanation: The centreline must lie in the midplane.
It is possible to use the belting reverse direction without violating the law of belting.
Explanation: Law of belting is violated if belt is used in reverse direction.
A shorter centre distance is always preferred in belt drives.
Explanation: It is more stable and compact.
If velocity ratio is less than 3, then centre distance is given by D+.5d.
Explanation: It is given by D+1.5d.
If velocity ratio is more than 3, then centre distance is given by 2D.
Explanation: It is given by D
Is it possible to reduce the centre distance as much as we want?
Explanation: It depends on physical dimension and the minimum angle of wrap required to transfer the required power.
The diameter of the shorter pulley in leather belt drive is 265mm. It is rotating at 1440 rpm. Calculate the velocity of the belt.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992721.31/warc/CC-MAIN-20210513014954-20210513044954-00228.warc.gz
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CC-MAIN-2021-21
| 2,077 | 28 |
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=1461386&contentType=Journals+%26+Magazines
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math
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Skip to Main Content
In the emerging nanotechnologies, faulty components may be an integral part of a system. For the system to be reliable, the error of the building blocks has to be smaller than a threshold. Therefore, finding exact error thresholds for noisy gates is one of the most challenging problems in fault-tolerant computations. Under the von Neumann's probabilistic computing framework, we show that computation by circuits built out of noisy NAND gates with an arbitrary number of K inputs under worst case operation can be readily described by nonlinear discrete maps. Bifurcation analysis of such maps naturally gives the exact error thresholds above which no reliable computation is possible. It is further shown that the maximum threshold value for a K-input NAND gate is obtained when K=5. This implies that if one chooses NAND gate as basic building blocks, then the optimal number of inputs for the NAND gate may be very different from the conventional value of 2. The analysis technique generalizes to other types of gates and circuits that use voting to improve reliability, as well as a network built out of the so-called para-restituted NAND gates recently proposed by Sadek et al. Nonlinear dynamics theory offers an interesting perspective to study rich nonlinear interactions among faulty components and design nanoscale fault-tolerant architectures.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823670.44/warc/CC-MAIN-20160723071023-00247-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 1,377 | 2 |
https://www.instructables.com/id/How-to-Add-9/
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math
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Introduction: How to Add
... using mental arithmetic tricks. I'm not going to teach you how to do long addition on paper, although I will assume you are comfortable with doing it. This Instructable is for those times when you don't have paper or a calculator handy.
Step 1: Borrow Ones
"From where?", I hear you cry. Essentially from nowhere- sometimes you can make an addition (or sometimes a subtraction or multiplication) easier by borrowing a one, doing the sum and putting the one back. Example:
13+29 is a bit of a pain to do in your head. If you like the previous technique you could call it thirty-twelve, but to do that precise addition is a little awkward. 13+30 is much easier, however. Borrowing ones essentially means you say "13+29 is hard- I'm going to borrow a one and add it to the 29, 13+30 is 43, then I put back the one I borrowed so the answer is 42". It sounds complicated, but with a little practise I now do all of those steps in my head much faster than just trying to add 13+29.
Borrowing ones can also work in reverse by "burying" a one you would rather ignore for the time being- for example, 13+31 can be turned into 13 + 30 = 43 and then you add the one you ignored earlier, but additions that become easier by "burying" a one are less common that those made easier by borrowing.
Pros: simple, conceptually easy
Cons: limited application, doesn't allow very large additions.
Step 2: Match Pairs
What is special about the pairs (1 and 9), (3 and 7), (4 and 6)?
They sum to 10. There are only five of these pairs so anyone who has spent a while doing maths should instantly recognise them, and they can make your life a whole lot easier when doing additions.
Take 13+27. Recognising the matched pair 3 and 7 in the ones place tells you the answer will be a multiple of ten, so you have to add 10, 20 and the 10 resulting from (3+7) to get 40- you have effectively simplified the addition from 13+27 to (1+2+1) * 10. Good for you.
If you become proficient at this technique, you may be able to combine it with the previous technique- if you saw 14+25 you might recognise that you can borrow a one to turn it into 14+26 then use this technique.
Pros: very quick, conceptually simple, quite general
Cons: requires practise for recognition, slightly limited application.
Step 3: See Subtractions
This is a similar technique to borrowing ones, but can be extended to numbers other than one. If you tried to do 98+97 using traditional means there would be a lot of carries. The easier way to do this addition is to recognise that 98 = (100-2) and 97 = (100-3) so the result is the sum of these, namely (200-5) or 195. Many people can do this intuitively given a case like 99+99=198, but with a little practise you can make it much more general by recognising larger subtractions. The result may become very confusing if the subtractions sum to more than 10 (for instance, 93 + 94 = 200 - 13), so beware of replacing an awkward addition with an equally awkward subtraction.
Pros: general, work with large numbers
Cons: needs a conceptual shift, requires some practise
Step 4: Make Groups
The previous few techniques have been delaing with adding two large-ish numbers. This one is more suited to "restaurant bill" type additions where you are adding a lot of very small numbers (or not very small, depending where you choose to eat).
This technique uses the fact that most people who have done maths for any length of time recognise most single-digit additions without even having to think about them- 2+2 is the obvious example but any maths student should be able to do 5+7 or 8+8 without too much thought.
When confronted by a string of numbers to add, you can simplify it by spotting groups that you can combine using the instinctive additions above. As a simple example, 2+2+3+4 could become 4+3+4 by pairing the twos, then 8+3 by pairing the 4s. If the numbers are out of order the pairs may be scattered, but in a longer example like the above you could even group all of the similar digits together and turn them into a multiplication, so you could start 2+5+7+2+7+3+8+2+4+6+2 by removing the four twos and adding an eight.
Pros: conceptually simple, general
Cons: requires holding a lot of working in your head, at risk of "losing count" and making mistakes.
Step 5: Running Total
In a similar manner to the previous technique, a string of small additions may be best handled by simply keeping a running total as the numbers are added in order. 2+2+3+4+5 = 4+3+4+54 = 7+4+5 = 11+5 = 16. A more experienced mental mathematician could probably reduce the number of steps with larger recognitions- if you recognise from sight that 2+2+3=7, compress that into one step and skip to 7+4+5.
Pros: conceptually simple, very general
Cons: not a great speed improvement
Step 6: Multiply
"But wait," I hear you cry, "this Instructable is meant to be about adding!"
But we've already invented a handful of new digits and borrowed numbers from out of thin air, so a simple multiplication shouldn't be too hard.
What is 55+66? The conventional method involves lots of carries and is (like many of the examples in this Instructable) a bit awkward. However, I'm sure many people will notice that 55 is 11*5 and 66 is 11*6, so the sum is naturally 11*11. Depending on how far your multiplication tables went you may know 11*11=121 off the top of your head, but other multiplications (the 5 and 9 times table, for instance) feature a lot of rules for working them out so may be of use in this technique.
63+18 might be a pain to work out in your head explicitly but a knowledge of the 9 times table will tell you that it is 7*9 + 1*9 = 9*9 = 81. For small numbers this method may not be much quicker than simple addition but certain problems may be greatly simplified.
Step 7: Runs
This is the most obscure of the techniques I am going to present. It's not as simple a method as the others and has limited application, but also has some incredibly powerful uses. The story goes that when he was a child, the mathematician Carl Friedrich Gauss was asked to mentally add all the integers between 1 and 100 to keep him busy for a period. It didn't work, as he summed all the number in seconds by realising that they form a simple pattern.
Gauss saw that he could break the numbers down into matched pairs, remove an amount from the high number and add it to the low number to make all the pairs the same. Taking the numbers 1 to 5 as a simpler example, you would take 2 from the 5 and add it to the 1, take 1 from the 4 and add it to the 2. This turns 1+2+3+4+5 into the rather more manageable 3+3+3+3+3 or 15.
To do this for the numbers 1 to 100 is a little trickier because there are an even number of them so the pairs end up summing to 50.5 (the mean average of all the numbers). The general rule is that to add a run of increasing integers, add the first and last together, halve the value and multiply by the number of numbers you are adding together. To go back to our smaller example, 1+5=6, 6/2=3 and 3*5=15. The diagram below shows in a more visual way why this works. The intricacies of this technique are outside the scope of this Instructable, but for now you can remember the formula (first+last)/2 * number of numbers
Again, this method isn't particularly general because it requires an addition of the form 1+4+7 (properly, an arithmetic series), but when it is applicable it is a very powerful method (as Gauss demonstrated). Runs of evenly-spaced additions are unlikely to come up much in "real life" (unless you go to restaurants with mathematicians) but pure maths features them more often.
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CC-MAIN-2020-34
| 7,619 | 39 |
http://cas.umt.edu/math/reports/sriraman/abstract_8.html
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math
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The University of Montana
Department of Mathematical Sciences
Technical report #12/2005
and the Evolution of Rigor
The University of Montana, USA
Guillermina Waldegg (Posthumously)
In this paper we discuss the origins and the evolution of rigor in mathematics in relation to the creation of mathematical objects. We provide examples of key moments in the development of mathematics that support our thesis that the nature of mathematical objects is co-substantia1 with the operational inventions that accompany them and that determine the normativity to which they are subjected.
Keywords: Arithmetic; Calculus; Geometry; History of mathematics; Mathematics foundations; Normativity; Non-Euclidean Geometry; Operationality; Proof
Classification: 01, 03, 97
Pre-print of: Moreno-Armella, L., Sriraman, B.,& Waldegg, G . Mathematical Objects and the evolution of rigor. In press in the Mediterranean Journal for Research in Mathematics in Mathematics Education.
Download Technical Report: Pdf (95 KB)
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s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997893859.88/warc/CC-MAIN-20140722025813-00010-ip-10-33-131-23.ec2.internal.warc.gz
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CC-MAIN-2014-23
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http://www.tellmehowto.net/answer/how_do_you_clean_the_green_3341
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math
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How do you clean the green algae of garden pebbles and rockery stones?
Question asked by: tresha
Asked on: 13 Apr 2009
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s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929832.32/warc/CC-MAIN-20150521113209-00196-ip-10-180-206-219.ec2.internal.warc.gz
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CC-MAIN-2015-22
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http://www.aes.org/e-lib/browse.cfm?elib=12913
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math
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Due to its simplicity and accuracy, quadratic peak interpolation in a zero-padded Fast Fourier Transform (FFT) has been widely used for sinusoidal parameter estimation in audio applications. While general criteria can guide the choice of window type, FFT length, and zero-padding factor, it is sometimes desirable in practice to know more precisely the requirements for achieving a prescribed error bound. In this paper, we theoretically predict and numerically measure the errors associated with various choices of analysis parameters, and provide precise criteria for designing the estimator. In particular, we determine 1) the minimum zero-padding factor needed for a given error bound in quadratic peak interpolation, and 2) the minimum allowable frequency separation for a given window length, for various window types.
Click to purchase paper as a non-member or login as an AES member. If your company or school subscribes to the E-Library then switch to the institutional version. If you are not an AES member and would like to subscribe to the E-Library then Join the AES!
This paper costs $33 for non-members and is free for AES members and E-Library subscribers.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867885.75/warc/CC-MAIN-20180625131117-20180625151117-00466.warc.gz
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CC-MAIN-2018-26
| 1,172 | 3 |
https://realestate.lohud.com/property/ny/newburgh-city/12550/-/47-dubois-street/5d6f681b2fe35459b30000b4/
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math
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Rehab, Renovate and Revive this Historic Newburgh Community. This Property Can Be sold as part of a package deal On Dubois Street...
Can Be Sold As A Package Deal
13 Dubois MLS#5042962-3 UNIT
25 Dubois MLS#5042967-2 DUPLEX
45 Dubois MLS# 5042972-INN/LODGE
47 Dubois MLS#5043001- REHAB
219-221 Dubois MLS#5043006-SFR +LOT
- Style Two Story
Listing Agent: Stacie R Laskin
Updated: 21st October, 2019 4:14 PM.
47 Dubois Street Newburgh City, NY
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987795403.76/warc/CC-MAIN-20191022004128-20191022031628-00067.warc.gz
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CC-MAIN-2019-43
| 441 | 11 |
http://www.chegg.com/homework-help/questions-and-answers/let-find-limxrightarrow16-f-x-determine-f-x-continuous-x-16-show-work-must-limit-notation--q4146617
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math
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Show transcribed image text
Show transcribed image text Let Find limxrightarrow16 f(x) and determine if f(x) is continuous at x = 16. Show all work and you must limit notation. State the Intermediate Value Theorem Use the Intermediate Value Theorem to show the equation sin(x) + x = 2 has a solution in the interval (0. Pi/2).
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s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471983580563.99/warc/CC-MAIN-20160823201940-00063-ip-10-153-172-175.ec2.internal.warc.gz
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CC-MAIN-2016-36
| 326 | 2 |
http://www.haihongyuan.com/xuekejingsai/762623.html
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math
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姓名 班次 分数
1. Yy 2. Cc 3. Mm
4. Ii 5. Vv 6. Ff
sandwich weekend drink hotel house hot dog post office bank festival cinema
1.make ghost mask ________ 2.电影院________ 3. turn left _________ 4. 旅行________ 5 .milk the cow ________ 6.play games ________ 四．单项选择。（20分，每小题4分）
( ) 1 ---What did you do? --- We＿ a big party.
A. has B. had C. have ( ) 2. --- ___ was your trip to Guangzhou?
A. What B. Where C. How
( ) 3.---Where ___she yesterday? ---I ___ in the gym.
A. were; were B. was; were C. were; was ( ) A. How do you do? B. I’m fine, thank you. C. Hello ( ) 5. ---Why are you here?
---___ I live here.
B. Because C. Since
where , last night(昨晚)，go
2. played the drums, I, yesterday (.)
六．阅读理解，正确的写T，错误的写F。（10分） My home is not far from school. I usually walk to school. In My name is Sally. I’m 12 years old. My city is Changsha. the morning, I usually eat a sandwich .Today is a rainy day. So I go to school by bus. I always do my homework.
1. ( ) My home is far from school. 2. ( ) I usually go to school by bus. 3. ( ) Today is a sunny day.
4. ( ) I usually eat a sandwich in the morning. 5. ( ) I never do my homework. ________
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123635.74/warc/CC-MAIN-20170423031203-00521-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,230 | 17 |
https://www.federalreserve.gov/econres/notes/feds-notes/low-risk-as-a-predictor-of-financial-crises-accessible-20180509.htm
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math
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Low risk as a predictor of financial crises Accessible Data
Figure 1: The relationship between volatility and financial crises. A flow chart shows that low volatility leads to an increase in the risk appetite. This in turn can increase lending on one hand, and makes issued loans riskier on the other hand. In time, loan defaults increase, leading to a banking crisis and high volatility.
Figure 2: Volatility as predictor of crises. A line chart plots a linear relationship between volatility and crises. X-axis is volatility, y-axis is the probability of crises, and an increasing line represents the view that increasing volatility means crises are more likely. This view is rejected by the data.
Figure 3: Low and high volatilities as predictors of crises. A line chart plots another possible relationship between volatility and crises. X-axis is de-trended volatility, y-axis is the probability of crises. On the left-hand side (volatility below trend), a solid decreasing line is plotted, on the right-hand side (volatility above trend), both a dashed increasing line (labeled as V shape) and a solid zero line (labeled as hockey stick shape) are plotted. The top of the V on the left is labeled "Low volatility; Strong evidence," and the top of the V on the right is labled "High volatility; Weak evidence."
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585302.56/warc/CC-MAIN-20211020024111-20211020054111-00676.warc.gz
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CC-MAIN-2021-43
| 1,314 | 4 |
https://link.springer.com/article/10.1007%2Fs00454-009-9198-7
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math
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Oriented Mixed Area and Discrete Minimal Surfaces
- 134 Downloads
Recently a curvature theory for polyhedral surfaces has been established, which associates with each face a mean curvature value computed from areas and mixed areas of that face and its corresponding Gauss image face. Therefore a study of minimal surfaces requires studying pairs of polygons with vanishing mixed area. We show that the mixed area of two edgewise parallel polygons equals the mixed area of a derived polygon pair which has only the half number of vertices. Thus we are able to recursively characterize vanishing mixed area for hexagons and other n-gons in an incidence-geometric way. We use these geometric results for the construction of discrete minimal surfaces and a study of equilibrium forces in their edges, especially those with the combinatorics of a hexagonal mesh.
KeywordsOriented mixed area Discrete curvatures Geometric configurations Discrete minimal surfaces Reciprocal parallelity
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540530452.95/warc/CC-MAIN-20191211074417-20191211102417-00455.warc.gz
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CC-MAIN-2019-51
| 979 | 4 |
https://rojhelat.info/en/map.php?pub_id=2&five=ff-free-math-homework-help-with-steps
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math
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Free math homework help with steps
Step-by-Step Math Problem Solver
- 75 Free Homework Help Sites
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Free Homework Help for Military Family Homework Kansas Live Homework Help free math homework help with steps Math Kentucky Homework Help Problem Homework Help Description Solver answers algebraic homework help from parents Homework Help Rocket Boy Questions and StepbyStep ap chemistry homework help Explanations. Production and Operation Management Task Help App Yup Homework Help Probability and Task Help Statistics provides anytime homework help for free math homework help with steps math, chemistry and physics and online oxford public library help with live tasks anywhere. You can connect with expert tutors hours a day, days a week for academic support. The yahooligans homework help service has a subscription to the homework help twitter rate, but free math homework help with steps your balto story homework help can sign up for a free trial to start tutoring. Free calculus help. Junior High School Homework Help For more information on our collection of online math resources from, and more free math homework help with steps as links to other doctoral dissertation writing services vancouver great free math homework help with steps math sites, see: There are also some free online calculators that can be very helpful in solving these difficult calculation problems and checking your answers. WebMath free math homework help with steps is designed to help you with homework solve your math problems. Composed of forms to fill in and then return the analysis of the Celtic warrior primary task to help solve a problem and when possible, the free online Algebra task help free math homework help with steps provides a stepbystep solution. Covers arithmetic, algebra, geometry, calculus, and statistics.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510810.46/warc/CC-MAIN-20231001073649-20231001103649-00446.warc.gz
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CC-MAIN-2023-40
| 4,275 | 17 |
https://www.neles.com/flow-control-manual/mathematical-simulation-of-control-valve-behavior/
|
math
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6 Mathematical simulation of control valve behavior
The use of computational science has resulted in a control valve simulation program that can be used to describe the dynamic behavior of control valves.
6.2 Use of simulation
Use of simulation can be divided into three areas:
In development of new products.
In support for customer's process applications.
In training of personnel about fluid flow control and control valves.
In the development of new products, simulation can be used to test new ideas, and to develop and optimize constructions before a prototype is manufactured. Simulation thus reduces the number of prototypes required. It can also be used to study the effects of different disturbances on control valves.
Before the delivery to a customer, the operation of a control valve packages can be simulated in conditions that equal the real process conditions. Simulation makes it possible to study the operation of the whole control loop including the customer's process. The simulation program can also be used to study various questions relating to the safety of process plants.
When training the personnel in the area of control valves, simulation can be used to illustrate the operation of different control valve units in process pipelines. In addition, simulation makes it possible to examine different control valve characteristics in the whole control loop.
Simulation of customer's control applications is a state-of-the-art service designed to study the control valve dynamic behavior before delivery. A detailed dynamic analysis performed in simulated process conditions enhances the optimal control valve selection for customers' demanding control valve applications.
6.3 Mathematical model of a control valve
The starting point for the control valve simulation program is a comprehensive mathematical model describing the operation of the control valve, right from the control signal from the controller to the fluid flow through the valve.
The dynamics equation of a quarter-turn control valve can be found using the basic equations (84) and (85).
Equations (84) and (85) can be used to produce the equations for the dynamics of an installed quarter-turn control valve as in equation (86).
The actuator coefficient (b) used in equation (86) is a function of the actuator turning angle (ψ) and friction coefficient (μ). Figure 74 shows the actuator coefficient for one manufacturer's actuator as a function of actuator relative travel (h) when the friction coefficient (μ) is assumed to be constant.
The non-linearity of the actuator coefficient (b) depends on the lever mechanism of the actuator. In practice, actuator friction coefficients vary greatly as a function of velocity. This means that in reality, the actuator coefficient is less linear than indicated in figure 74.
Figure 75 shows the non-linearity of the derivatives in equation (86) for the actuator examined, as a function of actuator relative travel (h). The first derivative in figure 74 describes the non-linearity between the actuator piston position (x) and the valve turning angle (ψ). The non-linearity of the derivatives depends on the lever mechanism of the actuator.
As the control valve dynamic equation (86) includes pressures pA and pB, affecting both sides of the actuator piston, they must be solved from the mathematical models describing positioner dynamics and actuator thermodynamics.
In equation (86), the valve load has been divided into the load caused by friction (Mvμ) and the load caused by dynamic torque (Md), since the dynamic torque usually tends to close the valve. The valve load consists of the seat friction, gland packing friction, bearing frictions, and dynamic torque of the valve. A mathematical model is needed to solve these torques as a function of valve travel (h) and the pressure difference (∆p) across the valve throttling element. Because the pressure difference (∆p) over the throttling element changes considerably in a control situation, especially with large travel changes, the mathematical model of the control valve must include a dynamic model of pipe flow.
Unsteady pipe flow control is calculated using the continuity equation (87) and the equation of motion, equation (88).
6.4 Control valve simulation program
The solution of mathematical models describing control valve action in space-time is not, however, mathematically possible as such, because the equations are complicated and nonlinear. For this reason, a numerical solution produced by a computer program has to be adopted. One advantage of the computer program is that the non-linearities in the control valve do not have to be linearized. Furthermore, the computer program is flexible because different changes and disturbance factors, depending on time and state, are easy to insert.
6.5 Friction model
A large decrease in the friction coefficient right after the valve starts to move is an important factor in the dynamics of a control valve equipped with a pneumatic cylinder actuator. This means that the correct modeling of friction behavior is decisive for proper functioning of the simulation program.
Lubrication mechanisms can be divided into contact lubrication and fluid lubrication. In contact lubrication, the sliding bearing surfaces touch each other, although the lubricant limits the contact area by penetrating between the contact points. In fluid lubrication, the pressure generated in the bearings prevents any contact between surfaces, and the friction force is created only by the shear stress of the lubricant.
The starting point for the contact friction model used is the exponential friction model, in which the friction force depends exponentially on relative slide velocity (vr). Applying the model gives the equations (89) and (90) for the contact friction coefficients.
The control valve friction model can be determined by approximating the contact friction, using the exponential friction coefficient, and by assuming that the fluid friction is directly proportional to velocity.
6.6 Testing and implementing the simulation program
Testing position control
The created simulation program was first tested with a single-stage pneumatic positioner, a double-acting cylinder actuator, and a valve with a load factor (Lp). In this case, the actuator load factor (Lp) is the valve load divided by the actuator nominal output torque. Figures 76 and 77 show one form of step response calculated with the simulation program, and the corresponding valve relative travel (h) measured when the relative input signal (I) changes from value 0.4 to value 0.45. As becomes apparent from the step responses presented in figure 76, the form of the response calculated theoretically using the simulation program is fairly consistent with the corresponding response measured in a laboratory by means of an oscilloscope.
Studies of an installed control valve
Figure 78 shows a preliminary study of a water-hammer with three different inherent flow characteristic curves. The calculations are based on a single-stage pneumatic positioner, a double-acting cylinder actuator and linear, equal percentage, and constant gain inherent flow characteristics.
The characteristic pressure difference ratio (DPf) describing the pipeline is determined using equation (91).
The starting point for the case is a constant gain inherent flow characteristic valve which performs the signal change from 100% to 10%. For the equal percentage opening valve with a corresponding steady-state pressure difference and flow rate change, the signal change is from 100% to 12.0%. For a linear valve, the corresponding signal change is from 100% to 3.2%.
Figure 78 shows that the water-hammer caused by a valve with a linear inherent flow characteristic is very strong and sharp. With equal percentage and constant gain inherent flow characteristics, water-hammers are considerably smaller. Note that in the contant gain inherent flow characteristics, the change in flow rate is almost linear as a function of time.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949093.14/warc/CC-MAIN-20230330004340-20230330034340-00789.warc.gz
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CC-MAIN-2023-14
| 8,022 | 36 |
https://wikieducator.org/Normal_force
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math
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1. Normal Force:
What is a Normal force? • .The normal force comes into play any time two bodies are in direct contact with one another • It always acts perpendicular to the body that applies the force. Let’s take the example of a block resting on a horizontal surface.
Clearly a gravitational force acts on the block, pulling it down, perpendicular to the surface. Since the block is not accelerating, another force must act to counteract the gravitational force. This force is applied by the surface and is called the normal force, and is referred to as FN .Let’s now draw a free body diagram to understand the case. Free body diagram (FBD) : While studying mechanics, when we examine the forces acting on an object there are five "classic" types that are usually considered:
weight normal friction tensions applied forces
We use freebody diagrams to illustrate the magnitude and direction of all of the forces acting directly on a single object (usually represented by a rectangle). Consider a scenario in which a mass is being pulled across a table by a cord.
The weight vector begins at the object's center of mass and points towards the center of the earth.
A normal vector begins at the point of contact between the mass and its supporting surface. It is directed perpendicularly away from the surface and passes through the object's center of gravity.
Tensions are forces conducted along strings, ropes, and wires. They begin at the point of contact and point in the direction in which they are pulling.
Friction forces begin at the same point as the normal and act parallel to the sliding surface. They always oppose motion.
Applied forces is a catch-all, generic category encompassing any other interactions. In our current example, there are no generic applied forces.
