Constraining inverse stefan design problems

A new formulation possessing stable numerical characteristics is presented for inverse Stefan design processes. In such processes, the goal of the analysis is to design transient boundary conditions which produce the desired interfacial surface motion. This subclass of mildly ill-posed mathematical problems is amenable to the proposed solution methodology. This investigation presents a fixed-front differential formulation from which a weighted residual statement is developed. Orthogonal collocation is used to obtain numerical results illustrating the merit of imposing physical constraints in the mathematical model. These mathematical constraints can be viewed as design specifications and are available to the designer or experimentalist. The proposed methodology is flexible and can be generalized to problems involving continuous casting or crystal growth. Finally, symbolic manipulation is used for augmenting the computational methodology.     

A regularization method for stationary maxwell equations in an inhomogeneous conducting medium

We consider the problem of defining a vector potential of a magnetic field with a nonstandard calibration in an inhomogeneous conducting medium. The problem in question is one with constraints on the right-hand side and on the solution itself. A generalized and regularized statement of this problem without constraints is proposed and substantiated. Such a problem statement is equivalent to the original generalized problem with constraints.     

A reciprocal confluence tree unit and its applications

A theorem by Jaeschke is generalized in this paper and a fast and efficient implementation called Reciprocal Confluence Tree unit for implementing the new theorem is sketched. We shall show that it can be used to solve two problems: a hashing algorithm design problem and an access control mechanism design problem.     

Solvability of physically and geometrically nonlinear problem of the theory of sandwich plates with transversally-soft core

The paper presents a generalized statement of geometrically and physically nonlinear problem of the equilibrium of sandwich plate with transversally-soft core. Generalized statement is formulated as a problem of finding a saddle point of a functional. We investigate the properties of this functional. These properties allow to prove a theorem of solvability of variational problem under consideration.     

Siegel zeros and the Goldbach problem

It is generally known that under the generalized Riemann hypothesis one could establish the Goldbach conjecture by the circle method provided one could obtain a certain estimate for the integral of the representation function over the minor arcs. Here it is first shown that the generalized Riemann hypothesis in the above statement can be weakened to the assumption that Siegel zeros do not exist. The case when Siegel zeros do exist is then considered.     

A projection approach to optimal control of elastic beam dynamics

Controlled lateral motions of an elastic beam – extended body with a cuboid shape – are studied. A generalized statement of the initial-boundary value problem is given in the frame of 3D linear elasticity based on the integral formulation of constitutive relations. A numerical approach relying on the Fourier method and semi-discretization technique is proposed to design the optimal boundary control that moves the beam to a given final state and minimizes a quadratic cost function. Some results of numerical simulation and quality analysis are presented and discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diophantine equations and the generalized Riemann hypothesis

We show that, for a listable set P of polynomials with integer coefficients, the statement “for all roots θ of all polynomials in P, the generalized Riemann hypothesis for Q(θ) holds” is Diophantine. That is, the statement is equivalent to the unsolvability of a particular Diophantine equation. This is achieved by finding a decidable property P such that the aforementioned statement may be written in the form “P holds for all natural numbers”.     

Iterative methods for finding the boundaries of unrecovered viscoplastic oil in multilayer beds

We suggest a generalized statement of the problem of finding the boundaries of limit-equilibrium unrecovered viscoplastic oil in multilayer beds in the form of a mixed variational inequality. We analyze the solvability of the problem. For its solution, we suggest an iterative method whose each step can essentially be reduced to the solution of the Dirichlet problem for the Poisson equation.     

Generation of efficient frontiers in multi-objective optimization problems by generalized data envelopment analysis

In many practical problems such as engineering design problems, criteria functions cannot be given explicitly in terms of design variables. Under this circumstance, values of criteria functions for given values of design variables are usually obtained by some analyses such as structural analysis, thermodynamical analysis or fluid mechanical analysis. These analyses require considerably much computation time. Therefore, it is not unrealistic to apply existing interactive optimization methods to those problems. On the other hand, there have been many trials using genetic algorithms (GA) for generating efficient frontiers in multi-objective optimization problems. This approach is effective in problems with two or three objective functions. However, these methods cannot usually provide a good approximation to the exact efficient frontiers within a small number of generations in spite of our time limitation. The present paper proposes a method combining generalized data envelopment analysis (GDEA) and GA for generating efficient frontiers in multi-objective optimization problems. GDEA removes dominated design alternatives faster than methods based on only GA. The proposed method can yield desirable efficient frontiers even in non-convex problems as well as convex problems. The effectiveness of the proposed method will be shown through several numerical examples.     

