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# What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament," and foun...
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GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 18 Dec 2018, 17:28 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customize...
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IEE Proceedings H - Microwaves, Antennas and Propagation Filter Results Displaying Results 1 - 14 of 14 • Rigorous field theory analysis of quasiplanar waveguides Publication Year: 1985, Page(s):1 - 6 Cited by:  Papers (11) | | PDF (525 KB) An accurate field theory solution for calculating the hybrid eigenmodes of ...
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# Thread: Functions of several variables 1. ## Functions of several variables How do you go about solving this? Find the dimension of the rectangular box of least surface area that has a volume of 1000 cubic inches. 2. Well i'm not sure if we have enough information to completely solve this. But here's a start. Le...
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You are given a 0-indexed binary string s and two integers minJump and maxJump. In the beginning, you are standing at index 0, which is equal to '0'. You can move from index i to index j if the following conditions are fulfilled: • i + minJump <= j <= min(i + maxJump, s.length - 1), and • s[j] == '0'. Return true if ...
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# Difference between revisions of "stat841f14" ## Principal components analysis (Lecture 1: Sept. 10, 2014) ### Introduction Principal Component Analysis (PCA), first invented by Karl Pearson in 1901, is a statistical technique for data analysis. Its main purpose is to reduce the dimensionality of the data. Suppose...
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#### Similar Solved Questions ##### One kg. mole of liquid water at 25C is injected into an evacuated copper chamber immersedin a thermostat at 25 C and vaporised completely to steam at 15.84 torr pressure.Equilibrium vapour pressure of water is 23.76 torr at 25 C. Calculate the Gibbs free energychange for this proces...
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# IEEE Transactions on Antennas and Propagation ## Filter Results Displaying Results 1 - 25 of 65 Publication Year: 2012, Page(s):C1 - 3550 | PDF (50 KB) • ### IEEE Transactions on Antennas and Propagation publication information Publication Year: 2012, Page(s): C2 | PDF (40 KB) • ### Minimum $Q$ Electrically Small...
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Referencing is a key element of your assessed work at university.  It involves acknowledging your sources of information/ideas/theories. Absent or inadequate referencing shows a lack of academic integrity. This book will explain: 1.Why referencing is important 2. What referencing involves • How to reference in your...
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## IBPS Quant Test 21 Instructions In these questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate option. a: If x > y b: If x < y c: If x ≥ y d: If x ≤ y e: If x = y or the relationship cannot be established Question 1 I. $$x^{2} - 11x + 30 = 0$$ II. $$2...
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program to detect h00ks/detours/hijacked functions Recommended Posts nuclear123    119 im curious as to how this can be done? say i wanted to make a program that will then scan for hooks made by a program! any advice/knowledge would be greatfull on where to start or how i could perform such a task! hook/detour/hijac...
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## Convergence and Asymptotic Results September 24, 2015 By $\overline{X}_n\ \xrightarrow{\text{a.s.}}\ \mathbb{E}(X)$ Last week, in our mathematical statistics course, we’ve seen the law of large numbers (that was proven in the probability course), claiming that given a collection  of i.i.d. random variables, with T...
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# Why are physicists interested in graph theory? Can you tell me how graph theory comes into physics, and the concept of small world graphs? (inspired to ask from comment from sean tilson in): which areas in physics overlap with those of social network theory for the analysis of the graphs? Best, - Both answers ha...
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1. ## Vector vector u= 2i - 5j w= -i -6j find the magnitude of w-u 2. Originally Posted by SHORTY vector u= 2i - 5j w= -i -6j find the magnitude of w-u Originally Posted by scrappy if the magnitude of the vector v= 1/2 and a= 113 degrees write the vector v in terms of i and j u= 2i -5j w= -i -6j Are you guys in the ...
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# SIR Model for COVID-19: Estimating $R_0$ Roberto Berwa, MIT [berwa.mit.edu] At the beginning of pandemic with a limited amount of data and knowledge of the transmission mechanisms behind COVID-19, various models from the scientific community, mathematicians, and epidemiologists, were useful in gauging a general vie...
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# Chern insulator vs topological insulator What is the basic distinction between a Chern Insulator and a Topological Insulator? Right now I know that a Chern Insulator has "topologically non-trivial band structure" and that a Topological Insulator has "symmetry protected surface states". • Chern insulators must break...