If a force acts at an angle, then we usually work with its x- and y-components.
If an object is in static (at rest) or dynamic (constant velocity) equilibrium, then all of the forces acting on it are balanced.
The magnitude of the forces acting to the left equals the magnitude of the forces acting to the right. The magnitude of the forces acting upwards equals the magnitude of the forces acting downwards.
In this case:
x: f = T cos θ y: + T sin θ = mg
If the forces were not balanced, then the object would be accelerated in the direction of the unbalanced force. For example, using the same forces as in our previous example, if T cos θ were greater than f, then Newton's Second Law will allow us the ability to calculate the object's acceleration towards the right as it starts gaining speed.
net F = ma T cos θ - f = ma (a > 0)
However, if T cos θ were less than f, then the object would still move towards the right but it would be losing speed.
net F = ma T cos θ - f = ma (a < 0)
Now let’s apply the concept of free body diagram.
There are only two forces in the system in figure above. The forcemg which is the weight of the block, and is acting on the surface. R1 = mg through its centre (since the body is symmetric). From FBD, we can see that net external force on the block is zero. That is why; it is stationary on the surface.
• The normal force can also be seen as a direct consequence of Newton's Third Law. • Since the normal force is a reactive force, its magnitude is independent of the nature of the force causing it. • The most common normal force is caused by gravity, as seen on the block resting on a plane surface. However, there can be additional forces that also cause a normal force.
1. The surface experiences a total force of 25 N, and reacts with a normal force of 25 N, keeping the block in equilibrium. 2.
2. The Normal Force on an Inclined Plane
Consider the case of a block resting on an inclined plane. In this instance, the gravitational force on the block is not perpendicular to the plane.
Free Body Diagram of an Inclined Plane
In order to calculate the normal force for this situation we must find the component of the gravitational force that is perpendicular to the plane. What does our free body diagram predict in this case? To find out we analyze all forces acting upon the object. • The perpendicular gravitational force ( F cosθ ) cancels exactly with the normal force ( F N ) • The left out parallel gravitational force ( F sinθ ), which points down the plane. Thus the block will accelerate down the incline. • The normal force applies in any situation in which a force is exerted on an object by direct contact from another object.
1.We solve the problem by drawing a free body diagram, and resolving all force vectors into components parallel and perpendicular to the plane:
The component of the gravitational force perpendicular to the plane is given by: F GP = F Gsin 45 o = 10 sin 45 o = 7.07N
Similarly, the component of the applied force perpendicular to the plane is: F HP = F sin 45 o = 10 sin 45 o = 7.07N
Thus the normal force on the block is simply the sum of the two perpendicular forces, or 14.14N .
Question 1 What is the normal force acting on a 8-kg mass that is at rest on a horizontal surface?
0.8 N 0 N 1.2 N 78.4 N
Question 2 What is the normal force acting on a 8-kg mass that is sitting on the floor of an elevator which is accelerating upwards at a rate of 10 m/sec2?
89.8 N 78.4 N 158.4 N 1.60 N
Question 3 What is the normal force acting on a 8-kg mass that is sitting on the floor of an elevator which is accelerating downwards at a rate of 5 m/sec2?
3.02 x 101 N 3.84 x 101 N 7.84 x 101 N 4.98 x 101 N
Question 4 What is the normal force acting on a 8-kg mass that is being pulled up a 40º frictionless inclined plane at a constant velocity of 10 m/sec?
7.84 x 101 N 6.01 x 101 N 5.04 x 101 N 5.04 x 102 N
Question 5 What is the normal force acting on a 8-kg mass which is being pulled at a constant velocity of 10 m/sec by a rope having a tension of 28 newtons at an angle of 40º to the horizontal?
78.4 N 96.4 N 60.4 N 57.0 N
Question 6 What is the normal force acting on a 8-kg mass which is being pushed at a constant velocity of 10 m/sec by a force of 28 newtons along a rigid handle that makes an angle of 40º to the horizontal?
96.4 N 60.4 N 99.8 N 57.0 N
References: 1)http://dev.physicslab.org/PracticeProblems/Worksheets/APB/normals/assortment.aspx 2) http://dev.physicslab.org/Document.aspx?doctype=3&filename=Dynamics_FreebodyDiagrams.xml 3) http://www.askiitians.com/iit-jee-physics/mechanics/free-body-diagram.aspx 4)http://www.sparknotes.com/physics/dynamics/newtonapplications/section3.rhtml
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141750841.83/warc/CC-MAIN-20201205211729-20201206001729-00601.warc.gz
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CC-MAIN-2020-50
| 6,501 | 44 |
https://intellectualarchive.com/?link=item&id=2038
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math
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M. F. Bessmertnyi. Groups Of Nonlinear Congruences And Geodesic Lines On The Ordered Set Of Positive Definite Matrices
Submitted on: Mar 09, 2019, 04:38:51
Natural Sciences / Mathematics / nonlinear analysis
Description: A family of nonlinear transformation groups of Hermitian matrices preserving the basic linear congruences properties is constructed. Each group generates a structure of a partially ordered vector multispace on the set of Hermitian matrices. Determinant inequalities which allow as to find geodesic lines for an analog of indefinite metric on positive definite matrix set are obtained.
The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.
To read the article posted on Intellectual Archive web site please click the link below.
GROUPS OF NONLINEAR CONGRUENCES AND GEODESIC LINES ON THE ORDERED SET OF POSITIVE DEFINITE MATRICES.pdf
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817650.14/warc/CC-MAIN-20240420122043-20240420152043-00328.warc.gz
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CC-MAIN-2024-18
| 879 | 7 |
https://fr.slideserve.com/ciqala/the-basics-of-physics-with-calculus-powerpoint-ppt-presentation
|
math
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The Basics of Physics with Calculus AP Physics C
Pythagoras started it all…6th Century Pythagoras first got interested in music when he was walking past a forge and heard that the sounds of the blacksmiths' hammers sounded good together. He talked to the blacksmiths and found out that this was because the anvils they were using were scaled down copies of each other: one full size, one half size, and one two thirds size. He got an idea that maybe a simple fraction relationship in the size of two instruments is what makes them sound good together. This idea led to the belief that mathematics was tied to the physical world.
Galileo Galilei Galileo too grew up around music as his father was a musician. His father, however, felt that the Pythagorean Harmonies were too simple for the now emerging Italian Renaissance. Galileo, like his father, was dealing with this same idea as well. His studies with kinematics (motion) were too abstract and too simple to explain complicated motion.
Differential Calculus – More sophisticated! 25 years later Isaac Newton and Gottfried Leibniz developed a sophisticated language of numbers and symbols called Calculus based on work. Newton began his work first but it was Leibniz who first published his findings. Both led the other towards accusations of plagiarism.
What is calculus? Calculus is simply very advanced algebra and geometry that has been tweaked to solve more sophisticated problems. Question: How much energy does the man use to push the crate up the incline?
The “regular” way For the straight incline, the man pushes with an unchanging force, and the crate goes up the incline at an unchanging speed. With some simple physics formulas and regular math (including algebra and trig), you can compute how many calories of energy are required to push the crate up the incline.
The “calculus” way For the curving incline, on the other hand, things are constantly changing. The steepness of the incline is changing— and not just in increments like it’s one steepness for the first 10 feet then a different steepness for the next 10 feet — it’s constantly changing. And the man pushes with a constantly changing force — the steeper the incline, the harder the push. As a result, the amount of energy expended is also changing, not every second or every thousandth of a second, but constantly changingfrom one moment to the next. That’s what makes it a calculus problem.
What is calculus? It is a mathematical way to express something that is ……CHANGING! It could be anything?? But here is the cool part: Calculus allows you to ZOOM in on a small part of the problem and apply the “regular” math tools.
Learn the lingo! Calculus is about “rates of change”. A RATEis anything divided by time. CHANGE is expressed by using the Greek letter, Delta, D. For example: Average SPEED is simply the “RATE at which DISTANCE changes”.
The Derivative…aka….The SLOPE! Since we are dealing with quantities that are changing it may be useful to define WHAT that change actually represents. Suppose an eccentric pet ant is constrained to move in one dimension. The graph of his displacement as a function of time is shown below. At time t, the ant is located at Point A. While there, its position coordinate is x(t). At time (t+ Dt), the ant is located at Point B. While there, its position coordinate is x(t + Dt) B x(t +Dt) A x(t) t + Dt t
The secant line and the slope Suppose a secant line is drawn between points A and B. Note: The slope of the secant line is equal to the rise over the run. B x(t +Dt) A x(t) t + Dt t
The “Tangent” line READ THIS CAREFULLY! If we hold POINT A fixed while allowing Dt to become very small. Point B approaches Point A and the secant approaches the TANGENT to the curve at POINT A. B x(t +Dt) A A x(t) A t + Dt t We are basically ZOOMING in at point A where upon inspection the line “APPEARS” straight. Thus the secant line becomes a TANGENT LINE.
The derivative Mathematically, we just found the slope! Lim stand for "LIMIT" and it shows the delta t approaches zero. As this happens the top numerator approaches a finite #. This is what a derivative is. A derivative yields a NEW function that defines the rate of change of the original function with respect to one of its variables. In the above example we see, the rate of change of "x" with respect to time.
The derivative In most Physics books, the derivative is written like this: Mathematicians treat dx/dt as a SINGLE SYMBOL which means find the derivative. It is simply a mathematical operation. The bottom line: The derivative is the slope of the line tangent to a point on a curve.
Derivative example Consider the function x(t) = 3t +2 What is the time rate of change of the function? That is, what is the NEW FUNCTION that defines how x(t) changes as t changes. This is actually very easy! The entire equation is linear and looks like y = mx + b . Thus we know from the beginning that the slope (the derivative) of this is equal to 3. Nevertheless: We will follow through by using the definition of the derivative We didn't even need to INVOKE the limit because the delta t's cancel out. Regardless, we see that we get a constant.
Example Consider the function x(t) = kt3, where k = proportionality constant equal to one in this case.. What happened to all the delta t's ? They went to ZERO when we invoked the limit! What does this all mean?
The MEANING? For example, if t = 2 seconds, using x(t) = kt3=(1)(2)3= 8 meters. The derivative, however, tell us how our DISPLACEMENT (x) changes as a function of TIME (t). The rate at which Displacement changes is also called VELOCITY. Thus if we use our derivative we can find out how fast the object is traveling at t = 2 second. Since dx/dt = 3kt2=3(1)(2)2= 12 m/s
THERE IS A PATTERN HERE!!!! • Now if I had done the previous example with kt2, I would have gotten 2t1 • • Now if I had done the above example with kt4, I would have gotten 4t3 • • Now if I had done the above example with kt5, I would have gotten 5t4
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053657.29/warc/CC-MAIN-20210916145123-20210916175123-00593.warc.gz
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CC-MAIN-2021-39
| 6,059 | 18 |
https://math.answers.com/Q/When_you_subtract_a_negative_number_by_a_positive_number_is_the_number_positive_or_negative
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math
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That is correct. If you subtract a positive number from a negative number, your result is negative.
Subtract and add the sign of the greater number.
A little awkwardly phrased, so I'll answer both ways. To subtract a negative from anything, add its positive. To subtract a positive from a negative, the equation is treated as though you are adding two postives, the result is negative.
-5+-3 = -8 ++ Add -- Add +- Subtract -+ Subtract
It's the same as adding a positive number.
you subtract the numbers then he higher number to start out with is the awnser. example: negative 3 - positive 7= 3-7=4 the higher number is 7 so i is positive. the final answer is positive 4
the number gets lower
subtract the positive number
it depends if the numbers are positive or negative. if its a positive minus a negative, or switched, it will be the sign of the greater number.
If you subtract a positive from a negative, you will get a negative.
take any negative number, and subtract a positive number..that is the same as adding a negative number and two negative numbers added together are a negative number.
BC= negative number AD= Positive number
It depends on what you do with the negative and positive. If you multiply or divide a positive number and a negative number, then the answer is negative. If you add or subtract a positive number and a negative number, the answer could be negative or positive depending on the numbers involved. If you put a negative sign in front of a positive number, the result is a negative number. If you put a positive sign in front of a negative number (like +(-7)), the result is still negative.
You will get a positive integer. If you subtract a negative number, you will be adding it. I think of it like 2 minuses equals a plus. :P
If you mean when you subtract a negative from a positive what does it make? If so, you will get a positive answer. This is because the two negative symbols are basically multiplied, and if you multiply two negatives you get a positive, so a positive number minus a negative number becomes a positive number plus a positive number. 6 - (-5) = 11 2 - (-10) = 12 125 - (-15) = 140
If the 2nd number is larger than the 1st number, and you subtract it from the 1st number, the result of the subtraction is negative.
always a negative number. just think about going backwards on a number line.
Yes, because subtrating a negative number is the same thing as adding a positive number.
positive is to add and negative is to subtract in math
No, you add the positive to the negative.
No. When you subtract negative numbers, they have the same effect as if you added a positive number. In this scenario as described, the only result would be a positive number.
Yes. to subtract a negative is to add that number, so the number will be higher than the first number which is positive and can't go below zero.
No.If you subtract a positive number, you move to the left.If you subtract a negative number, you move to the right.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00553.warc.gz
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CC-MAIN-2022-05
| 2,975 | 23 |
https://www.jiskha.com/display.cgi?id=1315869827
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math
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posted by jeff .
A fishtank with inside dimensions of 30.5 cm X 61 cm X 30.5 cm is filled with water. What is the volume in cm3 of water required? What is the mass in grams of the water required? What is the mass in kilograms?
The fishtank above measures 1 ft X 2 ft X 1 ft in English dimensional units. If water weights 62.4 lbs/ft3, what is the weight in lbs of the water filling the tank?
The second qustion:
weight= volume*density=2ft^3 * 62.4lbs/ft^3
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109670.98/warc/CC-MAIN-20170821211752-20170821231752-00287.warc.gz
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CC-MAIN-2017-34
| 455 | 5 |
https://fullhomework.com/downloads/expert-answers-179-2/
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math
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1 Which of the following is most likely Section 1231 property (assume that each item has been held long-term and is used in a trade or business)?
Section 1245 property
Section 1250 property
Each of the above items is Section 1231 property
2. Which of the following would MOST LIKELY require an adjustment for the alternative minimum tax?
A casualty loss deduction
A deduction for state income taxes
A charitable contribution deduction
Each of the above items requires an adjustment for the alternative minimum tax
3. Which of the following is most likely Section 1245 property (assume that each item has been held long-term and is used in a trade or business)?
4. Mustufa was at risk for $25,000 in Partnership X and $25,000 in Partnership Z on January 1, 2013. Both partnerships are passive activities to Mustufa (these are Mustufa’s only passive activities). Mustufa’s share of net income from Partnership X during 2013 is $10,000. Mustufa’s share of losses from Partnership Z during 2013 is $40,000. How much is Mustufa at risk for Partnership X on January 1, 2014?
$35,000 – $25k +$10 k
5. Refer to the facts in the previous question. How much is Mustufa at risk for Partnership Z on January 1, 2014
$0 – can only be adjust to 0 no lower all other must be
6. Refer to the facts in the previous questions. What is Mustufa’s carryover under the at-risk rules for Partnership Z in 2013?
$0 – must be suspended loss not carried over, b/c already adjusted to 0
7. Refer to the facts in the previous question. What is Mustufa’s deductible loss for Partnership Z in 2013?
8. Refer to the facts in the previous question. What is Mustufa’s suspended loss under the passive loss rules for Partnership Z in 2013?
9. In 2013, Dennis invested in the BERNARDO Limited Partnership (“BERNARDO L.P.”) by paying $75,000 cash and contributing additional assets worth $50,000 (and having a basis equal to $25,000 on the date of the contribution). What amount did Dennis have at risk in BERNARDO L.P. as of January 1, 2014, if BERNARDO L.P. broke even in 2013 (i.e., if BERNARDO L.P. had no income or loss in 2013)?
10. Refer to the facts stated in the prior question. But, for this question, assume that BERNARDO L.P. allocated to Dennis net income of $20,000 from operations in 2013. What amount does Dennis have at risk in BERNARDO L.P. as of January 1, 2014?
11. In 2013, Kristine and Jason (who file a joint return) had an interest expense of $10,000 on a loan that was used to purchase a variety of stock and bonds (all producing taxable income). Assume further that, in 2013, Kristine and Jason had net investment income of $4,000. Assume they itemize deductions, what is their maximum interest expense deduction in 2013?
12. Assume that Jason and Joyce file a joint return and have the following items for 2013:
Taxable income: $75,000
Positive adjustments: $40,000
Regular tax ability: $10,608
What was their 2013 AMT?
13. Assume that a couple that filed a joint return had 2013 AMTI of $300,000. What was the amount of their actual 2013 exemption for the AMT?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038076454.41/warc/CC-MAIN-20210414004149-20210414034149-00257.warc.gz
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CC-MAIN-2021-17
| 3,074 | 27 |
https://magoosh.com/hs/sat/mental-math-division-sat-video-post/
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math
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How to Divide Numbers in Your Head on the SAT
A good way to think of division is the opposite of multiplication. For instance, if you know that 7 x 4 = 28 than it should be easy to figure out what 28/4 is. Just as we did with multiplication, we want to break down larger numbers into smaller bits. 280/7 is the same 28/7 but with a zero at the end of it. One way to think of this is to split up 280 into 28 x 10. Dividing it by 4, we get: 28/4 x 10 = 70.
Of course, not all numbers end in ‘0’. What if we have 175/5? Well, we can break 175 into 150 + 25 (notice how this doesn’t have a multiplication sign in the middle the way that 28 x 10). So when we divide by 5, we are dividing both of those numbers: 150/5 + 25/5 = 30 + 5 = 35.
This tactic works when the number you are dividing by (in this case ‘5’) divides evenly into both numbers. Say, for instance, that you have 216 and you are dividing it by ‘4’. It helps to notice that 16 is divisible by 4. In fact, a rule of dividing by 4 is that if the last two digits of the number are divisible by 4, the entire number is divisible by 4. So I can break up 216 into 200 and 16, giving me 200/4 and 16/4, which equals 50 + 4 = 54.
One final note, before a couple of practice questions: throughout this post, when I’m showing you these tactics, they are for mental math (meaning: no pencil and paper). So don’t write down 200/4 + 16/4. The reason I show you this is it is not too difficult to do those steps in your head. Try it below!
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300658.84/warc/CC-MAIN-20220118002226-20220118032226-00016.warc.gz
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CC-MAIN-2022-05
| 1,503 | 5 |
http://indiarailinfo.com/train/blog/509/810/835
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math
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Pictures from Yesteryear's Golden Memories.
Yesterday was Searching for Some Old Docs and also found a Old Photo Album and started browsing through it & Incidentally Found the Snaps I was looking for from Long Back. The Inaugural Pics of then "47- KAKINADA-SECUNDERABAD EXPRESS (GOUTHAMI EXPRESS).
Pic 1. Me a Small Kid aged around 4 Years on the Extreme Right Posing with My Uncle & Sister in-front of the Loco ready to do the Honours of the Inaugural run. Beautifully Decorated WDM2 of KZJ (Possible) Shed. My Dad was Clicking the Snap.
I was expecting the same post!!!!!
Darlings B'day party ekada mastaru!!!!
3rd Pic lo date untadi chalk toh raasi guard pakkana.
Meeru ooru vellaru memichestamu..
Sure ki choodam both are diff words
Sure Party, meeru kakinada ravali nenu undali daaniki choodam ani :)
30 years industry anamata....:)
My favorite train Gowthami Express turns 28 today. Hope you serve us in the same way..
Seen here is Bezawada WAP4 22589 in mps action with one of the best maintained trains in IR 12737 Kakinada Port - Secunderabad Jn Gowthami Superfast Express
Many more Happy returns to the Darling :)
3 to 4 years back e train timings change avutayani chepparu but change cheyaledu
it is always having a huge waiting list and this is only non ac available train from kakinada to secunderabad daily
it is better to introduce one more train from secunderabad to kotipally
so that the route will be utilized and extra rush will be cleared
secunderabad - kotipally express
secunderabad : 19:30
kazipet : 21:05
warangal : 21:20
samalkot : 3:40
kakinada : 4:00-4:20
draksharama : 5:20
Kotipally : 5:45
If this has to happen where will have the maintainence sir?? Kotipally can't have it, tough to think of SC having it.
Change chesaru AC express start chesinappudu but backfire avvatam valla same TT continue chestunnaru...
All festival rush.
sun-Jan 17 GNWL# 481 / WL# 399 GNWL# 76 / WL# 72 GNWL# 13 / WL# 10 Avbl 5
For Sept 12th, the availability status from SC to TDD is RAC 137. If I book a berth now,will it get confirmed by the the journey date or shall I look other options for a confirmed berth between SC and TDD ?
The chances of confirmation is gud, book it
I found that RJY-SC has been made GNWL, instead of PQWL. Is it correct. It means I need not book my ticket from Samalkot as I used to all these days!!
book from rjy only from now
Yes from AUG 15 RJY will be converting into GNWL see this
Fri-Aug 14 Avbl 38 Avbl 5 Avbl 4 PQWL# 6 / WL# 2
Sat-Aug 15 Avbl 220 Avbl 25 Avbl 14 Avbl 2
Sun-Aug 16 Avbl 213 Avbl 18 Avbl 23 GNWL# 4 / WL# 4
Mon-Aug 17 Avbl 167 Avbl 24 Avbl 32 GNWL# 3 / WL# 2
Fri-Aug 14 regret / PQWL# 50 PQWL# 23 / WL# 6 regret / PQWL# 11 PQWL# 5 / WL# 3 2m old Refresh
Sat-Aug 15 GNWL# 244 / WL# 102 GNWL# 57 / WL# 28 GNWL# 32 / WL# 10 GNWL# 14 / WL# 7 2m old Refresh
Sun-Aug 16 GNWL# 266 / WL# 138 GNWL# 84 / WL# 39 GNWL# 30 / WL# 12 GNWL# 5 / WL# 2 2m old Refresh
Mon-Aug 17 GNWL# 136 / WL# 36 GNWL# 28 / WL# 12 GNWL# 5 / WL# 1 GNWL# 2 / WL# 1 2m old Refresh
Tue-Aug 18 GNWL# 66 / WL# 23 GNWL# 26 / WL# 12 GNWL# 19 / WL# 12 GNWL# 2 / WL# 2 2m old
Bza should be avoided from bza to sc at least for gnwl. Mtm and ns should have gnwl.
So it's going to run with 26 coaches from Aug 15th?
Not from Aug15th.. SCR has sent list of few trains to make 26coacher so i think they need to get permission from rb to increase coaches to 26.. Gowthami has fair chances to become 1st scr train to run with 26 coaches.
Thank God!! Saved on a few rupees!!
From Aug 15 all stations are given GNWL. Now BZA, WL also GNWL. Seems soon its get 26 coaches
Sat-Aug 15 PQWL# 93 / WL# 55 PQWL# 17 / WL# 12 PQWL# 14 / WL# 4 PQWL# 6 / WL# 2 0m old Refresh
Sun-Aug 16 GNWL# 227 / WL# 58 GNWL# 50 / WL# 29 GNWL# 36 / WL# 4 GNWL# 12 / WL# 5 0m old Refresh
Mon-Aug 17 GNWL# 383 / WL# 182 GNWL# 79 / WL# 41 GNWL# 44 / WL# 27 GNWL# 4 / WL# 4 0m old Refresh
Even return to WL, BZA converted as GNWL
Thu-Aug 13 PQWL# 101 / WL# 41 PQWL# 20 / WL# 7 PQWL# 21 / WL# 3 PQWL# / Avbl 0m old Refresh
Fri-Aug 14 regret / PQWL# 50 PQWL# 23 / WL# 6 regret / PQWL# 11 PQWL# 5 / WL# 3 0m old Refresh
Sat-Aug 15 GNWL# 244 / WL# 102 GNWL# 57 / WL# 28 GNWL# 32 / WL# 10 GNWL# 14 / WL# 7 0m old Refresh
Sun-Aug 16 GNWL# 266 / WL# 138 GNWL# 84 / WL# 39 GNWL# 30 / WL# 12 GNWL# 5 / WL# 2 0m old Refresh
Mon-Aug 17 GNWL# 136 / WL# 36 GNWL# 28 / WL# 12 GNWL# 5 / WL# 1 GNWL# 2 / WL# 1 0m old Refresh
Isn't it is valid case for Objection ? :)
Here posting both side availability. Its surprising change and help full to the people if started as separate posting.
why this train is maintaining as a super fast express ?
it is halting at so many stations in between vijayawada and secunderabad
only based on the speed it is telling as a super fast express but it is having more halts even than a normal express
This train is in service since 1980's. 70-80% of its present halts are there since its inception. Oneof the finest n best maintained train of SCR got superfast status in October 2006 after Ruby jubilee celebrations. It's not easy to remove an existing halt for a train that too a popular one. BTW, what extra halts does this train has when compared to others?
You are right all the halts for this same as of now which were before it was a SF...If my memory serves right Only Aler was added and deleted and again added.
This train has bit of reverse pattern to Godavari which has more halts in Godavari dists and less in between BZA-SC, where as this one has more halts between BZA-SC section and many use this as connectivity from there to various areas in godavari dists.
Gowthami also used to have a Sleeper Slip coach to Bitragunta in 1990's, that sleeper used to be attached to a passenger from BZA to Bitragunta.
Why is the base fare of Goutami is 265 from SCto RJY
Why is base fare of 07706 pushkaram spl HYB to VSK is 375 froom SC to RJY?
