Related papers: Moufang symmetry VIII. Reconstruction of Moufang l…

In this paper, we construct the fundamental theorem of UP-homomorphisms in UP-algebras. We also give an application of the theorem to the first, second, third and fourth UP-isomorphism theorems in UP-algebras.

It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold.

This is a revised version of Sh:430, section 6.

We identify those elements of the homeomorphism group of the circle that can be expressed as a composite of two involutions.

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.

We give a new proof of Lucas' Theorem in elementary number theory.

A proof is given of Rosenthal's \(\ell_1\) theorem.

We solve a problem of Belousov which has been open since 1967: to characterize the loop isotopes of F-quasigroups. We show that every F-quasigroup has a Moufang loop isotope which is a central product of its nucleus and Moufang center. We…

The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.

We unify various \'etale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semigroup. 3) Steinberg's reconstruction from a groupoid ring.…

The reconstruction theorem deals with dynamical systems that are given by a map $T:X\to X$ of a compact metric space $X$ together with an observable $f:X \to \R$ from $X$ to the real line $\R$. In 1981, by use of Whitney's embedding…

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.

A classification theorem for 4-dimensional conformally flat QK3-manifolds is proved.

We formulate and prove the analogue of Moser's stability theorem for locally conformally symplectic structures. As special cases we recover some results previously proved by Banyaga.

In the previous paper, the structure of the cut locus was determined for a class of surfaces of revolution homeomorphic to a cylinder. In this paper, we prove the structure theorem of the cut locus for a wider class of surfaces of…

Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering…