Also let S be the set of “sources” of some wave or the location of the wavefront at time t = 0. The discrete WDT finds at each pixel [i,j] the smallest sum of values of f over all possible discrete paths conn
The discrete nonlinear Schrödinger equation (DNLS) is a nonlinear differential equation that describes the evolution of a complex valued fieldFootnote 1 in a -dimensional space. For all times , each lattice site is associated with a value , and the time evolution of is given by (1.1) It...
There is, in general, no vector x that will satisfy this equation; however, we seek an x that minimizes the sum of the squares of the differences between the corresponding elements of Ax and b. It can be shown that such an x satisfies the equation ATAx=ATb, which is now an n × n...
The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates. The sin...
For example, you see the analysis in a minimal surface equation, but then you also realize it has connections with other geometric questions that are not just analysis. I am definitely very attracted to the idea that there are a lot of different facets in mathematics and seeing the ...
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Find a formula for the nth partial sum of each series and use it to find the series' sum if the series converges. \left. \begin{array} { l } { \text { 1. } 2 + \frac { 2 } { 3 } + \frac { 2 } { 9 } + Find the sum of the geo...
A differential equation is an equation that relates functions with their derivatives. Derivative indicates the rate of change. It is used to find the slope of the curve. A power series is an infinite series of the form {eq}\sum_{k=0}^{\infty }a_kx^k {/eq} where {...
We reduce the problem of finding the steady state probabilities for the Lindley equation to finding the generalized ordered Schur form of a matrix pair () where the size of these matrices are the sum, not the product, of the orders of individual arrival and service distributions. The approach...
We often use the sum of the drag force and inertial force, which are assumed to be unrelated, to express the wave force acting on an isolated vertical cylindrical pile, as shown in Equation (1-214), which is called the Morison equation. Although the assumptions of the Morison equation have...