we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations sparsify the separators in Nested Dissection based Householder QR factorization. First, modified version of used identify interiors/separators and reorder matrix. Then, classical factorize interiors, going from leaves root elim...

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

In this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets.

For a sparse linear system Ax = b, preconditioners of the form C = D + L+ U , where D is the block diagonal part of A (or incomplete factorization approximation of its blocks), and L and U are block strictly lower and upper triangular matrices composed of low-ranks approximations of the respective blocks of A, are examined. C is applied directly, by solving Cz = w, or partially, by applying one...

We describe δ-shock wave generation from continuous initial data in the case of triangular conservation law system arising from ”generalized pressureless gas dynamics model”. We use smooth approximations in the weak sense that are more general than small viscosity approximations. In this paper we investigate formation of δ-shock wave in the case of triangular system of conservation laws: ut + (...

In this paper, we introduce a class of lowest-order nonconforming immersed finite element (IFE) methods for solving two-dimensional Stokes interface problems. The proposed do not require the solution mesh to align with fluid and can use either triangular or rectangular meshes. On meshes, Crouzeix–Raviart is used velocity approximation, piecewise constant pressure. Rannacher–Turek rotated Q1-Q0 ...

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...

Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially large-scale hydrostatic calculations centrifugal acceleration. This paper proposes an unstructured method a filtered scheme to mitigate noise and avoid further influencing velocities water elevation. In pressure calc...