A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

We find IIb compactifications on Calabi-Yau orientifolds in which all Kähler moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and Trivedi.

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

I review the tunneling, Hartle-Hawking and Linde proposals for the wave function of the universe and comment on the recent work on quantum creation of open universes.

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

We use light-cone QCD sum rules to evaluate the strong coupling gf0K+K− which enters in several analyses concerning the scalar f0(980) meson. The result: 6.2 ≤ gf0K+K− ≤ 7.8 GeV is larger than in previous determinations.

An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

for a given graph $g=(v,e)$, let $mathscr l(g)={l(v) : vin v}$ be a prescribed list assignment. $g$ is $mathscr l$-$l(2,1)$-colorable if there exists a vertex labeling $f$ of $g$ such that $f(v)in l(v)$ for all $v in v$; $|f(u)-f(v)|geq 2$ if $d_g(u,v) = 1$; and $|f(u)-f(v)|geq 1$ if $d_g(u,v)=2$. if $g$ is $mathscr l$-$l(2,1)$-colorable for every list assignment $mathscr l$ with $|l(v)|geq k$ ...