相关论文: On The Symmetry Of Arithmetical Functions In Almos…
In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functions. We first study the axial symmetry and monotonicity of…
A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
The paper considers estimates for the asymptotics of summation functions of bounded multiplicative arithmetic functions. Several assertions on this subject are proved and examples are considered.
We investigate a conformal-like transformation for which the spacetime interval is invariant.
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…
Consider the number of integers in a short interval that can be represented as a sum of two squares. What is an estimate for the variance of these counts over random short intervals? We resolve a function field variant of this problem in…
We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
Asymptotic almost automorphy is introduced and studied in the context of some algebras of generalized functions. We also give applications to neutral difference differential systems in the framework of such generalized functions.
We study sums with multiplicative functions that take values over a non-homogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas such as the number of integers in a Beatty sequence…
We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems ${\stackrel{\circ}{W}}\vphantom{W}_2^r(-1,1)\hookrightarrow{\stackrel{\circ}{W}}\vphantom{W}_\infty^k(-1,1)$ for various $r$ and $k$. The sharp…