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• Spectral theorems associated to the Dunkl operators

In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^{p}_{k}-$norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on $\mathbb{R}^{d}$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

• Existence of solution for a fractional differential inclusion via nonsmooth critical point theory

This paper is concerned with the existence of solutions to the following fractional differential inclusion \begin{equation*} \left\{\begin{array}{l}- \frac{d}{dx}\left(p \ {}_0D_x^{-\beta}(u'(x))+q \ {}_xD_1^{-\beta}(u'(x))\right)\in \partial F_u(x,u),\hspace{0.5cm}x\in (0,1),\\ u(0)=u(1)=0, \end{array} \right. \end{equation*} where ${}_0D_x^{-\beta}$ and ${}_xD_1^{-\beta}$ are left and right Riemann-Liouville fractional integrals of order $\beta \in(0,1)$ respectively, $0<p=1-q<1$ and $F:[0,1]\times \Bbb{R}\rightarrow\Bbb{R}$ is locally Lipschitz with respect to the second variable. Due to the general assumption on the constants $p$ and $q$, the problem does not have a variational structure. Despite that, here we study it combining with an iterative technique and nonsmooth critical point theory, we obtain an existence result for the above problem under suitable assumptions. The result extends some corresponding results in the literatures.

• Studying on a skew ruled surface by using the geodesic Frenet trihedron of its generator

In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.

• Construction of the first layer of anti-cyclotomic extension

In this paper, using a theorem of Brink for prime decomposition of the anti-cyclotomic extension, we explicitly construct the first layer of the anti-cyclotomic Z3-extension of imaginary quadratic fields.

• A note on $\delta$-quasi fuzzy subnear-rings and ideals

In this paper, we discuss in detail some of the properties of the new kind of $(\in,\in\vee q)$-fuzzy ideals in Near-ring. The concept of $(\in,\in \vee q_0^\delta)$-fuzzy ideal of Near-ring is introduced and some of its related properties are investigated.

• Some remarks on the generalized order and generalized type of entire matrix functions in complete reinhardt domain

The main aim of this paper is to introduce the definitions of generalized order and generalized type of the entire function of complex matrices and then study some of their properties. By considering the concepts of generalized order and generalized type, we will extend some results of Kishka et al. [5].

• KRONECKER FUNCTION RINGS AND PRUFER-LIKE DOMAINS

Let D be an integral domain, D be the integral closure of D, * be a star operation of nite character on D, *w be the so-called *w-operation on D induced by *, X be an indeterminate over D, N* = ff 2 D[X]jc(f)* = Dg, and Kr(D; ) =f0g [ ff g j0 6= f; g 2 D[X] and there is an 0 6= h 2 D[X] such that (c(f)c(h))* (c(g)c(h))*g. In this paper, we show that D is a *-quasi-Prufer domain if and only if D [X]N* = Kr(D; *w). As a corollary, we recover Fontana-Jara-Santos's result that D is a Prufer *-multiplication domain if and only if D[X]N* = Kr(D; *w).

• Dynamical Bifurcation of the Burgers-Fisher equation

In this paper, we study dynamical Bifurcation of the Burgers-Fisher equation. We show that the equation bifurcates an invariant set $\mathcal{A}_n (\beta)$ as the control parameter $\beta$ crosses over $n^2$ with $n \in \mathbb{N}$. It turns out that $\mathcal{A}_n (\beta)$ is homeomorphic to $S^1$, the unit circle.

• A FIXED POINT APPROACH TO THE STABILITY OF QUARTIC LIE *-DERIVATIONS

We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+\frac{1}{2}a(a^2+1)f(x-y)+(a^4-1)f(y)= \,\,\frac{1}{2}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie $*$-derivation by using a directed method and an alternative fixed point method.

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