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Existance of certain almost invariant functions related to amenability and piece-wise transformations - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T20:06:59Z http://mathoverflow.net/feeds/question/98935 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/98935...
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IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q8 Calculus Level 3 Let $$f$$ be a twice differentiable function and $$g, h$$ be some functions, such that $$f''(x)=-f(x), f'(x)=g(x), h(x)=[f(x)]^2+[g(x)]^2, h(5)=11$$. Then which of the following is/are not incorrect? • (A) h(10)=11 • (B) h'(10)=0 • (C) ...
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# How can I type formula cosine of two vectors nice? I want to find cosine of two vectors, I define the command \cross for cross product of two vectors. I tried \documentclass[12pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{fourier} \usepackage{esvect} \usepackage[left=2cm,right=2c...
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# Linear Transformations with given basis Currently im on Lineal Algebra class, seing linear transformations with matrices. My question is what are the steps to resolve this question? $$\text{Let }T: \mathbb{R}^3 \longrightarrow \mathbb{R}^3 \text{ a lineal transformation. Consider the following basis of }\mathbb{R}^...
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# PoS(ICRC2017)025 Tracking cosmic-ray spectral variations with neutron monitor time-delay measurements at high cutoff rigidity during 2007-2017 C. Banglieng, D. Ruffolo, A. Sáiz, P. Evenson, T. Nutaro Contribution: pdf Abstract We present measurements of the leader fraction of neutron monitor counts that did not ...
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# Kooperativer Bibliotheksverbund ## Berlin Brandenburg and and An error occurred while sending the email. Please try again. Proceed reservation? Export • 1 Article In: Nature, Volume 468, Issue 7325, pp. 796-798 (2010) Description: Observations of the 21-centimetre line of atomic hydrogen in the early Universe di...
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# Saving from R Studio Does anyone have sample VBA (Excel) code for Accessing the AS400 in Windows 10 Hello One of our (non-IT) staff is using R to "... create an HTML or Notebook using RStudio...". The error is: R "C:/Users/CRISTEL/AppData/Local/Pandoc/pandoc" +RTS -K512m -RTS test.utf8.md --to html4 --from markd...
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Letter # Attosecond optical-field-enhanced carrier injection into the GaAs conduction band Accepted: Published online: ## Abstract Resolving the fundamental carrier dynamics induced in solids by strong electric fields is essential for future applications, ranging from nanoscale transistors1,2 to high-speed electro-...
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# How to get rid of the error message when evaluating a highly oscillatory numerical integral? I have a simple numerical integral with a highly oscillatory integrand: In[256]:= Integrate[Exp[-x^2] Cos[100 x], {x, -10, 10}] // N Out[256]= 5.11136*10^-46 + 0. I Using numerical integration, I used the method "LevinRul...
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# Asymptotic formula of $\sum_{n \le x} \frac{d(n)}{n^a}$ As the title says, I'm trying to prove $$\sum_{n \le x} \frac{d(n)}{n^a}= \frac{x^{1-a} \log x}{1-a} + \zeta(a)^2+O(x^{1-a}),$$ for $x \ge 2$ and $a>0,a \ne 1$, where $d(n)$ is the number of divisors of $n$. There is a post here dealing with the case $a=1$. Thi...
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# How do you solve 2x^2 - 32 = 0? Apr 17, 2016 $x = 4 , - 4$ #### Explanation: You can factor out a 2 as the GCF. $2 \left({x}^{2} - 16\right) = 0$ ${x}^{2} - 16$ is the difference of perfect squares, which are $\left(x - 4\right) \left(x + 4\right)$ Therefore, you now have $2 \left(x - 4\right) \left(x + 4\righ...
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# Paint Work CalculatorIS 15489 ## Paint Work Calculation Sq. ft. ft ft Nos ft ft Nos #### Total Paint Area 312.15 m2 | 3360.00 ft2 Sr. Material Quantity 1 Paint 33.60 liters 2 Primer 33.60 liters 3 Putty 84.00 kgs ## Paint-Work Calculation #### Paint Area Note: Approx Paint Area Including Wall And Ceiling ###...
