We study triangular lattice spin-1 /2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin-liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean-field states and their energetics is compared against magnetically ordered trial states. We find that in a range of the ring ex...

The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...

We use Kazhdan-Lusztig polynomials and subspaces of the polynomial ring C[x1,1, . . . , xn,n] to construct irreducible Sn-modules. This construction produces exactly the same matrices as the Kazhdan-Lusztig construction [Invent.Math 53 (1979)], but does not employ the Kazhdan-Lusztig preorders. It also produces exactly the same modules as those which Clausen constructed using a different basis ...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

A new ankylosaurid (Ankylosauria: Dinosauria), Ziapelta sanjuanensis, gen. et sp. nov., is based on a complete skull, an incomplete first cervical half ring, a possible fragment of the second cervical half ring, and additional fragmentary osteoderms. The holotype specimen is from the Upper Cretaceous (Upper Campanian, Kirtlandian Land-Vertebrate Age) Kirtland Formation (De-na-zin Member) at Hun...

Derivations, Jordan derivations, as well as automorphisms and Jordan automorphisms of the algebra of triangular matrices and some class of their subalgebras have been the object of active research for a long time [1, 2, 5, 6, 9, 10]. A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic different from 2 is either an isomorphism or an anti-iso...

We completely determine those natural numbers $n$ for which the full matrix ring $M_n(F_2)$ and triangular $T_n(F_2)$ over two elements field $F_2$ are either n-torsion clean or almost clean, respectively. These results somewhat address settle a question, recently posed by Danchev-Matczuk in Contemp. Math. (2019) as well they supply more precise aspect nil-cleanness property of $n\times n$ all ...

We present a parallel algorithm for solving triangular systems of linear equations on distributed-memory multiprocessor machines. The parallelism is achieved by partitioning the rows of the coefficient matrix in segments of a fixed size and distributing these sets in a wrap-around fashion among the processors, connected in a ring. The granularity of the algorithm is controlled by varying the se...

2. Simultaneous similarity of tuples of matrices over C. Problem 1 is notoriously difficult. We show that for the local ring H0 this problem reduces to a Problem 2 for certain kind of matrices. We then discuss certain special cases of Problem 2 as simultaneous similarity of tuples of matrices to upper triangular and diagonal matrices. L-property of pairs of matrices, that discussed next, is clo...