the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix is divided into signal subspace and noise subspace. in this subspace division,each derivative of the singular values with respect to rank order is used ...

I construct a finite-dimensional quantum theory from general relativity by a homotopy method. Its quantum history is made up of at least two levels of fermionic elements. Its unitary group has the diffeomorphism group as singular limit. Its gravitational metrical form is the algebraic square. Its spinors are multivectors.

We show that many integrals containing products of confluent hypergeometric functions follow directly from one single integral that has a very simple formula in terms of Appell’s double series F2 . We present some techniques for computing such series. Applications requiring the matrix elements of singular potentials and the perturbed Kratzer potential are presented. PACS 03.65.Ge Integrals cont...

Let Fp denote the field with p elements and F̄p its algebraic closure. We show that the singular cochain functor with coefficients in F̄p induces a contravariant equivalence between the homotopy category of connected pcomplete nilpotent spaces of finite p-type and a full subcategory of the homotopy category of E∞ F̄p-algebras. Draft: January 26, 1998, 17:28

We characterize the compactness properties of the product of λ copies of the space ω with the discrete topology, dealing in particular with the case λ singular, using regular and uniform ultrafilters, infinitary languages and nonstandard elements. We also deal with products of uncountable regular cardinals with the order topology. 2010 Mathematics Subject Classification 54B10, 54D20, 03C75 (pri...

Let A be an M-matrix in standard lower block triangular form, with diagonal blocks Ai; irreducible. Let S be the set of indices a such that the diagonal block A"" is singular. We define the singular graph of A to be the set S with partial order defined by a > (3 if there exists a chain of non-zero blocks A,,;, A;i' .. . , AIi3" Let Al be the set of maximal elements of S, and define the p-th lev...

We establish an analogue of the classical Polya–Vinogradov inequality for $$GL(2, {\mathbbm {F}}_p)$$ , where p is a prime. In process, we compute ‘singular’ Gauss sums . As application, show that collection elements in $$GL(2,{\mathbbm {Z}})$$ whose reduction modulo are maximal order and matrix entries bounded by x has expected size as soon $$x\gg p^{1/2+\varepsilon }$$ any $$\varepsilon >0$$