Expansions of solutions of higher order evolution equations in series of generalized heat polynomials.
Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation () based Sharpe ratio for measuring...
Experimental comparison of traffic flow models on traffic data
Despite their deficiencies, continuous second-order traffic flow models are still commonly used to derive discrete-time models that help traffic engineers to model and predict traffic oflow behaviour on highways. We brie fly overview the development of traffic flow theory based on continuous flow-density models of Lighthill-Whitham-Richards (LWR) type, that lead to the second-order model of Aw-Rascle. We will then concentrate on widely-adopted discrete approximation to the LWR model by Daganzo's...
Explicit bounds on some nonlinear integral inequalities.
Explicit construction, uniqueness, and bifurcation curves of solutions for a nonlinear Dirichlet problem in a ball.
Explicit definition of an exact measure for the semiflow of a first order partial differential equation
Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis
We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
Explicit exponential decay bounds in quasilinear parabolic problems.
Explicit Finite Element Schemes for First Order Symmetric Hyperbolic Systems.
Explicit fundamental solutions of some second order differential operators on Heisenberg groups
Let p,q,n be natural numbers such that p+q = n. Let be either ℂ, the complex numbers field, or ℍ, the quaternionic division algebra. We consider the Heisenberg group N(p,q,) defined ⁿ × ℑ , with group law given by (v,ζ)(v’,ζ’) = (v + v’, ζ + ζ’- 1/2 ℑ B(v,v’)), where . Let U(p,q,) be the group of n × n matrices with coefficients in that leave the form B invariant. We compute explicit fundamental solutions of some second order differential operators on N(p,q,) which are canonically associated to...
Explicit integration of equations of motion solved on computer cluster
In the last decade the dramatic onset of multicore and multi-processor systems in combination with the possibilities which now provide modern computer networks have risen. The complexity and size of the investigated models are constantly increasing due to the high computational complexity of computational tasks in dynamics and statics of structures, mainly because of the nonlinear character of the solved models. Any possibility to speed up such calculation procedures is more than desirable. This...
Explicit inequalities for parabolic and pseudoparabolic equations with Neumann boundary conditions.
Explicit parametrix and local limit theorems for some degenerate diffusion processes
For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of McKean–Singer [J. Differential Geom.1 (1967) 43–69] type for the density. We therefrom derive an explicit gaussian upper bound and a partial lower bound that characterize the additional singularity induced by the degeneracy. This particular representation then allows to give a local limit theorem with the usual convergence...
Explicit solution for Lamé and other PDE systems
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.
Explicit solution of the jump problem for the Laplace equation and singularities at the edges.
Explicit solutions for a system of first-order partial differential equations. II.
Explicit solutions for a system of first-order partial differential equations.
Explicit solutions of Fisher's equation with three zeros.
Explicit solutions of generalized nonlinear Boussinesq equations.
Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints
MSC 2010: 44A35, 35L20, 35J05, 35J25In this paper are found explicit solutions of four nonlocal boundary value problems for Laplace, heat and wave equations, with Bitsadze-Samarskii constraints based on non-classical one-dimensional convolutions. In fact, each explicit solution may be considered as a way for effective summation of a solution in the form of nonharmonic Fourier sine-expansion. Each explicit solution, may be used for numerical calculation of the solutions too.