In this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in C[x1,x2, . . . ,xn] for n ≥ 3 always form a regular sequence and we state the conjecture when pa, pb, pc for given positive integers a < b < c forms a regular sequence in C[x1,x2,x3,x4]. We also provide evidence for this c...

Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...

INTRODUCTION Comparison of platform switched (PS), sloping shoulder, and regular implants on stress reduction in various bone densities with finite element analysis. MATERIALS AND METHODS A total of 12 three-dimensional finite element models were built to analyze the stress distribution model. Nobel Biocare 4.3 × 8 mm regular platform replace select implant with matching diameter easy abutmen...

Three machine implemented algorithms for computing with integral orders are described. The algorithms are: 1. For an integral order R given in terms of its left regular representation relative to any basis, compute the nil radical J(R) and a left regular representation of R/J(R). 2. For a semisimple order R given in terms of its left regular representation relative to any basis, compute a new b...

In this paper, finite element method is used to obtain thermal conductivity coefficients of single-walled carbon nanotube reinforced polypropylene. For this purpose, the two-dimensional representative volume elements are modeled. The effect of different parameters such as nanotube dispersion pattern, nanotube volume percentage in polymer matrix, interphase thickness between nanotube and surroun...

Let k be a field and S = k[x1, . . . , xn] be a polynomial ring over k. We consider finite sequences of homogeneous polynomials of positive degrees and their operation on non-trivial finitely generated graded S-modules (with grading in Z). Here and in the following, by a polynomial, we always mean an element of S. Moreover, by an S-module we mean in the following a graded S-module with grading ...

If u, v ∈ N, A is a u × v matrix with entries from Q, and ~b ∈ Q, then (A,~b ) determines an affine transformation from Q to Q by ~x 7→ A~x + ~b. In 1933 and 1943 Richard Rado determined precisely when such transformations are kernel partition regular over N, Z, or Q, meaning that whenever the nonzero elements of the relevant set are partitioned into finitely many cells, there is some element o...

Let r be a finite connecied regular bipartite 2-arc transitive graph. It is shown that r is a cover of a possibly smaller graph :E, which is also connecied and regular of the same valency as r, and there is a subgroup G of Aut :E such that G is 2-arc transitive on :E and every nontrivial normal subgroup of G has at most two orbits on vertices. Such graphs :E for which the subgroup G has an abel...