Is tatkal fare included in special train?
Yes, i guess, pushkaram spls are with tatkal charge.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443736676547.12/warc/CC-MAIN-20151001215756-00143-ip-10-137-6-227.ec2.internal.warc.gz
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CC-MAIN-2015-40
| 5,935 | 70 |
https://ez.analog.com/thread/40293-ad7609-common-mode-input-range-again
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math
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We have some trouble interpreting the AD7609 common-mode input range in companion with the Absolute Voltage Input specification.
How exactly is "common mode" defined in regard to the AD7609 inputs? Does is specify how much a full swing signal can be offset from AGND, or something else?
How exactly is "Absolute Voltage Input" defined? Is this the voltage with respect to AGND that is allowed to be applied at the VIN pins, or something else?
If I have a full swing input (Vdiff = 20V) with the max. allowed common mode voltage of 4V (as example VIN+ = 14 V, VIN- = -6 V), does the Absolute Voltage Input specification have impact here?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867217.1/warc/CC-MAIN-20180525200131-20180525220131-00002.warc.gz
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CC-MAIN-2018-22
| 636 | 4 |
https://www.jiskha.com/display.cgi?id=1287046012
|
math
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Calc Please Help
posted by Chelsea .
Are these correct?
lim x->0 (x)/(sqrt(x^2+4) - 2)
I get 4/0= +/- infinity so lim x->0+ = + infinity? and lim x->0- = + infinity?
lim x->1 (x^2 - 5x + 6)/(x^2 - 3x + 2)
I get 2/0, so lim x-> 1+ = - infinity? and lim x->1- = + infinity?
lim h->0 [(-7)/(2+h^2) + (7/4)]/h
I used a computational website to get (7/4) as the answer, but I did not get this. My work ends with: (-28)/(4(h+8) + (7(h+8)/(4(h+8)) and I end with -5.25 for an answer?
lim x-> neg. infinity (-2x^2 + 3x - 2)/(5x^3 + 4x -x + 1)
Don't even know about this one?
Please help. I would like to understand these.
The first two are correct.
Looking at the pattern of the third and considering the answer , I think you have a typo
The function appears to be f(x) = -7/x^2 and you are finding the derivative when x = 2
Instead of lim h->0 [(-7)/(2+h^2) + (7/4)]/h , it should be
lim h->0 [(-7)/(2+h)^2 + (7/4)]/h , notice the change in brackets.
then I get [-28 + 7(2+h)^2]/(4(2+h)^2) / h
= [ -28 + 28 + 28h + 7h^2]/(4(2+h)^2) / h
= h(28+7h)/(4(2+h)^2) / h
now as h ---> 0 this becomes
28/16 = 7/4
for the last one, how about dividing each term in both the numerator and denominator by the highest power of x that you see, that is , by x^3
to get the expression as
(-2/x + 3/x^2 - 2/x^3)/(5 + 4/x^2 - 1/x^2 + 1/x^3)
Now consider each term
As x becomes hugely negative, each of the terms would still be negative, but very very close to zero, so the top approaches zero, the bottom obvious approaches 5
so you have -0/5 which approaches 0 from the negative.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886117519.82/warc/CC-MAIN-20170823020201-20170823040201-00054.warc.gz
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CC-MAIN-2017-34
| 1,553 | 28 |
https://ittimepass.wordpress.com/2017/02/09/prove-the-distributive-law-of-boolean-algebra/
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math
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Prove the distributive law of Boolean algebra?
Answer: – The Distributive property is easy to remember, if you recall that “multiplication distributes over addition”. Formally, they write the property as “a(b + c) = ab + ac”. In number, this means that 2(3+4) = 2×3+2×4. Any time they refer in a problem to using the distributive property, they want you to take something through the parentheses (or factor something out); any time a computer depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the distributive property.
- Why is the following true? 2(x + y) = 2x + 2y
Since they distributed through the parentheses, this is true by the Distributive property.
- Use the Distributive property to rearrange: 4x – 8
The Distributive property either takes something through a parentheses or else factors something out. Since there aren’t any parentheses to go into, you must need to factor out of. Then the answer is “By the Distributive property, 4x – 8 = 4(x – 2)”
“But wait!” you say. “The Distributive property says multiplication distributes over addition, not subtraction! What gives?” You make a good point. This is one of those times when it’s best to be flexible. You can either view the contents of the parentheses as the subtraction of a positive number (“x – 2”) or else as the addition of a negative number (“x + (-2)”). In the latter case, it’s easy to see that the distributive property applies, because you’re still adding; you’re just adding a negative.
The other two properties come in two versions each: one for addition and the other for multiplication. (Note that the Distributive property refers to both addition and multiplication, too, but both within just one rule.)
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937193.1/warc/CC-MAIN-20180420081400-20180420101400-00247.warc.gz
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CC-MAIN-2018-17
| 1,808 | 8 |
https://ricerca.univaq.it/handle/11697/193162
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math
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Euler developed a program which aimed to transform analysis into an autonomous discipline and reorganize the whole of mathematics around it. The implementation of this program presented many difficulties, and the result was not entirely satisfactory. Many of these difficulties concerned the integral calculus. In this paper, we deal with some topics relevant to understand Euler’s conception of analysis and how he developed and implemented his program. In particular, we examine Euler’s contribution to the construction of differential equations and his notion of indefinite integrals and general integrals. We also deal with two remarkable difficulties of Euler’s program. The first concerns singular integrals, which were considered as paradoxical by Euler since they seemed to violate the generality of certain results. The second regards the explicitly use of the geometric representation and meaning of definite integrals, which was gone against his program. We clarify the nature of these difficulties and show that Euler never thought that they undermined his conception of mathematics and that a different foundation was necessary for analysis.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00369.warc.gz
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CC-MAIN-2022-49
| 1,231 | 3 |
http://www.elsevier.com/books/simulation/ross/978-0-12-598063-0
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math
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- Sheldon Ross, University of Southern California, Los Angeles, USA
Ross's Simulation, Fourth Edition introduces aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers learn to apply results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions about future outcomes. This text explains how a computer can be used to generate random numbers, and how to use these random numbers to generate the behavior of a stochastic model over time. It presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.
Senior/graduate level students taking a course in Simulation, found in many different departments, including: Computer Science, Industrial Engineering, Operations Research, Statistics, Mathematics, Electrical Engineering, and Quantitative Business Analysis.
Hardbound, 312 Pages
Published: August 2006
Imprint: Academic Press
- Preface; Introduction; Elements of Probability; Random Numbers; Generating Discrete Random Variables; Generating Continuous Random Variables; The Discrete Event Simulation Approach; Statistical Analysis of Simulated Data; Variance Reduction Techniques; Statistical Validation Techniques; Markov Chain Monte Carlo Methods; Some Additional Topics; Exercises; References; Index
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699924051/warc/CC-MAIN-20130516102524-00066-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 1,467 | 7 |
http://reupspot.com/tag/pro-era
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math
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Ah. Got it. Beast Coast is a supergroup that features members of Flatbush Zombies (Meechy Darko, Zombie Juice, and Erick Arc Elliott), Pro Era (Joey Bada$$, Kirk Knight, Nyck Caution, CJ Fly, Powers Pleasant) and […]
Stream Pro Era’s Scion AV-presented The Shift EP, featuring the Brooklyn collective of Joey Bada$$, CJ Fly, Kirk Knight, Nyck Caution, A La Sole, Dessy Hinds, Chuck Strangers, Powers Pleasant, The 47s (Dirty Sanchez, Roka-Mouth, […]
Joey Bada$$ and company liberate each track as part of their Secc$ Tap.e 2 EP.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540551267.14/warc/CC-MAIN-20191213071155-20191213095155-00356.warc.gz
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CC-MAIN-2019-51
| 534 | 3 |
http://www.tripadvisor.com/ShowTopic-g187147-i14-k651168-Train_Travel_in_France_and_Throughout_Europe_But_not-Paris_Ile_de_France.html
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math
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I only have an advanced Master's Degree so I am unable to decipher how these consecutive day rail passes work in travelling through France and the rest of Europe. It seems harder to crack than the "Da Vinci Code". I hope someone can help. Here is what I want to do:
1. I plan to arrive in Paris CDG from NYC JFK.
2. After spending a few days in Paris I want to travel on a HIGH SPEED train to other cities in France.
5. I plan to travel for a total of about 20 days.
My questions are:
1. What kind of pass do I buy (Eurorailpass, Railpass, Eurail, etc.)?
2. How much should it cost?
3. Are there supplements?
4. Do I need to make reservations each time I travel?
5. Is 1st Class Travel really worth it?
6. Where should I buy my ticket?
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s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430455241618.47/warc/CC-MAIN-20150501044041-00044-ip-10-235-10-82.ec2.internal.warc.gz
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CC-MAIN-2015-18
| 735 | 11 |
https://mynixworld.info/2012/11/15/understanding-emc2/
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math
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Even if physics was never the centre of my interest, I was always eager to understand "why" and "how" the world works as we know it does.
Over the time I understand more and more what is the value of a good teacher. I was in the school, of course, I got my education, but somehow it seems that the teachers that I had were never able to explain in easy words either "why" or "how".
These days I got the answer that I was looking for, maybe only partially, and it turns out that Einstein's equation E=mc2 represents the answer for the "why"- question.
The people from the SBS have made a wonderful documentary called "Einstein's big idea". It takes you from the beginning, when Emilie du Chatelet has discovered that the Leibnitz calculations about the kinetic energy were correct and not the Newton ones, that is (because they applies only at speeds v that are less than 10% of speed of light - the c from Einstein's equation), or later, when Lavoisier have been determined that nature is a closed system, when he have demonstrated with an experiment that in any transformation, no amount of matter(mass) is ever lost and non is gained. From general theory of relativity we know that mass(matter) and energy is equivalent. The movie goes even further, when Faraday define what we know as electromagnetic induction.
All these contributions to physics and chemistry had led Einstein in 1905 to that equation what we know today as E=mc2 (albeit the correct formula should be written as ).
So here is the movie:
- full movie: https://www.youtube.com/watch?v=hi2QUNSABH8
Thank you Einstein for unveiling the world so as we can see it as it really is. Now I understand E=mc2 and more important why and how. Check my Fysik category (written in Swedish but Google Translate does a good job nowadays) where I approached the theoretical part of the theory of relativity and the photoelectric effect (this is what the Einstein have got the Nobel for).
Now, if you think that this article was interesting don't forget to rate it. It shows me that you care and thus I will continue write about these things.
Latest posts by Eugen Mihailescu (see all)
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http://www.mywordsolution.com/question/find-an-optimal-solution-and-the-associated-cost/97965
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math
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A company produces small component for all industrial products at three plants and distributes them from three regional warehouses. The production capacities at each plant demand at each warehouse and unit shipping costs are presented in the following table:
problem1. Develop an initial feasible solution and the shipment cost using Northwest Corner Rule.
problem2. Find an optimal solution and the associated cost using Stepping - Stone Techniques. Illustrate out clearly your answer.
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CC-MAIN-2017-17
| 486 | 3 |
http://www.imgrum.org/tag/dieseltrucks
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math
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I don't think I've posted in a while, how much I LOVE this truck.
Yes... it IS just a material thing, and in the grand scheme of things, it means nothing. However...to me... it means a lot!!! Too me... it is my dream truck. Custom ordered brand new, with every little detail exactly how i wanted it.
I love the way owning it and driving it makes me feel. Showed up with only 26kms on it.. now it has over 41 thousand...all put on by me... nobody else
I love the peace of mind... that every time i get into it, i know is going to start. I love the feeling, of not worrying about if it will break down on the hwy or not.
I love the feeling... that i can load almost anything i want or need to load behind it, and it's not going to let me down.
I love how owning a truck like this... really helps to feel like a boss, because a boss IS what i am... But most of all... this big ass truck... is just a small physical bit of validation i sometimes need... to remind me of ALL the hard work I've put in... long before i ever could afford to buy it... all the 10, 16, 20hr even 40 hr shifts I've put in to get where i am today... the periods I've gone 12 weeks straight without 1 single day off. The risks I've taken... to get to a place where i could purchase such a spectacular machine.
No... i don't NEED this truck... i didn't even NEED to purchase one with all the options i did... however... it sure is a damn nice piece of validation, to help me feel like it has all be worth it.
Feeling pretty blessed!!! #blessed#levelup#hashtag#dodge#dodgeram#dodgeram2500#cummins#diesel#dieseltrucks#deiselpower#dirtyboyz#dirtyboys#quality#rednecks#redneckswithpaychecks#country#countryboy#countrylife#countryliving#nothingbutcountry
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https://www.distancecalculus.com/winter-session-2020/calculus-based-statistics/start-today/
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math
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Winter Session 2020 Enroll Now, Start Today - Calculus-Based Statistics Academic CreditsWinter Session 2020 @ Roger Williams University
Our Probability Theory course differs from a classroom/textbook-based course in that we employ Mastery Learning so that you complete all assignments at 100% to assure competancy, as well as our curriculum shifting the course to a laboratory-style course, where theorem/lemma/proof type exposition is replaced by running experiments in Mathematica as you would in a science laboratory to empirically deduce the concepts and behaviors of Probability Theory, both solvable (classically) via hand-based techiques, as well as studying Probability Theory that can only be solved and investigated graphically and numerically using a computer.
The Probability Theory curriculum is highly visual and based upon observations of experiments run in Mathematica.
Distance Calculus - Student Reviews
Date Posted: Dec 20, 2019
Review by: Bill K.
Courses Completed: Calculus I, Calculus II, Multivariable Calculus, Linear Algebra
Review: I took the whole calculus series and Linear Algebra via Distance Calculus. Dr. Curtis spent countless hours messaging back and forth with me, answering every question, no matter how trivial they might seem. Dr. Curtis is extremely responsive, especially if the student is curious and is willing to work hard. I don't think I ever waited much more than a day for Dr. Curtis to get a notebook back to me. Dr. Curtis would also make videos of concepts if I was really lost. The course materials are fantastic. If you are a student sitting on the fence, trying to decide between a normal classroom class or Distance Calculus classes with Livemath and Mathematica, my choice would be the Distance Calculus classes every time. The Distance Calculus classes are more engaging. The visual aspects of the class notebooks are awesome. You get the hand calculation skills you need. The best summary I can give is to say, given the opportunity, I would put my own son's math education in Dr. Curtis's hands.
Transferred Credits to: None
Date Posted: Aug 16, 2020
Review by: Jennifer S.
Courses Completed: Calculus I
Review: The course was intense and required a lot of hard work. Professors ready available to assist when needed. Professors presented and explained materials/course work in detail and provided explanations and resources.
Transferred Credits to: University of New Haven, West Haven, CT
Date Posted: Apr 30, 2020
Review by: Hannah J.
Courses Completed: Probability Theory
Review: Probability Theory was a great course. Very very thorough. I thought it would never end :). I was very prepared for my coursework in economics. Excellent refereshher of derivatives and integrals - really forced me to remember that stuff from freshman cal.
Transferred Credits to: Boston University
Distance Calculus - Curriculum Exploration
- Y0: Getting Started:
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https://www.arxiv-vanity.com/papers/0906.2367/
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math
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Uniqueness of Extremal Kerr and
Kerr-Newman Black Holes
Aaron J. Amsel, Gary T. Horowitz, Donald Marolf, and Matthew M. Roberts
Department of Physics, UCSB, Santa Barbara, CA 93106
We prove that the only four dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a longstanding gap in the black hole uniqueness theorems.
In the 1970’s, work by Hawking , Carter , and Robinson proved that the only stationary, asymptotically flat vacuum black hole with a (single) non-degenerate horizon is the nonextremal Kerr metric. In the early 1980’s, Mazur and Bunting extended this proof to the charged Kerr-Newman black hole. These uniqueness theorems have been the basis for most of the subsequent work on black holes for almost thirty years. This spans a wide range of topics from astrophysical black holes to no hair theorems to studies of black hole thermodynamics and quantum aspects of black holes.
A similar uniqueness theorem for the extremal Kerr or Kerr-Newman black hole has not been available. The existing techniques were not sufficient to obtain a proof in this case. Two recent developments have encouraged us to reexamine this longstanding problem. First, it was shown that stationary rotating (analytic) extremal black holes must be axisymmetric [6, 7]. This extended the well known result for nonextremal black holes [1, 8, 9, 10] to the extremal case. Second, building on earlier work , it has recently been shown that the near horizon geometry of any extremal vacuum black hole must agree with the extremal Kerr metric . Similarly, the near horizon geometry of any extremal electrovac black hole must agree with the extremal Kerr-Newman solution .111See [13, 14] for related results. At first sight, these local uniqueness theorems seem surprising since one might expect that adding stationary matter outside the black hole could distort the horizon. However, extremal horizons are infinitely far away from any matter outside and do not get distorted. We will show that these new results can be combined with existing methods of proving black hole uniqueness to finally prove the uniqueness of the extremal Kerr and Kerr-Newman solution.
2 Uniqueness of the Extremal Kerr Solution
Before proceeding to the uniqueness proof, we briefly review the near horizon geometry of an extremal Kerr black hole [15, 16]. Since the horizon of an extremal Kerr black hole is infinitely far away (in spacelike directions) from events outside the horizon, one can extract a limiting geometry by taking a certain scaling limit. The general Kerr metric is labeled by two parameters, a mass and angular momentum In Boyer-Lindquist coordinates , the metric takes the form
Consider the extremal solution, . Defining a one-parameter family of new coordinate systems
and taking the scaling limit yields
with . The shift in is needed so that is null on the horizon . Since is not changed, the rotation axis () in this limiting geometry agrees with the axis in Kerr near the horizon. This spacetime is known either as the extremal Kerr throat or as the Near-Horizon Extreme Kerr (NHEK) geometry. It has recently attracted considerable attention in connection with a proposed Kerr/CFT correspondence . For fixed , the term in square brackets becomes the metric on in Poincaré coordinates. In fact, the NHEK geometry inherits all the isometries of AdS. It has an isometry group.
We are now ready to state and prove our uniqueness theorem for the extremal Kerr solution:
Theorem 1: The only stationary, rotating, asymptotically flat (analytic) vacuum solution with a single degenerate horizon is the extremal Kerr black hole.
Proof: We follow the approach in [18, 19] which is based on earlier work by Mazur . Many aspects of our proof are identical to the one proving uniqueness of nonextremal black holes. For those aspects, we will just give the main ideas. For technical details, we refer the reader to [18, 19, 7].
It has recently been shown that stationary (analytic) extremal black holes must be axisymmetric if they are rotating [6, 7].222The unlikely possibility of a stationary (but not static) extremal black hole with zero angular velocity has not yet been ruled out. It therefore suffices to consider stationary, axisymmetric metrics. Such metrics can always be written in Weyl-Papapetrou form
where are functions of and only. Given a solution for and , is then determined in terms of them by first order equations. Rather than work with , it is convenient to introduce the potential for the twist of the Killing field:
The twist potential (and Weyl-Papapetrou coordinates) are globally well defined in the domain of outer communication.
A key role in the proof will be played by the following 2 x 2 matrix constructed from the norm and twist of :
The matrix is symmetric, has positive trace and unit determinant. It is therefore positive definite and can be written for some matrix with . The equation satisfied by is most easily expressed by viewing and as cylindrical coordinates in an auxiliary flat Euclidean , with derivative . Viewing as a rotationally invariant matrix in this space, the vacuum Einstein equation implies
where this equation holds everywhere except possibly the axis .
Suppose we have two axisymmetric solutions and to this equation with the same angular momentum. Set
In terms of the norm and twist of the Killing field,
In this form, it is clear that One can show that away from the axis , satisfies the following “Mazur identity”
Note that the right hand side of (12) is nonnegative.
The requirements that and impose strong constraints on . If we can show that is globally bounded on (including the axis) and vanishes at infinity then must vanish everywhere [20, 21]. This, in turn, implies that and hence the two solutions agree.
We now show that is indeed globally bounded. Since the key step is the behavior near the horizon, we consider this first. It was shown in that the near horizon geometry of any extremal rotating vacuum black hole is given by the NHEK solution (5). To put this into standard form (6), note that the part of the metric is conformal to , so if one sets
then (5) takes the form (6). In other words, the radial coordinate in (5) is the standard radial coordinate in the auxiliary space . In particular, the horizon corresponds to the origin of this space.
Since the angular momentum can be expressed in terms of a Komar integral involving , the value of in the NHEK metric must agree with the value computed at infinity. This fixes the free parameter in (5) to be . For the NHEK geometry, the twist potential is
and is a function of only333The large symmetry group of the NHEK geometry ensures that all geometric quantities are functions of only.:
So has a direction dependent limit at the horizon and diverges near the axis.
To show that remains bounded we consider the two terms in (11) separately. Since is the norm of the rotational Killing field, it must be smooth near the horizon. The near horizon geometry must be given by the NHEK metric with , so we have where is smooth and vanishes on the horizon. It follows that the ratio goes to one everywhere on the horizon including the axis. This shows that in the auxiliary space , the second term in (11) vanishes at , in a direction independent manner. Now consider the first term. For or , is nonzero, and vanishes near the horizon since both must approach (15). So again vanishes, at least for . Before discussing these points, we first consider the axis away from the horizon.
Smoothness near the axis requires , so the second term in (11) is bounded everywhere on the axis. Since the rotational Killing vector vanishes on the axis, its twist vector vanishes there and hence the twist potential is constant along the axis. The difference between on the axis and axis can be related to the Komar integral for and is given by . Hence given two extremal black holes with the same angular momentum, one can add a constant to the twist potential if necessary, so that on the axis. Since must vanish on the axis, near the axis. It now follows from (11) that remains bounded near the axis. (This argument is the same as in the nonextremal black hole case.) It remains to check that the coefficient of the term remains bounded as you approach the extremal horizon. However it follows from (7) that the limit of as along the axis must approach which vanishes by (15). So not only does the first term remain bounded as you approach the extremal horizon along the axis, it actually vanishes. We have thus shown that is bounded along the axis and vanishes at in a direction independent way.
The treatment at infinity is the same as for nonextremal black holes, with the result that vanishes asymptotically. For points off the axis, this follows from the fact that for any asymptotically flat spacetime, subleading terms and remains bounded asymptotically. The axis requires a little more work but has the same conclusion. Hence is globally bounded on and vanishes at infinity. Therefore it must vanish everywhere and . This completes the proof.
3 Uniqueness of the Extremal Kerr-Newman Solution
We now show that the above result can be extended to extremal rotating and charged black holes. The near horizon geometry of the extremal Kerr-Newman solution is discussed in [15, 16, 22]. It depends on a second parameter and smoothly interpolates between the solution (5) and . The Kerr-Newman metric has exactly the same form as (1), except that , where is the electric charge and the factor in is replaced by . The extremal limit corresponds to , and the horizon is at with area . To obtain the throat metric, we can use the same scaling of as in (4), but the scaling of is modified to
where now . The near horizon geometry becomes
Notice that when , this metric reduces to as expected. The Maxwell field in the extremal throat is where the nonzero components of the vector potential are:
We can now prove:
Theorem 2: The only stationary, rotating, asymptotically flat (analytic) Einstein-Maxwell solution with a single degenerate horizon is the extremal Kerr-Newman black hole.
The proof that stationary, rotating (analytic) extremal black holes must be axisymmetric in applies not just for vacuum spacetimes but also for Einstein-Maxwell solutions. So our solution must be axisymmetric and can be put into the Weyl-Papapetrou form (6). To prove Theorem 2, we will follow the original approach of Mazur [4, 23], which is based on the fact that the stationary, axisymmetric Einstein-Maxwell equations have an symmetry.444Setting the Maxwell field to zero, one recovers a uniqueness proof for Kerr based on the symmetry of the vacuum equations. It will look slightly different from the proof given in the previous section, because we have used the equivalence of to to write that proof in terms of real matrices. Given a stationary and axisymmetric Maxwell field, one can introduce two scalar potentials and as follows: Let be the rotational Killing field as before, and let be the vector potential, , in a gauge in which it is Lie derived by . Similarly, we introduce a dual vector potential and pick a gauge in which is Lie derived by . Then the scalar potentials are defined by and . We now define two complex Ernst potentials
where is the norm of the rotational Killing field as before. The definition of must be modified since the twist vector is no longer a gradient for Einstein-Maxwell solutions. Instead, we set
The metric and Maxwell field are completely determined in terms of .
Consider a complex three dimensional vector space with hermitian metric with signature (1,2). So this is a complex analog of three dimensional Minkowski space. Let be the vector defined by
Using a bar to denote the complex conjugate vector, one can easily check that , so is in fact a unit timelike vector. We now set
This is a Hermitian matrix which is positive definite. In fact, one can view the second term as changing the sign of the time-time component of the original metric . leaves the metric invariant in the sense that
Using to raise and lower indices, this implies that . It follows that has unit determinant and so defines an element of .
The equation satisfied by is most easily expressed by again viewing and as cylindrical coordinates in an auxiliary flat Euclidean , with derivative . Viewing as a rotationally invariant matrix in this space, the Einstein-Maxwell equations imply
where, as before, this equation holds everywhere except possibly the axis . Since is positive, we can again write , and the proof now proceeds almost exactly as before.
Suppose we have two axisymmetric solutions and to (25). Set
In terms of our original quantities:
where etc. In this form, it is clear that One can show that away from the axis , satisfies the following “Mazur identity”
Note that the right hand side of (29) is again nonnegative.
As in section 2, it suffices to show that is globally bounded and vanishes at infinity [20, 21]. Consider the horizon first. It was shown in that the near horizon geometry of any extremal rotating and charged black hole is given by (18). The part of this metric is still conformal to so one can use (14) to put the metric into coordinates. The horizon again corresponds to the origin of .
