Solvability Set Research Articles

Stability of multiobjective NLP problems with fuzzy parameters in the objectives and constraints functions

This paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the objectives and constraints functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of the notions (solvability set, stability sets of the first kind and of the second kind) in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of α-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding α-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.

Parametric nash coalitive differential games

In this paper we present the qualitative and quantitative analysis of open loop coalitive Nash equilibrium solutions to differential games of fixed duration with general parameters in the cost functions. The solvability set and the stability sets of the first and the second kind are defined and algorithms for determining these sets are presented. Finally an illustrative example is given.

A fully dispersive weakly nonlinear model for water waves

A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm–coupling technique , in which the velocity field is represented by a few vertical–dependence functions having different wave–numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth–dependence functions to represent a random wave–field with diversely varying wave–numbers. The new wave equations are valid for arbitrary ratios of depth to wavelength and therefore it is possible to recover all the well–known linear and weakly nonlinear wave models as special cases. Numerical simulations are carried out to demonstrate that a wide spectrum of waves, such as random deep water waves and solitary waves over constant depth as well as nonlinear random waves over variable depth, is well reproduced at affordable computational cost.

The stability notions for fuzzy nonlinear programming problem

This paper deals with the stability of fuzzy multiobjective nonlinear programming (FMONLP) problem. The stability and the stability notions of parametric nonlinear programming problem are extended to redefine and analyze the stability and stability notions of FMONLP. The concept of α-fuzzy efficient was introduced in which the ordinary efficient solution is extended based on the α-fuzzy numbers. A necessary and sufficient condition for such a solution is established. The basic notions of stability (the solvability set and the stability set of the first kind) are redefined and analyzed qualitatively and quantitatively for the problem. An example is given for the sake of illustration.

A parametric study of multiobjective NLP problems with fuzzy parameters in the objective functions

This paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of the notions (solvability set, stability sets of the first kind and of the second kind) in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of α-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding α-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.

Spectroscopic Wave Function Imaging and Potential Inversion

An accurate imaging technique of complex nonstationary wave functions and a method of inversion of excited-state potentials is developed. The wave function imaging is accomplished by using both frequency-resolved and time-resolved fluorescence data, thereby reducing the problem to a solvable set of linear algebraic equations. The procedure is demonstrated for excited-state Na2 wave packets created by ultrashort pulse excitations. A method for evaluating the sign of the transition-dipole amplitudes from the spectral line strengths is developed. Using the transition-dipole amplitudes thus generated, plus the transition frequencies and the ground state potential, we show how to obtain excited-state potentials. Contrary to the RKR procedure, this inversion scheme is not limited to diatomic molecules and is capable of yielding potentials at energies above the dissociation thresholds. Highly accurate inversions of the and Na2(B1Πu) excited-state potentials are demonstrated.

Stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints

This paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraint functions. These fuzzy parameters are characterized by fuzzy numbers. Qualitative and quantitative analysis of the basic notions like the set of feasible parameters, the solvability set, the stability sets of the first kind and of the second kind, will be reformulated under the concept of α-pareto optimality. An illustrative example is given to clarify the obtained results.

Stability on multiobjective linear programming problems with fuzzy parameters

This paper deals with multiobjective linear programming problems with fuzzy parameters (FMOLP). For such problems, some stability notions as the solvability set and the stability set of the first kind (SSK1) are defined and characterized. Two algorithms for the determination of the set (SSK1) are proposed. One of these algorithms is applied when the fuzzy multiobjective problem remains linear after introducing the so-called α-level set of the fuzzy numbers, while the other algorithm is applied when the fuzzy multiobjective problem becomes nonlinear. Finally, a numerical example is given to illustrate the theory developed in the paper.

Imaging of wave functions and potentials from time-resolved and frequency-resolved fluorescence data

Imaging of the amplitude and phase of time-evolving wave functions and excited-state potentials, using fluorescence data, is performed. The method relies on the use of both frequency-resolved and time-resolved fluorescence to reduce the problem of wave function imaging to a solvable set of linear algebraic equations. The potential inversion is performed by a new formula which expresses an excited state potential in terms of the ground state potential, the transition frequencies, and the transition-dipole matrix elements, whose sign is shown to be derivable from the spectral line strengths.

Finite-difference equations in relativistic quantum mechanics

Relativistic Quantum Mechanics suffers from structural problems which are traced back to the lack of a position operator $\hat{x}$, satisfying $[\hat{x},\hat{p}]=i\hbar\hat{1}$ with the ordinary momentum operator $\hat{p}$, in the basic symmetry group -- the Poincar\'e group. In this paper we provide a finite-dimensional extension of the Poincar\'e group containing only one more (in 1+1D) generator $\hat{\pi}$, satisfying the commutation relation $[\hat{k},\hat{\pi}]=i\hbar\hat{1}$ with the ordinary boost generator $\hat{k}$. The unitary irreducible representations are calculated and the carrier space proves to be the set of Shapiro's wave functions. The generalized equations of motion constitute a simple example of exactly solvable finite-difference set of equations associated with infinite-order polarization equations.

A study on parametric multiobjective programming problems without differentiability

Great efforts have been done for studying basic notions like the solvability and stability sets for parametric multiobjective programming problems of the first and second kind. In this paper, these notions have been defined and analyzed without differentiability assumptions on the considered functions. New stability notions like the stability sets of the third and fourth kind have been also defined and analyzed for this problem.

