An analogue for composite moduli m ≥ 2 of the Wilson quotient is studied. Various congruences are derived, and the question of when these quotients are divisible by m is investigated; such an m will be called a “Wilson number”. It is shown that numbers in certain infinite classes cannot be Wilson numbers. Eight new Wilson numbers up to 500 million were found.

The K-groups, the range of trace on K0, and isomorphism classifications are obtained for simple infinite dimensional quotient C*-algebras of the group C*-algebras of six lattice subgroups, corresponding to each of the six non-isomorphic 5-dimensional connected, simply connected, nilpotent Lie groups. Connes’ non-commutative geometry involving cyclic cocycles and the Chern character play a key r...

how to cite this article: ordooei m, mottaghipisheh h, fallah r, rabiee a. cognitive outcomes for congenital hypothyroid and healthy children: a comparative study. iran j child neurol. 2014 autumn;8(4): 28-32. abstract objective early diagnosis and treatment of congenital hypothyroidism (ch) and the prevention of developmental retardation is the main goal of public health national screening pro...

The Rayleigh Quotient Iteration (RQI) was developed for real symmetric matrices. Its rapid local convergence is due to the stationarity of the Rayleigh Quotient at an eigenvector. Its excellent global properties are due to the monotonie decrease in the norms of the residuals. These facts are established for normal matrices. Both properties fail for nonnormal matrices and no generalization of th...

The articles [8], [1], [4], [2], [3], [5], [7], [12], [13], [6], [9], and [10] provide the notation and terminology for this paper. We follow the rules: h, r, r1, r2, x0, x1, x2, x3, x4, x5, x, a, b, c, k denote real numbers and f , f1, f2 denote functions from R into R. Next we state a number of propositions: (1)1 ∆[f ](x, x+ h) = ( ~ ∆h[f ])(1)(x) h . (2) If h 6= 0, then ∆[f ](x, x+ h, x+ 2 ·...

The papers [2], [7], [13], [3], [1], [6], [9], [4], [14], [8], [5], [15], [11], [12], and [10] provide the notation and terminology for this paper. We adopt the following rules: n denotes an element of N, h, k, x, x0, x1, x2, x3 denote real numbers, and f , g denote functions from R into R. Next we state a number of propositions: (1) If x0 > 0 and x1 > 0, then loge x0 − loge x1 = loge( x1 ). (2...

Let G be a locally compact Abelian group; I’ the dual group of G; CO(l_’)the algebra of continuous functions on r which vanish at infinity; CB(17)the continuous, bounded functions on r; M(G) the algebra of bounded Borel measures on G; Ll(G) the algebra of absolutely continuous measures; and M(G)A the algebra of l?ourier-Stielt jes transforms. Let E denote a compact subset of I’, and let A(E) be...

Quotient space theory (QST), a new granule computing tool dealing with imprecise, incomplete and uncertain knowledge, uses a triplet, including the universe, its structure and attributes, to describe a problem space or simply a space. As one of important theories of granular computing (GrC), QST is very helpful to the study of cognitive informatics (CI). This article summarizes the quotient spa...

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic, but also in probabilistic and classical logic. This relation is presented by a long series of examples, some of them easy, and some also highly non-trivial (es...