Amazing properties of binomial coefficients
... Now let us prove by induction that there exists a bijection between T Hn and Pn , such that the vertices of the triangle Pn correspond to the configurations A1 , A2 , A3 . The base n = 1 is evident. Proof of the step of induction. Assume that the bijection between T Hn and Pn has been constructed. T ...
... Now let us prove by induction that there exists a bijection between T Hn and Pn , such that the vertices of the triangle Pn correspond to the configurations A1 , A2 , A3 . The base n = 1 is evident. Proof of the step of induction. Assume that the bijection between T Hn and Pn has been constructed. T ...
Part1
... • The only way of minimizing the errors is by knowing and understanding why they occur and how we can diminish them. • The most frequent errors are: – Rounding errors, due to the fact that computers can work only with a finite representation of numbers. – Truncation errors, due to differences betwee ...
... • The only way of minimizing the errors is by knowing and understanding why they occur and how we can diminish them. • The most frequent errors are: – Rounding errors, due to the fact that computers can work only with a finite representation of numbers. – Truncation errors, due to differences betwee ...
29(2)
... opus; and (5) the letter to Master Theodorus, the shortest of his extant writings. This useful letter has been somewhat neglected by historians of mathematics, a tendency I would like to see reversed. To understand Fibonacci's outstanding contributions to knowledge, it is necessary to know something ...
... opus; and (5) the letter to Master Theodorus, the shortest of his extant writings. This useful letter has been somewhat neglected by historians of mathematics, a tendency I would like to see reversed. To understand Fibonacci's outstanding contributions to knowledge, it is necessary to know something ...
Numerical Algorithms and Digital Representation
... In these notes we cover the basic numerical algorithms such as interpolation, numerical root finding, differentiation and integration, as well as numerical solution of ordinary differential equations. In the area of digital understanding we discuss digital representation of numbers, text, sound and ...
... In these notes we cover the basic numerical algorithms such as interpolation, numerical root finding, differentiation and integration, as well as numerical solution of ordinary differential equations. In the area of digital understanding we discuss digital representation of numbers, text, sound and ...
Probability Essentials. Springer, Berlin, 2004.
... Gauss (1777–1855), and Laplace (1749–1827). For a nice history of Probability before 1827 (the year of the death of Laplace) one can consult [21]. In the twentieth century it was Kolmogorov (1903–1987) who saw the connection between the ideas of Borel and Lebesgue and probability theory and he gave ...
... Gauss (1777–1855), and Laplace (1749–1827). For a nice history of Probability before 1827 (the year of the death of Laplace) one can consult [21]. In the twentieth century it was Kolmogorov (1903–1987) who saw the connection between the ideas of Borel and Lebesgue and probability theory and he gave ...
![arXiv:math/0703236v1 [math.FA] 8 Mar 2007](http://s1.studyres.com/store/data/016433271_1-576581ae87603d2aee90a405a983700e-300x300.png)
On Advanced Analytic Number Theory
... = C (Euler’s constant). Proposition 1 is thus proved. The constant C lies between 0 and 1. It is not known whether it is rational or irrational; very probably, it is irrational. One could determine the constants a1 , a2 , . . . also explicitly but this is more complicated. We shall consider now an a ...
... = C (Euler’s constant). Proposition 1 is thus proved. The constant C lies between 0 and 1. It is not known whether it is rational or irrational; very probably, it is irrational. One could determine the constants a1 , a2 , . . . also explicitly but this is more complicated. We shall consider now an a ...
Introduction to Queueing Theory and Stochastic
... 17, various aspects of a single server queue with Poisson arrivals and general service times are studied, mainly focussing on mean value results as in [13]. Then, in Chapter 18, some selected results of a single server queue with a general arrival process and general service times are provided. Next ...
... 17, various aspects of a single server queue with Poisson arrivals and general service times are studied, mainly focussing on mean value results as in [13]. Then, in Chapter 18, some selected results of a single server queue with a general arrival process and general service times are provided. Next ...
Introduction to Queueing Theory and Stochastic Teletraffic Models
... Stochastic Teletraffic Models Moshe Zukerman EE Department, City University of Hong Kong email: [email protected] c 2000–2016. Copyright M. Zukerman This book can be used for educational and research purposes under the condition that it (including this first page) is not modified in any way. ...
... Stochastic Teletraffic Models Moshe Zukerman EE Department, City University of Hong Kong email: [email protected] c 2000–2016. Copyright M. Zukerman This book can be used for educational and research purposes under the condition that it (including this first page) is not modified in any way. ...
Sample pages 1 PDF
... board, and five bond issues. The ballot instructs voters to choose up to four people running for city council, rank up to three candidates for the school board, and approve or reject each bond issue. How many different ballots may be cast, if partially completed (or empty) ballots are allowed? 8. Co ...
... board, and five bond issues. The ballot instructs voters to choose up to four people running for city council, rank up to three candidates for the school board, and approve or reject each bond issue. How many different ballots may be cast, if partially completed (or empty) ballots are allowed? 8. Co ...
Products of random variables and the first digit phenomenon
... symbol {x} stands for the fractional part of a real x; we write Z+ for the set of positive integers; the standard abbreviations a.s., r.v. and i.i.d. stand respectively for almost surely (or almost sure), random variable and independent and identically distributed; all the r.v.’s in consideration ar ...
... symbol {x} stands for the fractional part of a real x; we write Z+ for the set of positive integers; the standard abbreviations a.s., r.v. and i.i.d. stand respectively for almost surely (or almost sure), random variable and independent and identically distributed; all the r.v.’s in consideration ar ...
