On Balanced Products of the Distributions X
نویسنده
چکیده
Results on products of the distributions xa± and δ (x) with coinciding singularities are derived when the products are balanced so that they exist in the distribution space. These results follow the idea of a known result on distributional products published by Jan Mikusiński in 1966. They are obtained in Colombeau algebra G(R)of generalized functions that contains the distribution space and the notion of ’association’ in it allows obtaining results in terms of distributions.
منابع مشابه
Balanced Colombeau products of the distributions x −p ± and x −p
Results on singular products of the distributions x ± and x −p for natural p are derived when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in Colombeau algebra of generalized functions, which is most relevant algebraic construction for...
متن کاملBalanced Reciprocal Translocation t(X;1) in a Girl with Tall Stature and Primary Amenorrhea
AbstractChromosomal translocations constitute one of the most important, yet uncommon, causes of primary amenorrhea and gonadal dysgenesis. Although X-autosome translocations are frequently associated with streak gonads and clinical features of the Turner syndrome, the majority of X-autosome carriers may present with a variable phenotype, developmental delay, and recognizable X-linked syndrome ...
متن کاملA Monte Carlo Study on Dose Enhancement by Homogeneous and Inhomogeneous Distributions of Gold Nanoparticles in Radiotherapy with Low Energy X-rays
Background: To enhance the dose to tumor, the use of high atomic number elements has been proposed.Objective: The aim of this study is to investigate the effect of gold nanoparticle distribution on dose enhancement in tumor when the tumor is irradiated by typical monoenergetic X-ray beams by considering homogeneous and inhomogeneous distributions of gold nanoparticles (GNPs) in the tumor.Method...
متن کاملA Note on the Bivariate Maximum Entropy Modeling
Let X=(X1 ,X2 ) be a continuous random vector. Under the assumption that the marginal distributions of X1 and X2 are given, we develop models for vector X when there is partial information about the dependence structure between X1 and X2. The models which are obtained based on well-known Principle of Maximum Entropy are called the maximum entropy (ME) mo...
متن کاملDispersive Ordering and k-out-of-n Systems
Extended Abstract. The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than that of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to ...
متن کامل