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# Expectation values, induction and conditioning Suppose I have a series $X_t$ of random variables, $t \in \mathbb{N}_0$. I am not sure if the following reasoning is sound: Let $f(x)$ be a function of the random variables. Let $E[f(X_t)]$ denote the expectation value of $f$ for variable $t$, and let $E[f(X_t) | X_{t...
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# Issues in Empirical Finance Research 2020-10-27 ## The challenge • I will discuss some issues in using plain OLS models in Corporate Finance & Governance Research • I will avoid the word “endogeneity” as much as I can • I will also avoid the word “identification” because identification does not guarantee causality...
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Algebraic Complete Integrability of the Bloch-Iserles System The goal of this paper is the proof of the algebraic complete integrability of the Bloch-Iserles Hamiltonian system [5]. This result was conjectured in [4], based on its validity in certain special cases. Published in: International Mathematics Research Not...
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# What is mathematical basis for the percent symbol (%)? Percent means 1 part of 100 or 1/100 and is indicated with %. Per mille means 1 part of 1000 or 1/1000 and is indicated with ‰, so it seems that these symbols indicate the mathematical operations that they perform (i.e., the divisor in per mille is 10X greater. ...
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# Z bosons from radioactive elements? 1. Jun 15, 2010 ### Yevgenia So I heard a little rumor that Beta decays in certain isotopes release an electron at "ultrarelativistic" speeds. I also heard a rumor that Z bosons can be created temporarily by a positron annihilating an electron when the two collide. My question ...
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Advanced Search Article Contents Article Contents Characterizing ethnic interactions from human communication patterns in Ivory Coast • Towards the consolidation of peace and national development, Ivory Coast must overcome the lack of cohesion, responsible for the emergence of two civil wars in the last years. As in ...
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# Inverse Problems and Data Assimilation Wiki and International Community ### Site Tools global_atmospheric_state_determination_every_three_hours # Inverse Blog: Global Atmospheric State Determination Every Three Hours! Example Infrared radiation, image by German Meteorological Service (DWD) Tue, July 29, 2014. L...
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# 1 X 5 X 2 4 X 2 1 X 5 X 2 4 X 2 ## Limit Calculator with steps Limit calculator helps you find the limit of a function with respect to a variable. It is an online tool that assists you in calculating the value of a function when an input approaches some specific value. Limit calculator with steps shows the step-b...
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# Analysis of Variance and the Completely Randomized Design In this section we show how analysis of variance can be used to test for the equality of k population means for a completely randomized design. The general form of the hypotheses tested is We assume that a simple random sample of size Hj has been selected fr...
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# Properties Label 2.3.ae_k Base field $\F_{3}$ Dimension $2$ $p$-rank $2$ Ordinary yes Supersingular no Simple no Geometrically simple no Primitive yes Principally polarizable yes Contains a Jacobian yes # Related objects ## Invariants Base field: $\F_{3}$ Dimension: $2$ L-polynomial: $( 1 - 2 x + 3 x^{2} )^{2}$...
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# Simple Harmonic Motion and time period 1. Sep 5, 2005 ### dpsguy A particle follows SHM with its eqn.of motion being s(x,y)=Asinwt i + 3Asin3wt j What is its time period? Also find the expression for total mechanical energy wrt time. I tried it in the following way V=Awcoswt i + 3Awcos3wt j = Aw[(coswt)^2 +9(co...
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# On best proximity points for pseudocontractions in the intermediate sense for non-cyclic and cyclic self-mappings in metric spaces Manuel De la Sen Author Affiliations Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644, Bilbao, 48080, Spain...
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# Do one-relator groups satisfy Haagerup property? The question is in the title: Do one-relator groups satisfy Haagerup property? I think the answer is known at least in some specific cases, but is the problem completely solved? • Most 1-relator groups are known to be free-by-(virtually solvable) (which implies Haa...
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:: Bounding boxes for compact sets in ${\calE}^2$ :: by Czes{\l}aw Byli\'nski and Piotr Rudnicki :: :: Copyright (c) 1997-2018 Association of Mizar Users Lm1: for X being Subset of REAL st X is bounded_below holds -- X is bounded_above proof end; Lm2: for X being non empty set for f being Function of X,REAL st f is ...
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## Indicators • Similars in SciELO ## On-line version ISSN 1807-0302 ### Comput. Appl. Math. vol.30 no.3 São Carlos  2011 #### http://dx.doi.org/10.1590/S1807-03022011000300010 Operational Tau approximation for a general class of fractional integro-differential equations S. Karimi Vanani; A. Aminataei Department...
