This work connects two mathematical fields – computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system, deciding solvability of a linear system, computing inverse matrix, eigenvalues, checking positive (semi)definiteness or stability. We discuss these problems and relati...

A topological algebra is a complex associative algebra which is also a Hausdorff topological vector space such that the multiplication is separately continuous. A locally convex algebra is a topological algebra whose topology is determined by a family of seminorms. A complete metrizable locally convex algebra is called a B0-algebra. The topology of a B0-algebra A may be given by a countable fam...

Given a von Neumann algebra M with a faithful normal semi-finite trace τ, we consider the non commutative Arens algebra Lω(M, τ) = ⋂ p≥1 Lp(M, τ) and the related algebras L2 (M, τ) = ⋂ p≥2 Lp(M, τ) and M + L2 (M, τ) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L2 (M, τ) is inner and...

Lie group methods for nonautonomous semi-discretized in space, partial differential equations are considered. The choice of frozen vector field and its corresponding algebra action on the manifold for such problems is discussed. A new exponential integrator for semilinear problems based on commutator free Lie group methods with algebra action arising from the solutions of differential equations...

This paper provides a review on major ergodic features of semiindependent hyper MV –algebra dynamical systems. Theorems are presented to make contribution to calculate the entropy. Particularly, it is proved that the total entropy of those semi-independent hyper MV –algebra dynamical systems that have a generator can be calculated with respect to their generator rather than considering all the ...

We study a q-deformation for the semi-direct product of the symmetric group Sn with the Clifford algebra on n anticommuting generators. We obtain a q-version of the projective analogue for the classical Young symmetrizer introduced by the second author. Our main tool is an analogue of the Hecke algebra of complex valued functions on the group GLn over a p-adic field relative to the Iwahori subg...

A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has...

We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis to algebras generated by semi-algebraic functions. In which case the standard global optimization problem with constraints given by elements of the same algebra is reduced via a natural change of variables to the better understood case ...

It is proved that if an algebra R over a field can be endowed with a pointed and finite-dimensional .nfiltration such that the associated .n-graded algebra T is semi-commutative, then R is left and right finitely partitive. In order to do this, a multi-variable Poincare! series for every finitely generated graded T-module is considered and it is shown that this Poincare! series is a rational fu...

A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g. a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous vector bundle over homogeneous spaces. In this paper, we study the relationship between partial flag and complete flag cases. Our main result is that the locally ...