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## Post-Buckling Range of Plates in Axial Compression with Uncertain Initial Geometric Imperfections

### Applications of Mathematics (2002-01-01) 47: 25-44 , January 01, 2002

The method of reliable solutions alias the worst scenario method is applied to the problem of von Karman equations with uncertain initial deflection. Assuming two-mode initial and total deflections and using Galerkin approximations, the analysis leads to a system of two nonlinear algebraic equations with one or two uncertain parameters-amplitudes of initial deflections. Numerical examples involve (i) minimization of lower buckling loads and (ii) maximization of the maximal mean reduced stress.

## Regularity of Pressure in the Neighbourhood of Regular Points of Weak Solutions of the Navier-Stokes Equations

### Applications of Mathematics (2003-12-01) 48: 573-586 , December 01, 2003

In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.

## Portfolio optimization for pension plans under hybrid stochastic and local volatility

### Applications of Mathematics (2015-04-01) 60: 197-215 , April 01, 2015

Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result is a generalization of Merton’s strategy in terms of the stochastic volatility and the elasticity of variance.

## Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow

### Applications of Mathematics (2003-12-01) 48: 437-453 , December 01, 2003

We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.

## Complexity of an algorithm for solving saddle-point systems with singular blocks arising in wavelet-Galerkin discretizations

### Applications of Mathematics (2005-06-01) 50: 291-308 , June 01, 2005

The paper deals with fast solving of large saddle-point systems arising in wavelet-Galerkin discretizations of separable elliptic PDEs. The periodized orthonormal compactly supported wavelets of the tensor product type together with the fictitious domain method are used. A special structure of matrices makes it possible to utilize the fast Fourier transform that determines the complexity of the algorithm. Numerical experiments confirm theoretical results.

## Wave Front Tracking in Systems of Conservation Laws

### Applications of Mathematics (2004-12-01) 49: 501-537 , December 01, 2004

This paper contains several recent results about nonlinear systems of hyperbolic conservation laws obtained through the technique of Wave Front Tracking.

## Single-use reliability computation of a semi-Markovian system

### Applications of Mathematics (2014-10-01) 59: 571-588 , October 01, 2014

Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first and second moments of the single-use reliability. The model and the validity of the results are illustrated through a numerical example.

## Unbounded solutions of BVP for second order ODE with p-Laplacian on the half line

### Applications of Mathematics (2013-04-01) 58: 179-204 , April 01, 2013

By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.

## On a high-order iterative scheme for a nonlinear love equation

### Applications of Mathematics (2015-06-01) 60: 285-298 , June 01, 2015

In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L.T.P.Ngoc, N.T. Long (2011); L.X.Truong, L.T. P.Ngoc, N.T. Long (2009)) to get a convergent sequence at a rate of order *N* ⩾ 2 to a local unique weak solution of the above mentioned equation.

## Stable Solutions to Homogeneous Difference-Differential Equations with Constant Coefficients: Analytical Instruments and an Application to Monetary Theory

### Applications of Mathematics (2004-08-01) 49: 373-386 , August 01, 2004

In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we present a general method for determining the stability of any solution to a homogeneous linear difference-differential equation with constant coefficients and advancing arguments.