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 “Shidov Property” and a Formation Satisfying It

If G is a nonsoluble finite group, the intersection of the maximal subgroups of G which are not nilpotent is the Frattini subgroup of G. This was proved by Shidov (1971 Shidov , L. I. ( 1971 ). On maximal subgroups of finite groups . Sibirsk. Mat. Zh. 12 ( 3 ): 682 – 683 . [Google Scholar]). The authors here present a new formation ? larger than the formation of the nilpotent groups for which the analogous of the theorem of Shidov holds. The theorem makes use of the classification of finite simple groups.     

On the complete integrability and linearization of a Burgers– Korteweg–de Vries-type nonlinear equation

In this work, on the basis of the Bogolyubov–Prykarpats’kyi gradient–holonomic algorithm for the investigation of the integrability of nonlinear dynamical systems on functional manifolds, the exact linearization of a Burgers–Korteweg–de Vries-type nonlinear dynamical system is established. As a result, we describe the linear structure of the space of solutions and show its relation to the convexity of certain functional subsets. The bi-Hamiltonian property of the Burgers–Korteweg–de Vries dynamical system is also established, and the infinite hierarchy of functionally independent invariants is constructed.     

On the “function” and “lattice” definitions of a narrow operator

We prove that the function and lattice definitions of a narrow operator defined on a Köthe Banach space E on a finite atomless measure space \((\Omega , \Sigma , \mu )\) are equivalent if and only if the set of all simple functions is dense in E. This answers Problem 10.3 from Popov and Randrianantoanina (Narrow operators on function spaces and vector lattices, De Gruyter studies in mathematics 45, De Gruyter, Berlin, 2013).     

On conjugate complex time – II: equipotential effect of gravity retrodicts differential and predicts apparent anomalous rotation of the sun

Equipotential effect of gravity (EEG), as opposed to radial interactions between bodies, is introduced here as the impact of a tangential potential. EEG causes frequency decrease that was observed in two specially devised and several indirect experiments. It depends on the distance that is measured along equipotential parts of trajectories and can explain an extraneous frequency decrease found in radio signals emitted by navigational positioning systems. It retrodicts the observed differential rotation of the sun without the assumed drag of the sun's photosphere as its cause, and predicts apparent anomalous rotation of the sun, for from the shifts in spectra taken from the sun's limb it should appear as if the sun rotates away faster than it does towards an observer on earth. The value predicted by it is over 10.56% excess over Einstein's value of deflection of light near the sun and agrees with the 10–15% excess estimated from the data that was obtained in numerous, quite independent experiments.     

On solutions of a common generalization of the Go?a?b-Schinzel equation and of the addition formulae

Under some additional assumptions we determine solutions of the equation

f(x+M(f(x))y)=f(x)○f(y),     

On channel coordination under price-dependent revenue-sharing: can eBay's fee structure coordinate the channel?

This article deals with the problem of coordinating a vertically separated channel under consignment contracts with a price-dependent revenue-sharing (R-S) function. We consider the retailer being a channel leader who offers the vendor a leave-it-or-take-it contract, and the vendor being a price-setting firm who sells the one-of-a-kind goods through the exclusive channel. Under such a setting, the retailer decides on the term of R-S contract, and the vendor determines the retail price of the product. For each item sold, the retailer deducts an agreed-upon percentage from the price and remits the balance to the vendor. We model the decision-making of the two firms as a Stackelberg game, and carry out equilibrium analysis for both the centralized and decentralized regimes of the channel with consideration of three kinds of contracts: the fixed, the price-increasing, and the price-decreasing R-S percentage. Our analysis reveals that the contract with a price-decreasing R-S function, for example, the fee structure adopted by eBay.com, performs worse than the others. It persists in a consistent bias: the price-decreasing R-S induces the vendor to choose a higher price, and the retailer tends to receive a lower R-S percentage, which leads to less demand quantity, less profit, and channel inefficiency.     

Erratum to “On a Classical Theorem on the Diameter and Minimum Degree of a Graph”

The original version of the article was published in[1]. Unfortunately, the original version of this article contains a mistake:in Theorem 6.2 appears that β(n, Δ)=(n-Δ+5)/4 but the correct statement is β(n, Δ)=(n-Δ+4)/4. In this erratum we correct the theorem and give the correct proof.     

On “Pre-historic” Linear Programming and the Figure of the Earth

In this paper, we develop algorithms to solve generalized Fermat–Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.     

