Motivated, in part, by the desire to develop an information-theoretic foundation for compound Poisson approximation limit theorems (analogous to the corresponding developments for the central limit theorem and for simple Poisson approximation), this work examines sufficient conditions under which the compound Poisson distribution has maximal entropy within a natural class of probability measure...

For a permutationally invariant unconditional convex body K in R we define a finite sequence (Kj)j=1 of projections of the body K to the space spanned by first j vectors of the standard basis of R. We prove that the sequence of volumes (|Kj |)j=1 is log-concave.

Let Ωn stand for the volume of the unit ball in Rn for n ∈ N. In the present paper, we prove that the sequence Ω 1/(n lnn) n is logarithmically convex and that the sequence Ω 1/(n lnn) n Ω 1/[(n+1) ln(n+1)] n+1 is strictly decreasing for n ≥ 2. In addition, some monotonic and concave properties of several functions relating to Ωn are extended and generalized.

Graphene oxide/Ag nanoparticles (Ag/GO) was prepared and employed to synthesize antifouling polyethersulfone (PES) mixed matrix membranes. The performance of the membranes was evaluated in terms of flux, hydrophilicity and anti-biofouling properties. With increment of the Ag/GO from 0 to 0.1 wt.%, the pure water flux increased from 24.7 up to 54.1 kg/m2 h. The flux recovery ratio (FRR) of the m...

‎In this paper‎, ‎we generalize the proximal point algorithm to complete CAT(0) spaces and show‎ ‎that the sequence generated by the proximal point algorithm‎ $w$-converges to a zero of the maximal‎ ‎monotone operator‎. ‎Also‎, ‎we prove that if $f‎: ‎Xrightarrow‎ ‎]-infty‎, +‎infty]$ is a proper‎, ‎convex and lower semicontinuous‎ ‎function on the complete CAT(0) space $X$‎, ‎then the proximal...

The analysis of thermal radiation in multi-surface enclosures typically involves multiple integrals with four, five, or six variables. Major difficulties for the numerical evaluation of these integrals are non-convex geometries and singular integral kernels. This paper presents hierarchical visibility concepts and coordinate transformations which eliminate these difficulties. In the transformed...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

In their paper [D–M–M2], van den Dries, Macintyre and Marker give an explicit construction of a nonarchimedean model of the theory of the reals with restricted analytic functions and exponentiation. This model, called the logarithmic exponential power series field, lies in a generalized power series field. They use the results of Ressayre and Mourgues about truncation-closed embeddings to answe...

The geometric mean and the function (det(·))1/m (on the m-by-m positive definite matrices) are examples of “hyperbolic means”: functions of the form p1/m , where p is a hyperbolic polynomial of degree m. (A homogeneous polynomial p is “hyperbolic” with respect to a vector d if the polynomial t → p(x+ td) has only real roots for every vector x.) Any hyperbolic mean is positively homogeneous and ...