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# Changes ## Papacy , 3 years ago Papal influence The yearly change of papal influence is affected by the opinion of the Papal state towards a country, namely by 0.5% times this opinion. ::$\text{yearly papal influence}<h1>test</h1> = \left(1 + \frac\text{opinion of the Papal state}{200}\right)\sum \text{modifiers}$ ...
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# Sum of Cauchy sequences [duplicate] Possible Duplicate: Sum of Cauchy Sequences Cauchy? Let $(X,||\cdot||)$ be a normed space. Show that if $(x_{n})_{n}$ and $(y_{n})_{n}$ are Cauchy sequences in $X$, then the sequence $(x_{n}+y_{n})_{n}$ is also Cauchy in $X$. I have used the definitions: If $(x_{n})_{n}$ is Cau...
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Pauls Online Notes Home / Calculus II / Applications of Integrals / Surface Area Show Mobile Notice Show All Notes Hide All Notes Mobile Notice You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in lands...
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h h A malleable material can be pounded into a very thin sheet. g Polymers are usually ductile; however there are brittle polymers available. Malleable metals, like copper and nickel, are able to be stretched out into thin wires. DBTT can also be influenced by external factors such as neutron radiation, which leads to ...
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FEATool Multiphysics  v1.15.5 Finite Element Analysis Toolbox Vibration Modes of a Hollow Cylinder This model studies the vibration modes of a free and hollow cylinder using an axisymmetric approximation. No loads or constrains are applied as the free modes are sought. The cylinder is 10 m long, has a center diameter ...
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# Explain in detail Carnot engine 30 views in Science edited Explain in detail Carnot engine by (26.5k points) A carnot engine is a reversible heat engine operating between two temperatures, The steps involved in a carnot cycle are explained as follows. Step 1 : Isothermal expansion of gas from state (P1, V1, T1)...
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# Math Help - Problem with vectors 1. ## Problem with vectors Question Forces of magnitude 3 Newtons, 5 Newtons and 7 Newtons act along the vectors (-3,-2,-9) (8,5,-9) (4,-1,-9) Find the x component. I have the answer at 4.968 however i can not arrive at it, attached is my working out. d has been used instead of c...
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# Given a steady state vector is it possible to calculate the corresponding transition (probability) matrix Knowing that there is a probability matrix M (where all columns add to 1) which when applied to a given vector P produces the same vector P, what is the best solution to find M? I can get my head around it for a...
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# projection matrix least squares A linear model is defined as an equation that is linear in the coefficients. OLS in Matrix Form 1 The True Model † Let X be an n £ k matrix where we have observations on k independent variables for n observations. 1 1 0 1 A = 1 2 projs b = - Get more help from … The Linear Algebra Vie...
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132k views Where can I find examples of good Mathematica programming practice? I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ... 3k views Injecting a sequence of ...
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# Verify a credit card with Luhn This is my solution for the Credit problem on CS50's (Introduction to CS course) Pset1. It involves using Luhn's Algorithm to test the validity of the Credit Card Number entered and based on a few conditions attempts to identify the Credit Card Company. check_length attempts to find t...
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# Atomic hydrogen is excited to the nth energy level. The maximum number of spectral lines which it can emit while returning to the ground state, is : $\frac{1}{2}n\left(n-1\right)$ $\frac{1}{2}n\left(n+1\right)$ Please do not use chat terms. Example: avoid using "grt" instead of "great".
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regular expressions -- syntax for regular expressions A regular expression is a string that specifies a pattern that describes a set of matching subject strings. Typically the string is compiled into a deterministic finite automaton whose execution, guided by the subject string, determines whether there is a match. C...
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# Strictly Positive Rational Numbers are Closed under Multiplication ## Theorem $\forall a, b \in \Q_{>0}: a b \in \Q_{>0}$ ## Proof Let $a$ and $b$ be expressed in canonical form: $a = \dfrac {p_1} {q_1}, b = \dfrac {p_2} {q_2}$ where $p_1, p_2 \in \Z$ and $q_1, q_2 \in \Z_{>0}$. As $\forall a, b \in \Q_{>0}$ i...
