We consider the property of vanishing logarithmic term (VLT) for the fundamental solution of the shifted Laplace-d'Alembert operators + b (b a constant), on pseudo-Riemannian reductive symmetric spaces M. Our main result is that such an operator on the c-dual or Flensted-Jensen dual of M has the VLT property if and only if a corresponding operator on M does. For Lorentzian spaces, where the +b ...

The main idea behind the Laplace transformation is that we can solve an equation (or system of equations) containing differential and integral terms by transforming the equation in time (t) domain into Laplace (2) domain. For example, we can use Laplace transforms to turn an initial value problem into an algebraic problem which is easier to solve. After we solved the problem in Laplace domain w...

Dibromination of [2.2]paracyclophane (I) led to predominantly pseudo-ortho2 (11) and pseudo-para2 (111) disubstituted compounds, and to lesser amounts of pseudo-meta (IV) and para (V) isomers. Oxidation of these dibromides gave terephthalic acids whose esters were identified by vpc, and whose structures allowed homoannular and transannular bromination to be differentiated. Tetrabromination of I...

Measurements of CMB anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected(MC) compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. We numerically obtain the low-lying eigenmodes on a compact 3-hyperbolic space called m003(−2, 3) in the SnapPea using the ...

Relativistic massive bosons with spin one are considered in several quantization schemes. In all of them the system is shown described by a non-Hermitian Hamiltonian H 6= H and helicity operator Λ. Constructively we show that in all of the contemplated schemes both these operators H and Λ prove simultaneously PT −symmetric, i.e., pseudo-Hermitian with respect to a certain not too complicated in...

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x, t) of finding the walker at position x at time t is completely determined by the Lapla...