# Browse Our Mathematics and Statistics Journals

**Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.**

# Mathematics and Statistics

Column-row products have zero determinant over any commutative ring. In this paper we discuss the converse. For domains, we show that this yields a characterization of pre-Schreier rings, and for rings with zero divisors we show that reduced pre-Schreier rings have this property.

Finally, for the rings of integers modulo *n*, we determine the 2x2 matrices which are (or not) full and their numbers.

For a continuous and positive function w(λ), λ > 0 and μ a positive measure on (0, ∞) we consider the following*monotonic integral transform*

where the integral is assumed to exist for*T* a positive operator on a complex Hilbert space*H*. We show among others that, if β ≥ A, B ≥ α > 0, and 0 < δ ≤ (B − A)^{2} ≤ Δ for some constants α, β, δ, Δ, then

and

where

Applications for power function and logarithm are also provided.

Let ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a_{2}z^{2} + a_{3}z^{3} +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.

The authors have studied the curvature of the focal conic in the isotropic plane and the form of the circle of curvature at its points has been obtained. Hereby, we discuss several properties of such circles of curvature at the points of a parabola in the isotropic plane.

In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these new objects. We give general combinatorial identities and some recurrence relations. We also show some connections with other sequences such as poly-Cauchy numbers with higher level and central factorial numbers. To obtain our results, we use pure combinatorial arguments and classical manipulations of formal power series.

A space X is called *functionally countable* if ƒ (X) is countable for any continuous function ƒ : X → Ø. Given an infinite cardinal k, we prove that a compact scattered space K with d(K) > k must have a convergent k^{+}-sequence. This result implies that a Corson compact space K is countable if the space (K × K) \ Δ_{K} is functionally countable; here Δ_{K} = {(x, x): x ϵ K} is the diagonal of K. We also establish that, under Jensen’s Axiom ♦, there exists a compact hereditarily separable non-metrizable compact space X such that (X × X) \ Δ_{X} is functionally countable and show in ZFC that there exists a non-separable σ-compact space X such that (X × X) \ Δ_{X} is functionally countable.

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called *exponential* spaces.

We also find the exact value of the embedding constant which appears in the corresponding norm inequality.

Suppose that K and K' are knots inside the homology spheres Y and Y', respectively. Let X = Y (K, K') be the 3-manifold obtained by splicing the complements of K and K' and Z be the three-manifold obtained by 0 surgery on K. When Y' is an L-space, we use the splicing formula of [1] to show that the rank of ^{2}) = 0 and is bounded below by rank(

Let *k* ≥ 1. A *Sperner k-family* is a maximum-sized subset of a finite poset that contains no chain with *k* + 1 elements. In 1976 Greene and Kleitman defined a lattice-ordering on the set *S _{k}*(

*P*) of Sperner

*k*-families of a fifinite poset

*P*and posed the problem: “Characterize and interpret the join- and meet-irreducible elements of

*S*(

_{k}*P*),” adding, “This has apparently not been done even for the case

*k*= 1.”

In this article, the case *k* = 1 is done.