For , is finite in the limit . If and are two solutions with the same charge and angular momentum, the fact that they must agree near implies that subleading terms. Thus in the limit for all . Before discussing these points we consider the behavior of on the axis away from the horizon.
The first term in (27) can be treated exactly as in the vacuum case with the result that it is bounded on the axis and vanishes as for all including . We now consider the scalar potentials. Since and is globally well defined, on the axis. Smoothness requires , so the terms remain bounded on the axis. The dual vector potential is not globally defined since we have nonzero electric charge. Choosing a gauge so that the “Dirac string” lies along the axis, we have that is constant along the axis and . So given two solutions with the same charge, the values of along the axis will agree and . This ensures that the terms will also be bounded. The mixed terms in (27) are also and their contribution to remains bounded. Finally, the potential behaves as in the vacuum case: It is constant along the axis, and the difference between its values on the two axes is . So two solutions with the same angular momentum will have and the term is also bounded.
Let us now consider the limit as we approach the extremal horizon along the axis. In the throat geometry:
As one approaches the extremal horizon along the axis, each approach . Similarly each approach . So their difference vanishes. This shows that the limit of all terms in (27) involving the electrostatic potentials vanish as one approaches the horizon along the axis. Similarly, each approach the corresponding expression in the throat and hence the term vanishes. In short, all terms in the expression for vanish as one approaches the horizon along the axis.
One can again show that vanishes at infinity along the same lines as in the nonextremal proofs. Hence is globally bounded on and vanishes at infinity. Therefore it must vanish everywhere and . This completes the proof.
Note added: After completion of this work, we were informed of which contains a proof of the uniqueness of extremal Kerr (but not Kerr-Newman) assuming axisymmetry. Their proof uses a different approach from the one presented here.
It is a pleasure to thank S. Hollands, R. Wald, and G. Weinstein for discussions. This work was supported in part by the US National Science Foundation under Grant No. PHY05-55669, and by funds from the University of California.
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- H. Friedrich, I. Racz and R. M. Wald, “On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon,” Commun. Math. Phys. 204 (1999) 691 [arXiv:gr-qc/9811021].
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- J. M. Bardeen and G. T. Horowitz, “The extreme Kerr throat geometry: A vacuum analog of AdS(2) x S(2),” Phys. Rev. D 60 (1999) 104030. [arXiv:hep-th/9905099].
- M. Guica, T. Hartman, W. Song and A. Strominger, “The Kerr/CFT Correspondence,” arXiv:0809.4266 [hep-th].
- S. Hollands and S. Yazadjiev, “Uniqueness theorem for 5-dimensional black holes with two axial Killing fields,” Commun. Math. Phys. 283 (2008) 749 [arXiv:0707.2775 [gr-qc]].
- S. Hollands and S. Yazadjiev, “A uniqueness theorem for stationary Kaluza-Klein black holes,” arXiv:0812.3036 [gr-qc].
- G. Weinstein, “On the Dirichlet problem for harmonic maps with prescribed singularities”, Duke Math. J. 77 (1995) 135.
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- B. Carter, “Bunting Identity and Mazur Identity for Non-Linear Elliptic Systems Including the Black Hole Equilibrium Problem”, Commun. Math. Phys. 99 (1985) 563.
- R. Meinel, M. Ansorg, A. Kleinwachter, G. Neugebauer, and D. Petroff, Relativistic Figures of Equilibrium, (Cambridge University Press, 2008) section 2.4.
- G. Neugebauer, “Rotating bodies as boundary value problems,” Ann. Phys. (Leipzig) 9 (2000) 342; G. Neugebauer and R. Meinel, “Progress in relativistic gravitational theory using the inverse scattering method,” J. Math. Phys. 44 (2003) 3407.
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https://www.enotes.com/homework-help/find-radius-base-cylinder-whose-volume-1000-cm-3-75629
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math
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Find the radius of base of a cylinder whose volume is 1000 cm^3 and whose hight is 10 cm.
the radius of base of a cyinder is 5.64cm.the formula 3.14(phi)xr^2h for volume.h is height.(10).so the radius is 5.64
The volume V of the cylinder is given by :
V=pi*r^2*h, where r is the radius of the cylinder and h is the height of it.
Given are the values of volume V=1000cm^3 and height h= 10 cm. We substitute in the above formula and then solve for radius r:
We divide both sides by 10pi .
We take square root of both sides to get r.
Hope this helps.
the radius of base of a cylinder is5.64cm.the formula 3.14(phi)xr^2h for volume .h is height.(so the radius is 5.64 cm. long .
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887729.45/warc/CC-MAIN-20180119030106-20180119050106-00230.warc.gz
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https://www.beloit.edu/live/profiles/1112-math-390-special-projects
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math
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[MATH 390] Special Projects
Individual guided investigations of topics or problems in mathematics. Since such investigation is important to the development of mathematical maturity, the department encourages each major to do at least one such project.Edit my profile
.25 - 1.00
Prerequisite: approval of the project by the department chair; sophomore standing.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986666959.47/warc/CC-MAIN-20191016090425-20191016113925-00091.warc.gz
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| 360 | 4 |
http://mathhelpforum.com/calculus/21954-higher-limits-l-hospital-s-rule.html
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math
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I can't figure out how to solve this: = ?
Follow Math Help Forum on Facebook and Google+
You don't need to apply that Rule, just remember that
When I solve it, I get [1 + (Infinity / Infinity)]. I don't know what I'm doing wrong.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121869.65/warc/CC-MAIN-20170423031201-00309-ip-10-145-167-34.ec2.internal.warc.gz
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https://www.econstor.eu/handle/10419/92761
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math
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ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 544
Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition alpha + beta < 1. The former has the usual unit root distribution and the latter is a functional of a bivariate Brownian motion, as in Ling and Li (1998). Several unit root tests based on LS estimators, ML estimators, and mixing LS and ML estimators, are constructed. Simulation results show that tests based on mixing LS and ML estimators perform better than Dickey-Fuller tests which are based on LS estimators, and that tests based on the ML estimators perform better han the mixed estimators.
Asymptotic distribution Brownian motion GARCH model Least squares estimator Maximum likelihood estimator Unit root
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104704.64/warc/CC-MAIN-20170818160227-20170818180227-00617.warc.gz
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CC-MAIN-2017-34
| 906 | 3 |
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1155/2009/808720
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math
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- Research Article
- Open Access
Markov Inequalities for Polynomials with Restricted Coefficients
Journal of Inequalities and Applications volume 2009, Article number: 808720 (2009)
Essentially sharp Markov-type inequalities are known for various classes of polynomials with constraints including constraints of the coefficients of the polynomials. For and we introduce the class as the collection of all polynomials of the form , , , . In this paper, we prove essentially sharp Markov-type inequalities for polynomials from the classes on . Our main result shows that the Markov factor valid for all polynomials of degree at most on improves to for polynomials in the classes on .
In this paper, always denotes a nonnegative integer; and always denote absolute positive constants. In this paper will always denote a positive constant depending only on the value of which may vary from place to place. We use the usual notation to denote the Banach space of functions defined on with the norms
We introduce the following classes of polynomials. Let
denote the set of all algebraic polynomials of degree at most with real coefficients. Let
denote the set of all algebraic polynomials of degree at most with complex coefficients. For we introduce the class as the collection of all polynomials of the form
The following so-called Markov inequality is an important tool to prove inverse theorems in approximation theory. See, for example, Duffin and Schaeffer , Devore and Lorentz , and Borwein and Erdelyi .
Markov inequality. The inequality
holds for every
It is well known that there have been some improvements of Markov-type inequality when the coefficients of polynomial are restricted; see, for example, [3–7]. In , Borwein and Erdélyi restricted the coefficients of polynomials and improved the Markov inequality as in following form.
There is an absolute constant such that
for every .
We notice that the coefficients of polynomials in only take three integers: and . So, it is natural to raise the question: can we take the coefficients of polynomials as more general integers, and the conclusion of the theorem still holds? This question was not posed by Borwein and Erdélyi in [5, 6]. Also, we have not found the study for the question by now. This paper addresses the question. We shall give an affirmative answer. Indeed, we will prove the following results.
There are an absolute constant and a positive constant depending only on such that
Our proof follows closely.
Theorem 1.2 does not contradict [6, Theorem 2.4] since the coefficients of polynomials in are assumed to be integers, in which case there is a room for improvement.
2. The Proof of Theorem
In order to prove our main results, we need the following lemmas.
Let and . Suppose , is analytical inside and on the ellipse , which has focal points and , and major axis
Let be the ellipse with focal points and , and major axis
Then there is an absolute constant such that
The proof of Lemma 2.1 is mainly based on the famous Hadamard's Three Circles Theorem and the proof [6, Corollary 3.2]. In fact, if one uses it with replaced by and replaced by , Lemma 2.1 follows immediately from [6, Corollary 3.2].
Let with , . Suppose and . Then there is a constant such that
By Chebyshev's inequality, there is an such that
for every with . Therefore, Because of the assumption on , we can write
Recalling the facts that
, and we obtain
Now by Lemma 2.1 we have
Let , then there is an absolute constant such that
By Cauchy's integral formula and the above inequality, we obtain
The proof of Lemma 2.2 is complete.
Proof of Theorem 1.2.
Noting and the fact
proved by , we only need to prove the upper bound. To obtain
we distinguish four cases.
. Let be an arbitrary number in , then
and , where and denotes the number of zeros of at 1. Let be a positive integer. If satisfies the assumptions, then , and . Therefore, Markov inequality implies
So, the last inequality and imply
Now using Taylor's Theorem, Lemma 2.2 with , the above inequality, and the fact , we obtain
and . Let . We have , where and are the major axis and minor axis of , respectively, and . Let , we see
The solution of equation is
It is obvious that
So, and the assumption of Lemma 2.2 imply
And from (2.17) and Cauchy's integral formula, it follows that for every ,
and there holds
. Applying Lemma 2.1 with and , we obtain that there is constant such that
Indeed, noting that
we get the result want to be proved by a simple modification of the proof of Lemma 2.2. We omit the details. The proof of Theorem 1.2 is complete.
Duffin RJ, Schaeffer AC: A refinement of an inequality of the brothers Markoff. Transactions of the American Mathematical Society 1941,50(3):517–528. 10.1090/S0002-9947-1941-0005942-4
DeVore RA, Lorentz GG: Constructive Approximation, Grundlehren der Mathematischen Wissenschaften. Volume 303. Springer, Berlin, Germany; 1993:x+449.
Borwein P, Erdélyi T: Polynomials and Polynomial Inequalities, Graduate Texts in Mathematics. Volume 161. Springer, New York, NY, USA; 1995:x+480.
Borwein PB: Markov's inequality for polynomials with real zeros. Proceedings of the American Mathematical Society 1985,93(1):43–47.
Borwein P, Erdélyi T: Markov- and Bernstein-type inequalities for polynomials with restricted coefficients. The Ramanujan Journal 1997,1(3):309–323. 10.1023/A:1009761214134
Borwein P, Erdélyi T: Markov-Bernstein type inequalities under Littlewood-type coefficient constraints. Indagationes Mathematicae 2000,11(2):159–172. 10.1016/S0019-3577(00)89074-6
Borwein P, Erdélyi T, Kós G: Littlewood-type problems on . Proceedings of the London Mathematical Society 1999,79(1):22–46. 10.1112/S0024611599011831
The research was supported by the National Natural Science Foundition of China (no. 90818020) and the Natural Science Foundation of Zhejiang Province of China (no. Y7080235).
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Cite this article
Cao, F., Lin, S. Markov Inequalities for Polynomials with Restricted Coefficients. J Inequal Appl 2009, 808720 (2009). https://doi.org/10.1155/2009/808720
- Positive Constant
- Focal Point
- Major Axis
- Minor Axis
- Absolute Constant
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http://wpdevph.com/page/linear-mixed-model-anova-31113770.html
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math
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We see that because it is higher than 0. Statistical procedures and the justification of knowledge in psychological science. In this example the two results are the same, probably the large sample size helps in this respect. Related 1. Fitting a mixed effects model - the big picture The mixed effects model approach is very general and can be used in general, not in Prism to analyze a wide variety of experimental designs.
As mixed models are becoming more widespread, there is a lot of confusion about when to use these more flexible but complicated models and when to use the. 1) What is the difference between conducting a Linear Mixed Models and an ANOVA?
ANOVA models have the feature of at least one. › post › Repeated_measures_ANOVA_v_linea.
Fixed vs. For normally distributed data the points should all be on the line.
Mixedeffects models for repeatedmeasures ANOVA
Active 3 years, 2 months ago. For fixed effect we refer to those variables we are using to explain the model. Students within classroom, patients within hospital, plants within ponds, streams within watersheds, are all common examples.
Linear mixed model anova
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Video: Linear mixed model anova How to Perform a Mixed Model ANOVA in SPSS
Here you will find daily news and tutorials about Rcontributed by hundreds of bloggers. In contrast, exploratory analyses are based on statistical tests which are motivated by the pattern of results observed after data collection.
For example, in our hypothetical experiment the concurrent speech may have been provided by different multilingual speakers. The analysis of repeated measures designs: a review. However, it is important to realize that the use of LMMs is by no means restricted to complex grouping designs, and can also be used for experimental psychology studies with a single grouping factor of participant or subject.
Brainstorming: what other factors might influence the data?
multiple regression Linear Mixed Models and ANOVA Cross Validated
A mixed model analysis of variance (or mixed model ANOVA) is the right data analytic analyses in the context of linear mixed effects models. Simple ANOVAs.
Video: Linear mixed model anova Modern repeated measures analysis using mixed models in SPSS (1)
The goal of a linear mixed effects model is to attribute some of the error present in a To start with, let's make a comparison to a repeated measures ANOVA.
For example, we could include more variables:.
Choose your flavor: e-mailtwitterRSSor facebook False-positive psychology: undisclosed flexibility in data collection and analysis allows presenting anything as significant.
On multi-level modeling of data from repeated measures designs: a tutorial. However, what we can say by just looking at the coefficients is that rain has a positive effect on blight, meaning that more rain increases the chances of finding blight in potatoes. That P value is 0.
Oct;6(2) A comparison of the general linear mixed model and repeated measures ANOVA using a dataset with multiple missing data. Theoretical Background - Linear Model and ANOVA Linear Model The classic linear model forms the basis for ANOVA (with categorical. Linear mixed-effects models (LMMs) are increasingly being used for data may be analyzed with a standard analysis of variance (ANOVA).
Sphericity means that the variances of the difference scores between the three levels of language are similar.
Therefore this new model where clustering is accounted for is better than the one without an additional random effect, even though only slightly.
GraphPad Prism 8 Statistics Guide The mixed model approach to analyzing repeated measures data
With the function predict we can see estimate these new values using mod3. To check the details we can look at the summary table:. LMMgui uses the package lme4 Bates et al.
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https://myinvestingnotes.blogspot.com/2009/06/why-invest-in-stocks-example-in.html
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math
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Not all stocks are going to live up to their early promise, no matter how much time you devote to making a selection.
In the other hand, even if you pick your stocks blindfolded, you will have some winners.
Investing into Common Stocks
Let's suppose that you want to invest $100,000 in 20 stocks, or $5,000 in each. Some will work out and some won't.
So so news - 10 of 20 stocks will just plug along
Hypothetically, it does not seem unreasonable to project that 10 of these stocks will just plug along, making you neither rich nor poor. Suppose we assume that these 10 stocks will appreciate (rise in value) an average of only 7% per year over the next 10 or 20 years. Toss in a 2% annual dividend and the total return adds up to 9% per year. That is not exactly riches, since stocks over the last 75 years have averaged about 11%.At any rate, here is what your $50,000 will be worth at the end of:
10 years - $118,368
20 years - $280,221
Good news - 3 of 20 stocks performed above your wildest dreams
Next, let's look at the 3 stocks that performed above your wildest dreams. They appreciated an average of 15% per year. Add in a modest annual dividend of only 1%, and you have a total return of 16%.Assuming you invest $5,000 in each of these stocks, that $15,000 will be worth over the next:
10 years - $66,172
20 years - $291,911
Bad news - 2 of 20 stocks skid and never recovered
So far, so good. Now, for the bad news. Two of your stocks hit the skids and never recovered. Total results for the $10,000 invested in these losers is: zero
10 years - $00,000
20 years - $00,000
Fair news - 5 of 20 stocks performed about averageFinally, 5 of your 20 stocks do about average. They appreciate an average of 9% per year and I have an average yearly dividend of 2%. That's a total return of 11%. Since you have 5 stocks in this category, your total investment is $25,000. Here is what you end up with in the next:
10 years - $70,986
20 years - $201,558
Adding Up these Returns
If we add up these various results, the final figures make you look reasonably rich:
10 years - $255,525
20 years - $ 773,690
Investing into CDs
By contrast, had you acted in a cowardly manner and invested exclusively in CDs that gave an annual return of 4%, you would have only the following at the end of the two periods:10 years - $162,889
20 years - $265,330
One final note. If you figure in taxes, you look even better, since the capital gains (on your stocks ) are taxed at a much lower rate than ordinary income (which applies to CDs). And, you wouldn't even have to worry about capital gains on your stocks if you elected not to sell them.
(Comment: My personal guideline is this. Of 5 stocks you buy, expect 1 to do very well, 3 to be average, and 1 to do poorly.)
Why Invest in Stocks?
Why Invest in Stocks? Look at the Facts
Why Invest in Stocks? Investing for the Long Term
Why Invest in Stocks? Some Profitable Comparisons
Why Invest in Stocks? Why Doesn't Everyone Buy Common Stocks?
Why Invest in Stocks? An Example in Practice
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https://www.physicseasytips.com/vector-important-operation-concept/
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math
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Vector important operation concept
|Vector important operation concept|
suppose i have 4kg rice and you have 6kg rice if we add this we will get (4kg +6kg )=10kg rice no doubt, now take other example
you moved 4m in east and 3m in north, understand here 4m is displacement and 3m is also displacement if i asked how far you are from starting point now your answer will be 5m and 5 is also displacement how this addition comes 4m+3m = 5m, take one more example you move 3m in east this is displacement and take a sharp turn 180⁰and move 4m west 4m is also displacement now i ask how far you are from your starting point your answer will be 1m this 1m is also displacement again how this addition come 3m+4m = 1m this is the operation of vector addition and that is why vector is one separate topic this operation is totally different from scalar operation, now take a third operation you move 4m east this is displacement then move 3m at an angle of 60⁰ with east, 3m is also displacement now i ask how far you are from your starting point now it will not be 4m+3m = 7m nor 5m because it is not at right angle now so it will not be 5m here we have to take component method of addition then we will get the result or resultant so this operation is totally different from scalar operation we can’t add vector like rice, mass, time these all are scalar quantities so we need a separate topic for vector operation and it is important because all important quantities like displacement, velocity, acceleration, force, torque, electric field, magnetic field and many more all are vector quantities and will follow this rule for addition and other operation hence it is very important to understand vector algebra operation.
Vector Addition: now there are three method for vector addition.
1 Head – Tail method (basic method )
2 Parallelogram law method
3 Triangle law method
now for any vector addition we have to apply any one method to add vector according to situation which one can apply easily so lets start one by one method.
Head – Tail method : in this method suppose you want to add more than two vector it can be 3,5, 10 or more vector just add like this “join tail of next vector with head of previous vector and continue joining till last vector” and whenever you want answer or resultant then join tail of first vector with head of last vector here in vector answer is resultant.
This is basic only at right angle vector can be added through this method if two vector are at some angle this method is not applicable to find out resultant as above Red color vector is resultant so for this type of vector we use parallelogram method.
Parallelogram law method: This law is applicable to add any type of two vector “Join two vector from tail to tail as two adjacent side of a parallelogram complete parallelogram”
where R is resultant and its value is .
Vector tail to tail join MP and MN
Now here see ∠NMP = ? and ∠OMP = ? since MPON is a parallelogram so MN = PO and ∠NMP = ∠OPQ = ? now take in triangle OPQ we can write cos? = PQ/PO = PQ/B hence
PQ = Bcos? in same triangle sin? = OQ/OP = OQ/B OQ = Bsin?
Now see in tangle OMQ this is right angle triangle hence we can write OM² = MQ² + QO² also we can write as
OM² = (MP+PQ)² +QO² now put value MP = A, PQ = Bcos? and QO = Bsin? OM = R
R² = (A+Bcos?)² +(Bsin?)² = A²+B²cos?²+2ABcos? +B²sin?²
now simplify we will get R² = A²+B²+2ABCos?.
Now for direction of resultant in ∆OMQ we can write
tan? = OQ/MQ = tan? = Bsin?/(A+Bcos?)
important point for vector angle always take angle between two vector by joining tail to tail or head to head always student confused about angle determination so you must remember this point now we can do some simple basic problem on this topic.
Q Two vector of equal magnitude are added to give resultant which is of same magnitude as the two vectors find the angle between two vector.
Ans First read question carefully you will get condition from question here two vector A, B and resultant are equal from question hence A= B = R
Now use formula for resultant R.
R² = A²+B²+2ABCos? let R = A= B =x now put
x² = x²+x²+2x²Cos? now simplify we will get Cos? = -1/2
? = 120⁰ value of x#0 now you can solve any type of problem using this formula formula in next post we will continue more about vector operation thanks for reading.
Vector important operation concept
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https://b-ok.xyz/book/566203/81697c
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math
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Main Periodicity in Sequences Defined by Linear Recurrence Relations
Periodicity in Sequences Defined by Linear Recurrence RelationsEngstrom H. T.
MATHEMATICS: H. T. ENGSTROM VOL. 16, 1930 fore, Vf U 663 4.8-109 cm. Since the radius of the earth is R = 6.35.108, we can sayVIA = 7.6 R. If we replace in expressions (16), (17), (18) the sign of inequality by that of equality, they will give us directly the maximum angular distance 0m from the magnetic pole, in which an electron can strike the surface of the earth. We obtain for the three special cases, (I) 7.6 sin /2" = 2.41, (19) 6 (m) = 60. = (IIa) 7.6 sin11/2m = 1, (20) 0(2) = 10 7.6 sin2 Om = 1 + /1 + Sin2 Om, (21) () = 320. The net result of our considerations is, therefore, that electrons of 109 volt energy cannot hit the earth outside of two limited zones around the magnetic poles." Our analysis does not permit us to say whether the maximum distance from the pole of 320 is actually reached. I Bothe and Kolhoerster, Zs. Physik, 54, 686 (1929). (IIb) 2 B. Rossi, Rend. Acc. dei Lincei, 2, 478 (1930). 3 M. A. Tuve, Phys. Rev., 35, 651 (1930). 4 L. M. Mott-Smith, Ibid., 35, 1125 (1930). 5 For electrons of energy 108 volt the maximum distance would be 170, for 2.109 volt it would be 400. PERIODICITY IN SEQUENCES DEFINED BY LINEAR RECURRENCE RELATIONS By H. T. ENGSTROM* DEPARTMENT OF MATHEMATICS, CALIFORNIA INSTITUTE OF TECHNOLOGY Communicated August 18, 1930 A sequence of rational integers Uo, Ub, U2, .. (1) is defined in terms of an initial set u0, ul, ..., Uk-1 by the recurrence relation (2) "+k + a, U.+i + ... + akU. = a, n > 0, where a,, a2, ..., ak are given rational integers. The author examines (1) for periodicity with respect to a rational integral modulus m. Carmichael' has shown that (1) is periodic for (ak, p) = 1 and has given periods (mod 664 MA THE MA TICS: H. T. ENGSTROM PROC. N. A. S. m) for the case where the prime divisors of m are greater than k. The present note gives a period for (1) (mod m) without restriction on m. The results include those of Carmichael. The author also shows that if p divides ak (1) is periodic after a determined number of initial terms and obtains a period. The algebraic equation + ak = 0 (3) F(x) =xk + aXk- + is said to be associated with (2). In considering (1) for the prime modulus p we may replace F(x) by any polynomial f(x) which is congruent to F(x) (mod p) and of degree k with leading coefficient unity. The following lemma gives a convenient choice for f(x). LEMMA 1. We may choose f(x) = F(x) (mod p) with the following properties: (1) f(x) is irreducible and of degree k with leading coefficient unity. (2) p does not divide the index of f(x). (3) If 0 is a root of f(x) and p contains precisely the ath power of a prime ideal p in K(8) then f'(0) contains precisely pa-l+p, where p = 1 or o according as a is or is not divisible by p. (4) 1 - 0 0 (mod p2) for any prime ideal divisor p of p in K(a). If 01, 02, .., k are the roots of f(x) = 0, the general term of any sequence associated with f(x) is given by a + 12 02+ + .+ 13k8k, n= f() + 10L+ (4) where j = and yj, 3j are integers in Let fi(6) ~~~~~~~~(5) a8 ++ (1 - O)f'(02) K(0j). (6) 0,(X)er (mod p) where the Oi(x) are prime functions (mod p) whose degrees we denote by ki. By the theorem of Dedekind (6) implies the prime ideal decomF(x) _ fl(X)e1f2(X)e2 ... position p p e1 e, q2j1 e2 P er k Npij=p, (7) in K(0j). Lemma 1 gives the power of these ideals dividing the denominators in (5). By use of the theorem of Fermat in algebraic fields we obtain the periodicity of (1) directly from (4). We say that ir is a general period (mod m) of the recurrence (2) if every sequence (1) satisfying (2) has the period ir (mod m). The minimum period of any particular sequence (1) will be a divisor of 7r. We write VOL. 16, 1930 MA THEMA TICS: H. T. ENGSTROM 665 e = max e, in (6) and I equal to the least common multiple of pki - 1, i = 1, 2, . . ., r. The following theorems give a general period of (2) for the case (ak, P) = 1. THEOREM 1. If (ak, p) $ 1, and either a = 0 (mod p) or F(1) p 0 (mod p), then (2) has the general period I (mod p). < e < p+', e > 0 then (2) has the THEOREM 2. If (ak, P) = 1 and p. general period pe+i I (mod p). If p divides ak we obtain the following theorem from (4). -g o THEOREM 3. If the last s coefficients in (2) are divisible by p, aks (mod p), then (1) is periodic (mod p) after s terms and a period is given by Theorems 1 and 2. A general period ir of (2) for the prime power modulus pa is obtained from a period (mod p) by the following theorem which may be proved quite directly by noting that (ufl+T - u")/p is again a sequence satisfying the recurrence (2) with a = 0. THEOREM 4. If (ak, p) = 1, and the recurrence (2) has the general period ir (mod p) then it has the general period pa-1ir(mod pa). If ak is divisible by p we obtain the theorem: THEOREM 5. If the last s coefficients of (2) are divisible by p, ak.. g 0 (mod p) then (1) is periodic (mod pa) after as terms and a period is given by Theorem 4. The following theorem suffices for obtaining a period of (1) for a general rational integral modulus m from the previous results. THEOREM 6. If m has the prime decomposition pla p ... pa, the least common multiple of a set of general periods 7ri of (2) (mod pi'i), i = 1, 2, ... t is a general period of (2) (mod m). * NATIONAL RESEARCH FELLOW. 1 R. D. Carmichael, "On Sequences of Integers Defined by Recurrence Relations," Quart. J. Math., 48, 343-372 (1920).
