On a heuristic treatment of the ‘Indices of dispersion’

Summary An elementary presentation of the ‘indices of dispersion’ tests used in detection of possible lack of homogeneity in successive samples from Poisson or binomial distributions is given. Various limiting distributions with an approximate form of the index are shown, in supplementing some empirical results obtained by ‘Monte Carlo’ methods on the I.B.M. 709 electronic computer.     

On the ‘Bayesability’ of chance-constrained programming problems

It was hoped that the aversions to risks of goal-attainment failures modeled by chance constraints could be equivalently embodied in some von Neumann-Morgenstern utility function, the expectation of which could be maximized in the standard Bayesian fashion to yield solution sets at all chance-constraint levels identical to those of the original chance-constrained program (CCP). But I shall show that a finite-act E-model CCP cannot have any such Bayesian equivalent if any goal modeled by a chance constraint can fail to be attained by a strategy which optimizes the chance-unconstrained objective function.     

On the ‘independence of trials-assumption’ in geometric distribution

In this note, it is shown through an example that the assumption of the independence of Bernoulli trials in the geometric experiment may unexpectedly not be satisfied. The example can serve as a suitable and useful classroom activity for students in introductory probability courses.     

A note ‘On a single machine-scheduling problem with separated position and resource effects’

This note concerns the paper [Janiak A, Kovalyov MY, Lichtenstein M. On a single machine-scheduling problem with separated position and resource effects. Optimization; 2013. doi:10.1080/02331934.2013.804077], which presents an analysis, a counterexample and a pseudocode related with our proof of optimality for a resource allocation algorithm given in [Rudek A, Rudek R. A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models. Comput. Math. Appl. 2011;62:1870–1878]. We show that the discussed analysis is based only on one part of our proof omitting its integral second part, which is the source of misunderstanding. The considered counterexample is applied for an algorithm, which was not the method presented in our paper, whereas our algorithm provides the correct result for the mentioned counterexample. The provided pseudocode of the resource allocation algorithm, which is presented as the correct method, is a pseudocode of the algorithm described in our paper. Therefore, we show that the results presented in our paper are correct.     

On the limit of conditional Spearman’s rho under the common factor model

Under the common factor structural model of credit risk, we study a limit of a conditional Spearman’s rho coefficient. The conditioning event is that the common factor stays below a threshold and the limit is taken as the threshold tends to ?∞. The main result is established through a relation with the classical theory of regular variation. We identify the relationship between the limiting Spearman’s rho and the tail thickness of the distribution function of the common factor. In particular, a necessary condition for the limiting Spearman’s rho to be strictly less than 1, is that the inverse cumulative distribution function of the common random variable is slowly varying at zero. As an illustration, the calculation of Stress Value-at-Risk for portfolio credit losses is discussed.     

On the local convergence of Newton’s method under generalized conditions of Kantorovich

Following an idea similar to that given by Dennis and Schnabel (1996) in [2], we prove a local convergence result for Newton’s method under generalized conditions of Kantorovich type.     

A possibility of realizing the Landau—Hopf scenario in the problem of tube oscillations under the action of a fluid flow

Theoretical and Mathematical Physics - We consider a boundary-value problem for a quasilinear partial differential equation describing tube oscillations under the action of a fluid flow. We show...     

On the geometric analysis of a quartic–quadratic optimization problem under a spherical constraint

Mathematical Programming - This paper considers the problem of solving a special quartic–quadratic optimization problem with a single sphere constraint, namely, finding a global and local...     

On the practical μ-stability of solutions of standard systems with delay

We study the problem of μ-stability of a dynamical system with delay. Conditions of the practical μ-stability are established for the general case and for a quasilinear system. The conditions suggested are illustrated by an example. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 204–213, February, 1999.     

On a serious mathematical error in the “Mathematical Encyclopedia” related to the solution of the Gibbs paradox

The solution of the Gibbs paradox in the “Mathematical Encyclopedia” [1] contained an error. It is also contained in many physics textbooks. A correct solution is given in this paper. New thermodynamic quantities taking into account the occurrence of dimers and clusters are introduced.     

On a Generalization of Martins’ Inequality

 Let be an increasing nonconstant sequence of positive real numbers. Under certain conditions on this sequence we prove the following inequality

On a Generalization of Martins’ Inequality

 Let be an increasing nonconstant sequence of positive real numbers. Under certain conditions on this sequence we prove the following inequality

On the Schrödinger–Maxwell equations under the effect of a general nonlinear term

In this paper we prove the existence of a nontrivial solution to the nonlinear Schrödinger–Maxwell equations in R³${\mathbb{R}}^3$, assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.     

On the geometry of O’N

We classify the rank two BCDL ₂₀₀₃-geometries of O’Nan and show that the maximal rank of a BCDL ₂₀₀₃-geometry for O’Nan is 4. This bound is sharp since it is satisfied by the rank four geometry given by Buekenhout (Contemp Math 45:1–32, 1985).