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Solving Linear Differential Equations: A Novel Approach
Linear Differential Equations Novel Approach Mathematical Physics
2012/5/24
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the...
Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
Fractional integro-differentiation fractional damping universal response electromagnetic field dielectric medium
2011/9/23
Abstract: We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equatio...
Exact polynomial solutions of second order differential equations and their applications
Polynomial solutions Bethe ansatz Quasi-exactly solvable systems
2011/9/21
Abstract: We find all polynomials $Z(z)$ such that the differential equation $${X(z)\frac{d^2}{dz^2}+Y(z)\frac{d}{dz}+Z(z)}S(z)=0,$$ where $X(z), Y(z), Z(z)$ are polynomials of degree at most 4, 3, 2 ...
Method of oscillation and spectral problem for four-order differential operator with self-similar weight
Method of oscillation spectral problem self-similar weight
2011/9/20
Abstract: Self-adjoint boundary problems for the equation $y^{(4)}-\lambda\rho y=0$ with generalized derivative $\rho\in W_2^{-1}[0,1]$ of self-similar Cantor type function as a weight are considered....
Self-adjoint commuting differential operators and commutative subalgebras of the Weyl algebra
Self-adjoint commuting differential operators commutative subalgebras the Weyl algebra Mathematical Physics
2011/9/13
Abstract: In this paper we give enough conditions when the operator of the fourth order included in a commutative ring of ordinary differential operators of rank 2 is formally self-adjoint. In the cas...
Differential-difference equations associated with the fractional Lax operators
Lax pair discretization Bogoyavlensky lattice Sawada Kotera equation Kaup Kupershmidt equation
2011/9/30
Abstract: We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference ...
Nonparametric model reconstruction for stochastic differential equation from discretely observed time-series data
Nonparametric model reconstruction stochastic differential equation discretely observed time-series data
2011/8/2
Abstract: We develop a scheme for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from a time-series data. There is no need to have any prior knowledg...
Measurement of the gas-flow reduction factor of the KATRIN DPS2-F differential pumping section
gas flow RGA residual gas analyzer vacuum measurement free molecular flow turbo-molecular gas flow RGA residual gas analyzer vacuum measurement free molecular flow turbo-molecular
2011/8/1
Abstract: We determined the gas-flow reduction factor of the second forward Differential Pumping Section (DPS2-F) for the KATRIN experiment using a dedicated vacuum-measurement setup and by detailed m...
Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative
local fractional calculus fractal time-space local fractional derivative local fractional differential equation
2011/7/26
Abstract: This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing eq...
On rings of commuting partial differential operators
partial differential operators Algebraic Geometry
2011/7/27
Abstract: We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings ...
Differential geometric formulation of the Cauchy Navier equations
differential geometry differential forms lie derivatives linear elasticity Cauchy Navier equations
2011/7/25
Abstract: The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equ...
General relativity, differential geometry, and unitary theories in the work of Mira Fernandes
General relativity differential geometry unitary theories
2010/12/27
An analysis of the work of Mira Fernandes on unitary theories is presented.
General relativity, differential geometry, and unitary theories in the work of Mira Fernandes
General relativity differential geometry unitary theories
2010/12/21
Aureliano de Mira Fernandes, born in 1884 in Portugal, was professor of Differential and Integral Calculus and Rational Mechanics, at Instituto Superior T´ecnico,from its foundation in 1911, onw...
Recurrence and differential relations for spherical spinors
spherical spinors spinor spherical harmonics angular momentum
2011/1/7
We present a comprehensive table of recurrence and differential relations obeyed by spin
one-half spherical spinors (spinor spherical harmonics) μ(n) used in relativistic atomic.
Physical applications of second-order linear differential equations that admit polynomial solutions
Criteria for polynomial solutions Asymptotic iteration method Confluent Heun equation Bicon-fluent Heun equation General Heun equation Davidson potential Exactly solvable differential equations
2010/10/21
to have polynomial solutions are given. Several application of these results to Schr¨odinger’s equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation ...