Corrigendum to “congruences for certain binomial sums”

Theorem 1 of J.-J. Lee, Congruences for certain binomial sums. Czech. Math. J. 63 (2013), 65–71, is incorrect as it stands. We correct this here. The final result is changed, but the essential idea of above mentioned paper remains valid.     

Tabu search for discrete–continuous scheduling problems with heuristic continuous resource allocation

Problems of scheduling non-preemptable, independent jobs on parallel identical machines under an additional continuous renewable resource to minimize the makespan are considered. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation that minimize the makespan. A heuristic procedure for allocating the continuous resource is used. The tabu search metaheuristic to solve the considered problem is presented. The results produced by tabu search are compared with optimal solutions for small instances, as well as with the results generated by simple search methods – multi-start iterative improvement and random sampling for larger instances.     

Solving inverse problems for variational equations using “generalized collage methods,” with applications to boundary value problems

A number of inverse problems involving deterministic and random differential equations may be viewed in terms of the problem of approximating a target element $x$ of a complete metric space $(X,d)$ by the fixed point $\stackrel{?}{x}$ of a contraction mapping $T:X\to X$. Most practical methods rely on a reformulation of this problem due to the “Collage Theorem,” a simple consequence of Banach’s Fixed Point Theorem: They search for a contraction mapping that minimizes the “collage distance” $d(x,Tx)$. One may consider the collage method as a kind of regularization procedure for the inverse problem. In this paper, after recalling some applications of the Collage Theorem to the solution of inverse problems for fixed point equations and applications of it to initial value problems, with the help of the Lax–Milgram representation, we develop some generalizations of the collage method in order to solve inverse problems for variational equations. We consider both deterministic and stochastic problems. We then show some applications to inverse boundary value problems.     

Corrigendum to “on the restricted partition function”

The Ramanujan Journal - This article is a corrigendum to our paper (Cimpoea? and Nicolae in Ramanujan J 473:565–588, 2018).     

Parallel Dantzig–Wolfe decomposition of petroleum production allocation problems

This article discusses the optimization of a petroleum production allocation problem through a parallel Dantzig–Wolfe algorithm. Petroleum production allocation problems are problems in which the determination of optimal production rates, lift gas rates and well connections are the central decisions. The motivation for modelling and solving such optimization problems stems from the value that lies in an increased production rate and the current lack of integrated software that considers petroleum production systems as a whole. Through our computational study, which is based on realistic production data from the Troll West field, we show the increase in computational efficiency that a parallel Dantzig–Wolfe algorithm offers. In addition, we show that previously implemented standard parallel algorithms lead to an inefficient use of parallel resources. A more advanced parallel algorithm is therefore developed to improve efficiency, making it possible to scale the algorithm by adding more CPUs and thus approach a reasonable solution time for realistic-sized problems.     

Monotone-iterative method for mixed boundary value problems for generalized difference equations with “maxima”

In this paper the authors investigate special type of difference equations which involve both delays and the maximum value of the unknown function over a past time interval. This type of equations is used to model a real process which present state depends significantly on its maximal value over a past time interval. An appropriate mixed boundary value problem for the given nonlinear difference equation is set up. An algorithm, namely, the monotone iterative technique is suggested to solve this problem approximately. An important feature of our algorithm is that each successive approximation of the unknown solution is equal to the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima”, and a formula for its explicit form is given. Also, each approximation is a lower/upper solution of the given nonlinear boundary value problem. Several numerical examples are considered to illustrate the practical application of the suggested algorithm.     

An alternative approach to the Faber–Krahn inequality for Robin problems

We give a simple proof of the Faber–Krahn inequality for the first eigenvalue of the p-Laplace operator with Robin boundary conditions. The techniques introduced allow to work with much less regular domains by using test function arguments. We substantially simplify earlier proofs, and establish the sharpness of the inequality for a larger class of domains at the same time.     

Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problems

Summary In contrast to Hölmgren uniqueness for linear equations and to the similar uniqueness result for first order scalar nonlinear equations, this paper gives elementary examples of analytic nonlinear higher order equations, for which uniqueness ofC solutions to the non characteristic Cauchy problem fails.Oblatum 11-V-1992 & 19-X-1992     

Single periodic Riemann problems for null-solutions to polynomially Cauchy–Riemann equations

In this paper, we focus on single periodic Riemann problems for a class of meta-analytic functions, i.e. null-solutions to polynomially Cauchy–Riemann equation. We first establish decomposition theorems for single periodic meta-analytic functions. Then, we give a series expansion of single periodic meta-analytic functions, and derive generalised Liouville theorems for them. Next, we introduce a definition of order for single periodic meta-analytic functions at infinity, and characterise their growth at infinity. Finally, applying the decomposition theorem for single periodic meta-analytic functions, we get explicit expressions of solutions and condition of solvability to Riemann problems for single periodic meta-analytic functions with a finite order at infinity.     

Correction to “Queue-proportional rate allocation with per-link information in multihop wireless networks”

There is a gap in the proofs of both Propositions 3 and 4 in the correspondence “Queue-Proportional Rate Allocation with Per-Link Information in Multihop Wireless Networks,” previously published in the Queueing Systems (see Li and Srikant 2016). We filled this gap in the proofs for the multihop networks (see Li and Srikant in Queueing Syst 84:203–210, 2016), where each route at most has two links. In this note, we completely fill the gap in the proofs in our original paper (see Li and Srikant in Queueing Syst 83:329–359, 2016).     

Time-marching algorithms for initial-boundary value problems based upon “approximate approximations”

New time marching algorithms for solving initial-boundary value problems for semi-linear parabolic and hyperbolic equations are described. With respect to the space variable the discretization is based upon a method of approximate approximation proposed by the second author. We use approximate approximations of the fourth order. In time the algorithms are finite-difference schemes of either first or second approximation order. At each time step the approximate solution is represented by an explicit analytic formula. The algorithms are stable under mild restrictions to the time step which come from the non-linear part of the equation. Some computational results and hints on crucial implementation issues are provided.Supported by the Center for Applied and Industrial Mathematics, Department of Mathematics, Linköping University, Sweden.     

Corrigendum to “Some problems of Wielandt revisited” [J. Algebra 302 (1) (2006) 167–185]

An error in the proof of Theorem 2 in [W. Knapp, Some problems of Wielandt revisited, J. Algebra 302 (1) (2006) 167–185] (concerning the action of semisimple groups) is corrected.     

Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints

In this paper we consider strong bilevel vector equilibrium problems and introduce the concepts of Levitin–Polyak well-posedness and Levitin–Polyak well-posedness in the generalized sense for such problems. The notions of upper/lower semicontinuity involving variable cones for vector-valued mappings and their properties are proposed and studied. Using these generalized semicontinuity notions, we investigate sufficient and/or necessary conditions of the Levitin–Polyak well-posedness for the reference problems. Some metric characterizations of these Levitin–Polyak well-posedness concepts in the behavior of approximate solution sets are also discussed. As an application, we consider the special case of traffic network problems with equilibrium constraints.