For a bivariate random vector (X, Y ), symmetry conditions are presented that yield stochastic orderings among |X|, |Y |, |max(X, Y )|, and |min(X, Y )|. Partial extensions of these results for multivariate random vectors (X1, ..., Xn) are also given.

legal terms are as heritage of civilization and arising out of social developments of nations. however, public order in international law is required in international instruments and is cited repeatedly by international tribunals and authors but still have a vague concept in practice. what is studied in this article is analyze of concept and nature of international public order in considering v...

Automatic Differentiation (AD) is increasingly an important component of Machine Learning (ML) packages. For evaluating the gradient, the first order reverse mode also known as back-propagation, is optimal and is widely used. However, the functionalities of current mainstream ML packages for evaluating second and higher order derivatives are limited. One reason is that high order derivatives ar...

This paper is a contribution to Harvey Friedman’s project of reverse mathematics in which one tries to classify theorems of ordinary mathematics by the set theoretic axioms required to prove them. All of the result in this paper are formalized in RCA0, the weakest of the standard systems in reverse mathematics, and concern classical theorems about countable ordered groups. The reader who is not...

Recent research has pointed out the importance of the inequational exchange law (P ∗Q) ; (R∗S) ≤ (P ;R)∗ (Q ;S) for concurrent processes. In particular, it has been shown that this law is equivalent to validity of the concurrency rule for Hoare triples. Unfortunately, the law does not hold in the relationally based setting of algebraic separation logic. However, we show that under mild conditio...

Sorites is an ancient piece of paradoxical reasoning pertaining to sets with the following properties: (Supervenience) elements of the set are mapped into some set of “attributes”; (Tolerance) if an element has a given attribute then so are the elements in some vicinity of this element; and (Connectedness) such vicinities can be arranged into pairwise overlapping finite chains connecting two el...

In 1999, Wei [M.Wei, Reverse order laws for generalized inverse of multiple matrix products, Linear Algebra Appl., 293 (1999), pp. 273-288] studied reverse order laws for generalized inverses of multiple matrix products and derived some necessary and sufficient conditions for An{1}An−1{1} · · ·A1{1} ⊆ (A1A2 · · ·An){1} by using P-SVD (Product Singular Value Decomposition). In this paper, using ...

We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA0, WKL0, or ACA0. We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA0 over RCA0.

payment order in eft can be a negotiable instrument in two ways; it can be an instrument based on custom and regulation meaning that whether it should be considered as new instrument or be incorporated in one of the current instruments. in light of iranian legal system and against common law, it is not acceptable that a new negotiable instrument be created by custom because some characteristics...