The algebra of O(3, 3) is contracted to that of E(2)-like groups in the infinite-momentum limit. It is shown through this process that there are 18 different possibilities for the representations of E(2)-like algebra if they are to be expressed in terms of Dirac γmatrices. It is also pointed out that the generators of this algebra are independent of the particular representation of the γ-matric...

The probability distribution function of n random elements subjected to the flexible boundary condition is derived. The probability density is a descending curve and converges to a delta function as n tends to infinity. The distribution of the minimum value is discussed in context of ordered statistics.

We introduce another powerful method of solving PDEs. First, we need to consider some preliminary definitions and ideas. Definition [Delta Function] The δ-function is defined by the following three properties, δ (x) = 0, ∞, x � = 0, x = 0, ∞ δ (x) dx = 1 −∞ ∞ f (x) δ (x − a) dx = f (a) −∞ where f is continuous at x = a. The last is called the sifting property of the δ-function. To make proofs w...

The ∆ decay in the nuclear medium is calculated in the relativistic mesonnucleon model. The delta spreading width is calculated and compared with the Pauli-blocked πN decay width. The influence of relativistic mean fields is also studied. We stress the importance of understanding the delta spreading width in interpreting experiments involving delta resonances.

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

A large number of results in analysis of algorithms contain fluctuations. A typical result might read “The expected number of . . . for large n behaves like log2 n + constant + delta(log2 n), where delta(x) is a periodic function of period one and mean zero.” Examples include various trie parameters, approximate counting, probabilistic counting, radix exchange sort, leader election, skip lists,...

Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical...

The phase field model is a highly successful computational technique for capturing the evolution and topological change of complex interfaces. The main computational advantage of phase field models is that an explicit tracking of the interface is unnecessary. The regularized Dirac delta function is an important ingredient in many interfacial problems that phase field models have been applied. T...