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Jordan-Hölder Theorem with Uniqueness for Semimodular Lattices
In 2011 Czédli and Schmidt proved the strongest form of Jordan-Hölder theorem for lattices, which they called Jordan-Hölder theorem with uniqueness:...
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Bianalytic functions of Hölder classes in Jordan domains with nonanalytic boundaries
We consider some boundary behavior effect for bianalytic functions related to the Dirichlet problem solvability. It is proved that there exist such...
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Structure of semisimple rings in reverse and computable mathematics
This paper studies the structure of semisimple rings using techniques of reverse mathematics, where a ring is left semisimple if the left regular...
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Octonionic Calabi–Yau Theorem
On a certain class of 16-dimensional manifolds a new class of Riemannian metrics, called octonionic Kähler, is introduced and studied. It is an...
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The Artin–Wedderburn Theorem
In this chapter, we shall obtain the full structure theorem for semisimple rings. This result, due to J. H. M. Wedderburn (1907) for semisimple...
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Hermitian Yang–Mills connections on pullback bundles
We investigate hermitian Yang–Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions...
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Kellogg’s theorem for diffeomophic minimizers of Dirichlet energy between doubly connected Riemann surfaces
We extend the celebrated theorem of Kellogg for conformal diffeomorphisms to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic...
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A Donaldson–Uhlenbeck–Yau theorem for normal varieties and semistable bundles on degenerating families
In this paper, we first prove a Donaldson–Uhlenbeck–Yau theorem over projective normal varieties smooth in codimension two. As a consequence we...
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Examples of Finite Dimensional Algebras which do not Satisfy the Derived Jordan–Hölder Property
We construct a matrix algebra Λ( A , B ) from two given finite dimensional elementary algebras A and B and give some sufficient conditions on A and B ...
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Normal Series
To give insights into the structure of a group G, we study a normal series of G. The idea of normal series of a group and solvability yields...
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Approximation by Entire Functions on a Countable Set of Continua. The Inverse Theorem
AbstractIn approximation theory, statements in which functions from certain classes are approximated by functions from other fixed classes (for...
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Semimodularity and the Jordan–Hölder theorem in posets, with applications to partial partitions
Lattice-theoretical generalizations of the Jordan–Hölder theorem of group theory give isomorphisms between finite maximal chains with same endpoints....
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Two Flags in a Semimodular Lattice Generate an Antimatroid
A basic property in a modular lattice is that any two flags generate a distributive sublattice. It is shown (Abels 1991, Herscovici 1998) that two...
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Schwarz Problem for J-Analytic Functions in an Ellipse
AbstractThe Schwarz problem for functions analytic in the sense of Douglis in an ellipse is considered. Necessary and sufficient conditions on the
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Almost-simple affine difference algebraic groups
Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic...
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A d-dimensional analyst’s travelling salesman theorem for subsets of Hilbert space
We are interested in quantitative rectifiability results for subsets of infinite dimensional Hilbert space H . We prove a version of Azzam and Schul’s d ...
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Initial–Boundary Value Problems for Homogeneous Parabolic Systems in a Semibounded Plane Domain and Complementarity Condition
AbstractWe consider initial–boundary value problems for homogeneous parabolic systems with coefficients satisfying the double Dini condition with...