On solving the chaotic Chen system: a new time marching design for the variational iteration method using Adomian’s polynomial

This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving the chaotic Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This research implements the multistage variational iteration method with an emphasis on the new multistage hybrid of variational iteration method with Adomian polynomials. Numerical comparisons are made between the multistage variational iteration method, the multistage variational iteration method using the Adomian’s polynomials and the classic fourth-order Runge-Kutta method. Our work shows that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage variational iteration method.     

Imperfect recall and time inconsistencies: an experimental test of the absentminded driver “paradox”

Absentmindedness is a special case of imperfect recall, in which a single history includes more than one decision node in an information set. Put differently, players, after making a decision, sometimes face it again without recalling having ‘been there before’. Piccione and Rubinstein (Game Econ Behav 20(1):3–24, 1997b) have argued that absentmindedness may lead to time inconsistencies. Specifically, in certain cases, a player’s optimal strategy as calculated when called to choose an action (the action stage) deviates from the optimal strategy as calculated in a preceding planning stage, although preferences remain constant and no new information is revealed between the two stages. An alternative approach assumes that the player maximizes expected payoff in the action stage while considering his actions at other decision nodes to be immutable. With this approach, no time inconsistencies arise. The present paper explores this issue from a behavioral point of view. We elicit participants’ strategies in an experimental game of absentmindedness, separately for a planning stage and an action stage. We find systematic and robust time inconsistencies under four variations of the experiment and using ten different parameterizations of the game. We conclude that real decisions under absentmindedness without commitment are susceptible to time inconsistencies.     

Counterexample to the paper “On the Gorenstein injective dimension and Bass formula”

In this note, we give a counterexample for Theorem 2.3 of the above mentioned paper that is a generalization of the Grothendieck non-vanishing theorem to a class of modules larger than finitely generated modules.     

On Markov?CKrein characterization of the mean waiting time in M/G/K and other queueing systems

We propose a new research direction to reinvigorate research into better understanding of the M/G/K and other queueing systems??via obtaining tight bounds on the mean waiting time as functions of the moments of the service distribution. Analogous to the classical Markov?CKrein theorem, we conjecture that the bounds on the mean waiting time are achieved by service distributions corresponding to the upper/lower principal representations of the moment sequence. We present analytical, numerical, and simulation evidence in support of our conjectures.     

On the location of the maximum of a process: Lévy,Gaussian and Random field cases

ABSTRACT

We show how the techniques presented in Pimentel [On the location of the maximum of a continuous stochastic process, J. Appl. Prob. 51 (2014), pp. 152–161] can be extended to a variety of non-continuous processes and random fields. For the Gaussian case, we prove new covariance formulae between the maximum and the maximizer of the process. As examples, we prove uniqueness of the location of the maximum for spectrally positive Lévy processes, Ornstein–Uhlenbeck process, fractional Brownian Motion and the Brownian sheet among other processes.     

Mixed convexity and optimization results for an (S ? 1, S) inventory model under a time limit on backorders

Das (Oper Res 25(5):835–850, 1977) considered the optimization of a cost function associated with an (S ? 1, S) inventory model assuming the parameters to be the initial number of items in the stock and the service rate. A similar optimization problem associated with an M/E _k /1 queueing system with parameters being the number of servers and the service rate was considered by Kumin (Manag Sci 20:126–129, 1973). Both carried out case-dependent computations and indicated the difficulty of finding general convexity and optimization results for functions with both integer and real variables. In this paper, generalized mixed convexity and computational optimization results for the cost function associated with the (S ? 1, S) inventory system suggested by Das are provided. The generalized convexity results determine the convexity region of the cost function, and therefore the region of possible minimal values of the cost function in the domain. In addition, algorithms to determine the generalized convexity and computational optimization results for the cost function are given.     

On optimal partitions,individual values and cooperative games: Does a wiser agent always produce a higher value?

We consider an optimal partition of resources (e.g. consumers) between several agents, given utility functions (“wisdoms”) for the agents and their capacities. This problem is a variant of optimal transport (Monge–Kantorovich) between two measure spaces where one of the measures is discrete (capacities) and the costs of transport are the wisdoms of the agents. We concentrate on the individual value for each agent under optimal partition and show that, counter-intuitively, this value may decrease if the agent’s wisdom is increased. Sufficient and necessary conditions for the monotonicity with respect to the wisdom functions of the individual values will be given, independently of the other agents. The sharpness of these conditions is also discussed. Motivated by the above we define a cooperative game based on optimal partition and investigate conditions for stability of the grand coalition.