This paper is devoted to studying the representation of measures non-generalized compactness, in particular, noncompactness, non-weak compactness and non-super weak etc., defined on Banach spaces its applications. With aid a three-time order-preserving embedding theorem, we show that for every space X, there exist function C(K) some compact Hausdorff K an affine mapping $$\mathbb{T}$$ from supe...

Erdős, Hajnal and Szemerédi proved that any subset $G$ of vertices a shift graph $\text{Sh}_{n}^{k}$ has the property independence number subgraph induced by satisfies $\alpha(\text{Sh}_{n}^{k}[G])\geq \left(\frac{1}{2}-\varepsilon\right)|G|$, where $\varepsilon\to 0$ as $k\to \infty$. In this note we prove for $k=2$ $n \to \infty$ there are graphs $G\subseteq \binom{[n]}{2}$ with $\alpha(\text...

The cannulation method and cardioplegia solution used during cardiopulmonary bypass (CPB) may both influence plasma potassium concentrations ([K+]) and mean arterial blood pressure (MAP). Bi-caval or right atrial cannulation methods are routinely used in conjunction with crystalloid or blood cardioplegia. We investigated the influence of cannulation method and cardioplegia solutions on plasma [...

Abstract The circular $$L(j,k)$$ L ( j , k ) -labeling problem with $$k\ge j$$ ≥ arose from the code assignment in wireless network of computers. Given a graph $$G$$ G ...

In this paper, we prove the following result conjectured by Z.-W. Sun: (2n− 1) ( 3n n ) ∣∣∣∣ n ∑ k=0 ( 6k 3k )( 3k k )( 6(n− k) 3(n− k) )( 3(n− k) n− k ) by showing that the left-hand side divides each summand on the right-hand side.

A singularly perturbed convection–diffusion problem, posed on the unit square in $${\mathbb {R}}^2$$ , is studied; its solution has both exponential and characteristic boundary layers. The problem solved numerically using local discontinuous Galerkin (LDG) method Shishkin meshes. Using tensor-product piecewise polynomials of degree at most $$k>0$$ each variable, error between LDG true proved to...

We deduce a family of six new series for $1/\pi $; example, $$\sum _{n=0}^\infty \frac {41673840n+4777111}{5780^n}W_n\left(\frac{1444}{1445}\right) =\frac{147758475}{\sqrt{95}\,\pi},$$ where $W_n(x)=\sum_{k=0}^n\binom nk\binom{n+k}k\binom{2k}k\binom{2

in this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{a}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{a}(t)) dt +mathbf{c}$. we also observe that the effective force $mathbf{f}_e$ on that particle due to pseudo-force $mathbf{a}(t)$, is given by $ mathbf{f}_e= mathbf{f} mat...

data mining is a powerful tool for firms to extract knowledge from their customers’ transaction data. one of the useful applications of data mining is segmentation. segmentation is an effective tool for managers to make right marketing strategies for right customer segments. in this study we have segmented retailers of a hygienic manufacture. nowadays all manufactures do understand that for sta...