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We derive the derivatives of inverse exponential functions using implicit differentiation. Geometrically, there is a close relationship between the plots of $$ and $$, they are reflections of each other over the line $$: One may suspect that we can use the fact that $$, to deduce the derivative of $$. We will use imp...
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Randomforest code taking longer time every iteration I have a prediction code that runs RandomForestRegressor and RandomForestClassifier. I call the functions 9 times each respectively and it is optimised by GridSearchCV. The first time it ran, it took around 2 Hrs, 20 mins to run and almost after every run cycle, t...
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# Do I have to transform all Observables (all Operators) simultaneously? Let's say I have a quantum system with 2 observables $\hat{O}_1$ and $\hat{O}_2$. Those are supposed to be "functions"of $\hat{X}$ and $\hat{P}$. Let's say I want to Transform $\hat{O}_1$ using an unitary transformation: $$\hat{O}_1' = \hat{U}^{-...
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## IB Individuals & Societies MYP G8 Welcome to IB Individuals & Societies MYP: Integrated Humanities Introduction: In this course you will be introduced to the Humanities through a survey of human social and cultural life in a global setting. By investigating the social, artistic, religious, and economic development...
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# zbMATH — the first resource for mathematics Anticipative diffusion and related change of measures. (English) Zbl 0804.60072 The authors consider anticipating drifts of the form $$G(t)= \int_ 0^ t g(s,w) ds$$, $$t\in [0,1]$$, in the standard Wiener space $$\Omega$$. If $$g$$ is square integrable, under some assumptio...
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# Code review of code to strip 0 from decimal series The following code would strip 0 (all numbers ending with 0, it can contain 0, eg: 105 can be is valid but 150 should be eliminated) and return a number in decimal series if all numbers ending with 0 were stripped. Example : 0 -> 1, 10 -> 11, 19 -> 22. I would just ...
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## Cryptology ePrint Archive: Report 2008/049 An Efficient Protocol for Secure Two-Party Computation in the Presence of Malicious Adversaries Yehuda Lindell and Benny Pinkas Abstract: We show an efficient secure two-party protocol, based on Yao's construction, which provides security against malicious adversaries. Y...
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Matrix is the most powerful tool in mathematics. We use matrices in certain branches of science as far as in economics, computer, psychology and management. A matrix is an arrangement of numbers or symbols in rectangle array. The items in a matrix are called elements of matrix. Given below is an example of a matrix wi...
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Generalized Multi-Output Gaussian Process Censored Regression @article{Gammelli2022GeneralizedMG, title={Generalized Multi-Output Gaussian Process Censored Regression}, author={Daniele Gammelli and Kasper Pryds Rolsted and Dario Pacino and Filipe Rodrigues}, journal={Pattern Recognit.}, year={2022}, volume={129}, page...
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Two closed geodesics on compact simply connected bumpy Finsler manifolds.(English)Zbl 1357.53086 Author’s abstract: We prove the existence of at least two distinct closed geodesics on a compact simply connected manifold $$M$$ with a bumpy and irreversible Finsler metric, when $$H^{\ast }(M;\mathbf Q)\cong T_{d,h+1}(x)...
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## Sunday, July 17, 2011 ### Quicksort partitioning During my years in school and at university I was always exposed to only one algorithm of quicksort partitioning. Let's take a look at some ways to partition a list for sorting. Quicksort itself works by taking a list, picking an element from the list which is refe...
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## Binary Search - Problem: Glyph Recognition In this task you will have to solve problem G from NWERC 2017. Read the problem statement below. Since the goal of this task is not to teach you geometry, you can use the following class that represents a regular polygon with $$n$$ vertices and radius $$r$$. static doubl...
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# Math Help - Proving Horrible exponent 1. ## Proving Horrible exponent Hi All, Prove $\frac{a}{ (\sqrt[3]{ax}}^2 = \frac{\sqrt[3]{ax}{x}$ $\frac{a}{ (ax)^{1/3} )^2 = \frac{a}{(ax)^{2/3} }$ $\frac{a}{ (ax)^{1/3} \times (ax)^{1/3}}$ Had Latex trouble (again); question is in attachment below. Thanks 2. ## Re: Pro...
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# recursion – How to perform AND on binary “recursive repeating sequences”? Suppose, we have a two binary sequences, encoded as “recursive repeating sequences” (I don’t know exactly how to name them). Each sequence can contain other sequences and has number related to how many times this sequence is repeated, or can c...