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https://www.ecmweb.com/power-quality-archive/standard-1459-2000-new-way-measure-power
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math
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Over the years, engineers have developed many definitions for measuring power with distorted voltages and currents. However, none of these definitions successfully characterize all of the distinguishing power components necessary for billing purposes, nor do they explain how to compensate for components that are not useful. To deal with this problem, the Institute of Electrical and Electronics Engineers (IEEE) organized a task force, chaired by Dr. Alex Emmanuel of Worcester Polytechnic Institute. The task force developed Standard 1459-2000, the “IEEE Trial Use Standard for Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions.” This standard is the subject of this month's column.
In the power business, nothing is more basic and important than measuring delivered energy for billing purposes. In addition to active (or real) delivered power, industry personnel often measure reactive power and/or total apparent power (definitions to follow). This allows them to factor in the additional system capacity required to supply a load's total power requirements.
Conventional induction disk watt-hour meters provide accurate real-power measurements. Engineers can use the same meters to measure reactive power by shifting the voltage 90 deg. Recently, engineers have developed electronic meters that accurately measure voltages and currents and calculate different power and energy quantities of interest. They also provide additional capabilities, including flexible demand periods, time-of-use rate calculations, and power quality measurements.
All of this works great for the assumed conditions of balanced systems and sinusoidal voltages and currents. The definitions and formulas used today for active, reactive, and apparent power have been used since the 1940s. When these definitions were developed, loads were dominated by motors, lighting, and other linear loads. This allowed the calculations to be simplified by taking advantage of the nondistorted voltages and currents and relatively balanced systems.
But what happens when harmonic components distort voltages and currents? This is an important question, considering the increasing applications of electronic equipment in all customer categories. Power electronic devices such as computer power supplies, adjustable-speed motor drives, phase-controlled rectifiers, thyristor-controlled loads, fluorescent lighting with electronic ballasts (including compact fluorescents) are everywhere. These nonlinear, harmonic-producing loads result in distorted voltages and currents that change the characteristics of the power delivered and the system capacity required to supply it.
Let's begin by reviewing the definitions for balanced and sinusoidal conditions. In these cases, we can use single-phase measurements for single-phase and 3-phase systems.
The instantaneous power (p) is defined as the instantaneous voltage (v) multiplied by the instantaneous current (i). Now divide this power into two components — active and reactive.
Active power (P), measured in watts, is the integral of the instantaneous power signal over some integral number of cycles:
Where: T=1/f = the period of one cycle in seconds, k is an integer number, and τ is the time at which the measurement starts.
This is the power component that utilities normally charge for and the component measured by a watt-hour meter. It results from the component of the current that is inphase with the voltage. In the case of a sinusoidal system, the active power is given by:
Where: V is the rms voltage magnitude, I is the rms current magnitude, and θ is the angle between the voltage and the current.
Reactive power (Q), measured in vars, is the power associated with the component of the current that is out-of-phase (in quadrature) with the voltage. This type of energy oscillates between the source and inductances, capacitances, and moving masses that pertain to electromechanical systems. The average value of this rate of flow is zero, and the net transfer of energy to the load is zero. It is obtained in a similar manner to active power, resulting in the following definition:
Note that reactive power is positive if the load is inductive and negative if the load is capacitive.
Apparent power (S) is the product of the rms voltage and current. It's measured in volt-amperes (VA):
Apparent power is important because it represents the total capacity that must be available to supply power to the load — even though only a portion of this is useful power. Some utilities use a demand charge based on the total apparent power to account for this system capacity requirement.
Power factor is defined as the ratio of active power (P) to total apparent power (S). This ratio represents the portion of the delivered power that is useful for performing work:
In sinusoidal situations, power factor is equal to the cosine of the angle between the voltage and current (cosθ).
Active, reactive, and apparent power form the power triangle shown in Fig. 1, on page 8.
Distorted Voltages and Currents
What happens when the voltage and current are not pure sinusoidal waveforms? In this case, it's useful to separate the voltage or current signals into two distinctive components — the power system fundamental frequency components v1 and i1, and the remaining terms vh and ih, which include all of the distortion components (both integer and noninteger harmonics). Consequently, the rms values of these components are related as follows:
These definitions provide the basis for the traditional measurements of total harmonic distortion (THD) in voltages and currents:
With harmonic distortion included, the power triangle that defines the power factor and the individual power components doesn't work. Some new definitions are needed. Rather than reviewing the whole history of definitions for power components that include harmonic distortion, we'll focus on the definitions developed for Standard 1459-2000 and the basis for this set of definitions.
The philosophy behind Standard 1459 involves defining a number of different components that could be useful in defining the responsibility and the costs associated with supplying power. These components can then be combined as necessary for particular situations. Here are the important components:
Active power (P) is divided into a fundamental component and a harmonic component. This is important because, typically, only the fundamental component benefits the load.
For example, motors produce no useful work from the power at harmonic frequency — they only cause additional heating in the motors. In most practical situations, the harmonic component of the active power is quite small.
Electronic meters can separate these two components if utility personnel want to base electricity charges on only the fundamental active power, rather than the total active power. (Currently, most electronic meters would not make this distinction and would try to accurately calculate the total active power). Conventional induction disk watt-hour meters can't make the distinction between the fundamental active power and the total active power. However, the responses of conventional watt-hour meters provide some attenuation at harmonic frequencies, which makes the meters focus primarily on the fundamental component of the active power.
It's possible to divide reactive power (Q) into two components in a similar manner. However, it's more useful to use a different breakdown of the nonactive power components because of distortion power components. The main purpose for defining a component called reactive power is to develop procedures and equipment for controlling the voltages and losses in a system at the fundamental frequency. Only fundamental frequency reactive power is important for these objectives.
For instance, you can size a capacitor bank to correct for fundamental frequency reactive power, but this capacitor bank would not compensate (and could magnify) nonfundamental frequency components.
The definition for total apparent power (S) remains the same — the product of the rms voltage and rms current (which now both include harmonic components). However, it's a good idea to separate the apparent power into fundamental and nonfundamental frequency apparent power. The fundamental frequency apparent power (S1) and its components (P1 and Q1) define the rate of flow of electromagnetic field energy associated with 50Hz and 60Hz voltages and currents.
These components can be used for power system design and evaluation in traditional manners.
The total apparent power will then consist of a number of additional components when the harmonic effects are taken into account. The expansion of rms voltages and currents into fundamental and harmonic terms is used to resolve the apparent power into its different components as follows:
Where: SN is the nonfundamental frequency apparent power:
Distortion Power Components
The breakdown of the total apparent power helps determine three different distortion power components that make up the nonfundamental frequency apparent power (SN).
Current distortion power (vars). The harmonic distortion in the current interacting with the fundamental frequency component of the voltage causes this component. It's usually the largest of the distortion power components. To develop penalties for harmonic current injection into the power system, you might use this component as the basis for these calculations.
Voltage distortion power (vars). This component is caused by the harmonic distortion in the voltage interacting with the fundamental frequency current. It's usually not as significant because voltage distortion tends to be smaller than current distortion. Also, because many people consider voltage quality to be the responsibility of the utilities, it may not be wise to make this the basis of charges for nonfundamental frequency apparent power.
Harmonic apparent power (VA). This is usually the smallest of the nonfundamental frequency apparent power components. It is defined as follows:
Sometimes it may be useful to divide harmonic apparent power into two separate components, one of which we have already defined above (PH).
The other term, DH, can be called harmonic distortion power (vars).
Power factor. The definitions for power factor do not change. Power factor is a measure of how efficiently the active power is being supplied. However, only the fundamental frequency power factor is useful for designing traditional power factor correction solutions that help improve voltage profiles and losses due to fundamental frequency reactive power flows on the system. This is sometimes referred to as displacement power factor. We will use the symbol PF1 for this quantity. Here are the power factor definitions:
There are simplified calculations for true power factor based on realistic distortion levels in voltages and currents, but we will not address those in this article.
Table 1, on page 12, summarizes the different definitions presented and groups them according to their use and whether they are associated with fundamental frequency or harmonic components. These are the definitions proposed by meter (and other monitoring equipment) manufacturers.
Standard 1459 provides a simple example that illustrates these calculations in a practical situation. The example is based on supplying a thyristor-controlled load, such as a dimmer switch controlling a light. The voltage and current waveforms at the metering point are shown in Fig. 2.
The important quantities needed to calculate the different power components are as follows:
The fundamental frequency apparent power (S1) for this example is 1229.7VA. Table 2, on page 12, summarizes the different power components in percentages of this base value. The true power factor is 0.58 and the displacement power factor is 0.696. Note that an electronic power supply load might have a similar true power factor but could have a displacement power factor close to unity. Also note that the nonfundamental frequency apparent power (684VA) is a significant component of the total apparent power in this example. This will be true in any case where current distortion is significant. To correct for this component, you would have to use some type of harmonic control rather than traditional power factor correction.
You may have noticed that we did not address unbalanced conditions in this article. This is because unbalanced conditions make situations even more complicated. You may want to investigate this further by obtaining the standard from the IEEE (www.ieee.org).
The definitions proposed in Standard 1459-2000 provide a blueprint for meter manufacturers and other monitoring equipment manufacturers to implement accurate power measurements in environments with significant distortion using a standardized approach. The standard breaks the power measurements into components that can characterize three things: the useful real power delivered to the load, the reactive power that can be compensated with conventional power factor correction, and the power components that require other methods of compensation (such as active filters). If we are going to charge for the system capacity required to supply these harmonic components, we must agree on standard definitions to measure them.
Mark McGranaghan directs power quality projects and product development at Electrotek Concepts in Knoxville, Tenn. You can reach him at [email protected].
Erich Gunther is responsible for technology development at Electrotek Concepts in Knoxville, Tenn. He is also the chief architect for the Dranetz-BMI Signature System™. You can reach him at [email protected].
The authors wish to thank Alex Emmanuel for his significant contributions to the article.
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https://www.answers.com/Q/What_kind_of_questions_can_science_answer
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math
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Science can answer questions about our physical world.
Questions that are not factual (eg religious questions).
Science cannot answer questions that contain the immeasurable. In other words, the question must contain quantifiable, finite components.
Science questions are science questions.
scientists can only answer questions about the physical world *APEX*
Something about cells, our body, about animals, about plants, about the parts of anything.
No, science can attempt to answer the questions that are testable.
Science can only answer questions about the physical world.
Science can only answer science questions but it can not answer most others. The answers to those have to come from other sorts of experts.
There are 40 questions on the science Aspire test.
Science can't answer some questions because science can only answer questions that can be proved, and some questions cannot be proved. A question like "Does God exist?" cannot be answered by science because it has not been proven that He exists yet. Science is all about answering questions that can be proved and known for a fact.
Science can only answer questions with the information available at the time. Science can answer some questions but not all because not all information is available all the time.
You can find a suitable resource for questions about medical science on sciencebasedmedicine.org/nine-questions-nine-answers/
Science is concerned with objective reality, therefore it does not answer subjective questions, vaguely worded questions, or meaningless questions.
Questions are important to life science because you want to find out the right answer.
Daily Science is something that your science teachers give you and it has questions on it about science it is stupid
As a general rule, science answers questions about objective reality, and does not answer questions about subjective opinion.
Science can't answer questions about values. For example, there is no scientific answer to the questions, which of these flowers is prettier? Or, which smells worse, a skunk or a skunk cabbage? • Science can't answer questions of morality. The problem of deciding good and bad, right and wrong, is outside the determination of science. • Finally, science can't help us with questions about the supernatural.
Because some of life's questions are too deep and complicated for science to answer.
Skepticism raises questions and questions spark investigation which is the underlying reason for science.
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http://slideplayer.com/slide/3808267/
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math
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Presentation on theme: "First Generation Marginalists"— Presentation transcript:
1 First Generation Marginalists We will look at the three individuals regarded as the co-founders of marginalist economics in the 1870sCarl Menger, W. S. Jevons, Leon WalrasSignificant differences in method and approach, particularly in terms of the use of mathematics and concepts of scienceNeither Menger nor Jevons dealt adequately with production
2 Carl MengerBecame a professor of economics at the University of Vienna and was the founder of what became the Austrian school of economicsIndividualistic and subjectivist approachNon-mathematicalInvolved in methodological debate with the historical schoolMenger believed in the importance of general economic principles and wanted to sharply distinguish between historical and statistical studies and exact laws of theoretical economics
3 Valuation of Consumption Goods For something to be an economic goodThere must be a wantThe object must have want satisfying powerConsumers have to be aware of its want satisfying powerMust be availableMust be scarce relative to wantsGoods that are not scarce may be very useful but are not economic goods
4 Valuation of Consumption Goods Economic goods have to be economizedAllocate goods to the most important want firstBut will begin to satisfy wants of lesser importance before fully satisfying the most important wantConcept of diminishing marginal utility but not stated in these termsDid see this as a solution to the Classical water/diamond paradox
5 Valuation of Consumption Goods WANTSIIIIIIIVVVI10987654321The numbers in the cells are an indication ofthe want satisfying power of a unit of a goodwith that want satisfying power. Possibly an ordinal ranking.
6 Valuation of Consumption Goods The value of a good is defined in terms of the want satisfaction that would be lost if the last unit of the good was not availableMenger did not formally derive the condition for a consumer maximum but seems to be what he had in mindPeople are constantly weighing up and choosing which needs shall be met and which not
7 Menger’s Theory of Factor Valuation Menger produces no analysis of the cost side but does discuss the valuation of higher order goods (production goods or factors of production)Emphasis on complementarity of production goodsProduction goods derive their value from the value of final consumption goodsTheory of “imputation”Value of a factor is the value of the production that would be lost if the last unit was withdrawn from production
8 W. S. Jevons 1835-1882 Biographical Details Born and raised in England Scientific training--ChemistryLived in Australia ( ) working as Assistant Assayer to the Royal Mint in SydneyStudied meteorology, but became interested in social scienceReturned to University of LondonProfessor of Economics at Manchester and then London
9 W. S. Jevons 1835-1882 Major Writings 1863 Pure Logic 1865 The Coal Question1862 Investigations in Currency and Finance1871 Theory of Political Economy1874 Principles of Science: A Treatise on Logic and the Scientific Method1875 The Solar Period and the Price of Corn
10 W. S. Jevons 1835-1882 Scientific background Interest in logic and “laws of the mind”Did experimental workIndex numbers and time series observationsNotion of equilibrium as a mechanical balance
11 Theory of Political Economy Opens with an attack on the Classical economics of Ricardo and MillCritical of labour theory of value and wage fund doctrineArgues for use of mathematical methods—calculusThe theory is arrived at deductively—role of intuition in providing basic premises—but Jevons also interested in measurement and empirical workWants to demonstrate that “value depends entirely upon utility”
12 Utility TheoryIndividuals seek to maximize pleasure/minimize pain (hedonism, based on Bentham)The purpose of production is consumptionConsumption choices based on utilityUtility is not intrinsic to a good, but a matter of individual valuationHow does utility vary with quantity?
13 Law of Variation of Utility Assumes continuous utility functionsTotal utility (u)Degree of utility (Δu/Δx)“The degree of utility varies with the quantity of the commodity, and ultimately decreases as quantity increases”Clear distinction between total and marginal utilitySolution of the water/diamond paradox
14 Law of Variation of Utility MUMU’MUxxx’As quantity of x increases, the degree of utility(MU) must eventually fall. If the individual hasx’ of x the “final degree of utility” is MU’
15 Exchange TheoryJevons does not go on from his theory of utility to derive demand curves, but considers the problem of exchangeIndividuals start with given endowments of goods, but depending on the final degrees of utility they may wish to exchange some of their goods for other goods in order to maximize utilityInitially, Jevons interested in the “limits of exchange” or how much would be traded between individuals at given prices
16 Exchange TheoryJevons takes the case of given supplies of two goods distributed to two individuals (one holds all the beef the other all the corn)He assumes competition and perfect information and an established ratio of exchangeEach individual will exchange up to the point where the ratio of the marginal utilities is equal to the ratio of exchangeThis is equivalent to the utility maximizing condition of each person trading until MUc/MUb = Pc/Pb
17 Exchange TheoryJevons tried to extend this analysis to the case of many traders and to the formation of market pricesConcept of a “trading body” as the aggregate of the buyers or sellers in a marketLaw of indifference or law of one priceExample of two trading bodies each with a given supply of two goods. To begin with one has all the beef and the other all the wheatAssumes that utility functions can be aggregated
18 Exchange theory MU corn MU beef a a’ m b’ b Q beef Q corn Trading body 1 starts at point a which representsa given endowment of corn and with MUfunctions as shown. Trading body 2 starts from bwhich represents a given endowment of beef(with the same MU functions). If 1 exchangescorn for beef and moves to a’ there is a utility gain.Similarly for 2 with the exchange of beef for cornAnd the movement from b to b’
19 Equation of ExchangeIf, ultimately y of beef is exchanged for x of corn the ratio of exchange can be expressed as y/x (which is equivalent to Px/Py)Trading body 1 will be left with (a-x) corn and y of beef and trading body 2 will have (b-y) of beef and x of cornFor this to be an equilibrium the equation of exchange must hold:Φ1(a-x)/ψ1(y) = y/x = Φ2(x)/ψ2(b-y)Where Φ1(a-x) is the final degree of utility of corn for trading body 1, etc.However, Jevons does not show how the ratio of exchange is determined but implicitly assumes it.
20 ProductionAs noted above Jevons wanted to show that value depends entirely on utilityTreatment of exchange assumed given suppliesWhat determines supply?Cost of production determines supplySupply determines final degree of utilityFinal degree of utility determines valueThis is not satisfactory as it suggests supply is determined first and before priceDemand and supply jointly determine price (Walras, Marshall)
21 Factor SupplySupply of effort a matter of the utility derived from income as against the disutility of workDiminishing MU of income and eventually increasing marginal disutility of workLabour becomes more tiring the more hours workedSupply effort to the point that the marginal utility of income is just equal to the marginal disutility of workWage increases and the supply of effort?
22 Supply of Effort Utility +ve MU income Hours worked -ve M disutility -veM disutilityOf workDisutility
23 Applied Economics: Resources Although Jevons’ theory was deductive he was also interested in empirical work and in a number of applied areasExhaustible resources and British coal supply—application of Malthusian theory to the issue of limited supply of coalJevons did not forsee the development of substitutes for coal
24 Applied Economics Cycles Jevons conducted a great deal of empirical work on cyclical fluctuations—he was one of the pioneers of trade cycle researchPioneered use of semi-log graphs, index numbers, geometric means, moving averages in time series analysisDeveloped a theory based on changes in weather produced by the solar period (sunspot cycle)
25 Sunspot theoryGood weather produces good harvests in India, China and other countries, after a time this increases demand for manufactured goods from Europe, so spreading prosperityAt that point the decline in solar radiation produces poor harvests in India and China reducing incomes and reducing demandTime series graphsDifficulties with the empirical evidence and the implied leads and lags in the theory
26 Government Policy Jevons a utilitarian and followed Bentham The greatest good for the greatest numberCase by case judgmentState enterprise in cases such as the post officeGenerally anti-trade union but certainly not an apologist for private business—pragmatic reform position
27 Leon Walras 1834-1910 Biographical details His father, Augustin Walras a professor of philosophy and economicsLeon Walras trained in engineeringTurned to economics in 1858Elements of Pure Economics 1874 and 1877Professor of Economics at University of LausanneMethod was mathematical and concerned with general equilibrium
28 Utility and DemandLike Jevons, Walras developed the idea of diminishing marginal utilityAssumes a cardinally measurable utility: “a standard measure of intensity of wants”Walras develops the condition for a utility maximum: that the ratio of marginal utilities must equal the ratio of pricesWalras then derives demand curves from this consumer utility maximizing condition—this is what Jevons failed to do
29 Derivation of Demand Curves Deals first with simple two commodity case but then moves on to assume many (m) commoditiesSelect one as the numeraireThe numeraire is the good in terms of which the prices of all other goods are expressed (P1=1)Consumer maximumMU1=MU2/P2=MU3/P3=MUm/PmWalras argues that it follows from this that a decrease in price of a good will lead to an increase in the quantity demandedThis ignores possibly perverse income effects
30 Walrasian Demand Curves QDPWalras sees Q as the dependent variableand places it on the vertical axis
31 General EquilibriumWhat most concerned Walras was the problem of general equilibriumIs it possible to have an equilibrium in all markets at the same time?Walras approached this first by assuming given quantities of goods and looking only at a pure exchange economy but then goes on to include production and factor marketsAssumes as given:initial factor endowments that individuals may use themselves or exchange for incomeMarginal utility functions for individuals for goods and self employed factor servicesTechnical coefficients of productionCompetitive conditions
32 General EquilibriumNeed to determine four sets of unknowns: the equilibrium prices of n productive services, the equilibrium quantities of n productive services, the equilibrium prices of m finished goods, and the equilibrium quantities of m finished goodsThat is 2m+2n unknownsOne price is a numeraire so we have (2m + 2n – 1) unknownsTo solve this need a set of (2m +2n – 1) simultaneous equations
33 General EquilibriumIndividuals supply factor services to factor markets and demand goods from goods marketsFirms demand factors from factor markets and supply goods to goods marketsIndividual demand functions for m goods will be of the formda= fa(pa, pb . . pm, pf1, pf2. . pfn)Individual factor supply functions for n factors will be of the formsf1= f1(pf1, pf2. . pfn, pa, pb . . pm)
34 General EquilibriumThese goods demand functions and factor supply functions can be aggregated over individuals giving m + n equationsThen need a set of n equations giving equilibrium in factor marketsIf coefficient af1 tells us how much of factor 1 is required to produce a unit of good a, then for factor market 1 to be in equilibriumaf1da+ bf1db mf1dm= sf1Have n such equations for each factor market
35 General EquilibriumLastly, need a set of m equations giving equilibrium in m goods marketsCondition for a long run equilibrium is zero economic profitaf1pf1+ af2pf afnpfn= paNow have (2m + 2n) equationsCan eliminate one equation by Walras’ law and are left with (2m+2n-1) equations and the same number of unknowns
36 General EquilibriumCounting of equations and unknowns only shows that there is a solution—a solution existsHowever, the solution may not be uniqueSolution may not be economically feasible (involve negative prices or quantities)Solution may not be stableDespite this Walras thought he had provided a rigorous demonstration of Smith’s invisible hand
37 Adjustment to a General Equilibrium Walras provides a description of adjustment to a general equilibrium through a process of “tatonnement” until no excess demand or supply exisitsIdea of the auctioneer who calls out pricesPrice adjustment leading to quantity adjustments (Q is the dependant variable)But the system will fail if there is any trading at non-equilibrium pricesAnalysis of an equilibrium system only
38 Walras and Applied Economics The pure theory of a competitive general equilibrium is “the guiding light for applied theory”Generally competitive conditions provide a maximum of utility for societyPolicy to remove obstacles and hindrancesSocial policy may involve state regulation or provisionSocial economics to examine principles of distribution and the framework of property rightsEnvisaged a “liberal-socialist” system
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https://www.electricalengineering.xyz/article/complex-vector-addition-in-electrical-engineering/
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math
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If vectors with uncommon angles are added, their magnitudes (lengths) add up quite differently than that of scalar magnitudes: (Figure below)
If two AC voltages — 90o out of phase — are added together by being connected in series, their voltage magnitudes do not directly add or subtract as with scalar voltages in DC. Instead, these voltage quantities are complex quantities, and just like the above vectors, which add up in a trigonometric fashion, a 6 volt source at 0o added to an 8 volt source at 90o results in 10 volts at a phase angle of 53.13o: (Figure below)
Compared to DC circuit analysis, this is very strange indeed. Note that it is possible to obtain voltmeter indications of 6 and 8 volts, respectively, across the two AC voltage sources, yet only read 10 volts for a total voltage!