Scalarization of Henig Properly Efficient Points in Locally Convex Spaces

Without any convexity assumption on feasible sets, we obtain two versions of scalarization of Henig properly efficient points with respect to a base of the ordering cone. Then we further deduce two corresponding versions of the scalarization of (resp. generalized) Henig properly efficient points, which only depend on the ordering cone, not referring to any special base. Moreover, we investigate the relationship between generalized Henig properly efficient points and Henig properly efficient points. Particularly, we give some conditions for generalized Henig properly efficient points to be Henig properly efficient points.     

On a class of essentially nonlinear elliptic differential-difference equations

An essentially nonlinear differential-difference equation containing the product of the p-Laplacian and a difference operator is considered. Sufficient conditions are obtained for the corresponding nonlinear differential-difference operator to be coercive and pseudomonotone in the case of nonvariational statement of the differential equation. The existence of a generalized solution to the Dirichlet problem for the nonlinear equation is proved.     

Local Solvability of the Problem of the Van Der Waals Gas Flow Around an Infinite Plane Wedge in the Case of a Weak Shock Wave

Studying the problem of a stationary supersonic van der Waals gas flow around an infinite plane wedge, we prove the local-in-time well-posedness of the generalized statement of the problem.     

Spectral problem in a waveguide with homogeneous bi-isotropic filling

A vector spectral problem in a rectangular waveguide with homogeneous bi-isotropic filling is considered. A generalized statement of this problem is proposed, which is used to develop a finite-element algorithm for calculating propagation constants with spurious solutions eliminated.     

Henig proper efficient points and generalized Henig proper efficient points

Applying the theory of locally convex spaces to vector optimization, we investigate the relationship between Henig proper efficient points and generalized Henig proper efficient points. In particular, we obtain a sufficient and necessary condition for generalized Henig proper efficient points to be Henig proper efficient points. From this, we derive several convenient criteria for judging Henig proper efficient points.     

Generalized set-valued mixed nonlinear quasi variational inequalities

In this paper we introduce and study a number of new classes of quasi variational inequalities. Using essentially the projection technique and its variant forms we prove that the generalized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations (normal maps). This equivalence enables us to suggest a number of iterative algorithms for solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational inequalities, we obtain a class of quasi variational inequalities studied by Siddiqi, Husain and Kazmi [35], but there are several inaccuracies in their formulation of the problem, the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of their results can be obtained as special cases from our main results.     

On the poisson output of queueing systems with dependent service times

In this paper a method is stated to conclude that the output of given queueing system is POISSON from the steady-state probabilities and from the behavior of the queueing system at jump epochs, i.e. at epochs when the system state can be changed. The corresponding statement for queueing systems described by Markov processes with denumber-able state space will be generalized to systems which can have arbitrary service time distributions if the steady-state probabilities are insensitive with respect to these distributions.     

Numerical Method for Damping String Vibrations with Unknown Initial State in the Class of Weak Generalized Solutions

The problem of positional boundary control is considered for the spatially one-dimensional wave equation. The objective of control is to transfer the system from an unknown initial state into the state of rest in finite time. A specific feature of the statement of the problem is the weakening of the requirements on the regularity of generalized solutions, observations, and control. The smoothing procedure is used to transfer the problem into the class of strong generalized solutions, where the method previously developed by the authors can be used. The procedure is mathematically justified, and the corresponding results of numerical experiments are given.     

Coproducts of bounded distributive lattices: infinite distributivity

Summary It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. In 1986, Yaqub proved that generalized Post algebras with a finite lattice of constants satisfy JID, and stated that, in general, it is not known whether a generalized Post algebra satisfies JID when its lattice of constants satisfies JID. In this note, the statement is proved.     

Efficient solutions in generalized linear vector optimization

This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized linear vector optimization problems is obtained. We also prove that the efficient solution set of a generalized linear vector optimization problem in a locally convex Hausdorff topological vector space is the union of finitely many generalized polyhedral convex sets and it is connected by line segments.