Related papers: Decomposition of a Nonlinear Multivariate Function…

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…

In this paper, we consider the dynamical zeta functions of Ruelle and Selberg associated with the geodesic flow of a compact hyperbolic odd dimensional manifold $X$. These functions are initially defined on one complex variable $s$ in some…

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of…

In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra $\mathfrak{sl}(2|1)$ generated by…

An efficient solution of the Dirac Hamiltonian flow equations has been proposed through a novel expandsion with the inverse of the Dirac effective mass. The efficiency and accuracy of this new expansion have been demonstrated by reducing a…

We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…

We derive a hydrodynamics formulation for a modified Dirac equation with a nonlinear mass term that preserves the homogeneity of the original Dirac equation. The nonlinear Dirac equation admits a symmetric split into the left and…

Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a…

We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain…

The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental…

We recall Dirac's early proposals to develop a description of quantum phenomena in terms of a non-commutative algebra in which he suggested a way to construct what he called `quantum trajectories'. Generalising these ideas, we show how they…

Remarks on the Kostant Dirac operator In 1999, Kostant [Kos99] indroduces a Dirac operator D_g/h associated to any triple (g, h,B), where g is a complex Lie algebra provided with an ad g-invariant non degenerate nsymetric bilinear form B,…

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…

Starting from the pseudo-differential decomposition $\mathbf{D}=(-\Delta)^{\frac{1}{2}}\mathcal{H}$ of the Dirac operator $\displaystyle \mathbf{D}=\sum_{j=1}^n\mathbf{e}_j\partial_{x_j}$ in terms of the fractional operator…

The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifolds that will play similar roles in the theory of holomorphic…

Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data. The results heavily rely on the choice of appropriate functional…

We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the…

In 1905, Einstein's theory of Brownian motion supported the molecular basis of the diffusion equation and introduced two complementary viewpoints: a deterministic field description and a probabilistic formulation based on stochastic…

In this work, we introduce the new class of functions which can use to solve the nonlinear/linear multi-dimensional differential equations. Based on these functions, a numerical method is provided which is called the Developed Lagrange…

We prove a sharp multiparameter integral inequality for the dyadic maximal operator which refines the one-parameter inequality that is given by A.Melas in [4] which in turn is applied for the evaluation of the Bellman function of two…