相关论文: Gaps between classes of matrix monotone functions

We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse…

Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…

The practically important classes of equal-input and of monotone Markov matrices are revisited, with special focus on embeddability, infinite divisibility, and mutual relations. Several uniqueness results for the classic Markov embedding…

An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…

A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.

In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…

In this paper, we introduce a new class of implicit function to prove common fixed point theorems in fuzzy metric space. Moreover we define a new altering distance in terms of integral and utilize the same to deduce integral type…

We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a monotone function of a bimodal interval map.

Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…

Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…

In this work we study the Artin-Mazur zeta function for piecewise monotone functions acting on a compact interval of real numbers. In the case of unimodal maps, Milnor and Thurston gave a characterization for the rationality of the…

In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and…

We apply matrix methods to arithmetic functions by associating matrices to the functions in a manner drawn from the theory of symmetric functions. Then we study the characteristic polynomials of the associated matrices.

We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.

We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.