This paper studies the numerical algorithm of stochastic control problems in investment optimization. Investors choose optimal to maximize expected return under uncertainty. The optimality condition, Hamilton–Jacobi–Bellman (HJB) equation, satisfied by value function and obtained dynamic programming method, is a partial differential equation coupled with One major computational difficulties irr...

A Riemann surface is associated with its Jacobian through the Abel map. Using a plane algebraic curve representation of the Riemann surface, we provide an algorithm for the numerical computation of the Abel map. Since our plane algebraic curves are of arbitrary degree and may have arbitrary singularities, the Abel map of any connected compact Riemann surface may be obtained in this way.

The Heisenberg hierarchy and its Hamiltonian structure are obtained respectively by use of the zero curvature equation trace identity. With help Lax matrix we introduce an algebraic curve $${\mathcal {K}}_{n}$$ arithmetic genus n, from which define meromorphic function $$\phi $$ straighten out all flows associated with under Abel–Jacobi coordinates. Finally, get explicit theta representations...

Using a corollary to Karamata’s main theorem [Math. Z. 32 (1930), 319—320], we prove that if a slowly decreasing sequence of real numbers is Abel summable, then it is convergent in the ordinary sense. Subjclass [2010] : 40A05; 40E05; 40G10.

Today, different formalisms exist to solve reasoning problems under uncertainty. For most of the known formalisms, corresponding computer implementations are available. The problem is that each of the existing systems has its own user interface and an individual language to model the knowledge and the queries. This paper proposes ABEL, a new and general language to express uncertain knowledge a...

Abstract On the basis of two sets Lenard recursion sequences and zero-curvature equation associated with a matrix spectral problem, we derive entire sine-Gordon hierarchy, which is composed all positive negative flows. Using theory hyperelliptic curves, Abel-Jacobi coordinates are introduced, from corresponding flows linearized. The algebro-geometric solutions hierarchy constructed by using asy...

Integral equations are in which the unknown function is found to be inside integral sign. N. H. Abel used equation analyze relationship between kinetic energy and potential a falling object, expressed by two equations. This called Abel's equation. Furthermore, these developed produce generalizations further for each study aims explain of first second kind Abel’s equations, find solution The met...

In this paper, having introduced a convergence of series on the root vectors in Abel-Lidskii sense, we present valuable application to evolution equations. The main issue paper is an approach allowing us principally broaden conditions imposed upon second term equation abstract Hilbert space. way, come definition function unbounded non-selfadjoint operator. Meanwhile, considering involve additio...

1Instituto de Ciências Biomédicas Abel Salazar, Universidade do Porto, Rua Jorge Viterbo Ferreira, no 228, 4050-313 Porto, Portugal 2Paediatric Gastroenterology Service, Department of Child and Adolescent, Centro Hospitalar do Porto, Largo Abel Salazar, 4099-001 Porto, Portugal 3Paediatric Service, Unidade Hospitalar de Famalicao, Centro Hospitalar do Médio Ave, Rua de Cupertino de Miranda, 476...