China 
Africa 
Explore chapters and articles related to this topic
Random Feedback Control, Group Invariants and Pattern Classification, Quantum Mechanics in Levy Noise, State Observer and Trajectory Tracking
Published in Harish Parthasarathy, Electromagnetics, Control and Robotics, 2023
where V1k is first order time dependent linear partial differential operator in q (i.e., the sum of a time dependent function of q and a time dependent vector field in q) while V2km(t) is a function of q, t, i.e., a multiplication operator. Using time dependent perturbation theory, we calculate the Schrodinger evolution operator U(T/I) generated by the Hamitonian H(t/I) at tiome T, i.e.,iU′(t|I)=H(t|I)U(t|I),t≥0,U(0|I)=I
Vector Visualization
Published in Alexandru Telea, Data Visualization, 2014
A second option is to compute the actual path x(t) of a particle in the time-dependent vector field, given by dx(t)dt=v(x(t),t)
Elements of Bioelectromagnetics
Published in Jitendra Behari, Radio Frequency and Microwave Effects on Biological Tissues, 2019
Second, the nature of the field may be such that one parameter only, such as its magnitude, is defined as scalar. The temperature field, for instance, inside a room or human body is a scalar field. On the other hand, in a vector field, a vector represents both the magnitude and the direction of the physical quality of points in space, and this vector field may also be static or time dependent. When plotting a static scalar field, that is, one quality, in points of space already requires some visualization effort. On the other hand, plotting a time-dependent vector field, which is described by a set of direction lines, also known as stream lines or flux lines.
On the Cauchy problem for a weakly dissipative Camassa-Holm equation in critical Besov spaces
Published in Applicable Analysis, 2022
Let . Let , , and let v be a time-dependent vector field such that for some and M>0, and Then the Equation (4) has a unique solution f in the space , if ;the space , if .
An inverse problem for the relativistic Schrödinger equation with partial boundary data
Published in Applicable Analysis, 2020
Venkateswaran P. Krishnan, Manmohan Vashisth
In this article, we prove unique determination of time-dependent vector and scalar potentials and appearing in (1) (modulo a gauge invariance for the vector potential) from partial boundary data. Our work is related to the result of Salazar [22] who showed uniqueness results for the relativistic Schrödinger operator from full Dirichlet to Neumann boundary data assuming such boundary measurements are available for infinite time. It extends the recent work of Kian [25], since we consider the full time-dependent vector field perturbation, whereas Kian assumes only a time derivative perturbation. We should emphasize that the approach using Carleman estimates combined with geometric optics (GO) solutions for recovering time-dependent perturbations, was first used by Kian in [26,27]. To the best of our knowledge, for time-independent perturbations, combination of these techniques to prove uniqueness results first appeared in [13] inspired by the work of Bukhgeim and Uhlmann [28] for the elliptic case.
On the Cauchy problem for a generalized Degasperis-Procesi equation
Published in Applicable Analysis, 2020
Let . Let and let v be a time-dependent vector field such that for some and and Then the Equation (4) has a unique solution f in the space if the space if .