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Question # Select the incorrect statement/ statements regarding the exchange rate management by the International Monetary Fund (IMF) using the code given below:1. Exchange rate of the member countries was managed by the IMF as per the 'fixed currency system' till $$1976$$. which did not allow the market forces.2. 'Fl...
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# The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume charge density  where A is a constant and r is the distance from the centre.  At the centre of the spheres is a point charge Q.  The value of A such that the electric field in the region between the spheres will be c...
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# Math Help - need help with this staticstics question (point me in right dirrection please) 1. ## need help with this staticstics question (point me in right dirrection please) Hello, sort of left an assignment to the last minute and am in desperate need of help The results are in for the paper toss game and we have...
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# Community cancel Showing results for Show  only  | Search instead for Did you mean: # Rich Content Editor HTML Cheatsheet Community Champion 87 26 74.2K Update 1/1/2020. The new rich content editor is available in beta and will be available in production in the January 2020 release. See my new post about the new ...
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## Parallel Axis Theorem If the inertia tensor for a set of axes with the center of mass at the origin is calculated, the tensor for any set of parallel axes can be easily derived. The translation of the coordinates is given by where is a constant vector. We now simply compute the inertia tensor for the new set of ax...
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# Fight Finance #### CoursesTagsRandomAllRecentScores Scores keithphw $6,011.61 Jade$1,815.80 Chu $789.98 royal ne...$750.00 Leehy $713.33 Visitor$650.00 ZOE HY $640.00 JennyLI$625.61 Visitor $590.00 Visitor$555.33 Visitor $550.00 Visitor$550.00 Visitor $540.00 Visitor$500.00 Yizhou $489.18 Visitor$480.00 Visitor $4...
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## The curvature of contact structure on 3-manifolds ##### Authors We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact structure on...
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Chapter 12.I, Problem 10RE ### Contemporary Mathematics for Busin... 8th Edition Robert Brechner + 1 other ISBN: 9781305585447 Chapter Section ### Contemporary Mathematics for Busin... 8th Edition Robert Brechner + 1 other ISBN: 9781305585447 Textbook Problem # Use Table 12-1 to calculate the future value of the ...
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# Homework Help: Understanding a problem that uses episolon delta defintion 1. Apr 10, 2014 ### Genericcoder let E = episolon and D = delta; the problem is as follows: let f(x) = (2x^2 - 3x + 3). prove that lim as x approaches 3 f(x) = 21, we write |f(x) - 21| = |x^2 + 2x - 15| = |x + 5||x - 3| to make this smal...
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# Applied Atomic Spectroscopy by H. Jäger (auth.), E. L. Grove (eds.) By H. Jäger (auth.), E. L. Grove (eds.) From the 1st visual appeal of the vintage The Spectrum research in 1885 to the current the sector of emission spectroscopy has been evolving and altering. over the past 20 to 30 years particularly there was a...
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# zbMATH — the first resource for mathematics The sharp Jackson inequality in the space $$L_p$$ on the sphere. (English. Russian original) Zbl 1058.41502 Math. Notes 66, No. 1, 40-50 (1999); translation from Mat. Zametki 66, No. 1, 50-62 (1999). The author gives a proof of his theorem which was announced in [”The Jack...
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# Hardness of Maximum Independent Set in 3-Colorable Graphs Let $$G = (V,E)$$ be an undirected graph such that there is a proper coloring of the vertices of $$G$$ in three colors. Question: In such graphs, are there known results for the hardness of finding a maximum independent set? e.g., can one find an Independent...
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# The Drake equation and the Cambrian explosion This summer billionaire Yuri Milner announced that he would spend upwards of 100 million dollars to search for extraterrestrial intelligent life (here is the New York Times article). This quest to see if we have company started about fifty years ago when Frank Drake poin...
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# Showing subgroups with equal Lie algebras are equal Let $$k$$ be a field. It might as well be algebraically closed, but I do not want to assume that it has characteristic $$0$$. I will write "group" for "affine group scheme over $$k$$", not assuming smoothness. Two groups can have the same Lie algebras without bein...
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# 2D array zeroing C++ style [closed] I have a valid code in C-style int arr[10][10] = {0}; // all elements of array are 0 What is the optimal way to do the same for C++ style array? My idea is #include <array> std::array<std::array<int, 10>, 10> arr = {0}; // is it correct? • This appears to be a general "best...
