From any given Frobenius manifold one may construct a so-called ‘dual’ structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying the WDVV equations of associativity. Jacobi group orbit spaces naturally carry the structures of a Frobenius manifold and hence there exists a dual prepotent...

The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol’nyi-type bound. We find all possible cylindrically symmetric vortex solutions and vortex-particle composites by examining the Einstein equations and the firstorder Bogomol’nyi equations. The underlying ...

An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Empl...

Finite-difference operators satisfying the summation-by-parts (SBP) rule can be used to obtain high-order accurate time-stable schemes for partial differential equations (PDEs), when the boundary and interface conditions are imposed weakly by the simultaneous approximation term method (SAT). The most common SBP-SAT discretizations are accurate of order 2p in the interior and order p close to th...

in this study the trend of technological change and its nature was studied in production of sugar beet in iran by using dual approach. this approach is useful for estimating the demand structure of the input price change and technology status. after estimating the various forms of flexible functions, by selection of translog cost function with cost share equations system is estimated using seem...

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

There is remarkable relation between self-dual Yang–Mills and self-dual Einstein gravity in four Euclidean dimensions. Motivated by this we investigate the Spin(7) and G2 invariant self-dual Yang–Mills equations in eight and seven Euclidean dimensions and search for their possible analogs in gravitational theories. The reduction of the self-dual Yang– Mills equations to one dimension results in...

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory for...