Related papers: iso-spectral Euler-Bernoulli beams \`a la Sophus L…
We discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular those of zero and constant curvature.…
We present the analytical formulation and the finite element solution of a fractional-order nonlocal continuum model of a Euler-Bernoulli beam. Employing consistent definitions for the fractional-order kinematic relations, the governing…
We study existence and uniqueness of distributional solutions to the differential equation of the Euler-Bernoulli rod with discontinuous coefficients and right-hand side. Upon checking the validity of a solution the occurring products of…
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
In this work, a new technique has been presented to find approximate solution of linear integro-differential equations. The method is based on modified orthonormal Bernoulli polynomials and an operational matrix thereof. The method converts…
We show that solutions for a specifically scaled nonlinear wave equation of nonlinear elasticity converge to solutions of a linear Euler-Bernoulli beam system. We construct an approximation of the solution, using a suitable asymptotic…
We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The…
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…
We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
The Euler-Poincar\'e characteristic of a finite-dimensional Lie algebra vanishes. If we want to extend this result to Lie superalgebras, we should deal with infinite sums. We observe that a suitable method of summation, which goes back to…
We explain how the unramified Plancherel formula in the relative Langlands program gives a natural way of constructing test vectors which satisfy the tame norm relations of an Euler system. This uniformly recovers many of the known Euler…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
Lie group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein's field equations for vacuum Bianchi spacetime geometries. The symmetries…
In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are…
We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles.…
We study the Euler-Bernoulli beam model with singularities at the points $x=\xi_1$, $x=\xi_2$ and with localized viscoelastic dissipation of Kelvin-Voigt type. We assume that the beam is composed by two materials; one is an elastic material…
We consider ${\cal N} =1$ supersymmetric gauge theories in the conformal window. The running of the gauge coupling is absorbed into the metric by applying a suitable matter superfield- and Weyl-transformation. The computation becomes…
Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex plane, is obtained via the Borel--Laplace transformation.…