For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2X can be extended to a Whitney map for 2X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Two-loop Gell-Mann–Low function of N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives. Abstract Two-loop Gell-Mann–Low function is calculated for N=1 supersymmetric Yang– Mills theory, regularized by higher covariant derivatives. The integrals, which define it, are shown to be reduced to total derivatives and can be easily calculated analytically .

We establish a sharp trilinear inequality for the extension operator associated to the paraboloid in R3. Our proof relies on a recent generalisation of the classical Loomis–Whitney inequality.

Abstract This paper studies a new Whitney type inequality on compact domain $\Omega \subset {\mathbb R}^d$ that takes the form $$ \begin{align*} \inf_{Q\in \Pi_{r-1}^d(\mathcal{E})} \|f-Q\|_p \leq C(p,r,\Omega) \omega_{\mathcal{E}}^r(f,\mathrm{diam}(\Omega))_p,\ \ r\in N},\ 0<p\leq \infty, \end{align*} where $\omega _{\mathcal {E}}^r(f, t)_p$ denotes r th order directional modulus of smoothn...

Design, trademark and patent are the intellectual properties that influence each other and become the core assets and ultimate commercial weapons of the companies. In this study, we researched the designs, trademarks and patents of Nike in depth. The secret of Nike brands are built up on the high technology. Nike also had very successful brands in the apparel and footwear industry. In 2006, Int...

In this paper, a q-analogue of r-Whitney-Lah numbers, also known as (q,r)-Whitney-Lah number, denoted by $L_{m,r} [n, k]_q$ is defined using the triangular recurrence relation. Several fundamental properties for the are established such vertical and horizontal relations, exponential generating functions. Moreover, an explicit formula (q, r)-Whitney-Lah number derived concept q-difference o...