Qualitative analysis of basic notions in an iterative approach to possibilistic goal programming

Abstract This paper deals with the qualitative analysis of basic notions in an iterative approach to possibilistic general goal programming problems. The problem is considered by incorporating possibilistic distribution into the parametric goals of the goal programming. As apparatus to cope with this problem, we use the concept of α-possibly optimal solutions for the problem. A necessary and sufficient condition for such a solution is established. The basic notions of stability (the solvability set, the stability set of the first kind and the stability set of the second kind) are redefined and analyzed qualitatively for the problem.

A Semenov approach to the modelling of thermal runaway of damp combustible material

Semenov theory for the self-heating of a reactive slab is extended to take account of the presence of water vapour. In this paper, mass changes due to evaporation/condensation are neglected but heat exchange is retained in the energy equation. By doing this, a simple easily solvable set of equations can be set up to represent the thermal behaviour of the slab. No account is taken of possible wet exothermic reactions in this paper. The aim is simply to understand the effects of evaporation/condensation on the overall thermal history. Using a simple model which treats the mass changes within the material as negligible, the competitive effects of condensation and evaporation are shown to produce a two-time situation which depends crucially on the surface mass transfer/heat transfer ratio h m

Use of Matrix Pencils for Parameter Identification in Analog Circuits

Abstract This paper provides new insight to the parameter identification problem in analog linear circuits by introducing the concept of n-pencils. With the given approach, the uniquely solvable set of parameters can be determined by the rank test of the Toeplitz matrix constructed from the parameter coefficient matrices which can be obtained from the topology of the network. This approach is a unified one in that it considers both the single and multiple excitation sets and yields constraints on the coefficient matrices for unique solvability of the parameters for both cases.

Inverse Dynamic Models of Closed-Chain Mechanisms With Contact Compliance

A general inverse dynamic model which is applicable to closed-chain mechanisms with contact compliance is presented. This class of mechanism has relatively rigid members and joints, but experiences compliant interactions with objects and the environment; examples include walking machines operating on natural terrain, devices for grasping a compliant object, and wheeled mobile robots. Previous approaches for formulating inverse dynamic models of compliant mechanisms have been approximations or limited to simple configurations and open-chain mechanisms. Inverse dynamic equations for closed-chain mechanisms with contact compliance are shown to be solvable sets of differential/algebraic equtaions (DAEs) which assures that stable and accurate solutions can be calculated; relevant characteristics and solutions of DAE systems are discussed.

The almost chebyshev property in linear semi-infinite programming

We consider a linear semi-infinite programming problem where the index set of the constraints is compact and the constraint functions are continuous on it. The set of all continuous functions on this index set as right hand sides are the parameter set. We investigate how large various unicity sets are.We state a condition on the objective function vector and the “matrix” of the problem which characterizes when the set of a parameters with a non-unique optimal point is a set of the first Baire category in the solvability set. This is the case if and only if the unicity set is a dense subset of the solvability set. Under the same assumptions it is even true that the interior of the strong unicity set is I also dense. If the index set of the constraints contains a dense subset with the property that each point1 is a G 8-set, then the parameters of the strong unicity set, such that the optimal point satisfies the linear independence constraint qualification, are also dense. We apply our results to a character...

On a construction related to the non-abelian tensor square of a group

LetG andGφ be isomorphic groups. We introduce and study a quotient ν(G) of the free productG *Gφ which is a group extention of the non-abelian tensor squareG ⊗G. This seems to bring computational advantages to calculate this last group. Looking over ν as an operator in the class of groups we prove that it preserves properties of the argumentG such as finiteness, set of prime divisors, nilpotency and solvability. For a finitep-groupG we find a good polynomial bound for the order of ν (G).

Geometrical SO(4, 1) gauge theory as a basis of extended relativistic objects for hadrons

The geometrical structure for a collective model description of extended relativistic single hadron systems is investigated by considering a Yang-Mills theory of the de Sitter group SO(4, 1). The full SO(4, 1) symmetry is broken down to that of its SO(3, 1) stability subgroup resulting in a set of Goldstone fields which are taken to represent coordinates of a point in the de Sitter fibre space and are used, along with the original linear gauge fields, to define the vierbein and spin connection on the restricted bundle: P'(M4, SO(3, 1)) contained in/implied by P(M4, SO(4, 1)). The symmetry breaking parameter is taken as a fundamental length relevant to hadron physics. The original linear gauge fields generate a type of parallel transport which is the curved space analogue of development into the flat affine tangent space and serves as the bridge between the geometrical and purely gauge-theoretic descriptions. Upon quantisation, the generator of development in the unitary gauge (Higgs mechanism), for a special class of horizontal Lorentz cross sections, goes over into the de Sitter space momentum which serves to break the mass-spin degeneracy inherent in the Poincare group description and supplies a curved space perturbation in the resulting relativistic Hamiltonian. The Hamiltonian is used to determine a completely solvable set of dynamical equations of motion resulting in the Zitterbewegung of the extended relativistic object.

Method of programmed iterations in pulse correction problems

Pulse correction problems are considered and a solution method based on programmed iterations is proposed. The structure of the solvability set of the pursuit problem with a fixed termination time is established subject to geometrical and mixed constraints on the set of control pulses.

A class of combinatorial problems with polynomially solvable large scale set covering/partitioning relaxations

On introduit ici toute une classe de problemes combinatoires qui peuvent se formuler comme des problemes de recouvrement/partitionnement de tres grandes dimensions dont les relaxations continues ou bien sont solubles en temps polynomial par l'algorithme des ellipsoides, ou bien peuvent etre resolues de facon efficace par des techniques de programmation lineaire generalisee. On montre que cette classe contient non seulement des problemes combinatoires bien connus, mais aussi un certain nombre de problemes apparemment nouveaux et decrits ici pour la premiere fois