共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Hlrabayashi 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2005,75(1):83-95
In 1994 and 1995 GIRSTMAIR gave (relative) class number formulas for the imaginary quadratic field $\mathbb{Q}(\sqrt { - p} )$ , P an odd prime with p ≡ 3 (mod 4) and p ≥ 7, using the coefficients of the digit expression of 1/p and z/p, respectively, where z is an integer with 1 ≤ z ≤p - 1. We extend the formulas to an imaginary abelian number field. 相似文献
2.
The classical Whitney formula relates the number of times an oriented plane curve cuts itself to its rotation number and the
index of a base point. In this paper we generalize Whitney’s formula to curves on an oriented punctured surface Σ
m, n
, obtaining a family of identities indexed by elements of π
1(Σ
m, n
). To define analogs of the rotation number and the index of a base point of a curve γ, we fix an arbitrary vector field on Σ
m, n
. Similar formulas are obtained for non-based curves. 相似文献
3.
The Wedderburn rank reduction formula and the Abaffy–Broyden–Spedicato (ABS) algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes such as Gram–Schmidt, conjugate direction and Lanczos methods. We present a rank reduction formula for transforming the rows and columns of A, extending the Wedderburn rank reduction formula and the ABS approach. By repeatedly applying the formula to reduce the rank, an extended rank reducing process is derived. The biconjugation process associated with the Wedderburn rank reduction process and the scaled extended ABS class of algorithms are shown to be in our proposed rank reducing process, while the process is more general to produce several other effective reduction algorithms to compute various structured factorizations. The process provides a general finite iterative approach for constructing factorizations of A and AT under a common framework of a general decomposition VTAP=Ω. We also show that the biconjugation process associated with the Wedderburn rank reduction process can be derived from the scaled ABS class of algorithms applied to A or AT. Finally, we provide a list of some well-known reduction procedures as special cases of our extended rank reducing process. The approach is general enough to produce various structured decompositions as well. 相似文献
4.
We find new partition identities arising from Ramanujan’s formulas of multipliers. Several of the identities are for overpartitions, overpartition pairs, and \(\ell \)-regular partitions. 相似文献
5.
S Bandyopadhyay S Bandyopadhyay 《The Journal of the Operational Research Society》2010,61(6):1057-1062
Several phenomena of interest like stock price movements, online auction bidprices or inventory levels, can be stylized as ‘momentum processes’,whereby the very start of activity (‘up’ or ‘down’) cantrigger subsequent activity in that direction. We calculate the transientprobabilities of being in a particular state (eg, stock price or current auctionbid level) in such activities. The calculations can be used to estimate theexpected time to reach a certain price, inventory level or bid. The processescan be modified to show the phenomenon where the lack of activity can have an‘inertia of rest’. 相似文献
6.
The Ramanujan Journal - In this paper, we give some extensions for Ramanujan’s circular summation formulas with the mixed products of two Jacobi’s theta functions. As applications, we... 相似文献
7.
We consider Poisson’s equation for discrete-time single-birth processes, and we derive its solutions by solving a linear system of infinitely many equations. We apply the solution of Poisson’s equation to obtain the asymptotic variance. The results are further applied to birth–death processes and the scalar-valued GI/M/1-type Markov chains. 相似文献
8.
We prove a Black–Scholes type formula when the geometric Brownian motion originates from approximations by multinomial distributions. It is shown that the variance appearing in the Black–Scholes formula for option pricing can be structured according to occurrences of different types of events at each time instance using a local limit theorem for multinomial distributions in Richter (1956). The general approach has first been developed in Kan (2005). 相似文献
9.
Largely absent from the emerging literature on flexibility is a consideration of experts’ flexibility. Do experts exhibit strategy flexibility, as one might assume? If so, how do experts perceive that this capacity developed in themselves? Do experts feel that flexibility is an important instructional outcome in school mathematics? In this paper, we describe results from several interviews with experts to explore strategy flexibility for solving equations. We conducted interviews with eight content experts, where we asked a number of questions about flexibility and also engaged the experts in problem solving. Our analysis indicates that the experts that were interviewed did exhibit strategy flexibility in the domain of linear equation solving, but they did not consistently select the most efficient method for solving a given equation. However, regardless of whether these experts used the best method on a given problem, they nevertheless showed an awareness of and an appreciation of efficient and elegant problem solutions. The experts that we spoke to were capable of making subtle judgments about the most appropriate strategy for a given problem, based on factors including mental and rapid testing of strategies, the problem solver’s goals (e.g., efficiency, error-free execution, elegance) and familiarity with a given problem type. Implications for future research on flexibility and on mathematics instruction are discussed. 相似文献
10.
The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series. 相似文献
11.
V. N. Belykh 《Doklady Mathematics》2016,93(2):197-201
An interpolation quadrature formula with a weight function from Lp[–1, 1] (1 < p < ∞) whose error is estimated in terms of Chebyshev smoothness characteristics is shown to be nonsaturable. 相似文献
12.
