共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we consider the mean value of the product of multiplicative arithmetic functions with shifted argument. The
investigated functions have to satisfy the following conditions: their moduli do not exceed 1; the values on the set of primes
are close to 1 for one of the functions and close to a fixed complex number for the other function. Some consequences for
the classical functions are given. 相似文献
2.
We study the characteristics of the mean values of multiplicative functions, given the values of the functions on primes. 相似文献
3.
Nonnegative matrix factorization (NMF) is the problem of approximating a given nonnegative matrix by the product of two nonnegative matrices. The multiplicative updates proposed by Lee and Seung are widely used as efficient computational methods for NMF. However, the global convergence of these updates is not formally guaranteed because they are not defined for all pairs of nonnegative matrices. In this paper, we consider slightly modified versions of the original multiplicative updates and study their global convergence properties. The only difference between the modified updates and the original ones is that the former do not allow variables to take values less than a user-specified positive constant. Using Zangwill’s global convergence theorem, we prove that any sequence of solutions generated by either of those modified updates has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. Furthermore, we propose algorithms based on the modified updates that always stop within a finite number of iterations. 相似文献
4.
Takeshi Izawa 《Proceedings of the American Mathematical Society》2003,131(11):3583-3588
We give a formula of the Riemann-Hurwitz type for classes defined by multiplicative sequences as corollaries of the Chern number formula for ramified coverings.
5.
By using the unsymmetrical scale instead of the symmetrical scale, the multiplicative intuitionistic fuzzy sets (MIFSs) reflect our intuition more objectively. Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number (MIFN) and is based on the unbalanced scale (i.e., Saaty’s 1-9 scale). In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively, in this paper, we firstly propose two new basic operational laws for MIFNs, which are the subtraction law and the division law. Secondly, we describe the change values of MIFNs when considering them as variables, classify these change values based on the basic operational laws for MIFNs, and depict the convergences of sequences of MIFNs by the subtraction and division laws. Finally, we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities, derivatives and differentials, and also give their application in selecting the configuration of a computer. 相似文献
6.
Vytas Zacharovas 《The Ramanujan Journal》2011,24(3):289-329
We prove a Tauberian theorem for the Voronoi summation method of divergent series with an estimate of the remainder term.
The results on the Voronoi summability are then applied to analyze the mean values of multiplicative functions on random permutations. 相似文献
7.
Zhaojuan Wang 《Journal of Mathematical Analysis and Applications》2011,384(1):160-172
In this paper we study the asymptotic dynamics for stochastic reaction-diffusion equation with multiplicative noise defined on unbounded domains. We investigate the existence of a random attractor for the random dynamical system associated with the equation. The asymptotic compactness of the random dynamical system is established by using uniform a priori estimates for far-field values of solutions and a cut-off technique. 相似文献
8.
Konstantin M. Dyakonov 《Journal d'Analyse Mathématique》1998,75(1):85-104
We study the multiplicative structure of holomorphic functions in the space BMOAφ, defined by a decrease condition on the mean oscillation. The inner and outer factors occurring in the canonical factorization
of such functions are completely characterized by explicit quantitative conditions. 相似文献
9.
In two previous papers,the first named author jointly with Florian Luca and Henryk Iwaniec,have studied the distribution modulo 1 of sequences which have linear growth and are mean values of multiplicative functions on the set of all the integers.In this note,we give a first result concerning sequences with linear growth associated to the mean values of multiplicative functions on a set of polynomial values,proving the density modulo 1 of the sequencem[∑((m2+1))(m2+1)(m≤n)]n.This result is but an illustration of the theme which is currently being developed in the PhD thesis of the second named author. 相似文献
10.
S. S. Volosivets 《Mathematical Notes》2011,89(3-4):311-318
We consider a new class of functions on the semiaxis for which the multiplicative Fourier transform can be defined. We prove equalities of Parseval type, an inversion formula and a condition for the validity of representation in the form of the multiplicative Fourier transform. 相似文献
11.
