We study the elliptic system \begin{equation*} \begin{cases} -\Delta u_1 - \kappa_1u_1 = \mu_1|u_1|^{p-2}u_1 + \lambda\alpha|u_1|^{\alpha-2}|u_2|^\beta u_1, \\ u_2 \kappa_2u_2 \mu_2|u_2|^{p-2}u_2 \lambda\beta|u_1|^\alpha|u_2|^{\beta-2}u_2, u_1,u_2\in D^{1,2}_0(\Omega), \end{cases} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb R^N$, $N\geq 3$, $\kappa_1,\kappa_2\in\mathbb R$, $\...

We show that the series expansions of certain $q$-products have \textit{matching coefficients} with their reciprocals. Several results are associated to Ramanujan's continued fractions. For example, let $R(q)$ denote Rogers-Ramanujan fraction having well-known $q$-product repesentation $$R(q)=\dfrac{(q;q^5)_\infty(q^4;q^5)_\infty}{(q^2;q^5)_\infty(q^3;q^5)_\infty}.$$ If \begin{align*} \sum_{n=0...

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...

The metabolic detoxication/bioactivation pathways, the levels and activity of enzymes, and endogenous cofactors mediating these reactions in crops have been well document‐ ed; however, much less evidence has been accumulated in weed species. The herbicide metabolism as a selectivity factor is summarized with special attention to acetyl-CoA car‐ boxylases (ACCase)-inhibiting aryloxyphenoxypropio...

It has been previously reported (7) that the administration of estrogens to the ovariectomized rat causes a pronounced response in the peroxi dase level of the uterus. Since the estrogens stimu late mitotic activity in the uterus, it was thought that the presence of peroxidase might be charac teristic of tissues undergoing proliferation. The studies to be presented in this paper mdi cate that a...

 In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.