in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

We show that if performance measures in stochastic and dynamic scheduling problems satisfy generalized conservation laws, then the feasible space of achievable performance is a polyhedron called an extended polymatroid that generalizes the usual polymatroids introduced by Edmonds. Optimization of a linear objective over an extended polymatroid is solved by an adaptive greedy algorithm, which le...

A comparison is made between the symmetries and conservation laws admitted by nonlinear telegraph NLT systems. Such systems are not variational. Unlike the situation for variational systems where all conservation laws arise from symmetries, there are many NLT systems that admit more conservation laws than symmetries. The results are summarized in a table which includes the numbers of symmetries...

This work deals with coding systems based on sparse graphs. The key issue we address is the relationship between iterative (in particular belief propagation) and maximum a posteriori decoding. We show that between the two there is a fundamental connection, which is reminiscent of the Maxwell construction in thermodynamics. The main objects we consider are EXIT-like functions. EXIT functions wer...

A complete and explicit classification of all independent local conservation laws of Maxwell’s equations in four dimensional Minkowski space is given. Besides the elementary linear conservation laws, and the well-known quadratic conservation laws associated to the conserved stress-energy and zilch tensors, there are also chiral quadratic conservation laws which are associated to a new conserved...

In [28] Rasin and Hydon suggested a way to construct an infinite number of conservation laws for the discrete KdV equation (dKdV), by repeated application of a certain symmetry to a known conservation law. It was not decided, however, whether the resulting conservation laws were distinct and nontrivial. In this paper we obtain the following results: (1) We give an alternative method to construc...