Xiaoyan Zhang Wei Xu Bingchang Zhou 《Communications in Nonlinear Science & Numerical Simulation》2009,14(12):4220-4225
The effect of any system parameter (include p, q, λ, τ1, τ2, τ3) on the mean first-passage time is investigated in a symmetric bistable system driven by multiplicative and additive colored noise with colored cross-correlation. Expression of the mean first-passage time (MFPT) has been obtained by applying the steepest-descent approximation. The effects of the additive noise intensity and the multiplicative noise intensity on the MFPT are mostly different only with bigger positive values of the strength of correlations between multiplicative and additive noise; and the MFPT has a maximum with the increase of the multiplicative noise intensity. The effects of the noise self-correlation times on the MFPT are quite different from that of the correlation time between the noises as the strength of correlations between multiplicative and additive noise is positive. 相似文献
12.
13.
《Quaestiones Mathematicae》2013,36(3):335-347
Abstract The value distribution problem for real-valued multiplicative functions defined on an additive arithmetical semigroup is examined. We prove that, in contrast to the classical theory of number-theoretic functions defined on the semigroup of natural numbers, this problem is equivalent to that for additive functions only under some extra condition. In this way, applying the known results for additive functions we derive general sufficient conditions for the existence of a limit law for appropriately normalized multiplicative functions. 相似文献
14.
We introduce Weierstrass multiplicative points and develop the theory of Weierstrass multiplicative points for multiplicative meromorphic functions and Prym differentials on a compact Riemann surface. We prove some analogs of the Weierstrass and Noether theorems on the gaps of multiplicative functions. We obtain two-sided estimates for the number of Weierstrass multiplicative points and q-points. We propose a method for studying the Weierstrass and Noether gaps and Weierstrass multiplicative points by means of filtrations in the Jacobi variety of a compact Riemann surface. 相似文献
15.
In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions. 相似文献
16.
Richard H. Hudson 《manuscripta mathematica》1981,35(3):353-370
In this paper we give proof of a conjecture of Emma Lehmer regarding the number of totally multiplicative functions taking on the values ±1 for which there are no positive integers a,a+1,a+3 with f(a)=f(a+1)=f(a+3)=+1. 相似文献
17.
Nancy Rallis 《manuscripta mathematica》1983,44(1-3):279-308
In this paper we develop a fixed point index theory for symmetric product mappings of ENR-spaces. For such mappings we show that an index can be defined which is an extension of the usual integer-valued fixed point index. Further, we show that the classical properties of the index hold in this setting: The index is additive, multiplicative and commutative, the index is preserving under homotopy, and finally, the index is equal to the Lefschetz number as defined by Maxwell [9]. 相似文献
18.
E. Y. Lerner 《Functional Analysis and Other Mathematics》2009,2(2-4):251-255
V.?I. Arnold has recently defined the complexity of a sequence of n zeros and ones with the help of the operator of finite differences. In this paper we describe the results obtained for almost most complex sequences of elements of a finite field, whose dimension n is a prime number. We prove that, with n→∞, this property is inherent in almost all sequences, while the values of multiplicative functions possess this property with any n different from the characteristic of the field. We also describe the prime values of the parameter n which make the logarithmic function almost most complex. All these sequences reveal a stronger complexity; its algebraic sense is quite clear. 相似文献
19.
Summary. Multilevel preconditioners are proposed for the iterative solution of the discrete problems which arise when orthogonal spline
collocation with piecewise Hermite bicubics is applied to the Dirichlet boundary value problem for a self-adjoint elliptic
partial differential equation on a rectangle. Additive and multiplicative preconditioners are defined respectively as sums
and products of independent operators on a sequence of nested subspaces of the fine partition approximation space. A general
theory of additive and multiplicative Schwarz methods is used to prove that the preconditioners are spectrally equivalent
to the collocation discretization of the Laplacian with the spectral constants independent of the fine partition stepsize
and the number of levels. The preconditioned conjugate gradient and preconditioned Orthomin methods are considered for the
solution of collocation problems. An implementation of the methods is discussed and the results of numerical experiments are
presented.
Received March 1, 1994 / Revised version received January 23, 1996 相似文献
20.
Julien Barral Jacques Peyrière Zhi-Ying Wen 《Probability Theory and Related Fields》2009,144(3-4):615-631
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of fixed points of smoothing transformations (i.e., some generalized stable laws). Studying this system leads to a central limit theorem and to its functional version. The limit Gaussian process can also be obtained as limit of an “additive cascade” of independent normal variables. 相似文献