Search results for "Mathematical analysis"

A velocity–diffusion method for a Lotka–Volterra system with nonlinear cross and self-diffusion

2009

The aim of this paper is to introduce a deterministic particle method for the solution of two strongly coupled reaction-diffusion equations. In these equations the diffusion is nonlinear because we consider the cross and self-diffusion effects. The reaction terms on which we focus are of the Lotka-Volterra type. Our treatment of the diffusion terms is a generalization of the idea, introduced in [P. Degond, F.-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11 (1990) 293-310] for the linear diffusion, of interpreting Fick's law in a deterministic way as a prescription on the particle velocity. Time discretization is based on the …

The energy minimization problem for two-level dissipative quantum systems

2010

In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Hamilton–Jacobi–Bellman equation. This analysis completed by numerical simulations based on adapted algorithms allows a computation of the optimal control law whose robustness with respect to the initial conditions and dissipative parameters is also detailed. In the final section, an application in nuclear magnetic resonance is presented.

General theory for cross-ply laminated beams

1997

We present a general formulation of the elasticity theory of the cross-ply composite laminated beam subjected to various loadings such as axial load, bending moment, shear/bending, and torsion. The formulation is based on the integral equation theory, and a direct approach is employed to obtain the boundary integral equations for the analysis of the laminated beam. The integral equations governing the elasticity problem are directly deduced from the reciprocity theorem, by using the singular solutions of the orthotropic elasticity explicitly derived. The numerical solution is achieved by the boundary element method, which gives, once the traction free boundary conditions and the interfacial…

Grafiska integrēšana un diferencēšana. Neperiodiskas līknes nolīdzinājuma atrašana

1931

Saturs: Funkcionāls sakars, tā attēlošana 3 Empirisks un racionāls nolīdzinājums 3 Pieskares konstrukcijas 6 Grafiska integrēšana 7 Grafiska diferencēšana 9 Līkņu veidi un nolīdzinājumi 10 Līkņu nolīdzinājumi pārveidotā koordinātu sistēmā 11 Deformācija 13 Līkņu pazīmes 13 Atsevišķi nolīdzinājumu veidi 17 Nolīdzinājuma atrašana, ja dots līknes zars 20 Piemēri 21 Nolīdzinājuma atrašana, kad doti līknes visi zari un īpaši punkti 25

A correction method for the analysis of continuous linear one-dimensional systems under moving loads

2008

A new correction procedure for dynamic analysis of linear, proportionally damped, continuous systems under traveling concentrated loads is proposed; both cases of non-parametric (moving forces) and parametric (moving mass) loads are considered. Improvement in the evaluation of the dynamic response is obtained by separating the contribution of the low-frequency (LF) modes from that of the high-frequency (HF) modes. The former is calculated, as usual, by classical modal analysis, while the latter is taken into account using a new series expansion of the corresponding particular solution. The advantage of the suggested method is immediately shown in the calculation of the stress distribution s…

Transparent boundary condition for acoustic propagation in lined guide with mean flow

2008

A finite element analysis of acoustic radiation in an infinite lined guide with mean flow is studied. In order to bound the domain, transparent boundary conditions are introduced by means of a Dirichlet to Neumann (DtN) operator based on a modal decomposition. This decomposition is easy to carry out in a hard‐walled guide. With absorbant lining, many difficulties occur even without mean flow. Since the eigenvalue problem is no longer selfadjoint, acoustic modes are not orthogonal with respect to the L2‐scalar product. However, an orthogonality relation exists which permits writing the modal decomposition. For a lined guide with uniform mean flow, modes are no longer orthogonal but a new sca…

The closure of the numerical range of an operator as spectral set

1964

Eigenvectors of k–ψ-contractive wedge operators

2008

Abstract We present new boundary conditions under which the fixed point index of a strict- ψ -contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k – ψ -contractive wedge operators.

Reflection and Refraction of Singularities for Wave Equations with Interface Conditions given by Fourier Integral Operators

1992

Cauchy problems for hyperbolic operators often have the property, that the singularities of the initial data propagate along the bicharacteristic strips of the operator (cf. e.g. [13]). We consider, in the linear case, the situation where the bicharacteristics hit transversally a spacelike interface, which is ‘active’ in the sense that the interface condition is given via certain Fourier integral operators. Taking the identity, we obtain classical transmission conditions. A suitable functional analytic setting is furnished by the interaction concept [3], [6], [7], which covers very general mutual influences of evolution phenomena on different domains.

Approximation properties of q-Kantorovich-Stancu operator

2015

In this paper we study some properties of Kantorovich-type generalizations of the q-Stancu operators. We obtain some approximation properties for these operators, estimating the rate of convergence by using the first and second modulus of continuity. Also, we investigate the statistical approximation properties of the q-Kantorovich-Stancu operators using the Korovkin-type statistical approximation theorem.