A k-factor of a graph G = (V (G), E(G)) is a k-regular spanning subgraph of G. A k-factorization is a partition of E(G) into k-factors. If V 1 , ..., V p are the p parts of V (K(n, p)) (the complete multipartite graph with p parts, each of size n), then a holey k-factor of deficiency V i of K(n, p) is a k-factor of K(n, p) − V i for some i satisfying 1 ≤ i ≤ p. Hence a holey k-factorization is ...

in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

I n o r d e r t o r e p r e s e n t u n c e r t a i n knowledge e s p e c i a l l y i n f e r e n c e r u l e s m a t c h i n g u n c e r t a i n knowledge s t r u c t u r e s s e v e r a l e x t e n s i o n s o f a r e p r e s e n t a t i o n schema a r e d e s c r i b e d . F i r s t a t w o d i m e n s i o n a l e v i d e n c e space i s i n t r o d u c e d t o e x p r e s s p o s i t i v e ...

<abstract><p>Let $ G be a simple connected graph with the vertex set V(G) and d_{B}(u, v) biharmonic distance between two vertices u v in $. The index BH(G) of is defined as</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ = \frac{1}{2}\sum\limits_{u\in V(G)}\sum\limits_{v\in V(G)}d_{B}^2(u, n\sum\limits_{i 2}^{n}\frac{1}{\lambda_i^2...

a m i t r a z, a n i ns e c t i c i d e /a ca ri c i de of the f o r m a m i d i n e p e st i c i d e s group, is a ? 2 a d r e n e r g i c ag on i st a nd of t he a m i d i ne c h e m i ca l f a m il y generally us e d to c o n t r ol animal e c top a r a s i t e s. poisoning due to am i t r a z i s r a r e and characterized by c e nt r a l n e r v ous s y st e m a nd r e sp ir a to r y d e p ...

ruminal, post-ruminal and total tract crude protein disappearance of alfalfa hay and barley grain were measured using in vivo, in situ mobile bag and three-step in situ/in vitro enzyme procedures (3-step). for in vivo, four baluchi lambs (49.4 ± 3.5 kg, body weight) were used in a 2 × 2 latin square design within 2 periods (24 days of each period). experimental diets were made of two alfalfa ha...

epilepsy is one of the common neurologic disorders in children. drug side-effects are one of the important problems in treating patients with epilepsy. using the antiepileptic medication may cause different side effects such as disorder in bone and vitamin d metabolism. sodium valproate is one of the antiepileptic medications used widely. some of its side effects include digestive disorder, inc...

Using elementary methods, the following results are obtalned:(1) If p is n n-m prime, 0 m n, 0 < b < ap n-m, and p ab, then (m) (-I)P-I(apb (rood pn). 2 A2_4B If r,s are the roots of x Ax-B, where (A,B) and D > 0, if n n u v rn+s n, and k > O, then (II) v =v (rood pn). n r-s n kpn kpn-1 (III) If p is odd and p D, then u (_D) u (rood pn); kp n P kp n-I (IV) u (_1)Bu n) n n-I (rood 2 k2 k2

Let G be a 2-connected graph with n ?: 3 vertices such that for any two vertices u, v at distance two in an induced subgraph K 1,3 or P4 of G, the inequality d(u) + d(v) ?: IN(u) U N(v) U N(w)ls holds for all w E N(u) n N(v). We prove that (i) if s = 1 and IN(u) n N(v)1 ?: 2, then G is hamiltonian or K p,p+1 ~ G ~ Kp + K p+1; (ii) if s = 0, then G is either pancyclic, or bipartite graph. This g...

In this paper, we study the multiplicity and concentration of positive solutions for following (p, q)-Laplacian problem: $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{p} u _{q} +V(\varepsilon x) \left( |u|^{p-2}u + |u|^{q-2}u\right) = f(u) &{} \text{ in } {\mathbb {R}}^{N}, \\ u\in W^{1, p}({\mathbb {R}}^{N})\cap q}({\mathbb {R}}^{N}), \quad u>0 \end{array} \right. \end{aligned}$$ where...