In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.

Let R be a commutative ring and Z(R) the set of all zero divisors R. Γ(R) is said to divisor graph if x,y ∈ V (Γ(R)) = (x,y) E(Γ(R)) only x.y 0. In this paper, we determine total vertex irregularity strength graphs associated with rings ℤp2 × Zq for p,q prime numbers.

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evol...

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

in this paper, a novel method for ranking of fuzzy numbers are proposed. in this method, decision maker is defined based on the center of mass at some cuts of a pair of fuzzy numbers in discreet version and center of mass on all of cuts of a pair of fuzzy numbers in continuous version. our method can rank more than two fuzzy numbers simultaneously. also, some properties of methods are described...

The notation and terminology used in this paper have been introduced in the following articles: [3], [4], [13], [5], [15], [6], [7], [16], [10], [1], [2], [8], [11], [18], [12], [17], and [9]. In this paper R, R1, R2 denote functions from N × N into R, r1, r2 denote convergent sequences of real numbers, n, m, N ,M denote natural numbers, and e, r denote real numbers. Let us consider R. We say t...

this research was an attempt to study reasons for creation of some of the important and sacred numbers and their reflection in architectural and urban spaces. this subject matter is important because significant and sacred numbers were used in design and construction of a number of historical spaces. the research objective was to discover some of the reasons for formation of important and sacre...

We adopt the following rules: r, x, y are real numbers, i, j are natural numbers, and p is a finite sequence of elements of R. The following proposition is true (1) For every closed-interval subset A of R and for every x holds x ∈ A iff inf A ¬ x and x ¬ supA. Let I1 be a finite sequence of elements of R. We say that I1 is non-decreasing if and only if the condition (Def. 1) is satisfied. (Def....

We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λn), n ∈ N be an unbounded sequence numbers. Costakis has proved following result. There exists entire function f with property: for every x, y R 0 , θ ∈(0,1) a there is subsequence natural (mn), such that, compact subset L ⊆ In present paper we show that constant cannot replaced by any non-constant G. This so ev...

In this paper r, s are real numbers. We now state several propositions: (1) 0 ¬ r + |r|. (2) 0 ¬ −r + |r|. (3) If |r| = |s|, then r = s or r = −s. (4) For all natural numbers i, j such that i < j and i 6= 0 holds i j is not integer. (5) {2 · k; k ranges over natural numbers: k > 1} is infinite. (6) For every function f and for all sets a, b, c such that a 6= c holds (f+·(a7−→ . b))(c) = f(c). (...