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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.

## Multiscale convergence and reiterated homogenization of parabolic problems

### Applications of Mathematics (2005-04-01) 50: 131-151 , April 01, 2005

Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂ *u*_{ɛ}/∂*t*−div (*a*(*x,x*/ɛ,*x*/ɛ^{2},*t,t*/ɛ ^{k})∇*u*_{ɛ})=*f*. It is shown that under standard assumptions on the function *a*(*x, y*_{1},*y*_{2},*t*,τ) the sequence {*u*_{ɛ}} of solutions converges weakly in *L*^{2} (0,*T*; *H*_{0}^{1}
(Ω)) to the solution *u* of the homogenized problem ∂*u*/∂*t*− div(*b*(*x,t*)∇*u*)=*f*.

## 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.

## 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.

## A Bayesian Estimate of the Risk of Tick-Borne Diseases

### Applications of Mathematics (2004-10-01) 49: 389-404 , October 01, 2004

The paper considers the problem of estimating the risk of a tick-borne disease in a given region. A large set of epidemiological data is evaluated, including the point pattern of collected cases, the population map and covariates, i.e. explanatory variables of geographical nature, obtained from GIS.

The methodology covers the choice of those covariates which influence the risk of infection most. Generalized linear models are used and AIC criterion yields the decision. Further, an empirical Bayesian approach is used to estimate the parameters of the risk model. Statistical properties of the estimators are investigated. Finally, a comparison with earlier results is discussed from the point of view of statistical disease mapping.

## A new non-interior continuation method for P 0-NCP based on a SSPM-function

### Applications of Mathematics (2011-09-09) 56: 389-403 , September 09, 2011

In this paper, we consider a new non-interior continuation method for the solution of nonlinear complementarity problem with *P*_{0}-function (*P*_{0}-NCP). The proposed algorithm is based on a smoothing symmetric perturbed minimum function (SSPM-function), and one only needs to solve one system of linear equations and to perform only one Armijo-type line search at each iteration. The method is proved to possess global and local convergence under weaker conditions. Preliminary numerical results indicate that the algorithm is effective.