We solve the matrix equation XA + AX = 0, where A ∈ Cnxn is an arbitrary given square matrix, and we compute the dimension of its solution space. This dimension coincides with the codimension of the tangent space of the congruence orbit of A. Hence, we also obtain the (real) dimension...
The path of least time is clearly AB. So some people might say, “Sometimes it is a maximum time.” It is not a maximum time, because certainly a curved path would take a still longer time! The correct statement is the following: a ray going in a certain particular path has the ...
On the Laplace equation in d-dimensionMathematical PhysicsWe develop a method to obtain the general solution of the Laplace equation in $d$-dimension in ultraspherical coordinates.doi:http://dx.doi.org/R. R. LandimPhysics
Let M be a differentiable manifold of finite dimension n. Consider a local coordinate system ( U , x 1 , … , x n ) (𝑈,𝑥1,…,𝑥𝑛) on M, simply denoted by ( x i ) (𝑥𝑖). Throughout this paper, we use similar abbreviations for the coordinate notations. Let k be...
The Hausdorff dimension of the Besicovitch functions is shown to be a linear function of the order of fractional integro-differentiation under some condition. We have shown some linear connection in Fig. 4, Fig. 5. by some numerical results. Meanwhile, the corresponding numerical results of the...
Dong, SH., Ma, ZQ. Levinson's Theorem for the Schrödinger Equation in One Dimension.International Journal of Theoretical Physics39, 469–481 (2000). https://doi.org/10.1023/A:1003604830131 February 2000 DOIhttps://doi.org/10.1023/A:1003604830131 ...
Our next result treats the dimension of the kernel of L_+ in H^1_{rad}(\mathbb {R}^n). To be more precise, if h \in H^1_{rad}(\mathbb {R}^n) \cap \textrm{Ker} L_+, then we can have stronger regularity properties (see Proposition 2.2 below) \begin{aligned} h \in H^...
late 19th century (in a sense relating to the number of times that a specific dimension is to be repeated in quantitive surveying): use as a verb of times expressing multiplication (dating from late Middle English). product n. 乘积(结果)the product of x and y : xy late Middle English...
5.4: Independence, Basis, and Dimension Model-Based Control of Humanoid Walking Model-Based Control of Humanoid Walking(19:38) Structural Analysis Using Finite Element Method in MATLAB | Finite Element Analysis in MATLAB, Part 1 Structural Analysis Using Finite Element Method in MATL...
, where d is the space-time dimension. the coefficients of the series are given in terms of generalized polylogarithms up to weight 3. the paper is organized as follows. in sect. 2 we present the partonic processes under consideration in more detail and we define their cross sections as ...