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We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type impossibility result, also shown in this article. We develop microlocal analysis in…
Wigner distributions for quantum mechanical systems whose configuration space is a finite group of odd order are defined so that they correctly reproduce the marginals and have desirable transformation properties under left and right…
We develop structure theory of finite Lie conformal superalgebras.
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
We study sets and groups definable in tame expansions of o-minimal structures. Let $\mathcal {\widetilde M}= \langle \mathcal M, P\rangle$ be an expansion of an o-minimal $\mathcal L$-structure $\cal M$ by a dense set $P$, such that three…
We study the U(M/N) supergroup keeping in mind its connection with electronic Hamiltonians. It is explicitly shown that the generators of the supergroup U(N/N) can be expressed by Clifford operators or Fermi operators. A multi-band…
We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers.…
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…
It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets,…
We use (nonconservative) dynamical semigroups to investigate the decay law of a quantum unstable system weakly coupled with a large environment. We find that the deviations from the classical exponential law are small and can be safely…
The spectral theory of semigroup generators is a crucial tool for analysing the asymptotic properties of operator semigroups. Typically, Tauberian theorems, such as the ABLV theorem, demand extensive information about the spectrum to derive…
We introduce the notion of Krull super-dimension of a super-commutative super-ring. This notion is used to describe regular super-rings and calculate Krull super-dimensions of completions of super-rings. Moreover, we use this notion to…
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…
In this article, we compare two different notions of partially defined group strutures, namely partial groups and pregroups, as introduced by Chermak and Stallings respectively. In particular we prove that the category of pregroups can be…
We survey the results regarding semi-extraspecial $p$-groups. Semi-extraspecial groups can be viewed as generalizations of extraspecial groups. We present the connections between semi-extraspecial groups and Camina groups and VZ-groups, and…
This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…
The structure of categorical at zero semigroups is studied from the point of view their likeness to categories.
We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive supergroups.
We use the Graph Minor Theorem to characterize infinite sequences of finite subsets of factorial and commutative semigroups (here semigroups have a unity element), e.g. the multiplicative semigroup of a unique factorization domain.
We define some formal moduli space of quasi-isogenies of isoclinic $p$-divisible groups with a non-reductive group as the "structure group". We then formulate new Arithmetic Fundamental Lemma conjectures for Bessel subgroups in the context…