An element f of a commutative ring A with identity element is called a von Neumann regular element if there is a g in A such that fg = f . A point p of a (Tychonoff) space X is called a P -point if each f in the ring C(X) of continuous realvalued functions is constant on a neighborhood of p. It is well-known that the ring C(X) is von Neumann regular ring iff each of its elements is a von Neuman...

Let T(X) be the full transformation semigroup on a set X, and let L(V) under composition of all linear transformations vector space V over field. For subset Y X subspace W V, consider semigroups $${\overline{T}}(X, Y) = \{f\in T(X):Yf \subseteq Y\}$$ $${\overline{L}}(V, W) L(V):Wf W\}$$ composition. We describe unit-regular elements in Y)$$ W)$$ . Using these, we determine when are unit-regular...

Let $$r\ge 3$$ be a positive integer and $${\mathbb {F}}_q$$ the finite field with q elements. In this paper, we consider r-regular complete permutation property of maps form $$f=\tau \circ \sigma _M\circ \tau ^{-1}$$ where $$\tau $$ is PP over an extension {F}}_{q^d}$$ $$\sigma _M$$ invertible linear map . When additive, give general construction CPPs for any r. not many examples regular field...

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

We present a simple, explicit construction of an infinite family F of bounded-degree ’unique-neighbor’ expanders Γ; i.e., there are strictly positive constants α and , such that all Γ = (X,E(Γ)) ∈ F satisfy the following property. For each subset S of X with no more than α|X| vertices, there are at least |S| vertices in X \ S that are adjacent in Γ to exactly one vertex in S. The construction o...

We introduce the concept of regular super-functions at a fixed point. It is derived from the concept of regular iteration. A super-function F of h is a solution of F(z+1)=h(F(z)). We provide a condition for F being entire, we also give two uniqueness criteria for regular super-functions. In the particular case h(x)=bˆx we call F super-exponential. h has two real fixed points for b between 1 and...

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...

Abstract In this paper, we will use the coincident gauge to investigate new solutions of $$f(\mathbb {Q})$$ f ( Q ) theory applied in context black holes, regular and black-bounce spacetime. For each these approaches, compute linear wit...