This article is concerned with Galois theory for iterative differential fields (ID-fields) in positive characteristic. More precisely, we consider purely inseparable Picard-Vessiot extensions, because these are the ones having an infinitesimal group scheme as iterative differential Galois group. In this article we prove a necessary and sufficient condition to decide whether an infinitesimal gro...

This paper is continuation of the study of the 1-box pattern in permutations introduced previously by the authors. We derive a two-variable generating function for the distribution of this pattern on 132-avoiding permutations, and then study some of its coefficients providing a link to the Fibonacci numbers. We also find the number of separable permutations with two and three occurrences of the...

My main focus, as requested by the editors, is the changing governance of welfare. But changes in this regard are inseparable from broader changes in the welfare regimes that emerged in advanced western capitalist states in the postwar Atlantic Fordist boom. Thus I will also discuss the social and economic functions that current welfare regimes are expected to perform and the scales on which th...

In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General biCohen-Macaulay graphs are classified up to separation. The inseparable bi-CohenMacaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.

Technology has become an inseparable part of everyday life, as we use it at home, at work, in school etc. For education, technology is frequently used as a tool to support classroom-based learning. However, an emerging challenge is the application of technology, beyond the traditional classroom, to a diverse mix of pedagogical techniques. Traditional education is based on the process of transmi...

Numerous convolution neural networks increase accuracy of classification for remote sensing scene images at the expense models' space and time sophistication. This causes model to run slowly prevents realization a trade-off among running time. The loss deep characteristics as network gets deeper makes it impossible retrieve key aspects with sample double branching structure, which is bad classi...

Generalizing the notion of a recursively enumerable (r.e.) set to sets of real numbers and other metric spaces is an important topic in computable analysis (which is the Turing machine based theory of computable real number functions). A closed subset of a computable metric space is called r.e. closed, if all open rational balls which intersect the set can be effectively enumerated and it is ca...

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n × n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT. Quantum entangled states have become one of the key resources in quantum in...

In this work, we use similarly separable vectors in Hilbert spaces to provide generalized integral results related majorization, Niezgoda, and Ćebysév type inequalities. Next, furnish some refinements of these Theorems obtained work extend improve several known the literature. An important aspect our is that inequalities are directly Arithmetic, Geometric, Harmonic, Power means. These means hav...