There is no suitable DC analogy for what we’re seeing here with two AC voltages slightly out of phase. DC voltages can only directly aid or directly oppose, with nothing in between. With AC, two voltages can be aiding or opposing one another to any degree between fully-aiding and fully-opposing, inclusive. Without the use of vector (complex number) notation to describe AC quantities, it would be very difficult to perform mathematical calculations for AC circuit analysis.
In the next section, we’ll learn how to represent vector quantities in symbolic rather than graphical form. Vector and triangle diagrams suffice to illustrate the general concept, but more precise methods of symbolism must be used if any serious calculations are to be performed on these quantities.
- DC voltages can only either directly aid or directly oppose each other when connected in series. AC voltages may aid or oppose to any degree depending on the phase shift between them.
Article extracted from: Lesson in Electric Circuits AC Volume Tony R Kuphaldt under Design Science License. Heading and title is modified/added.
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https://animorepository.dlsu.edu.ph/faculty_research/6070/
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math
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The bandwidth of tower graphs Tm,2 and Tm,3
College of Science
Mathematics and Statistics Department
The bandwidth problem deals with finding a labeling of a graph G using non-negative integers such that the maximum difference between adjacent vertices is minimized. This thesis is a study on the bandwidth of tower graphs Tm,2 and Tm,3. Furthermore, some theorems and properties of bandwidth-critical subgraphs included in the paper entitled The bandwidth problem: Critical subgraphs and solution for caterpillars by Maciej Syslo and Jerzy Zak were proven and were used in the proofs for the bandwidth of tower graphs Tm,2 and Tm,3.
Garcia, M. A. (2007). The bandwidth of tower graphs Tm,2 and Tm,3. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/6070
Graph theory; Graph labelings
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| 803 | 6 |
https://www.cusd80.com/domain/4620
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math
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2017 Summer School Options:
Dates: Monday, June 12th - Friday, June 30th
Breakfast and Lunch included
Courses offered:English 9, Sem. 1 and 2
English 10, Sem. 1 and 2 & English 11, Sem. 1 and 2Spanish 1 and 2, Sem. 1 and 2Intro to PE Males, Sem. 1 and 2Intro to PE Females, Sem. 1 and 2Comprehensive Health, offered both sessionsAlgebra 1, Sem. 1 and 2Geometry, Sem. 1 and 2Algebra 2, Sem. 1 and 2Algebra 2A (Juniors only) Sem. 1 and 2World History and Geography, Sem. 1 and 2AM/AZ History, FULL Year onlyUS Government, offered both sessionsECONOMICS, offered both sessionsMusic and Technology Camps also offered
Student MUST meet with their counselor first to receive an approval code for registration.
Classes will also be available through Chandler On Line AcademyFor more information please refer to this click hereStudent must meet with their counselor to receive approval
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| 877 | 7 |
https://rhc.de/en/lexikon/average-room-rate-occupancy-and-revenue-per-available-room/
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math
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The average achieved room rate is one of the key figures in the hotel industry. Together with the average room occupancy, can be combined into the so-called RevPar the “Revenue per Available Room”.
You calculate the average room rates as follows:
Method of calculation: NET lodging sales divided by the number of hired out rooms. For example, 80 rooms that were rented out for € 6,800 net lodging turnover per day, amount to a daily average room rate of € 85.00.
The average occupancy / utilization (English “Occupancy Rate” = OR), describes the proportion of rented out rooms. You calculate this key figure as follows:
Method of calculation: OR = total occupied rooms divided by the total rooms available
For example, a hotel has 100 rooms, of which 80 rooms were occupied
Calculation: 80 by 100 = 80%
Result: The hotel has therefore an occupancy rate of 80% on this day.
A key figure of “ARR” has little meaning without the other key figure of the occupancy rate. The average room price of € 200 should be barely economical with 10% of occupancy. Vice versa, 90 % occupancy at an average price of €10.00 for a 3 or 4 star hotel is not sufficient.
A useful combination results from the two key figures, thus, to compare various hotels it only needs this key number, the RevPar that is the revenue per available room:
You calculate the RevPar as follows:
Method of calculation: RevPAR = NET lodgings sales divided by the total number of rooms available.
Example: You make a lodging sale in one day of a NET amount of € 8,500 for 100 available rooms, of which 80 are occupied.
Calculation: 6,800 divided by 100 = € 68.00
Result: The lodgings revenue per available room (RevPar) on this day amounts to € 68.00
Copyrights © 2023 RHC Real Hotel Controlling. All Rights reserved.
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| 1,801 | 16 |
http://www.ma.utexas.edu/academics/courses/descriptions/M333L.php
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math
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M333L STRUCTURE OF MODERN GEOMETRY
Prerequisite and degree relevance: The prerequisite is one of 408D, M408L, M408S or upper-division standing and consent of the instructor. These requirements are set to ensure the mathematical maturity, rather than for content knowledge. They may be waived by the instructor in some cases, most notably a specialization in mathematics. M333L is required for students seeking certification to teach secondary school mathematics.
Course description: The course is designed to familiarize prospective mathematics teachers with the geometrical concepts which relate to two and three dimensional geometry and the mathematical techniques used in the study of geometry. The emphasis is both on the development of understanding of the concepts and the ability to use the concepts in proving theorems. The course includes study of axiom systems, transformational geometry, and an introduction to non-Euclidean geometries, supplemented by other topics as determined by the instructor. While the course is primarily designed for teachers, its content and approach may be of interest to other students of mathematics.
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CC-MAIN-2018-34
| 1,140 | 3 |
https://wikimili.com/en/Table_of_Newtonian_series
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math
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In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence written in the form
Mathematics includes the study of such topics as quantity, structure, space, and change.
Sir Isaac Newton was an English mathematician, physicist, astronomer, theologian, and author who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members. The number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and order matters. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers or the set of the first n natural numbers. The position of an element in a sequence is its rank or index; it is the natural number from which the element is the image. It depends on the context or a specific convention, if the first element has index 0 or 1. When a symbol has been chosen for denoting a sequence, the nth element of the sequence is denoted by this symbol with n as subscript; for example, the nth element of the Fibonacci sequence is generally denoted Fn.
is the binomial coefficient and is the rising factorial. Newtonian series often appear in relations of the form seen in umbral calculus.
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n, and it is given by the formula
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to 'prove' them. These techniques were introduced by John Blissard (1861) and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas, who used the technique extensively.
The generalized binomial theorem gives
A proof for this identity can be obtained by showing that it satisfies the differential equation
The digamma function:
The Stirling numbers of the second kind are given by the finite sum
In mathematics, particularly in combinatorics, a Stirling number of the second kind is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by or . Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions.
This formula is a special case of the kth forward difference of the monomial xn evaluated at x = 0:
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered:
A related identity forms the basis of the Nörlund–Rice integral:
where is the Gamma function and is the Beta function.
In mathematics, the gamma function is one of the extensions of the factorial function with its argument shifted down by 1, to real and complex numbers. Derived by Daniel Bernoulli, if n is a positive integer,
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by
The trigonometric functions have umbral identities:
The umbral nature of these identities is a bit more clear by writing them in terms of the falling factorial . The first few terms of the sin series are
which can be recognized as resembling the Taylor series for sin x, with (s)n standing in the place of xn.
In analytic number theory it is of interest to sum
where B are the Bernoulli numbers. Employing the generating function its Borel sum can be evaluated as
The general relation gives the Newton series
where is the Hurwitz zeta function and the Bernoulli polynomial. The series does not converge, the identity holds formally.
Another identity is which converges for . This follows from the general form of a Newton series for equidistant nodes (when it exists, i.e. is convergent)
In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,
The Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.
In mathematics, the falling factorial is defined as the polynomial
In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers ℂ defined as the (m + 1)th derivative of the logarithm of the gamma function:
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function:
In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions. It is formally defined for complex arguments s with Re(s) > 1 and q with Re(q) > 0 by
In mathematics, the Lerch zeta function, sometimes called the Hurwitz–Lerch zeta-function, is a special function that generalizes the Hurwitz zeta function and the polylogarithm. It is named after the Czech mathematician Mathias Lerch.
In mathematics, the Barnes G-functionG(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the Gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written in terms of the double gamma function.
In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function. Specifically, given a real number x, the rational zeta series for x is given by
In mathematics, the Nørlund–Rice integral, sometimes called Rice's method, relates the nth forward difference of a function to a line integral on the complex plane. As such, it commonly appears in the theory of finite differences, and also has been applied in computer science and graph theory to estimate binary tree lengths. It is named in honour of Niels Erik Nørlund and Stephen O. Rice. Nørlund's contribution was to define the integral; Rice's contribution was to demonstrate its utility by applying saddle-point techniques to its evaluation.
In combinatorics, the binomial transform is a sequence transformation that computes its forward differences. It is closely related to the Euler transform, which is the result of applying the binomial transform to the sequence associated with its ordinary generating function.
In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem from the same underlying principle; that is, the relation for one special function can be derived from that for the others, and is simply a manifestation of the same identity in different guises.
In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a q-analog of the Pochhammer symbol. It is defined as
In mathematics, Ramanujan's master theorem is a technique that provides an analytic expression for the Mellin transform of an analytic function.
Gregory coefficientsGn, also known as reciprocal logarithmic numbers, Bernoulli numbers of the second kind, or Cauchy numbers of the first kind, are the rational numbers
The Bernoulli polynomials of the second kindψn(x), also known as the Fontana-Bessel polynomials, are the polynomials defined by the following generating function:
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CC-MAIN-2021-31
| 8,056 | 42 |
https://beta.geogebra.org/m/d6hwkbEk
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math
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Graphing Linear Equations in Standard Form
Graph the line -2x + 3y = -6
We can find the x and the y intercepts of the line by the following:
- First, let . This can be done by writing it out, but it is easier to just cover up the x-term with your finger as if it isn't even there. Divide both sides by 3 to get . Plot the point on the y-axis. Click on and plot the point.
- Next, let . Once again, it is easier to just cover up the y-term with your finger. Divide both sides by -2 to get . Plot the point on the x-axis.
- Now, click on the icon in the menu to create a line the goes through both points.
Find the slope of -2x + 3y = -6
Now that the line has been graphed, let's find the slope of the line.
- Using the formula, , plug in the coordinates of the two points.
- On the menu, click on the icon and then arrow down to the icon Slope. Click on the line. The slope will be displayed as a decimal rounded to two decimal places.
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https://mathshistory.st-andrews.ac.uk/Biographies/Neumann_Bernhard/
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math
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Bernhard Hermann Neumann
BiographyBernhard Neumann's father was Richard Neumann, an engineer who worked for the electricity company AEG. The family lived in a wealthy district of Berlin. Bernhard attended school in Berlin spending three years in primary school followed by nine years at the Herderschule. As one might imagine mathematics was his best subject but at first he did not enjoy his other subjects very much at all. He found the teaching at the Herderschule rather uninspiring particularly the lessons on French and Latin. However, later in his school career things changed and Latin in particular became one of his favourite subjects. He began reading Latin for pleasure and found some Latin texts on scientific topics of particular interest.
Neumann entered the University of Freiburg to study mathematics in 1928 and spent two semesters there before moving to the Friedrich-Wihelms University in Berlin. There he was influenced by an impressive collection of teachers including Schmidt, Robert Remak and Schur, together with his assistant Alfred Brauer, and near contemporaries of Neumann such as Hurt Hirsch, Richard Rado and Helmut Wielandt. In fact it was Remak, more than any of the others, who influenced Neumann to turn towards group theory for at first he intended to become a topologist. Hopf had given him a love of topology and this seemed the topic on which he would undertake research. However his reading on the topic involved studying a paper by Jakob Nielsen, and he realised how a certain result on the number of generators of a group could be strengthened. Schur advised him to apply the same methods to prove results on wreath products of groups and his doctoral dissertation followed on naturally from this first excursion into group theory.
In November 1931 Neumann submitted his doctoral dissertation which was examined by Schur and Schmidt. He was awarded his doctorate by the University of Berlin in July 1932 and after that remained there attending lectures and acting as an unpaid assistant in the experimental physics laboratory. At the University of Berlin at this time he met Hanna von Caemmerer who was an undergraduate. A particularly difficult time was approaching, however, which would have a major effect on his life and that of Hanna von Caemmerer who later became Hanna Neumann after they married. When Hitler came to power in 1933, only a couple of months after Bernhard and Hanna first met, life in Germany became very hard for those of Jewish origin. Neumann realised immediately the dangers of remaining in Germany and quickly left the country, going first to Amsterdam before being advised that Cambridge was the best place for a mathematician to go. At the University of Cambridge he registered for a Ph.D. despite already holding a doctorate. In taking this course he followed the route adopted by most of those arriving in Cambridge fleeing from the Nazis, but in doing so he went against the advice of Hardy who said all that was necessary was to produce top quality mathematics.
Registering for a doctorate, Neumann was assigned Philip Hall as a supervisor. Hall gave him a research problem on rings of polynomials but Neumann did not make much progress on it. Returning to questions in group theory which he had studied while in Berlin, he made rapid progress and was awarded his second doctorate in 1935. Even a mathematician as outstanding as Neumann was not guaranteed a lecturing post at that time and he spent two years unemployed. He remained at Cambridge for a year teaching a preparatory course to give students the right background to take Olga Taussky-Todd's algebraic number theory course. He was appointed to an assistant lectureship in Cardiff in 1937, the post being a temporary one for three years. He was joined there by Hanna Neumann who left Germany in 1938 and the two were married in July of that year.
The year 1939 saw the start of World War II and now Neumann's position as a German in England became a difficult one despite having fled there to escape from the Nazis. He was briefly interned as an enemy alien but, in 1940, he was released. The University of Cardiff had not requested that he return there (if they had he would have been released earlier) so he joined the Pioneer Corps. Later he joined the Royal Artillery, and lastly the Intelligence Corps for the duration of the war. After the war ended Neumann volunteered for service in Germany with the Intelligence Corps and he was able to make contact with his wife's family at that time. Turning down an offer to return to Cardiff on the grounds that they had not helped him when he was interned, Neumann searched for an academic appointment again, and this time was appointed as a lecturer at Hull in 1946. The Neumann's were fortunate in that Hanna Neumann, who by this time had obtained her doctorate, was soon able to join him on the staff as an assistant lecturer in Hull.
In 1948 Neumann was appointed to the University of Manchester, after being approached by Max Newman, although he continued to live in Hull where Hanna still worked. In 1958 Hanna was appointed to a post in Manchester and the Neumanns then moved to a house in Manchester in which they lived for three years before Bernhard accepted an offer from the Australian National University of a professorship and the Head of the Mathematics Department at the Institute of Advanced Studies. He retired in 1974 but continued to live in Canberra.
Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them.
One of the questions raised in Neumann's thesis was the finite basis problem:-
Can each variety be defined by a finite set of laws?Neumann himself made many contributions to this question over many years but the answer to the problem was not given until 1969 when Ol'sanskii proved that the problem had a negative answer.
An indication of some of the topics which interested Neumann can be seen from looking at the material covered in Lectures on topics in the theory of infinite groups (1960). The notes provide an introduction to universal algebras, groups, presentations, word problems, free groups, varieties of groups, cartesian products and wreath products. He goes into greater detail when discussing varieties of groups, embedding theorems for groups and amalgamated products of groups. His methods here are based on wreath products and permutational products. Then he studies embeddings of nilpotent and soluble groups and finally looks at Hopfian groups. Frank Levin, reviewing the work, writes:-
The author's leisurely but informative style make these notes a pleasure to read and profitable even for the novice with no background in infinite groups.Among the many important concepts which Neumann introduced we should note in particular that of an HNN extension, which appears in the paper Embedding theorems for groups (1949) written jointly with Hanna Neumann and Graham Higman. Their results proved that every countable group can be embedded in a 2-generator group.
One of Neumann's many research students, Gilbert Baumslag, began a paper dedicated to Neumann on his 70th birthday with the paragraph:-
In 1955 when I first arrived in Manchester to work with B H Neumann he suggested that I read his paper 'Ascending derived series' which had only just been submitted for publication. This was a beautifully crafted paper, filled with ideas and very stimulating. The present note, written in gratitude, affection and esteem, in Bernhard Neumann's honour, comprises some simple variations on the themes of that paper.The history of mathematics first interested Neumann when he was at Manchester. At that time he was given access to the papers which had come from Augusta Ada Lovelace. These papers were loaned to him by the Lovelace family and he was particularly interested in the correspondence between Lovelace and her mathematics tutor De Morgan. In 1973 Neumann published a paper Byron's daughter in the Mathematical Gazette which gives an account of the mathematical activities of Ada Lovelace, her correspondence with De Morgan, and details of her friendship with Babbage. Following on from this work he later wrote a fascinating account of De Morgan's life which was published in the Bulletin of the London Mathematical Society in 1984.
But Bernhard Neumann's contribution to mathematics goes far beyond his leadership in research. As the authors of write:-
... he always had a very deep appreciation of the need to serve the mathematical community in other ways. He was a member of the Council of the London Mathematical Society between 1954 and 1961, and its Vice-President between 1957 and 1959. His scholarly influence stretched much further than Britain ... . His contributions to mathematics in Australia have been many and varied. Not only did he form a department of very able mathematicians at the ANU specialising in group theory and functional analysis, he also took a deep interest in the Australian Mathematical Society.Neumann served the Australian Mathematical Society as Vice-President on a number of occasions and was President during 1966-68. Neumann worked to set up the Bulletin of the Australian Mathematical Society and was editor for ten years after it was founded in 1969. He played a crucial role in setting up the Australian Association of Mathematics Teachers and the New Zealand Mathematical Society, see .
Many honours have been given to Neumann for his outstanding contribution and continue to be awarded. He received the Wiskundig Genootschap te Amsterdam Prize in 1949, and the Adams Prize from the University of Cambridge. He was elected a Fellow of the Royal Society of London in 1959 and a Fellow of the Australian Academy of Sciences in 1963.
- B H Neumann and H Neumann, Selected works of B H Neumann and Hanna Neumann (Six Volumes) (Winnipeg, MB, 1988).
- M Conder, Bernhard Hermann Neumann, New Zealand Math. Soc. Newslett. 47 (1989), 20-22.
- J Gani, and M F Newman, Bernhard Neumann's 70th birthday, Math. Sci. 4 (2) (1979), 69-76.
Additional Resources (show)
Other pages about Bernhard Neumann:
Other websites about Bernhard Neumann:
Honours awarded to Bernhard Neumann
Written by J J O'Connor and E F Robertson
Last Update May 2001
Last Update May 2001
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http://arc.lib.montana.edu/snow-science/item/1349
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math
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Item: Statistical Modelling of Snow Cover Stability in Mountain Slopes
Title: Statistical Modelling of Snow Cover Stability in Mountain Slopes
Proceedings: Proceedings of the 1994 International Snow Science Workshop, Snowbird, Utah, USA
- Pavel A. Chemouss [ Antiavalanche Service of Production Association Apatit, Kirovsk, Murmansk Region, 184230, Russia. ]
Abstract: New class of snow cover stability models are suggested. The base of such models are determined models of snow cover mechanical equilibrium and parameters of the models are stochastic functions. As an example of this class consider the model that is used for evaluation snowstorm snow stability. As a determined model was chosen simplified Boginsky's model in which comparison tensile stress with tensile strength is used for evaluation snow cover stability. For practical using the model was simplified by Boginsky additionally and instead of tensile stress was used snow mass of instability zone and instead of tensile strength - value of critical mass. The algorithm of the modelling is described briefly below. The profile of the slope is divided on segments with equal length in projection on horizontal plane. For each segment inclination uk and length lk are calculated. For each segment snow thickness hk, snow density Pk and shear strength ck are set. For each segment critical snow thickness is calculated with approximate formula (1). hk* = ck/Pkg (sinuk - fcosuk) (1) For each segment snow thickness hk is compared with critical one hk*. Zones in profile where snow thickness more then critical one are selected. Snow masses in selected zones are calculated. Calculated snow masses M are compared with critical one M* for each zone. It is considered, that snow is in unstable conditions in zones where snow masses more then critical one. In accordance with a friction coefficient f and a critical mass M* are effective constants which are determined by inverse calculation with data on avalanche releases.
Language of Article: English
Keywords: algorithm, snow model, stability, snow cover, statistics
Digital Abstract Not Available
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http://www.chegg.com/homework-help/questions-and-answers/office-building-billed-based-rate-structure-given-table-53-energy-charges-00732-kwh-demand-q4193132
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math
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An office building is billed based on the rate structure given in Table 5.3 (Energy charges is $0.0732/KWh and demand charge is $9 / mo-kw. As a money saving strategy, during the 21 days per month that the office is occupied, it has been decided to shed 10 kW of load for an hour during the period of peak demand in the summer. a. How much energy will be saved (kWh/mo)? b. By what amount will their bill be reduced ($/mo) during those months? c. What is the value of the energy saved in �/kWh?
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http://www.ams.org/journals/proc/1981-081-04/S0002-9939-1981-0601718-6/home.html
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math
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Simple subrings of algebras over fields
Abstract: In this note we shall prove that if is a not necessarily associative algebra over a field and is a simple subring of with centroid then .
Since we do not use polynomial identities in a proof of this result then we have obtained an affirmative answer to the 11th question from , posed by I. N. Herstein.
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
- Ring theory, Lecture Notes in Pure and Applied Mathematics, vol. 40, Marcel Dekker, Inc., New York, 1978. Edited by F. van Oystaeyen. MR 522810
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17A99
Retrieve articles in all journals with MSC: 17A99
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https://www.webnextconf.eu/mathematica-4-2-for-macos-x-and-mac-os/
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math
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Mathematica 4.2 for MacOs X and Mac OS – Macitynet.it
The new version of Mathematica was released yesterday and available for purchase. Introduced in November 2001 also for Mac OS X, the software offers a significant increase in speed and stability compared to the previous release for MacOs Classic. " The Mach 3.0 kernel – reads a press release – and the Unix foundations of MacOs X allow this version to far surpass the old versions of mathematics in speed, scalability, stability "" MacOs X – it is read again – the first system operating from a workstation developed as an operating system for a personal computer. We have used Mathematica for MacOs X for three years internally and have worked closely with Apple to optimize performance "
Mathematica is one of the five main scientific applications and is intensively used by scientists and researchers to perform complex calculations. The program is also very popular in the USA both in high schools and colleges. The price set on the American market of $ 1,495.
Here are the news of version 4.2 available as an update. Transparent integration of Java with J / Link 2.0 and Java Runtime Engine built in improved simplificator, linear programming and optimization, improvements on statistics that include the new ANOVA package. The new Combinatorics packages have been introduced and AuthorTools for technical publications, a slide show environment for presentations. New import and export formats include FITS and STDS. XML extensions allow Mathematica notebooks and expressions to be recorded in XML format: the XML package Tool allows the manipulation of symbolic XML. XHTML export including style sheets is also supported and MathML 2.0 Extended is supported.
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https://www.generationgenius.com/area-circumference-of-circles/
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math
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You can use formulas to calculate the distance around a circle (called the circumference) and the area of a circle. The formulas use a special number called pi.
To better understand the area & circumference of circles…
LET’S BREAK IT DOWN!
Review Perimeter and Area
Perimeter is the distance around a shape. For example, a rectangle that is 5 units long and 10 units wide has a perimeter of 30 units. Area is the amount of space inside a 2D shape. Area is measured in square units. To find the area of the rectangle, multiply the length by the width. 5 units × 10 units = 50 square units. Try this one yourself: A rectangle has length 4 units and width 8 units. What is its perimeter? What is its area?
Circumference of a Frisbee
In ultimate frisbee, the frisbee has to have a circumference of 66 centimeters. How can you find the circumference of a frisbee? Circumference is the distance around a circle. One way to find the circumference is to use a string. Measure around the frisbee with the string, and then measure the string with a meter stick. It is about 44 cm. What if you don’t have a string? You can calculate the circumference from the diameter. The diameter is the distance straight across a circle. The diameter always passes through the center point of the circle. The frisbee has a diameter of 14 cm. The circumference of a circle is always about 3.14 times the diameter. So the circumference of the frisbee is approximately 14 × 3.14 = 43.96 cm. The number 3.14 is an approximation. The actual number has a decimal that never ends. It is 3.141592653589793238.... This number is called pi. You can approximate pi as 3.14. You can always find the circumference of a circle by multiplying the diameter by pi. Try a small frisbee: the diameter is 7 cm, so the circumference is about 7 × 3.14 = 21.98 cm. Try a big frisbee: the diameter is 21 cm, so the circumference is about 21 × 3.14 = 65.94 cm. Pi is a ratio of the circumference of a circle to its diameter. If the diameter is 1 cm, then the circumference is about 3.14 cm. If the diameter is 2 cm, then the circumference is about 6.28 cm, and so on. Circumference divided by diameter equals pi. You can use letters instead of names: d for diameter and C for circumference. Try this one yourself: A circle has diameter 10 units. What is its circumference? Use 3.14 for pi.
Circumference of a Table
A table border wraps around a circular table for decoration. The border is 15.7 feet long. How big is the diameter of the table if the border wraps around it perfectly? You know the circumference and now you need to find the diameter. Rearrange the equation C = πd. Divide both sides by π. On the right side, the pi symbols cancel out, since pi divided by pi equals 1. So, C ÷ π = d. Substitute 15.7 feet into the equation for C. Then evaluate: 15.7 ÷ 3.14 = 5. So, the table border fits around a table with diameter 5 feet. Try this one yourself: A circle has circumference 25.12 meters. What is the diameter of the circle? Use 3.14 for pi.
