In the present paper, we study normalized solutions with least energy to following system: $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+\lambda _1u=\mu _1 |u|^{p-2}u+\beta r_1|u|^{r_1-2}|v|^{r_2}u\quad &{}\hbox {in}~{{\mathbb {R}}^N},\\ v+\lambda _2v=\mu _2 |v|^{q-2}v+\beta r_2|u|^{r_1}|v|^{r_2-2}v\quad \int _{{{\mathbb {R}}^N}}u^2=a_1^2\quad \hbox {and}\quad {R}}^N}}v^2=a_2^2, \end{a...

We extend the notion of dissipative particle solutions [5] to case Hamiltonian flow in space probability measures $ \mu \in \mathscr{P}( \mathbb {R}^d \times {R}^d) sense [3]. The is form \begin{equation*} H(\mu) = \int V(q,p) \mu(dqdp) + \frac{1}{2} W(q,p,q',p') \mu(dqdp)\mu(dq'dp'), \end{equation*} with at most quadratic growth, so that a conservative \dot q \nabla_p V W \mu, \quad p - \nabla...

Let $(u, v)$ be a solution to semilinear parabolic system $$ \mbox{(P)} \qquad \left\{ \begin{array}{ll} \partial_{t} u = D_1 \Delta u+v^{p} \quad \mbox{in} \mathbf{R}^{N} \times (0, T),\\ v D_2 v+u^{q} u, \geq 0 (u(\cdot, 0), v(\cdot, 0)) (\mu, \nu) \mathbf{R}^N, \end{array} \right. where $N 1$, $T > 0$, $D_1 $D_2 $0 < p \leq q$ with $pq 1$ and $(\mu, \nu)$ is pair of Radon measures or nonnega...

Dementia is a common cognitive syndrome reflecting a wide spread chronic progressive disease as an extension to normal aging process. Oxidative stress has been implicated in dementia and antioxidants have become attractive therapeutic agents. Among the antioxidants vitamin E is the most potent in the treatment of dementia. Study was conducted in 20 patients suffering from dementia in the age gr...

Reaction of the uranium(III) tris(anilide) complex (THF)U(N[t-Bu]Ar)(3) (1, THF = tetrahydrofuran; Ar = 3,5-Me(2)C(6)H(3)) with MN(3) (M = Na, [N(n-Bu)(4)]) results in the formation of the bimetallic diuranium(IV/IV) complexes M[(mu-N)(U(N[t-Bu]Ar)(3))(2)] (M[3]), which feature a single nitride ligand engaged as a linear, symmetric bridge between two uranium centers. The stability of the U=N=U ...

We now define random walks on weighted graphs. We will let A denote the adjacency matrix of a weighted graph. We will also the graph to have self-loops, which will correspond to diagonal entries in A. Thus, the only restriction on A is that is be symmetric and non-negative. When our random walk is at a vertex u, it will go to node v with probability proportional to au,v: mu,v def = au,v ∑ w au,w .

Let G be a connected graph, nu(e) is the number of vertices of G lying closer to u and nv(e) is the number of vertices of G lying closer to v. Then the Szeged index of G is defined as the sum of nu(e)nv(e), over edges of G.. The PI index of G is a Szeged-like topological index defined as the sum of [mu(e)+ mv(e)], where mu(e) is the number of edges of G lying closer to u than to v, mv(e) is the...

HAS-V is a cryptographic hash function which processes 1024-bit message blocks and produces a hash value of variable length. The design of the hash function is based on design principles of the MD4 family. Recently, weaknesses have been shown in members of this family. Therefore, the analysis of the HAS-V hash function is of great interest. To the best of our knowledge this is the first article...