A Dynamic Algorithm for Constructing the Dual Representation of a Polyhedral Cone

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

Download Full-text

An Analytic and Numerical Investigation of a Differential Game

Axioms ◽

10.3390/axioms10020066 ◽

2021 ◽

Vol 10 (2) ◽

pp. 66

Author(s):

Aviv Gibali ◽

Oleg Kelis

Keyword(s):

Differential Game ◽

Equation Approach ◽

Linear Quadratic ◽

Control Cost ◽

Dual Representation ◽

Cost Functional ◽

Variational Derivatives ◽

Zero Sum ◽

The Cost ◽

Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

Download Full-text

Dual subtractions

Journal of High Energy Physics ◽

10.1007/jhep06(2021)089 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Renato Maria Prisco ◽

Francesco Tramontano

Keyword(s):

Field Theory ◽

Quantum Field ◽

Matrix Elements ◽

Leading Order ◽

Initial State ◽

Final State ◽

Dual Representation ◽

Subtraction Scheme ◽

Theoretical Predictions ◽

Perturbative Quantum

Abstract We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

Download Full-text