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# Fill the plane with pentagons as tightly as possible in a regular way I wrote a small python script with recursion to create a "lattice" of non-overlapping pentagons. Below one can see the first stages of recursion. One can see that 5 small pentagons are missing in the second stage of recursion. The code in python ...
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Preprint A774/2016 On OM-decomposable sets Alfredo Noel Iusem | Maxim Todorov Keywords: Motzkin decomposable sets | convex sets | convex cones We introduce and study the family of sets in a finite dimensional Enclidean space which can be written as the Minkowsky sum of an open, convex  and bounded set and a closed and...
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# matrix.py¶ Define the base Matrix class. class openmdao.matrices.matrix.Matrix(comm, is_internal)[source] Bases: object Base matrix class. This class is used for global Jacobians. Parameters commMPI.Comm or <FakeComm> Communicator of the top-level system that owns the <Jacobian>. is_internalbool If True, thi...
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# How can I prove that a sequence such that every converging subsequence coverges to the same limit, converges? I want to claim that if $(x_n)_{n\in N}$ is a sequence, and there is $a$ such that if $(x_{n_k})$ converges, so $\lim x_{n_k} = a$ (it means that all converging subsequences have the same limit), then $(x_n)...
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# The omega one of chess, CUNY, March, 2013 This is a talk for the New York Set Theory Seminar on March 1, 2013. This talk will be based on my recent paper with C. D. A. Evans, Transfinite game values in infinite chess. Infinite chess is chess played on an infinite chessboard.  Since checkmate, when it occurs, does ...
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# How to approach this sum-minimization problem I am new to math. How to approach the following problem? $\min_{a,b} \sum_{t=1}^N (-4aX_t\sin(Z_tb) -4aY_t\cos(Z_tb)+a^2Z_t^2 + X_t^2 + Y_t^2)$ where $X_t,Y_t,Z_t$ for $t\in \{1,...N\}$ are given. Say $N$ is around 800. Do I need software? Which? I am not having luck ...
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Coder's Cat 2020-02-07 ## Challenge Description Given an array of size n, find the majority element. The majority element is the element that appears more than ⌊ n/2 ⌋ times. You may assume that the array is non-empty and the majority element always exist in the array. Example 1: Example 2: ## Naive Solution It...
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# Suppose a plot of inverse wavelength vs frequency has slope equal to 0.388, what is the... ###### Question: Suppose a plot of inverse wavelength vs frequency has slope equal to 0.388, what is the speed of sound traveling in the tube to 2 decimal places? #### Similar Solved Questions ##### I would like to you spen...
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# 8.9. Density Functional Theory (DFT)¶ ## 8.9.1. Many Body Schrödinger Equation¶ We use (Hartree) atomic units in this whole section about DFT. We use the Born-Oppenheimer approximation, which says that the nuclei of the treated atoms are seen as fixed. A stationary electronic state (for electrons) is then described...
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KNM MFF UK Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Analysis of algebraic flux correction schemes • ID: 2737, RIV: 10330010 • ISSN: 0036-1429, ISBN: not specified • source: SIAM Journal on Numerical Analysis • keywords: algebraic flux correction method; linear boundar...
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# 'Tightness' of Alternating Series Error term vs Lagrange Error term when a Taylor polynomial can have both Is it true that, if a Taylor expansion of a function has the form of an alternating series, then the alternating series error will always be a 'tighter' estimate of the true error than the Lagrange error?
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# Monte Carlo integration An illustration of Monte Carlo integration. In this example, the domain D is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*12) can be estimated by the ratio (0.8) of the points inside the circle (40) to the t...
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# Fault detection¶ We’ll consider a problem of identifying faults that have occurred in a system based on sensor measurements of system performance. # Problem statement¶ Each of $$n$$ possible faults occurs independently with probability $$p$$. The vector $$x \in \lbrace 0,1 \rbrace^{n}$$ encodes the fault occurrenc...
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## { Information = Comprehension × Extension } • Discussion 14 Information and optimization go hand in hand — discovering the laws or constraints naturally governing the systems in which we live is a big part of moving toward our hearts’ desires within them.  I’m engaged in trying to clear up a few old puzzles about i...
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