Radii of starlikeness and convexity of a cross-product of Bessel functions

To illustrate vertical and horizontal equidistributions of Kloosterman sums, we prove two relevant central limit theorems by some analytic and combinatorial properties of Chebyshev polynomials and independence of monodromy groups of Kloosterman sheaves. The first one supports a short interval version of Katz’s vertical Sato–Tate distribution theorem, and the second one coincides with the horizontal conjecture of Katz in the statistical sense.     

A new heuristic and an exact approach for a production planning problem

Central European Journal of Operations Research - We deal with a very complex and hard scheduling problem. Two types of products are processed by a heterogeneous resource set, where resources have...     

A simple method to find out when an ordinary differential equation is separable

In many statistical discussions, especially in data analysis, the idea of polynomials plays a key role. For example, Dwyer [1] employed polynomials to express factorial moments of discrete distribution in terms of cumulative totals. Traditionally, polynomials are derived using the difference operator method (see [2], p. 134]). In this article, using the differential equation approach as an alternative method, we obtain generalized exponential and logarithmic polynomials, and find their special cases appearing in statistical signal‐noise models.     

Characterization of mean transformations

The mean transformations M(A,?B) are linear mappings and they are analogues of the matrix means of A,?B?≥?0. They are defined by operator monotone functions. In this article several properties are described and a part of them characterize the concept.     

Maschke Type Theorems for Nonassociative Hopf Algebras

In this article, we give necessary and sufficient conditions for a possibly nonassociative comodule algebra over a nonassociative Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the associative setting. Also, from this result we deduce a version of Maschke's Theorems and the consequent characterization of projectives for (H, B)-Hopf triples associated with a nonassociative Hopf algebra H and a nonassociative right H-comodule algebra B.     

Risk models for the Prize Collecting Steiner Tree problems with interval data

Given a connected graph G=(V,E)with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree(PCST)problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c+e]while taking risk(c+e xe)/(c+e c e)of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p+v]for its inclusion in T while taking risk(yv p v)/(p+v p v)of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.     

On differential properties for bivariate orthogonal polynomials

In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.      

Toward the computer-aided discovery of FabH inhibitors. Do predictive QSAR models ensure high quality virtual screening performance?

Antibiotic resistance has increased over the past two decades. New approaches for the discovery of novel antibacterials are required and innovative strategies will be necessary to identify novel and effective candidates. Related to this problem, the exploration of bacterial targets that remain unexploited by the current antibiotics in clinical use is required. One of such targets is the \(\beta \) -ketoacyl-acyl carrier protein synthase III (FabH). Here, we report a ligand-based modeling methodology for the virtual-screening of large collections of chemical compounds in the search of potential FabH inhibitors. QSAR models are developed for a diverse dataset of 296 FabH inhibitors using an in-house modeling framework. All models showed high fitting, robustness, and generalization capabilities. We further investigated the performance of the developed models in a virtual screening scenario. To carry out this investigation, we implemented a desirability-based algorithm for decoys selection that was shown effective in the selection of high quality decoys sets. Once the QSAR models were validated in the context of a virtual screening experiment their limitations arise. For this reason, we explored the potential of ensemble modeling to overcome the limitations associated to the use of single classifiers. Through a detailed evaluation of the virtual screening performance of ensemble models it was evidenced, for the first time to our knowledge, the benefits of this approach in a virtual screening scenario. From all the obtained results, we could arrive to a significant main conclusion: at least for FabH inhibitors, virtual screening performance is not guaranteed by predictive QSAR models.     

Spring-block approach for crack patterns in glass

Fracture patterns resulting from point-like impact acting perpendicularly on the plane of a commercial sodalime glass plate is modelled by a spring-block system. The characteristic patterns consist of crack lines that are spreading radially from the impact point and concentric arcs intersecting these radial lines. Experimental results suggest that the number of radial crack lines is scaling linearly with the energy dissipated during the crack formation process. The elaborated spring-block model reproduces with success the observed fracture patterns and scaling law.