1 errors - New Age International
... The magnitude of the error in the value of the function due to cutting (truncation) of its series is equal to the sum of all the discarded terms. It may be large and may even exceed the sum of the terms retained, thus making the calculated result meaningless. (iii) Round-off Errors: When depicting e ...
... The magnitude of the error in the value of the function due to cutting (truncation) of its series is equal to the sum of all the discarded terms. It may be large and may even exceed the sum of the terms retained, thus making the calculated result meaningless. (iii) Round-off Errors: When depicting e ...
Bell numbers, partition moves and the eigenvalues of the random
... and nt these are few, and occur for particular choices of the parameters t and n. References are given to the new sequences arising from this work. 2. Proof of Theorem 1.1 We prove the first equality in Theorem 1.1 using an explicit bijection. This is a special case of the bijection in the proof of ...
... and nt these are few, and occur for particular choices of the parameters t and n. References are given to the new sequences arising from this work. 2. Proof of Theorem 1.1 We prove the first equality in Theorem 1.1 using an explicit bijection. This is a special case of the bijection in the proof of ...
BPS states of curves in Calabi–Yau 3–folds
... Theorem 1.9 Let Cn,g be number of degree n, connected, complete, étale covers of a curve of genus g , each counted by the reciprocal of the number of automorphisms of the cover. Let µ be the Möbius function: µ(n) = (−1)a where a is the number of prime factors of n if n is square-free and µ(n) = 0 ...
... Theorem 1.9 Let Cn,g be number of degree n, connected, complete, étale covers of a curve of genus g , each counted by the reciprocal of the number of automorphisms of the cover. Let µ be the Möbius function: µ(n) = (−1)a where a is the number of prime factors of n if n is square-free and µ(n) = 0 ...
CIS541_08_MonteCarlo
... Random v. Pseudo-random • Random numbers have no defined sequence or formulation. Thus, for any n random numbers, each appears with equal probability. • If we restrict ourselves to the set of 32-bit integers, then our numbers will start to repeat after some very large n. The numbers thus clump with ...
... Random v. Pseudo-random • Random numbers have no defined sequence or formulation. Thus, for any n random numbers, each appears with equal probability. • If we restrict ourselves to the set of 32-bit integers, then our numbers will start to repeat after some very large n. The numbers thus clump with ...
Fuchsian groups, coverings of Riemann surfaces, subgroup growth
... Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of ...
... Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of ...
Minimal number of periodic points for C self
... a sequence of indices of iterations. He considered a map f : U → X , where U ⊂ X is an open subset of an ENR, satisfying the following fixed-compactness condition. We denote inductively U0 = U , Un+1 = f −1 (Un ) i.e. Un = {x ∈ U : x, f (x), ..., f n (x) ∈ U }. We assume that the fixed point set Fix ...
... a sequence of indices of iterations. He considered a map f : U → X , where U ⊂ X is an open subset of an ENR, satisfying the following fixed-compactness condition. We denote inductively U0 = U , Un+1 = f −1 (Un ) i.e. Un = {x ∈ U : x, f (x), ..., f n (x) ∈ U }. We assume that the fixed point set Fix ...
19(5)
... In a recent paper [2], Scott, Delaney, and Hoggatt discussed the Tribonacci numbers Tn defined by TQ = 1, T± = 1, T2 = 2 and Tn = T n _ x + Tn-i + T n _ 3 , for n >_ 3, ...
... In a recent paper [2], Scott, Delaney, and Hoggatt discussed the Tribonacci numbers Tn defined by TQ = 1, T± = 1, T2 = 2 and Tn = T n _ x + Tn-i + T n _ 3 , for n >_ 3, ...
Notes on Combinatorics - School of Mathematical Sciences
... Fifteen schoolgirls go for a walk every day for a week in five rows of three. Is it possible to arrange the walks so that every two girls walk together exactly once during the week? This is certainly plausible. Each girl has to walk with fourteen others; every day there are two other girls in her ro ...
... Fifteen schoolgirls go for a walk every day for a week in five rows of three. Is it possible to arrange the walks so that every two girls walk together exactly once during the week? This is certainly plausible. Each girl has to walk with fourteen others; every day there are two other girls in her ro ...
mean square of quadratic Dirichlet L-functions at 1
... mean square result over (all) discriminants with error term O(X 2/5+ε ). The sum over primitive characters, and the proof for (1.1), are considered later in Chapter 4. The mean square of primitive L-functions is obtained by sieving out the primitive characters from the sum over all characters by usi ...
