Related papers: A sharp version of Shimizu's theorem on entire aut…
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…
In 1997 B. Weiss introduced the notion of measurably entire functions and proved that they exist on every arbitrary free C- action defined on standard probability space. In the same paper he asked about the minimal possible growth of…
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the…
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…
We formulate and prove the local twist version of the Yamanaka-Oshikawa-Affleck theorem, an extension of the Lieb-Schultz-Mattis theorem, for one-dimensional systems of quantum particles or spins. We can treat almost any translationally…
This thesis has three goals related to the automorphism groups of finite $p$-groups. The primary goal is to provide a complete proof of a theorem showing that, in some asymptotic sense, the automorphism group of almost every finite…
We give an explicit and versatile parametrization of all positive selfadjoint extensions of a densely defined, closed, positive operator. In addition, we identify the Friedrichs extension by specifying the parameter to which it corresponds.…
It is known that the dynamics of $f$ and $g$ vary to a large extent from that of its composite entire functions. Using Approximation theory of entire functions, we have shown the existence of entire functions $f$ and $g$ having infinite…
In this paper we study holomorphic properties of infinite dimensional spin factors. Among the infinite dimensional Banach spaces with homogeneous open unit balls, we show that the spin factors are natural outlier spaces in which to ask the…
In his seminal paper from 1936, Alan Turing introduced the concept of non-computable real numbers and presented examples based on the algorithmically unsolvable Halting problem. We describe a different, analytically natural mechanism for…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…
A $k$-orbit maniplex is one that has $k$ orbits of flags under the action of its automorphism group. In this paper we extend the notion of symmetry type graphs of maps to that of maniplexes and polytopes and make use of them to study…
We show that the third order approximation function $M_f$, proposed by S. Amat, S. Busquier, S. Plaza, in \textit{J. Math. Anal. Appl.}, 366(2010), 24--32, for functions $f$ twice continuously differentiable and such that both $f$ and its…
Beginning from 1981 one of the present authors (S.Novikov) published a series of papers, (some of them in collaboration with I.Schmelzer and I.Taimanov) dedicated to the development of the analog of Morse theory for the closed 1-forms --…
We hereby present a class of multidimensional higher derivative theories of gravity that realizes an ultraviolet completion of Einstein general relativity. This class is marked by a "non-polynomal" entire function (form factor), which…
Frucht's theorem is the statement that "every group is the automorphism group of a graph". This was shown over ZFC independently by Sabidussi and deGroot, by induction using a well ordered generating set for the group. Sabidussi's proof is…
Classical modular curves are of deep interest in arithmetic geometry. In this survey we show how the work of Fumiyuki Momose is involved in order to list the classical modular curves which satisfy that the set of quadratic points over…
We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto-Sivashinky equation. These two results are based on writing down the existence of periodic orbits as zeros of functionals. This…
Given a number field $k$, and a quadratic rational function $f(x) \in k(x)$, the associated arboreal representation of the absolute Galois group of $k$ is a subgroup of the automorphism group of a regular rooted binary tree. Boston and…