In this article, first we generalize the concept of complete parts in hyperrings by introducing the concept R-parts in hyperrings and then we study R-closures in hyperrings. Finally we characterize R-closures in hyperfields.

We show that for Lebesgue almost all $d$-tuples $(\theta\_1,\ldots,\theta\_d)$, with $|\theta\_j|>1$, any self-affine measure a homogeneous non-degenerate iterated function system ${Ax+a\_j}\_{j=1}^m$ in\~$\mathbb{R}^d$, where $A^{-1}$ is diagonal matrix the entries has power Fourier decay at infinity.

Hindered convection of macromolecules in gels was studied by measuring the sieving coefficient (theta) of narrow fractions of Ficoll (Stokes-Einstein radius, r(s) = 2.7-5.9 nm) in agarose and agarose-dextran membranes, along with the Darcy permeability (kappa). To provide a wide range of kappa, varying amounts of dextran (volume fractions < or = 0.011) were covalently attached to agarose gels w...

An $(n,r,h,a,q)$ -Local Reconstruction Code (LRC) is a linear code over notation="LaTeX">$\mathbb {F}_{q}$ of length notation="LaTeX">$n$ , whose codeword symbols are partitioned into notation="LaTeX">$n/r$ local groups each size nota...

Given a smooth projective curve X, we give effective very ampleness bounds for generalized theta divisors on the moduli spaces SUX(r, d) and UX(r, d) of semistable vector bundles of rank r and degree d on X with fixed, respectively arbitrary, determinant.

The list Ramsey number R ℓ ( H , k ) ${R}_{\ell }(H,k)$ recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list-coloring variant of the classical number. They showed that if $H$ fixed r $r$ -uniform hypergraph not -partite colors $k$ goes to infinity, e Ω ≤ O ${e}^{{\rm{\Omega }}(\sqrt{k})}\le {R}_{\ell }(H,k)\le {e}^{O(k)}$ . We prove = Θ }(H,k)={e}^{{\rm{\Theta }}(k)}$ ...

Abstract We generalize the Rindler-Ishak (2007) result for lensing deflection angle in a SdS spacetime, to case of general spherically symmetric fluid beyond cosmological constant. thus derive an analytic expression first post-Newtonian order static metric form $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(d\theta ^2 +\sin \theta d\phi ^2)$ with $f(r) 1 - \frac{2m}{r}-\sum _{i} b_i\,\, r_0^{-q_...

In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta ]$-submodules of $R_{n}=R[x;\theta ]/\langle x^{n}-1\rangle $. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an...

We investigate here the following weighted degenerate elliptic system $$\begin{aligned} &-\Delta _{s} u =\Big(1+\|\mathbf{x}\|^{2(s+1)}\Big)^{ \frac{\alpha }{2(s+1)}} v^{p}, \quad -\Delta v= \Big(1+\| \mathbf{x}\|^{2(s+1)}\Big)^{\frac{\alpha }{2(s+1)}}u^{\theta }, \\ &\quad u,v>0 \mbox{in }\; \mathbb{R}^{N}:=\mathbb{R}^{N_{1}}\times \mathbb{R}^{N_{2}}, \end{aligned}$$ where $\Delta _{s}=\Delta ...