... mean square result over (all) discriminants with error term O(X 2/5+ε ). The sum over primitive characters, and the proof for (1.1), are considered later in Chapter 4. The mean square of primitive L-functions is obtained by sieving out the primitive characters from the sum over all characters by usi ...
(pdf)
... In this paper we intend to explore the elementaries of partition theory, taken from a mostly graphic perspective, culminating in a theorem key in the proof of Euler's Pentagonal Number Theorem. A partition λ= (λ1 λ2 . . . λr ) of a positive integer n is a nonincreasing sequence of positive integers ...
... In this paper we intend to explore the elementaries of partition theory, taken from a mostly graphic perspective, culminating in a theorem key in the proof of Euler's Pentagonal Number Theorem. A partition λ= (λ1 λ2 . . . λr ) of a positive integer n is a nonincreasing sequence of positive integers ...
Fibonacci numbers, alternating parity sequences and
... So i is made up of consecutive entries of of alternating parities, and it is maximal under these conditions. The i ’s are uniquely determined, and called a.p. components of . The length of i will be denoted by ri . The formulas given in Theorems 4.3 and 4.4 for LR are homogeneous in the sens ...
... So i is made up of consecutive entries of of alternating parities, and it is maximal under these conditions. The i ’s are uniquely determined, and called a.p. components of . The length of i will be denoted by ri . The formulas given in Theorems 4.3 and 4.4 for LR are homogeneous in the sens ...
SGN-2506: Introduction to Pattern Recognition
... million components. The most part of this data is useless for classification. In feature extraction, we are searching for the features that best characterize the data for classification The result of the feature extraction stage is called a feature vector. The space of all possible feature vectors i ...
... million components. The most part of this data is useless for classification. In feature extraction, we are searching for the features that best characterize the data for classification The result of the feature extraction stage is called a feature vector. The space of all possible feature vectors i ...
Recursion Over Partitions
... A partition of a number n is a way to present it as a sum of non negatives integer numbers when the order has no signicant. An example to a partition of 3 is 3=1+2. The partition function is the number of dierent partitions of a specic number n and it is written as p(n). The partition function is ...
... A partition of a number n is a way to present it as a sum of non negatives integer numbers when the order has no signicant. An example to a partition of 3 is 3=1+2. The partition function is the number of dierent partitions of a specic number n and it is written as p(n). The partition function is ...
Advanced Topics in Markov chains
... E[Mk+1 |Fk0 ] = E E[Mk+1 |Fk ]|Fk0 ] ≥ E[Mk |Fk0 ] = Mk ({k, k + 1} ⊂ I), which shows that M is also an Fk -submartingale. In particular, a stochastic process M is a submartingale with respect to some filtration if and only if it is a submartingale with respect to its own filtration (FkM )k∈I . In t ...
... E[Mk+1 |Fk0 ] = E E[Mk+1 |Fk ]|Fk0 ] ≥ E[Mk |Fk0 ] = Mk ({k, k + 1} ⊂ I), which shows that M is also an Fk -submartingale. In particular, a stochastic process M is a submartingale with respect to some filtration if and only if it is a submartingale with respect to its own filtration (FkM )k∈I . In t ...
40(1)
... Articles should be submitted using the format of articles in any current issues of THE FIBONACCI QUARTERLY. They should be typewritten or reproduced typewritten copies, that are clearly readable, double spaced with wide margins and on only one side of the paper. The full name and address of the auth ...
... Articles should be submitted using the format of articles in any current issues of THE FIBONACCI QUARTERLY. They should be typewritten or reproduced typewritten copies, that are clearly readable, double spaced with wide margins and on only one side of the paper. The full name and address of the auth ...
infinite series
... This was discovered independently by Leibniz and James Gregory in the 1670s, and was known 300 years earlier by Madhava in India.1 If we try to use (2) to compute π, we’re faced with the reality that this series is very slowly convergent. For instance, the sum of the first 100 terms in (2) is approx ...
... This was discovered independently by Leibniz and James Gregory in the 1670s, and was known 300 years earlier by Madhava in India.1 If we try to use (2) to compute π, we’re faced with the reality that this series is very slowly convergent. For instance, the sum of the first 100 terms in (2) is approx ...