Area of a Circular Pen
A tortoise lives in a circular pen. What is the area of the pen? Remember, area is the space inside a 2D shape. The area of a circle can be calculated with the formula A = π x r2, where r stands for radius. The radius is the measurement from the center of the circle to its edge. The radius is half of the diameter. So, to find the area of the pen, multiply pi times the radius squared. When you square a number, you multiply it by itself. The radius of the pen is 2 meters. In the formula, substitute in 2 for r. 22 = 2 × 2 = 4. Then, 3.14 × 4 = 12.56. So, the area of the pen is about 12.6 square meters. Where did the area formula come from? You can cut a circle into slices, like a pizza. Then, rearrange the pieces into a shape like a parallelogram. The area of a parallelogram is its base times its height. In this parallelogram-like shape, the height is the radius of the circle, or r. The base is half the circle’s circumference. The circumference is pi times the diameter, so half the circumference is pi times the radius, or π x r. So, the area of the shape is π x r x r, or π x r2. Try this one yourself: A circle has radius 3 meters. What is the area of the circle? Use 3.14 for pi.
Area of a Pool
A circular pool has diameter 6 meters. What is its area? The formula for area is A = π x r2. Find the radius by dividing the diameter in half: 6 meters divided by 2 is 3 meters. So, the radius is 3 meters. Then, square the radius: 3 × 3 = 9. Then, multiply 9 × 3.14 = 28.26. The area of the pool is about 28 square meters. Try this one yourself: A circular pool has diameter 7 meters. What is its area? Use 3.14 for pi.
AREA & CIRCUMFERENCE OF CIRCLES VOCABULARY
AREA & CIRCUMFERENCE OF CIRCLES DISCUSSION QUESTIONS
What is the radius of a circle? What is the diameter of a circle? How are they related?
What is pi?
What is the circumference of a circle? What is the formula for circumference?
What is the area of a circle with radius 6 cm?
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https://electricalstudent.com/question/17-24-a-chain-of-four-inverters-whose-sizes-are-scaled-by-a-factor-x-is-used-to-drive-a-load-capacitance-cl-1600-c-where-c-is-the-input-capacitance-of-the-standard-inverter-which-is-the-first-in-t/
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math
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17.24 A chain of four inverters whose sizes are scaled by a factor x is used to drive a load capacitance CL = 1600 C, where C is the input capacitance of the standard inverter (which is the first in the chain).
(a)Without increasing the number of inverters in the chain, find the optimum value of x that results in minimizing the overall delay tP and find the resulting value of tP in terms of the time constant CR, where R is the output resistance of the standard inverter.
(b)If you are allowed to increase the number of inverters in the chain, what is the number of inverters and the value of x that result in minimizing the total path delay tP? What is the value of tP achieved?
(a) x = 6.32; tp = 25.3 CR (b) n = 7; x = 2.87; tp = 20.1 CR
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https://www.coursehero.com/sitemap/schools/1105-MIT/courses/1753500-MATH18901/
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math
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Proof of the Well-ordering Theorem
We follow the pattern outlined in Exercises 2-7 on pp. 72-73 of the text.
be well-ordered sets; let
the following are equivalent:
or a section
is order preser
Compactly generated spaces
the following condition:
is said to be compactly generated if it satisfies
for each compact subspace
is open in
is open in
Said differently, a space is compactly generated
Locally Euclidean Spaces
The basic objects of study in differential geometry are certain topological
spaces called manifolds.
Oe crucial property that manifolds possess is
that they are locally just like euclidean space.
that for each such s
Tychonoff via well-ordering,
We present a proof of the Tychonoff theorem that uses the well-ordering
theorem rather than Zorn's lemma.
A be a collection of basis elements for the topology
of the product space
It follows the o
Normality of quotient spaces
For a quotient space, the separation axioms-even the
are difficult to verify.
We give here three situations in which the quotient
space is not only Hausdorff, but normal.
is normal, then
Normality of Linear Continua
is normal in the order topology.
Every linear continuum
and no smallest element.
form a new ordered set
by taking the disjoint union of
to be less than every element of
The separation axioms
We give two examples of spaces that satisfy a given separation
axiom but not the next stronger one.
is a familiar space,
and the second is not.
Teorem F.1. If
of R J
is of cou
Set Theory and Logic: Fundamental Concepts
(Notes by Dr. J. Santos)
A.1. Primitive Concepts. In mathematics, the notion of a set is a primitive
notion. That is, we admit, as a starting point, the existence of certain objects
(which we call sets), whic
The Long Line
We follow the outline of Exercise 12 of 24.
denote the set
denote the smallest element of
[o 0 X 0, ckX 0]
has the order type of
0 in 5
Sppose the lemma holds for all
We show it holds for 3.
We have studied four basic countability properties:
The first countability axiom.
(2) The second countability axiom,
The Lindel6f condition.
tse condition that the space has
a countable dense subset.
We know that condit
The Pruifer Manifold.
;The so-called Prufer mnanifold is a space that is locally 2-euclidean
and Hausdorff, but not normal.
In discussing it, we follow the outline of
Exercise 6 on p. 317.
be! the following subspace of
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https://www.physicsforums.com/threads/black-hole-horizon-confusion.808297/page-6
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math
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I don't know what you are referring to. I commented on the latest post you made prior to mine.Regretfully you did not comment on the correction to the erroneous statement.
Yes, they do. See below.Light signals in the other direction don't add information for this question
Fine. Now tell me what "clock rate is reduced in a gravitational field" actually means, in terms of direct observables. See below.it is generally acknowledged that clock rate is reduced in a gravitational field.
You missed the key phrase "local inertial frame". You are not even addressing what I'm actually saying.As you see above, the interpretation that you advocate does not match all the observations
Once again, it doesn't seem like you are reading my posts. I specifically talked about a local inertial frame. The GPS satellite clock scenario (which I assume is what you are referring to) obviously cannot be covered by a single local inertial frame. Also, an orbiting satellite is a bad example because it is not at rest relative to an observer on the Earth's surface; it would be better to talk about an observer at rest on Earth's surface, compared to an observer at rest on, say, a platform high above the first observer.Satellite clocks are typically slowed down in order to run at the correct clock rate in space around the Earth; Doppler effects can only explain that by pretending that the Earth is exploding at almost 10 m/s2.
We agree on this; but I don't think we agree on what the bug is. Let me re-state the key points from my perspective.I think that this is probably a permanent bug
We want to compare two scenarios:
Scenario #1: A rocket accelerating in flat spacetime. Observer 1R is at the rear of the rocket; observer 1F is at the front.
Scenario #2: At rest in a gravitational field. Observer 2R is at rest at some altitude in the field; observer 2F is at rest at some higher altitude.
We stipulate that observers 1R and 2R feel the same proper acceleration, and observers 1F and 2F feel the same proper acceleration. We stipulate that the proper distance between observers 1R and 1F is the same as the proper distance between observers 2R and 2F, and that both proper distances are unchanging.
We have observer 1R send a light signal to observer 1F, and observer 2R send a light signal to observer 2F. Both light signals are redshifted when they are received. Why is this? We have two ways of analyzing it:
Local Inertial Frame Analysis: Pick a local inertial frame in which the R observer is at rest at the instant the light signal is emitted. Because both the R and F observers are accelerating in this frame, the F observer will be moving away from the light signal when it is received; so there will be a Doppler redshift.
Non-Inertial Frame Analysis: Construct a non-inertial frame in which the observers are at rest. For scenario #1, this will be Rindler coordinates; for scenario #2, it will be Schwarzschild coordinates. In this frame, there will be a "gravitational redshift"--or, if you don't like the term "gravitational" in the flat spacetime case, you can simply look at the timelike Killing vector field with respect to which the R and F observers are both following integral curves--both coordinate charts are adapted to this KVF, so that the KVF corresponds to the timelike basis vector and its integral curves are curves of constant spatial position. The invariant length of the KVF is different for the R and F observers--it is "shorter" for the R observer than for the F observer. This causes observer F to see light signals from observer R as redshifted (the math is simple and applies to any stationary spacetime).
So both analyses give the same answer. The advantage of the second analysis is that it can be extended beyond a single local inertial frame, so if you want to say you prefer it for that reason, that's fine. But that doesn't make the first analysis invalid; it just restricts its scope. If we're talking about the equivalence principle, the scope is restricted to a single LIF anyway.
However, there is another issue. You had claimed, in the post I originally responded to that started this subthread, that
"(to first order) the apparent difference in clock rates in an accelerating rocket is an artefact of using accelerating coordinates"
and I had responded that we can look at repeated round-trip light signals to verify that the difference in clock rates is not an artefact. You apparently still do not understand how that works. The scenario is simple: the R and F observers send repeated round-trip light signals back and forth, and each measures his own elapsed proper time between successive signals. The R observer finds less elapsed proper time than the F observer does from signal to signal. This is a direct observable that shows the difference in clock rates.
It is true that this result is simplest to derive in the non-inertial coordinates of the second analysis above, but that doesn't make it an "artefact" of using accelerating coordinates. Elapsed proper time along a given worldline between two given events is an invariant, independent of coordinate choice. So I am entirely unable to understand how you can justify your claim that I quoted above.
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CC-MAIN-2020-40
| 5,204 | 18 |
http://www.ck12.org/book/CK-12-Basic-Probability-and-Statistics-Concepts-A-Full-Course/r8/section/3.6/
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math
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What is the probability that when you toss a coin it will come up heads? If you tossed a coin 100 times and kept a record of your results would it be the same as the probability you expected? Would heads come up exactly 50% of the time?
First watch this video to learn about theoretical and experimental coin tosses.
CK-12 Foundation: Chapter3TheoreticalandExperimentalCoinTossesA
Then watch this video to see some examples.
CK-12 Foundation: Chapter3TheoreticalandExperimentalCoinTossesB
In an example in a previous concept, we were tossing 2 coins. If you were to repeat this experiment 100 times, or if you were going to toss 10 coins 50 times, these experiments would be very tiring and take a great deal of time. On the TI-84 calculator, there are applications built in to determine the probability of such experiments. In this section, we will look at how you can use your graphing calculator to calculate probabilities for larger trials and draw the corresponding histograms.
You can also use the randBin function on your calculator to simulate the tossing of a coin. The randBin function is used to produce experimental values for discrete random variables. You can find the randBin function using:
If you wanted to toss 4 coins 10 times, you would enter the command below:
To try other types of probability simulations, you can use the Texas Instruments Activities Exchange. Look up simple probability simulations on http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=9327.
Let’s try an example using the Toss Coins simulation.
A fair coin is tossed 50 times. What is the theoretical probability and the experimental probability of tossing tails on the fair coin?
To find the experimental probability, we need to run the Toss Coins simulation in the probability simulator. We could also actually take a coin and flip it 50 times, each time recording if we get heads or tails.
If we follow the same keystrokes to get into the Prob Sim app, we get to the main screen.
We see the frequency of tails is 30. Now we can calculate the experimental probability.
What if the fair coin is tossed 100 times? What is the experimental probability? Is the experimental probability getting closer to the theoretical probability?
To find the experimental probability for this example, we need to run the Toss Coins simulation in the probability simulator again. You could also, like in Example A, actually take a coin and flip it 100 times, each time recording if you get heads or tails. You can see how the technology is going to make this experiment take a lot less time.
Notice that the frequency of tails is 59. Now you can calculate the experimental probability.
With 50 tosses, the experimental probability of tails was 60%, and with 100 tosses, the experimental probability of tails was 59%. This means that the experimental probability is getting closer to the theoretical probability of 50%.
You can also use this same program to toss 2 coins or 5 coins. Actually, you can use this simulation to toss any number of coins any number of times.
2 fair coins are tossed 10 times. What is the theoretical probability of both coins landing on heads? What is the experimental probability of both coins landing on heads?
To determine the experimental probability, let’s go to the probability simulator. Again, you can also do this experiment manually by taking 2 coins, tossing them 10 times, and recording your observations.
The frequency is equal to 4. Therefore, for 2 coins tossed 10 times, there were 4 times that both coins landed on heads. You can now calculate the experimental probability.
Points to Consider
- How is the calculator a useful tool for calculating probabilities in discrete random variable experiments?
- How are these experimental probabilities different from what you would expect the theoretical probabilities to be? When can the 2 types of probability possibly be equal?
To produce experimental values for discrete random variables, use the randBin function on your TI calculator.
You are in math class. Your teacher asks what the probability is of obtaining 5 heads if you were to toss 15 coins.
a. Determine the theoretical probability for the teacher.
b. Use the TI calculator to determine the actual probability for a trial experiment of 10 trials.
a. Let’s calculate the theoretical probability of getting 5 heads in the 15 tosses. In order to do this type of calculation, let’s bring back the factorial function from an earlier concept.
In the example, you want to have 5 H's and 10 T‘s. Our favorable outcomes would be HHHHHTTTTTTTTTT, with the H's and T's coming in any order. The number of favorable outcomes would be:
The number of possible outcomes = 32,768
Now you just divide the numerator by the denominator:
Therefore, the theoretical probability would be 9.16% of getting 5 heads when tossing 15 coins.
b. To calculate the experimental probability, let’s use the randBin function on the TI-84 calculator.
From the list, you can see that you only have 5 heads 1 time in the 10 trials.
Therefore, the experimental probability can be calculated as follows:
- Use the randBin function on your calculator to simulate tossing 5 coins 25 times to determine the probability of getting 2 tails.
- Use the randBin function on your calculator to simulate tossing 10 coins 50 times to determine the probability of getting 4 heads.
- Calculate the theoretical probability of getting 3 heads in 10 tosses of a coin.
- Find the experimental probability using technology of getting 3 heads in 10 tosses of 3 coins.
- Calculate the theoretical probability of getting 8 heads in 12 tosses of a coin.
- Calculate the theoretical probability of getting 7 heads in 14 tosses of a coin.
3 coins were tossed 500 times using technology.
- According to the following screen, what is the experimental probability of getting 0 heads?
- According to the following screen, what is the experimental probability of getting 1 head?
- According to the following screen, what is the experimental probability of getting 2 heads?
- According to the following screen, what is the experimental probability of getting 3 heads?
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CC-MAIN-2017-17
| 6,166 | 48 |
https://www.ansaroo.com/types/graphs+algebra
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math
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Ch2: Frequency Distributions and Graphs Santorico -Page 30 For quantitative variables we have grouped and ungrouped frequency distributions. An Ungrouped Frequency Distribution is a frequency distribution where each class is only one unit wide. Meaningful when the data does not take on many values.
5.2 - Reference - Graphs of eight basic types of functions The purpose of this reference section is to show you graphs of various types of functions in order that you can become familiar with the types. You will discover that each type has its own distinctive graph.
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CC-MAIN-2021-17
| 566 | 2 |
http://nrich.maths.org/public/leg.php?code=31&cl=1&cldcmpid=5728
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math
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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Can you hang weights in the right place to make the equaliser balance?
Use the number weights to find different ways of balancing the equaliser.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Choose a symbol to put into the number sentence.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
If you have only four weights, where could you place them in order to balance this equaliser?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
A game for 2 players. Practises subtraction or other maths operations knowledge.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Ben has five coins in his pocket. How much money might he have?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Find all the numbers that can be made by adding the dots on two dice.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
You have 5 darts and your target score is 44. How many different ways could you score 44?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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CC-MAIN-2017-34
| 5,971 | 50 |
https://tex.stackexchange.com/questions/495995/does-the-apa6-class-keywords-do-anything-but-formatting
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math
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I was wondering if the "Keyword" command from the APA6 class does anything more than just formatting. (e.g. pass as PDF keywords or similar?)
It does not
: does anyone know how these are formatted?
Thank you in advance for your efforts and answers.
PS: concerning 2 Abstracts in apa6 Document
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670558.91/warc/CC-MAIN-20191120111249-20191120135249-00511.warc.gz
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CC-MAIN-2019-47
| 292 | 5 |
http://gmatclub.com/forum/what-is-the-value-of-x-y-4-1-the-product-of-x-and-y-is-18771.html?fl=similar
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math
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What is the value of (x-y)^4
(1) The product of x and y is 7
(2) x and y are integers
To know its value it will not be sufficient to know xy=7 or to know that both x and y are integers.
Combined we know that x and y can only be (1,7) or (-1,-7). (The order is not important.) The quadratic terms make the negative signs go away so the value of (x-y)^4 would be unique.
I agree with C.
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
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CC-MAIN-2015-32
| 510 | 9 |
http://lfessayfopy.njdata.info/research-papers-on-abstract-algebra.html
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math
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We provide students with custom example papers such as example essays, term paper examples, example research papers, example dissertations/theses of high quality. Algebra analysis applied foundations to understand abstract concepts, this book details how to write a research paper, . The following is meant as a guide to the structure and basic content of a mathematical research paper the basic structure of the paper is as follows: abstract . Abstract algebra is an important course in the undergraduate empirical research studies attest to students teaching and learning group theory 139. On this page you ca get sample pages of a research paper research paper topics pertaining to algebra research paper topics pertaining to geometry research paper topics on calculus how we can help research paper topics on mathematical logic probability and statistics topics research paper topics on differential equations research paper topics on .
How do i sell out with abstract algebra what happens in day-to-day work in any industry is very far removed from what you read in research papers. What is the best introductory abstract algebra textbook why multiple research papers what is it like to do research in abstract algebra. Topics structure and methods : 11 great women in mathematics hypatia, maria agnesi sophie germain sonya kovalevsky emmy noether (contributions to abstract. What is an abstract do abstracts vary by discipline don’t just cut and paste sentences from your research paper into your abstract .
Our research covers the spectrum of as such the algebra group sits naturally among a operator theory, including unbounded operators, and abstract . Classical education research papers discuss the style of education that focuses student move from factual to more abstract thought and use logic in algebra. Abstract algebra introduction to abstract algebra e-study guide for abstract research papers sony vgn tx770pt laptops owners manual sony vgn ux230p laptops.
De bock, deprez, van dooren, roelens, verschaffel 111 papers were mostly based on kaminski’s (2006) dissertation, in which students’ need for concrete instantiations to learn abstract concepts was explicitly questioned. Sample apa research paper sample title page the abstract summarizes the problem, research has focused mainly on how nutrition affects cognition. Free algebra papers, essays, and research - effective teaching of abstract algebra abstract algebra is one of the important bodies of knowledge that the .
A descriptive, survey research study of the student characteristics influencing the abstract of dissertation a descriptive, survey research study of the student. Research & white papers a first course in abstract algebra is an in-depth introduction to abstract algebra paper fraleigh: . Research could include some here one only needs background in linear and abstract algebra pseudo-random number generation, middlebury college thesis . How to write an effective title and abstract and choose appropriate keywords velany we focus on how to write a research paper abstract that is concise and .
Abstract-ness the beauty of if you use it as a noun the one i tend to associate is the abstract of research paper, distills the essence of the research paper. Arthur ogus arthur ogus math 113--introduction to abstract algebra math research papers and presentations. Math 252: abstract algebra ii research topics the paper should be 6-8 pages in length if your paper is slightly shorter or substantially longer, you will not be penalized.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510867.6/warc/CC-MAIN-20181016201314-20181016222814-00149.warc.gz
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CC-MAIN-2018-43
| 3,534 | 6 |
http://workforcemanagementsoftware15.zemir.org/aa/12-by-12-room-size-in-square-feet.html
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math
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Calculate square feet meters yards and acres for flooring carpet or tiling projects.
12 by 12 room size in square feet.
Square footage is also known as a k a square feet square ft sqft sq ft sq ft ft2 ft 2 this calculator also calculates square inches total height in feet total height in inches total length in feet and total length in inches.
To measure the approximate square footage of a space you measure the length and width of a space.
How to calculate the square footage of a house example.
30 sq in 0 00694 sq ft sqin 0 208333 sq ft.
12 x 12 144 assuming the room is measured in feet which most are the area is 144 square feet.
A square foot is basically a square that s 12 inches 30 5 cm on each side.
Calculate project cost based on price per square foot square yard or square meter.
However in our research it was not uncommon to find bedrooms that were as large as 12 feet by 12 feet or as small as 10 feet by 10 feet.
You can enter feet only inches only or any combination of the two.
Let s compute the how many square feet in a 12 12 room.
If your room is 10 feet long by 10 feet wide 10 10 100 square feet.
To make it clear a 12 12 feet room has exactly 144 square feet.
Calculate square footage square meters square yardage and acres for home or construction project.
How many square feet are in an acre.
For example a table that s 4 feet 122 cm by 3 feet 91 cm would be about 12 square feet.
The procedure of converting square inches to square feet or from acres to sq ft is the same as converting from square meters to square feet.
In homes below 2500 square feet the average bedroom size in the united states is 11 feet by 12 feet or 132 square feet in total area.
In the following examples you will find the most common of these conversions.
Use the calculator above to calculate your square footage.
The length and the width of the room are both equal with 12 feet.
For example if your room has a rectangular shape write down in the calculator only width and depth of it and specify the measure s units.
To answer this question we simply multiply the length of the room by the width.
How to calculate square footage for rectangular round and bordered areas.
The surface value will be.
S length width s 12 12 144 square feet.
1 acre 43 560 square foot 1 square yard 9 square foot 1 square meter 10 76 square foot 1 square inch 0 00064516 square foot calculating cost per square foot.
Enter measurements in us or metric units.
Then you multiply the numbers to get the total square feet.
Dividing the room into the particular number of separate sections is an effective way to calculate the room s precise size when it has a unique shape.
1 acre 43 560 sq ft acre 43 560 sq ft.
When painting a house installing flooring or building a home the square footage of the property is often used to determine cost or materials to be used.
Supposing you want to measure the square footage of an area that isn t one single rectangle.
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CC-MAIN-2021-21
| 2,942 | 34 |
http://cprpulleys.com.au/maximising-pulley-performance-through-stress-and-finite-element-analysis/
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math
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Maximising Pulley Performance through Stress and Finite Element AnalysisFebruary 26, 2019
Finite element analysis is a mathematically based method of solving physical problems. Think of it as a problem-solving aid, a way of breaking mechanical systems down until they become pure numbers. Stress factors on one side, design parameters on the other, mechanical structures develop as formula-balancing solutions. Here, on bringing the mathematical tools together, we’ll carry out an FEA study on a series of heavy-duty conveyor system pulleys.
Assigning the Mathematical Identities
Let’s assume a hypothetical pulley is undergoing the design process. One option here is to build a dozen prototypes. Each variant is built to provide a slightly different set of operational parameters. Only, this approach would be incredibly wasteful. Ideally, we want the fewest number of prototypes possible. This is an opportunity for a finite element analysis program to produce a mathematically accurate model, one that emulates the physical performance characteristics of a heavy-duty prototype. Stress factors are assigned first. They’re used to calculate how the pulley will respond to a number of statistically analyzed loading scenarios. Will the cylinder deform under the load? Will it experience premature wear and fatigue? Belt wrap angles and tensioning data are added to the formulas now, so the model becomes more detailed, more realistic.
What Is FEA Science Based Upon?
Sometimes referred to as the Finite Element Method (FEM), the mathematics used here are not easy to comprehend. Partial differential equations and exotic domain parameters blend into unfathomable figures and calculations. Making the science that much easier to wield, there are FEA software packages available. They simulate pulley stresses, calculate cylinder deformation characteristics, and they generally model pulley shell outlines so that a system designer can maximize pulley performance. Again, by pulling off this work inside a mathematically created workspace, fewer prototypes are required. At the end of the day, a handful of prototypes and a slew of experimental data should be enough to model a cylinder/shell profile that will endure.
The partial differential calculations are useless by themselves. We need to determine the deformation forces and stress factors that are applied by a system. On calculating those stress forces, they’re plugged into the finite element analysis software. All the building blocks are in place, so the modelling run commences. With all of the experimental data and mathematical figures in place, the FEA formulae, whether manually calculated or run within a computer simulation package, creates a vast number of virtual prototypes. It’s easy to fine-tune any material option or dimensional value when everything is moving inside a virtual workspace. But make no mistake, FEA studies solve real-world physical problems. They do resolve pulley performance challenges.
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- How to Judge the Wear Resistance Performance of Pulley Rubber Lagging
- Popular Conveyor Design Trends for 2019
- What are Troughing Idlers for?
- Understanding Self-Cleaning Pulleys: How Do They Really Work?
- The Importance of Meeting the Minimum Run-out Tolerance for Conveyor Idlers
- What Does a Crowned Pulley Mean?
- Plain Rubber, Chevron, and Diamond Groove Pulley Lagging: What are their Differences?
- Understanding the Differences Between Live Shaft and Dead Shaft in Pulleys
- The Different Types and Functions of Idler Rollers
- Self-Cleaning Spiral and Winged Pulleys: How Do These Pulleys Work?
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CC-MAIN-2020-29
| 3,634 | 18 |
http://xrcourseworkcwge.locksmith-bellevue.us/mathematics-education-dissertation.html
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math
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Mathematics education dissertation
(last updated: 4/28/2015) graduate students in the master of science in mathematics education program at boise state university are encouraged to consider the following suggested formats as they work to frame the topic and scope for their culminating project or thesis general information candidates enroll in 4-7 credits of project or thesis. Students interested in pursuing postgraduate research in mathematics education can find a list of potential research projects here. This study was carried out to investigate the effect of using animated computer 3-d figures illustration (actdfi) in the learning of polyhedron in geometry. Here is a list of phd and edd theses completed in the recent past at the faculty of education. Mathematics education ms 1992 georgia state university mathematics education this dissertation is the story of my journey as a mathematics teacher in this dissertation, i share my experiences of introspection, examination, change and. Dissertations, theses and capstone recommended citation rimpola, raquel caampued, examining the efficacy of secondary mathematics inclusion co-teachers (2011)dissertations, theses and capstone projectspaper 457 dr sanchez' expertise in mathematics education informed important.