We construct extremal stochastic integrals
of a deterministic function with respect to a random Fréchet () sup-measure. The measure is sup-additive rather than additive and is defined over a general measure space , where is a deterministic control measure. The extremal integral is constructed in a way similar to the usual stable integral, but with the maxima replacing the operation of summation. It is well-defined for arbitrary , and the metric metrizes the convergence in probability of the resulting integrals.This approach complements the well-known de Haan's spectral representation of max-stable processes with Fréchet marginals. De Haan's representation can be viewed as the max-stable analog of the LePage series representation of stable processes, whereas the extremal integrals correspond to the usual stable stochastic integrals. We prove that essentially any strictly stable process belongs to the domain of max-stable attraction of an Fréchet, max-stable process. Moreover, we express the corresponding Fréchet processes in terms of extremal stochastic integrals, involving the kernel function of the stable process. The close correspondence between the max-stable and stable frameworks yields new examples of max-stable processes with non-trivial dependence structures.This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University of Michigan and the NSF Grant DMS-0505747 at Boston University. 相似文献
13.
Queueing Systems - Donsker’s theorem is perhaps the most famous invariance principle result for Markov processes. It states that, when properly normalized, a random walk behaves... 相似文献
14.
Touchard–Riordan-like formulas are certain expressions appearing in enumeration problems and as moments of orthogonal polynomials. We begin this article with a new combinatorial approach to prove such formulas, related to integer partitions. This gives a new perspective on the original result of Touchard and Riordan. But the main goal is to give a combinatorial proof of a Touchard–Riordan-like formula for q-secant numbers discovered by the first author. An interesting limit case of these objects can be directly interpreted in terms of partitions, so that we obtain a connection between the formula for q-secant numbers, and a particular case of Jacobi’s triple product identity. Building on this particular case, we obtain a “finite version” of the triple product identity. It is in the form of a finite sum which is given a combinatorial meaning, so that the triple product identity can be obtained by taking the limit. Here the proof is non-combinatorial and relies on a functional equation satisfied by a T-fraction. Then from this result on the triple product identity, we derive a whole new family of Touchard–Riordan-like formulas whose combinatorics is not yet understood. Eventually, we prove a Touchard–Riordan-like formula for a q-analog of Genocchi numbers, which is related with Jacobi’s identity for (q;q)3 rather than the triple product identity. 相似文献
15.
Xiaoxia Huang 《Fuzzy Optimization and Decision Making》2012,11(4):451-463
Portfolio selection is concerned with selecting an optimal portfolio that can strike a balance between maximizing the return and minimizing the risk among a large number of securities. Traditionally, security returns were regarded as random variables. However, there are cases that the predictions of security returns are given mainly based on experts’ judgements and estimations rather than historical data. In this paper, we introduce a new type of variable to reflect the subjective estimations of the security returns. A risk index for uncertain portfolio selection is proposed and a new safe criterion for judging the portfolio investment is introduced. Based on the proposed risk index, a new mean-risk index model is developed and its crisp forms are given. In addition, to illustrate the application of the model, two numerical examples are also presented. 相似文献
16.
17.
V. P. Kurenok 《Lithuanian Mathematical Journal》2007,47(4):423-435
The time-dependent SDE dX
t
= b(t, X
t−)dZ
t
with X
0 = x
0 ∈ ℝ, and a symmetric α-stable process Z, 1 < α ⩽ 2, is considered. We study the existence of nonexploding solutions of the given equation through the existence of solutions
of the equation
in class of time change processes, where
is a symmetric stable process of the same index α as Z. The approach is based on using the time change method, Krylov’s estimates for stable integrals, and properties of monotone
convergence. The main existence result extends the results of Pragarauskas and Zanzotto (2000) for 1 < α < 2 and those of T. Senf (1993) for α = 2.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 517–531, October–December, 2007. 相似文献
18.
WANG Bin XIANG Kainan & YANG Xiangqun Department of Mathematics Hunan Normal University Changsha China 《中国科学A辑(英文版)》2006,49(10):1315-1326
A measure-valued diffusion process describing how the measures evolve under flows or "imaginary" flows on Rd is constructed in this paper. The interest of the process is that on the one hand, it can be viewed as a measure-valued flow; on the other hand, the general stochastic flows of measurable maps or kernels do not cover it. 相似文献
19.
Gorman Gilbert 《The Journal of mathematical sociology》2013,37(1):139-145
For at least twenty‐five years, the concept of the clique has had a prominent place in sociometric and other kinds of sociological research. Recently, with the advent of large, fast computers and with the growth of interest in graph‐theoretic social network studies, research on the definition and investigation of the graph theoretic properties of clique‐like structures has grown. In the present paper, several of these formulations are examined, and their mathematical properties analyzed. A family of new clique‐like structures is proposed which captures an aspect of cliques which is seldom treated in the existing literature. The new structures, when used to complement existing concepts, provide a new means of tapping several important properties of social networks. 相似文献
20.
Yasuho Masuda 《The Ramanujan Journal》2013,32(2):281-314
The kernel function of Cauchy type for type BC is defined as a solution of linear q-difference equations. In this paper, we show that this kernel function intertwines the commuting family of van Diejen’s q-difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type BC. We also construct a new infinite family of commuting q-difference operators for which the Koornwinder polynomials are joint eigenfunctions. 相似文献