The Worpitzky identity for the groups of signed and even-signed permutations

Journal of Algebraic Combinatorics - The well-known Worpitzky identity $$\begin{aligned} (x+1)^n = \sum \limits _{k=0}^{n-1} A_{n,k} {{x+n-k} \atopwithdelims (){n}} \end{aligned}$$ provides a...     

Finite Groups with Subnormal Residuals of Sylow Normalizers

Siberian Mathematical Journal - Considering a nonempty formation $ {\mathfrak{X}} $ of nilpotent groups, we prove that a group $ G $ is an extension of a nilpotent group by an $...     

Entanglement entropy of a near-extremal black hole

Theoretical and Mathematical Physics - We study how the entanglement entropy of the Hawking radiation derived using the island recipe for the Reissner–Nordström black hole behaves as the...     

A New Proof of a Result Concerning a Complete Description of $$ (n,n + 2) $$ -Graphs with Maximum Value of the Hosoya Index

Mathematical Notes - The Hosoya index is an important topological index of graphs defined as the number of their matchings. At present, for any $$ n $$ and $$ k \in \{- 1,0,1,2 \}$$ , all connected...     

Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Methodology and Computing in Applied Probability - This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to...     

Network manipulation algorithm based on inexact alternating minimization

In this paper, we present a network manipulation algorithm based on an alternating minimization scheme from Nesterov (Soft Comput 1–12, 2020). In our context, the alternative process mimics the natural behavior of agents and organizations operating on a network. By selecting starting distributions, the organizations determine the short-term dynamics of the network. While choosing an organization in accordance with their manipulation goals, agents are prone to errors. This rational inattentive behavior leads to discrete choice probabilities. We extend the analysis of our algorithm to the inexact case, where the corresponding subproblems can only be solved with numerical inaccuracies. The parameters reflecting the imperfect behavior of agents and the credibility of organizations, as well as the condition number of the network transition matrix have a significant impact on the convergence of our algorithm. Namely, they turn out not only to improve the rate of convergence, but also to reduce the accumulated errors. From the mathematical perspective, this is due to the induced strong convexity of an appropriate potential function.

     

Oxidation of propene in the gas phase

A series of laboratory and modelling experiments on the oxidation of propene in the gas phase has been undertaken to determine conditions which give high yields of propene oxide. The conditions under which the experiments were conducted were 505–549 K and up to 4 bar pressure. It is proposed that propene oxide is formed from propene by reaction with several peroxy radicals including HO₂ and CH₃CO₃. However, one of the more important radicals is hydroxypropylperoxy. Its reaction with propene, under these conditions is more important than concerted decomposition to formaldehyde and acetaldehyde. © 1995 John Wiley & Sons, Inc.     

Elastic instabilities in cone- and -plate flow: Small gap theory

Consider the axisymmetric, inertialess cone- and -plate flow of a viscoelastic fluid. A perturbation method is used to obtain more tractable equations that describe the flow when the gap angle is small. A linear stability analysis of the base viscometric flow shows that there is a loss of stability when an elasticity parameter =DeWe, increases past a critical value. This purely elastic instability is of the oscillatory type. We obtain expressions for the critical elasticity number, frequency and wave number. The critical Deborah number varies as , the wave length as . and the wave speed as , where . is the gap angle. The most unstable mode exhibits infinitely many logarithmically-spaced roll cells which propagate inward towards the apex of the cone. These results are in agreement with experimental and numerical results.     

A two-phase algorithm for the partial accessibility constrained vehicle routing problem

In the partial accessibility constrained vehicle routing problem, a route can be covered by two types of vehicles, i.e. truck or truck + trailer. Some customers are accessible by both vehicle types, whereas others solely by trucks. After introducing an integer programming formulation for the problem, we describe a two-phase heuristic method which extends a classical vehicle routing algorithm. Since it is necessary to solve a combinatorial problem that has some similarities with the generalized assignment problem, we propose an enumerative procedure in which bounds are obtained from a Lagrangian relaxation. The routine provides very encouraging results on a set of test problems.