Objective(s): Oxidative stress has a pivotal role in the pathogenesis of diabetic retinopathy (DR). Juglans regia L. (JRL) leaf extract has hypoglycemic and antioxidative properties. This study aimed to determine the ameliorative effects of JRL against diabetic retinopathy. Materials and Methods: The DR rat model was generated by injection of streptozotocin (STZ). A subset of the diabetic rats ...

Let $$S\subset\mathbb R^n$$ be a nonempty set. Given $$d\in [0,n)$$ and cube $$\overline{Q}\subset\mathbb with side length $$l=l(\overline{Q}) \in (0,1]$$ , we show that if the $$d$$ -Hausdorff content $$\mathcal H^d_{\infty}(\overline{Q}\cap S)$$ of set $$\overline{Q}\cap S$$ satisfies inequality S)<\overline{\lambda}l^{d}$$ for some $$\overline{\lambda}\in (0,1)$$ then $$\overline{Q}\setminus...

We study semiclassical sequences of distributions \(u_h\) associated with a Lagrangian submanifold phase space \(\mathcal {L}\subset T^*X\). If is distribution, which concentrates at maximal rate on {L},\) then the asymptotics are well understood by work Arnol’d, provided {L}\) projects to X stable simple singularity. establish sup-norm estimates under much more general hypotheses it concentrat...

in this paper, we study the chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. in particular, we prove that if t is a remotal subset of an inner product space h, and f is a star-shaped set at a relative chebyshev centre c of t with respect to f, then llx - qt (x)1i2 2 ilx-cll2 + ilc-qt (c) 112 x e f, where qt : f + t is any choice function s...

we introduce center-like subsets z*(r,f), z**(r,f) and z1(r,f), where r is a ring and f is a map from r to r. for f a derivation or a non-identity epimorphism and r a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of r.

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

For simplicity, we adopt the following rules: x denotes a set, r, s denote real numbers, n denotes a natural number, V denotes a real linear space, v, u, w, p denote vectors of V , A, B denote subsets of V , A1 denotes a finite subset of V , I denotes an affinely-independent subset of V , I1 denotes a finite affinelyindependent subset of V , F denotes a family of subsets of V , and L1, L2 denot...

For simplicity, we use the following convention: i, i1, i2, j, j1, j2, k, m, n, t denote natural numbers, D denotes a non empty subset of E2 T, E denotes a compact non vertical non horizontal subset of E2 T, C denotes a compact connected non vertical non horizontal subset of E2 T, G denotes a Go-board, p, q, x denote points of E2 T, and r, s denote real numbers. The following propositions are t...

Let V be a real linear space. The functor ConvexComb(V ) yielding a set is defined by: (Def. 1) For every set L holds L ∈ ConvexComb(V ) iff L is a convex combination of V . Let V be a real linear space and let M be a non empty subset of V . The functor ConvexComb(M) yielding a set is defined as follows: (Def. 2) For every set L holds L ∈ ConvexComb(M) iff L is a convex combination of M . We no...