一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数

首先介绍广义Weierstrass型函数的Weyl-Marchaud分数阶导数,得到了带随机相位的广义Weierstrass型函数的Weyl-Marchaud分数阶导数图像的Hausdorff维数,证明了该分形函数图像的Hausdorff维数与Weyl-Marchaud分数阶导数的阶之间的线性关系.     

Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions

We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labeled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products Γ?S_n and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf algebras appear as natural analogs of McMahon’s multisymmetric functions. As a consequence, we obtain an internal product on ordinary multi-symmetric functions. We extend these constructions to Hopf algebras of colored parking functions, colored non-crossing partitions and parking functions of type B.     

Specialization of Appell's functions to univariate hypergeometric functions

Univariate specializations of Appell's hypergeometric functions F₁, F₂, F₃, F₄ satisfy ordinary Fuchsian equations of order at most 4. In special cases, these differential equations are of order 2 and could be simple (pullback) transformations of Euler's differential equation for the Gauss hypergeometric function. The paper classifies these cases, and presents corresponding relations between univariate specializations of Appell's functions and univariate hypergeometric functions. The computational aspect and interesting identities are discussed.     

On progressive functions

Progressive functions at time t involve only the progressive functions at time before t and some nice compactly supported function at time t. We give sufficient conditions and explicit formulas to construct progressive functions with exponential decay and characterize the conditions on which the positive integer translates of a progressive function are orthonormal or a Riesz sequence. We provide explicit ways for construction of orthonormal progressive functions and for construction of the biorthogonal functions of nonorthogonal progressive functions. Such progressive functions can be used to construct wavelets with arbitrary smoothness on the half line if they are generated by a smooth refinable compactly supported function.     

Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g=f⁻¹ satisfying the conditions that zf^′(z)/f(z) and zg^′(z)/g(z) are both subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.     

Dirichlet problem for pluriholomorphic functions of two complex variables

In this paper the Dirichlet problem for pluriholomorphic functions of two complex variables is investigated. The key point is the relation between pluriholomorphic functions and pluriharmonic functions. The link is constituted by the Fueter-regular functions of one quaternionic variable. Previous results about the boundary values of pluriharmonic functions and new results on L² traces of regular functions are applied to obtain a characterization of the traces of pluriholomorphic functions.     

On Finsler transnormal functions

In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition, when the function is defined on a compact analytic manifold M.     

Exceptional functions and normal families of meromorphic functions with multiple zeros

Let k be a positive integer with k?2; let h(?0) be a holomorphic function which has no simple zeros in D; and let F be a family of meromorphic functions defined in D, all of whose poles are multiple, and all of whose zeros have multiplicity at least k+1. If, for each function f∈F, f(k)(z)≠h(z), then F is normal in D.     

Factoring and recognition of read-once functions using cographs and normality and the readability of functions associated with partial k-trees

An approach for factoring general boolean functions was described in Golumbic and Mintz [Factoring logic functions using graph partitioning, in: Proceedings of IEEE/ACM International Conference on Computer Aided Design, November 1999, pp. 195-198] and Mintz and Golumbic [Factoring Boolean functions using graph partitioning, Discrete Appl. Math. 149 (2005) 131-153] which is based on graph partitioning algorithms. In this paper, we present a very fast algorithm for recognizing and factoring read-once functions which is needed as a dedicated factoring subroutine to handle the lower levels of that factoring process. The algorithm is based on algorithms for cograph recognition and on checking normality.For non-read-once functions, we investigate their factoring based on their corresponding graph classes. In particular, we show that if a function F is normal and its corresponding graph is a partial k-tree, then F is a read 2^k function and a read 2^k formula for F can be obtained in polynomial time.     

Algebraic and topological closure conditions for classes of pseudo-Boolean functions

We examine classes of real-valued functions of 0-1 variables closed under algebraic operations as well as topological convergence, and having a certain local characteristic (requiring that any function not in the class should have a k-variable minor not belonging to this class). It is shown that for k=2, the only 4 maximal classes with these properties are those of submodular, supermodular, monotone increasing and monotone decreasing functions. All the 13 locally defined closed classes are determined and shown to be intersections of the 4 maximal ones. All maximal classes for k≥3 are determined and characterized by the sign of higher order derivatives of the functions in the class.     

Properties for uniformly starlike and related functions under the Srivastava-Attiya operator

In the present paper, we introduce and investigate classes of analytic functions involving the Srivastava-Attiya operator. Basic properties for β-uniformly starlike functions of order γ are studied, such as inclusion relations, sufficient conditions, coefficient inequalities and distortion inequalities. The results are also extended to β-uniformly convex, close-to-convex, and quasi-convex functions. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.     

Some characterizations of strongly preinvex functions

In this paper, a new class of generalized convex function is introduced, which is called the strongly α-preinvex function. We study some properties of strongly α-preinvex function. In particular, we establish the equivalence among the strongly α-preinvex functions, strongly α-invex functions and strongly αη-monotonicity under some suitable conditions. As special cases, one can obtain several new and previously known results for α-preinvex (invex) functions.     

A note on hyperharmonic and polyharmonic functions

We show that the spaces of harmonic functions with respect to the Poincaré metric in the unit ball B^N in have many different properties depending upon whether N is even or odd.     

Subclasses of bi-univalent functions defined by convolution

In this paper, we introduced two new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution. Furthermore, we find estimates on the coefficients ∣a₂∣ and ∣a₃∣ for functions in these new subclasses.     

Integrals involving products of Airy functions, their derivatives and Bessel functions

A new integral representation of the Hankel transform type is deduced for the function Fn(x,Z)=Zn−1Ai(x−Z)Ai(x+Z) with x∈R, Z>0 and n∈N. This formula involves the product of Airy functions, their derivatives and Bessel functions. The presence of the latter allows one to perform various transformations with respect to Z and obtain new integral formulae of the type of the Mellin transform, K-transform, Laplace and Fourier transform. Some integrals containing Airy functions, their derivatives and Chebyshev polynomials of the first and second kind are computed explicitly. A new representation is given for the function ²|Ai(z)| with z∈C.     

A recursion formula for k-Schur functions

The Bernstein operators allow one to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t=1 based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to a combinatorial interpretation for the expansion coefficients of k-Schur functions at t=1 in terms of homogeneous symmetric functions.     

On the logarithmic coefficients of Bazilevic? functions

The objective of the present paper is to study the logarithmic coefficients of Bazilevic? functions. We obtain the inequality ∣γ_n∣ ? An⁻¹logn (A is an absolute constant) which holds for Bazilevic? functions.     

An improvement on the complexity of factoring read-once Boolean functions

Read-once functions have gained recent, renewed interest in the fields of theory and algorithms of Boolean functions, computational learning theory and logic design and verification. In an earlier paper [M.C. Golumbic, A. Mintz, U. Rotics, Factoring and recognition of read-once functions using cographs and normality, and the readability of functions associated with partial k-trees, Discrete Appl. Math. 154 (2006) 1465-1677], we presented the first polynomial-time algorithm for recognizing and factoring read-once functions, based on a classical characterization theorem of Gurvich which states that a positive Boolean function is read-once if and only if it is normal and its co-occurrence graph is P₄-free.In this note, we improve the complexity bound by showing that the method can be modified slightly, with two crucial observations, to obtain an O(n|f|) implementation, where |f| denotes the length of the DNF expression of a positive Boolean function f, and n is the number of variables in f. The previously stated bound was O(n²k), where k is the number of prime implicants of the function. In both cases, f is assumed to be given as a DNF formula consisting entirely of the prime implicants of the function.