Search results for "Mathematical analysis"
showing 10 items of 2409 documents
A robust forward-displacement analysis of spherical parallel robots
2009
The forward-displacement analysis of spherical parallel robots (SPRs) is revisited. A robust approach, based on the input–output (I/O) equation of spherical four-bar linkages, is proposed. In this approach, the closed-loop kinematic chain of a SPR is partitioned into two four-bar spherical chains, whose I/O equations are at the core of the analysis reported here. These equations lead to a trigonometric equation in the joint angles, which is solved semigraphically to obtain the joint variables for the determination of the moving plate orientation. Examples are included to demonstrate the application of the method.
Mappings of exponentially integrable distortion: Decay of the Jacobian
2018
We establish an integrability result on the reciprocal of the Jacobian determinant for a mapping of exponentially integrable distortion and thus answer a question raised by S. Hencl and P. Koskela.
A family of complex potentials with real spectrum
1999
We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.
A new result on impulsive differential equations involving non-absolutely convergent integrals
2009
AbstractIn this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations.
On the integrability of the extended nonlinear Schrödinger equation and the coupled extended nonlinear Schrödinger equations
2000
We consider the extended nonlinear Schr¨ (ENLS) equation which governs the propagation of nonlinear optical fields in a fibre with higher-order effects such as higher-order dispersion and self-steepening. We show that the ENLS equation does not pass the Painlev´ test. Similarly, we claim that the coupled ENLS equations and N -coupled ENLS equations which govern the simultaneous propagation of two and more nonlinear fields in optical fibres are also not integrable from the Painlev´ e analysis point of view.
Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion
2010
We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.
Mappings of Finite Distortion:¶Discreteness and Openness
2001
We establish a sharp integrability condition on the partial derivatives of a mapping with L p -integrable distortion for some p>n− 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.
Spatially chaotic configurations and functional equations with rescaling
1996
The functional equation is associated with the appearance of spatially chaotic structures in amorphous (glassy) materials. Continuous compactly supported solutions of the above equation are of special interest. We shall show that there are no such solutions for , whereas such a solution exists for almost all . The words `for almost all q' in the previous sentence cannot be omitted. There are exceptional values of q in the interval for which there are no integrable solutions. For example, , which is the reciprocal of the `golden ratio' is such an exceptional value. More generally, if is any Pisot - Vijayaraghavan number, or any Salem number, then is an exceptional value.
Algebriskā analīze: teorija un uzdevumi
1937
Reālās ģimnāzijas kurss.
Mapping properties of weakly singular periodic volume potentials in Roumieu classes
2020
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solut…