This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which has received particular attention is the class of hyperfinite Borel equivalence relations. These can be defined as the increasing unions of sequences of Borel equivalence relations all of whose equ...

let $h$ be a hopf algebra and $a$ an $h$-bimodule algebra‎. ‎in this paper‎, ‎we investigate gorenstein global dimensions for hopf‎ ‎algebras and twisted smash product algebras $astar h$‎. ‎results from‎ ‎the literature are generalized‎.

The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

‎‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpot...

We construct a mirabolic analogue of the geometric Satake equivalence. also prove an equivalence that relates representations supergroup with category $GL(N-1,{\mathbb C}[\![t]\!])$-equivariant perverse sheaves on affine Grassmannian $GL_N$. explain how our equivalences fit into more general framework conjectures due to Gaiotto and Ben-Zvi, Sakellaridis Venkatesh.

Subjects were exposed to a word-picture association training phase in which each of 2 arbitrary nonsense syllables printed in blue and red font, respectively, were paired with either sexual or aversive photographic images. Subjects were then exposed to an equivalence training procedure that led to the formation of 2 3-member equivalence relations, each containing 1 of the 2 nonsense syllables i...

After a brief review of the existing results on permutation binomials finite fields, we introduce notion equivalence among (PBs) and describe how to bring PB its canonical form under equivalence. We then focus PBs Fq2 Xn(Xd(q−1)+a), where n d are positive integers a∈Fq2⁎. Our contributions include two nonexistence results: (1) If q is even sufficiently large aq+1≠1, Xn(X3(q−1)+a) not Fq2. (2) 2...

The Hox gene lin-39 plays a crucial role in the establishment of the nematode vulva equivalence group. Mutations in lin-39 in Caenorhabditis elegans and Pristionchus pacificus result in a vulvaless phenotype because presumptive vulva precursor cells adopt non-vulval fates. Interestingly, the non-vulval fate of anterior and posterior epidermal cells differs between Caenorhabditis and Pristionchu...