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Bidemocratic Bases and Their Connections with Other Greedy-Type Bases
In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or...
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Sagbi-Gröbner Bases Under Composition
The process of substituting variables in a polynomial with other polynomials is dubbed polynomial composition. The behaviour of Gröbner bases and...
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Noncommutative Gröbner Bases and Ext Groups
We consider a theory of noncommutative Gröbner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer...
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On Some Classes of Bases in Finite-Dimensional Lie Algebras
AbstractIn the paper, Lie algebras having bases of a special form (nice and beautiful bases) are considered. For nice bases, it is proved that, in...
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Greedy-like bases for sequences with gaps
In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the
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Symmetric Bases for Finite Element Exterior Calculus Spaces
In 2006, Arnold, Falk, and Winther developed finite element exterior calculus, using the language of differential forms to generalize the Lagrange,...
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Symmetry and Invariant Bases in Finite Element Exterior Calculus
We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued...
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Extensions and New Characterizations of Some Greedy-Type Bases
Partially greedy bases in Banach spaces were introduced by Dilworth et al. as a strictly weaker notion than the (almost) greedy bases. In this paper,...
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Stable Unital Bases, Hyperfocal Subalgebras and Basic Morita Equivalences
We investigate Conjecture 1.5 introduced by Barker and Gelvin (J. Gr. Theory 25 , 973–995
2022 ), which says that any source algebra of a p -block ( p is... -
A study of bi-bases of ternary semigroups
In this paper, we introduce the bi-bases of a ternary semigroup. The results of this paper are based on the bi-ideals generated by a non-empty subset...
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Nicely structured positive bases with maximal cosine measure
The properties of positive bases make them a useful tool in derivative-free optimization and an interesting concept in mathematics. The notion of the c...
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Collisions of digit sums in bases 2 and 3
We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers n such that...
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Riesz bases by replacement
In this paper we provide a method for constructing new Riesz bases on separable Hilbert spaces and we use it to prove sufficient conditions for the...
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FINITE ELEMENTS IN ORDERED BANACH SPACES WITH POSITIVE BASES
We characterize finite elements, an order-theoretic concept in Archimedean vector lattices, in the setting of ordered Banach spaces with positive...
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An Extended Range of Stable Flux Reconstruction Schemes on Quadrilaterals for Various Polynomial Bases
An extended range of energy stable flux reconstruction schemes, developed using a summation-by-parts approach, is presented on quadrilateral elements...
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On Wieferich and Non-Wieferich Primes with Prime Bases
We study the matter of the density and the distribution of Wieferich and non-Wieferich primes and especially the issues related to bases that are...
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Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample
AbstractIn this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical)...