Core state standards for mathematics and the singapore mathematics curriculum framework heidi ann ertl part of themathematics commons, and thescience and mathematics education commons this thesis is brought to you for free and open access by uwm digital commons. Senior thesis and phd thesis at the mathematics department. Ames, lisa the effect of incorporating geometer's sketchpad in a high school geometry course to improve conceptual understanding, inductive reasoning, and motivation. A survey of college mathematics professors' reported instructional strategies in courses in which prospective of the requirements for the doctor of philosophy degree in teaching and learning (mathematics education) in the graduate thesis supervisor: associate professor carolyn colvin. The course of study for a phd in mathematics and statistics education includes 56-62 hours of courses and dissertation work after a master's degree. Thesis on education thesis topics for education education master thesis education thesis papers doctoral thesis in education.
Doctor of philosophy in mathematics education the doctor of philosophy (phd) degree emphasizes research competencies the degree requires a scholarly dissertation of intellectual merit and sound research methodology. This is a list of all dissertations that have been submitted in partial satisfaction for the degree of doctorate of philosophy (phd) in mathematics at ucsd.
Database of example education dissertations - these dissertations were produced by students to aid you with your studies. A research paper/thesis/dissertation submitted in partial fulfillment of the requirements for the master of science degree department of mathematics in the graduate school southern illinois university carbondale july, 2006. Find popular pages faster via the quick links on the right undergraduate prospective students sample dissertation page 001 page 002 page 003 page 004 page 005 page 006 page 007 page 008 page 009 school of mathematics, university of manchester, oxford road, manchester m13 9pl.
Mathematics education dissertation
Ph d requirements in addition to the information on this page by the math department in mathematics education may be used to satisfy the outside course requirement by students whose dissertation is not in mathematics education. Prideaux, jodi b, the constructivist approach to mathematics teaching and the active learning strategies used to enhance student understanding (2007) ms in mathematics, science, and technology education this thesis is available at fisher digital publications.
- The mathematics and science education (mse) interdisciplinary science education, and mathematics education her dissertation examined the potential that lesson study.
- Do you struggle with a master's or phd thesis in math do you need a good plan to start writing well, in this article you will find helpful information on how to get ready for writing a master's mathematics thesis step # 1 first, you should choose a topic for your mathematical thesis.
- University of wollongong research online university of wollongong thesis collection university of wollongong thesis collections 2014 improving mathematics education in the middle.
- Early childhood education dissertations early childhood education department 5-16-2014 a mixed-methods examination of inservice elementary school teachers' mathematics mentoring experiences in a mathematics master's degree program.
Technology adoption in secondary mathematics teaching in kenya: an explanatory this dissertation is brought to you for free and open access by the surface at surface it has been accepted for inclusion in dissertations debates on the uses of technology in mathematics education. To the graduate council: i am submitting herewith a dissertation written by renee lenise colquitt entitled social justice in mathematics education. Dissertations, theses and capstone projects 12-2014 understanding student mathematical ways of knowing: relationships among mathematical anxiety, attitude toward learning math, gender part of thescience and mathematics education commons. Dissertations from 2015 august 2015 dissertations from 2014 december 2014 yasemin gunpinar: teachers' instructional practices within connected classroom technology environment to support representational fluency (mathematics education. Master of science degree in mathematics (thesis, non-thesis, and non-thesis education track) mathematics graduate handbook. Maths dissertations dissertation in mathematics algebra, probability applied mathematics dissertations.
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https://www.cheric.org/research/tech/periodicals/view.php?seq=81883
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IEEE Transactions on Automatic Control, Vol.44, No.3, 619-622, 1999
Optimal control structure of an unreliable manufacturing system with random demands
This paper considers an unreliable manufacturing system with random processing times and random product demands. The system can produce many part types and its total capacity is constrained by a fixed constant. The objective is to find an optimal service-rate allocation policy between different part types by minimizing the expected discounted inventory and backlog cost. Structural properties of the optimal control policy are investigated, It is shown that the optimal policy is of a switching structure. For producing a one part type case, the optimal control is a threshold policy. For producing a two part types case, the optimal control can be described by three monotone switching curves and its asymptote properties are derived. Numeric examples are given to illustrate the results.
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| 943 | 3 |
https://www.data.ai/en/apps/mac/app/wizard-statistics-visualization/
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math
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Wizard is a Mac app that makes data analysis easier than ever. No programming, no typing — just click and explore. Wizard makes statistics accessible to beginners, but beneath the surface lies a full set of tools for doing professional research.
Featured by Apple! "New and Noteworthy" and "@Work: Apps for Business"
"You can be looking at statistical analyses less than a minute after importing your data." —MacFormat Magazine (UK)
It's true: within minutes of importing your first data set into Wizard, you'll be generating graphics, uncovering correlations, producing p-values, building models, and sharing insights with colleagues. Most customers find that the program pays for itself in just a few days of use. Explore Wizard's delightful feature set, including...
Wizard will start graphing your data as soon as you click on it. It uses native Mac graphics to give you crisp visual summaries — box-plots, scatterplots, histograms, survival curves, and more — in a fraction of a second.
EASY STATISTICAL MODELING
Build sophisticated statistical models in seconds with Wizard's intuitive modeling interface. Regression estimates are instantly recomputed as you play around with the controls and experiment with new specifications.
Wizard supports drag-and-drop, multi-level Undo, and other interface conveniences that Mac users expect from their software. An interactive tutorial will help you get started.
Dozens of functions are available to help you get data into the form you want. Compute quantiles, perform day-of-week calculations, multiply columns together, and more.
Export colorful graphics as web-friendly PNG or print-quality PDF. If you're surrounded by PC users, export your models as interactive spreadsheets that can be used to run "What if?" scenarios in any version of Microsoft Excel.
LIST OF STATISTICAL TESTS
Wizard supports the most common statistical tests and models, including...
+ Shapiro-Wilk test of normality
+ 1-sample Kolmogorov-Smirnov (normality and uniformity)
+ Pearson's goodness-of-fit (equal proportions)
+ Pearson's goodness-of-fit (chi-square)
+ t-test (paired and unpaired)
+ ANOVA (1-way, 2-way, and repeated measures)
+ Correlation and R²
+ Median tests: Mann-Whitney and Kruskal-Wallis
+ NEW: Wilcoxon signed-rank and Friedman tests
+ Survival analysis: Log-rank test
+ 2-sample and N-sample Kolmogorov-Smirnov
+ Linear regression (OLS)
+ Weighted linear regression (WLS)
+ Poisson and geometric regression
+ Logistic regression (Logit) and Probit
+ Multinomial Logit and Ordered Probit
+ Negative Binomial (NegBin-2)
+ Cox Proportional Hazards
+ Fixed effects
+ Robust standard errors
+ Clustered standard errors
+ Joint significance tests (Wald tests)
+ Odds ratios
+ Residual analysis
+ Sensitivity/specificity analysis (ROC curves)
+ Censoring of survival data (Cox models)
+ Interactive prediction assistant
+ Copy models as R code
Is there a missing feature you'd like to see? Just click "Email the Developer" from the Help menu and send me your thoughts.
LIST OF FILE FORMATS AND DATABASES
Although you have the option to enter data manually, more likely you'll want to import data from one of the following sources:
• Excel (.xls/.xlsx)
• Numbers ('09 and later)
• R workspace and single-object files (.RData and .rds)
• DBF and Microsoft Access
• Plain text (Comma-, tab-, and custom-delimited values)
To import and export other formats, including SPSS, Stata, and SAS, you can either buy In-App Purchases inside Wizard (Wizard > Unlock Pro Features...), or purchase Wizard Pro, also available in the Mac App Store. The set of included importers is the only difference between the Pro and Standard versions.
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https://masozlerankara.com/qa/question-how-do-you-know-if-something-is-discrete-or-continuous.html
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math
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- What is discrete numbers example?
- Is Money discrete or continuous?
- What’s the difference between continuous and discrete?
- How do you know if a variable is continuous?
- Is hours of sleep discrete or continuous?
- What is discrete series example?
- Is age a discrete or continuous?
- Is gender a discrete or continuous variable?
- Is blood pressure discrete or continuous?
- Is family size discrete or continuous?
What is discrete numbers example?
Examples of discrete data include the number of people in a class, test questions answered correctly, and home runs hit.
Tables, or information displayed in columns and rows, and graphs, or structured diagrams that display the relationship among variables using two axes, are two ways to display discrete data..
Is Money discrete or continuous?
A continuous distribution should have an infinite number of values between $0.00 and $0.01. Money does not have this property – there is always an indivisible unit of smallest currency. And as such, money is a discrete quantity.
What’s the difference between continuous and discrete?
Discrete data is information that can only take certain values. … Continuous data is data that can take any value. Height, weight, temperature and length are all examples of continuous data.
How do you know if a variable is continuous?
If you start counting now and never, ever, ever finish (i.e. the numbers go on and on until infinity), you have what’s called a continuous variable. If your variable is “Number of Planets around a star,” then you can count all of the numbers out (there can’t be an infinite number of planets).
Is hours of sleep discrete or continuous?
Amount of sleep is a variable. 3, 5, 9 hours of sleep are different values for that variable. Variables can be continuous or discrete. Question: Are these variables discrete or continuous?…Frequency distribution table:Score (X)Frequency (f)(Hours)(Number of people with this score)3142561 more row
What is discrete series example?
ADVERTISEMENTS: Discrete series means where frequencies of a variable are given but the variable is without class intervals. Here the mean can be found by Three Methods. … Here each frequency is multiplied by the variable, taking the total and dividing total by total number of frequencies, we get X.
Is age a discrete or continuous?
We could be infinitly accurate and use an infinite number of decimal places, therefore making age continuous. However, in everyday appliances, all values under 6 years and above 5 years are called 5 years old. So we use age usually as a discrete variable.
Is gender a discrete or continuous variable?
Variable Reference Table : Few ExamplesVariableVariable TypeVariable ScaleGenderDiscreteCategoricalGender as Binary 1/0 CodingDiscreteCategoricalTrue/FalseDiscreteCategoricalPhone NumberDiscreteNominal15 more rows•Oct 7, 2016
Is blood pressure discrete or continuous?
Is blood pressure an example of continuous or discrete data? Blood pressure is an example of continuous data. Blood pressure can be measured to as many decimals as the measuring instrument allows.
Is family size discrete or continuous?
when family size is measured as a continuous variable. Household size and number of computers are discrete variables. The range is an important descriptive statistic for a continuous variable, but it is based only on two values in the data set.
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https://nrich.maths.org/public/topic.php?code=-99&cl=3&cldcmpid=1186
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math
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Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Four small numbers give the clue to the contents of the four surrounding cells.
Find out about Magic Squares in this article written for students. Why are they magic?!
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
A pair of Sudoku puzzles that together lead to a complete solution.
Use the differences to find the solution to this Sudoku.
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
This Sudoku combines all four arithmetic operations.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
An introduction to bond angle geometry.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
Solve the equations to identify the clue numbers in this Sudoku problem.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Two sudokus in one. Challenge yourself to make the necessary connections.
This Sudoku requires you to do some working backwards before working forwards.
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
A Sudoku with clues as ratios.
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https://www.proofwiki.org/wiki/Definition:Mathematics/Historical_Note
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Jump to navigation Jump to search
Historical Note on Mathematics
The intellectual discipline of mathematics goes back at least $5000$ years.
Unlike most subjects, the truths discovered way back then are still valid, relevant and applicable now.
- 2004: Ian Stewart: Galois Theory (3rd ed.) ... (next): Historical Introduction
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https://brainsanswer.com/question/404849
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math
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Standard form is written this way:
However, in this case, we just have to simplify 8x-3y=6-4x, as it is already mostly in standard form.
So, to do this, we have to combine like terms.
The only like terms that can be combined are -4x and 8x.
So, we add 4x to both sides, and we get: .
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https://sanet.st/blogs/mecury-books/delay_ordinary_and_partial_differential_equations.4549695.html
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math
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English | 2023 | ISBN: 0367486911 | 434 pages | True PDF | 5.14 MB
Delay Ordinary and Partial Differential Equations is devoted to linear and nonlinear ordinary and partial differential equations with constant and variable delay. It considers qualitative features of delay differential equations and formulates typical problem statements. Exact, approximate analytical and numerical methods for solving such equations are described, including the method of steps, methods of integral transformations, method of regular expansion in a small parameter, method of matched asymptotic expansions, iteration-type methods, Adomian decomposition method, collocation method, Galerkin-type projection methods, Euler and Runge-Kutta methods, shooting method, method of lines, finite-difference methods for PDEs, methods of generalized and functional separation of variables, method of functional constraints, method of generating equations, and more. The presentation of the theoretical material is accompanied by examples of the practical application of methods to obtain the desired solutions. Exact solutions are constructed for many nonlinear delay reaction-diffusion and wave-type PDEs that depend on one or more arbitrary functions. A review is given of the most common mathematical models with delay used in population theory, biology, medicine, economics, and other applications. The book contains much new material previously unpublished in monographs. It is intended for a broad audience of scientists, university professors, and graduate and postgraduate students specializing in applied and computational mathematics, mathematical physics, mechanics, control theory, biology, medicine, chemical technology, ecology, economics, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on applied mathematics, mathematical physics, and differential equations for delivering special courses and for practical training.
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http://doverpublications.stores.yahoo.net/0486602699.html
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math
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This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric tr... read more
Quantum Mechanics for Applied Physics and Engineering by Albert T. Fromhold, Jr. For upper-level undergraduates and graduate students: an introduction to the fundamentals of quantum mechanics, emphasizing aspects essential to an understanding of solid-state theory. Numerous problems (and selected answers), projects, exercises.
Quantum Mechanics in Simple Matrix Form by Thomas F. Jordan With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Includes more than 100 problems and 38 figures. 1986 edition.
Group Theory: The Application to Quantum Mechanics by Paul H. E. Meijer, Edmond Bauer Upper-level undergraduate and graduate students receive an introduction to problem-solving by means of eigenfunction transformation properties with this text, which focuses on eigenvalue problems in which differential equations or boundaries are unaffected by certain rotations or translations. 1965 edition.
Relativistic Quantum Fields by Charles Nash This graduate-level text contains techniques for performing calculations in quantum field theory. It focuses chiefly on the dimensional method and the renormalization group methods. Additional topics include functional integration and differentiation. 1978 edition.
Philosophic Foundations of Quantum Mechanics by Hans Reichenbach Noted philosopher offers a philosophical interpretation of quantum physics that reviews the basics of quantum mechanics and outlines their mathematical methods, blending philosophical ideas and mathematical formulations to develop a variety of concrete interpretations. 1944 edition.
The Quantum Theory of Radiation: Third Edition by W. Heitler The first comprehensive treatment of quantum physics in any language, this classic introduction to basic theory remains highly recommended and widely used, both as a text and as a reference. 1954 edition.
Problems in Quantum Mechanics by I. I. Gol’dman, V. D. Krivchenkov A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. An ideal adjunct to any textbook in quantum mechanics.
Group Theory by W. R. Scott Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Quantum Mechanics and Path Integrals: Emended Edition by Richard P. Feynman, Albert R. Hibbs, Daniel F. Styer The Nobel Prize–winning physicist presents unique insights into his theory and its applications. Feynman starts with fundamentals and advances to the perturbation method, quantum electrodynamics, and statistical mechanics. 1965 edition, emended in 2005.
Abstract and Concrete Categories: The Joy of Cats by Jiri Adamek, Horst Herrlich, George E Strecker This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.
The Concept of a Riemann Surface by Hermann Weyl, Gerald R. MacLane This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
Applications of Group Theory in Quantum Mechanics by M. I. Petrashen, J. L. Trifonov This advanced text explores the theory of groups and their matrix representations. The main focus rests upon point and space groups, with applications to electronic and vibrational states. 1969 edition.
Quantum Mechanics of One- and Two-Electron Atoms by Hans A. Bethe, Edwin E. Salpeter This classic of modern physics includes a vast array of approximation methods, mathematical tricks, and physical pictures useful in the application of quantum mechanics to other fields. 1977 edition.
Group Theory and Quantum Mechanics by Michael Tinkham Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.
This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.
In the Author's Own Words: "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."
"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl
Critical Acclaim for Space, Time, Matter: "A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science
This book was printed in the United States of America.
Dover books are made to last a lifetime. Our US book-manufacturing partners produce the highest quality books in the world and they create jobs for our fellow citizens. Manufacturing in the United States also ensures that our books are printed in an environmentally friendly fashion, on paper sourced from responsibly managed forests.
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https://www.uu.se/en/admissions/freestanding-courses/course-syllabus/?kpid=38944&list=26873&kKod=1MA024&lasar=
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math
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Main field(s) of study and in-depth level:
Explanation of codes
The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:
G1N: has only upper-secondary level entry requirements
G1F: has less than 60 credits in first-cycle course/s as entry requirements
G1E: contains specially designed degree project for Higher Education Diploma
G2F: has at least 60 credits in first-cycle course/s as entry requirements
G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
GXX: in-depth level of the course cannot be classified.
A1N: has only first-cycle course/s as entry requirements
A1F: has second-cycle course/s as entry requirements
A1E: contains degree project for Master of Arts/Master of Science (60 credits)
A2E: contains degree project for Master of Arts/Master of Science (120 credits)
AXX: in-depth level of the course cannot be classified.
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
The Faculty Board of Science and Technology
Single Variable Calculus. Linear Algebra and Geometry I or Algebra and Geometry.
On completion of the course the student shall be able to:
be able to give an account of and use basic vector space concepts such as linear space, linear dependence, basis, dimension, linear transformation;
be able to give an account of and use basic concepts in the theory of finite dimensional Euclidean spaces;
be familiar with the concepts of eigenvalue, eigenspace and eigenvector and know how to compute these objects;
know the spectral theorem for symmetric operators and know how to diagonalise quadratic forms in ON-bases;
know how to solve a system of linear differential equations with constant coefficients;
be able to formulate important results and theorems covered by the course;
be able to use the theory, methods and techniques of the course to solve mathematical problems;
Linear spaces: subspaces, linear span, linear dependence, basis, dimension, change of bases. Matrices: rank, column space and row space. Linear transformations: their matrix and its dependence on the bases, composition and inverse, range and nullspace, the dimension theorem. Euclidean spaces: inner product, the Cauchy-Schwarz inequality, orthogonality, ON-basis, orthogonalisation, orthogonal projection, isometry. Quadratic forms: diagonalisation. Spectral theory: eigenvalues, eigenvectors, eigenspaces, characteristic polynomial, diagonalisability, the spectral theorem, second degree surfaces. Systems of linear ordinary differential equations.
Lectures and problem solving sessions. Test or written assignment.
Written examination at the end of the course.
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.
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| 3,116 | 29 |
https://deluxeknowledgeexchange.com/online-688
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math
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Online maths questions
Here, we debate how Online maths questions can help students learn Algebra. We can solving math problem.
The Best Online maths questions
Online maths questions can be found online or in math books. There’s an app for that. No, really. Photomath is an app that can solve math problems just by taking a photo of them. It’s available for free on iOS and Android, and it’s pretty darn accurate.
By inputting the letters that you have into the cheat, you can quickly find words that fit the puzzle. This can be a great way to save time and frustration when you are trying to complete a difficult word search.
There are a variety of ways to solve a system of three equations with three unknowns. One method is to use a 3x3 system of equations solver. This type of solver will typically ask for the values of the variables in the equations, and then use algebraic methods to solve for the unknowns. Some 3x3 system of equations solvers will also provide step-by-step solutions, so that you can see how the equations were solved.
There are a few things you can do to make solving math word problems easier. First, read the problem carefully and make sure you understand what it is asking. Once you know what the problem is asking, try to identify any key information or relevant equations that you will need to solve it. Once you have all of the necessary information, you can begin solving the problem. If you get stuck, don't be afraid to ask for help from a friend or a teacher.
Some common examples include questions about finding a particular numerical answer, identifying a specific mathematical pattern, or determining the best way to solve a given problem. No matter what the specific question is, there are a few key steps that can be followed in order to solve it. First, it is important to read the question carefully and identify any key information that is necessary for solving the problem. Next, it is helpful to devise
Triple integrals are often used in physics and engineering to solve problems involving three-dimensional objects or systems. The triple integral solver can be used to calculate the volume of a three-dimensional object, the moment of inertia of a three-dimensional object, or the center of mass of a three-dimensional object.
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https://scholarshare.temple.edu/handle/20.500.12613/6021
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math
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Interior gradient estimates for solutions to the linearized Monge-Ampère equation
Permanent link to this recordhttp://hdl.handle.net/20.500.12613/6021
MetadataShow full item record
AbstractLet φ be a convex function on a convex domain Sigma;CRn, n≥1. The corresponding linearized Monge-Ampère equation is. trace(φD2u)=f, where φ:=detD2φ(D2φ)-1 is the matrix of cofactors of D2φ. We establish interior Hölder estimates for derivatives of solutions to such equation when the function f on the right-hand side belongs to Lp(Ω) for some p>n. The function φ is assumed to be such that φbSigma;C(Ω) with φ=0 on ∂. Ω and the Monge-Ampère measure detD2φ is given by a density gSigma;C(Sigma;) which is bounded away from zero and infinity. © 2011 Elsevier Inc.
Citation to related workElsevier BV
Has partAdvances in Mathematics
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http://vcq.quantum.at/news/events/detail/95.html
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math
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Classical and quantum theory of electromagnetism made simple: The Riemann-Silberstein vector
Friday, 24 Jan. 2014, 10:00 - 12:00
Presenter: Iwo Bialynicki-Birula
Host: Anton Zeilinger
Where: Ernst Mach Hörsaal
In my lectures I will describe the salient properties of the classical and quantum electromagnetic field with the use of the complex combination of the electric and magnetic field: the Riemann-Silberstein vector. This formulation simplifies significantly various calculations and it also clarifies several fundamental issues. The lectures, in principle, will cover the material contained in our review paper [Journal of Physics A 46, 053001 (2013)]. However, the exposition will be far more pedagogical and some newer results will be included.
In the first part devoted to the classical theory I will concentrate on the those aspects that are usually not treated in the standard exposition (Whittaker construction of solutions of Maxwell equations, propagation of electromagnetic waves in the presence of the gravitational field, knotted light fields).
In the second part devoted to the quantum theory I will start from the nonstandard approach to quantization and then continue with the photon wave function and the uncertainty relations for photons.
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https://dearteassociazione.org/how-do-you-measure-the-temperature-of-the-sun/
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math
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$sigma=5.67*10^-8fracWm^2K^4$ (Stefan-Boltzmann constant)
$S = 1367fracWm^2$ (solar constant)
$D = 1.496*10^11 m$ (Earth-Sun median distance)
$R = 6.963*10^8 m$ (radius the the Sun)
$T = (fracPsigma A)^frac14 = (fracS4 pi D^2sigma 4pi R^2)^frac14=(fracSD^2sigma R^2)^frac14 = 5775.8 K$
(Wikipedia provides 5777K because the radius to be rounded come $6.96*10^8m$)
This calculate is perfectly clear.
You are watching: How do you measure the temperature of the sun
But in Gerthsen Kneser Vogel there is an exercise wherein Sherlock Holmes estimated the temperature of the sun only knowing the root of the portion of D and also R. Allows say, he estimated this portion to 225, so the square source is about 15, exactly how does he involved 6000 K ? The value $(fracSsigma)^frac14$ has around the worth 400. It cannot be the approximate mean temperature on earth, i m sorry is about 300K. What perform I miss ?
astrodearteassociazione.org temperature blackbody order-of-magnitude estimate
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edited Nov 14 "14 in ~ 14:10
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The partnership of temperature in between a planet and also a star based on a radiative power balance is provided by the adhering to equation (from Wikipedia):
$T_p = temperature of the planet$ $T_s = temperature of the star$ $R_s = radius of the star$ $alpha = albedo of the planet$ $epsilon = average emissivity of the planet$ $D = distance between star and planet$
Therefore if Sherlock to know $sqrtfracR_sD = 0.06818$ and can estimate the Earth"s temperature $T_p$ as well as $alpha$ and also $epsilon$ climate he have the right to calculate the temperature top top the surface of the sun which is the unknown variable $T_s$.
Both $alpha$ and $epsilon$ have true values between zero and one. Speak Sherlock assumed $alpha = 0.5$ and $epsilon = 1$ (perfect blackbody). Estimating the temperature of the planet $T_p$ to it is in 270 K and also plugging in every the numbers us have:
Which is really near the true typical temperature that the surface ar of the sun, 5870 K. Case closed!
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edited Jul 14 "15 at 14:15
answered Nov 14 "14 at 6:10
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A stormy estimate of a body"s temperature in the solar mechanism is $$T=frac280KsqrtD_AU$$if us calculate the AU fraction from the Sun"s "edge" come its center, R end D = $4.65x10^-3$, and also substitute this right into the formula, the Sun"s temperature would be around 4100K.Not an extremely close to her 5776 K, however utilizes the square source of the R D fraction.
The formula reflects efficient temperatures. Yet peak, so called sub-solar temperatures, room $sqrt2$ times effective temperatures, which would certainly yield about 5800K.Clever Sherlock!
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edited might 30 "14 in ~ 10:32
answered may 29 "14 in ~ 23:39
Michael LuciukMichael Luciuk
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