Bézier variant of Bernstein–Durrmeyer blending-type operators

In this paper, we construct the Bézier variant of the Bernstein–Durrmeyer-type operators. First, we estimated the moments for these operators. In the next section, we found the rate of approximation of operators [Formula: see text] using the Lipschitz-type function and in terms of Ditzian–Totik modulus of continuity. The rate of convergence for functions having derivatives of bounded variation is discussed. Finally, the graphical representation of the theoretical results and the effectiveness of the defined operators are given.

Selective functional inhibition of a tumor-derived p53 mutant by cytosolic chaperones identified using split-YFP in budding yeast

Life requires the oligomerization of individual proteins into higher-order assemblies. In order to form functional oligomers, monomers must adopt appropriate three-dimensional structures. Molecular chaperones transiently bind nascent or misfolded proteins to promote proper folding. Single missense mutations frequently cause disease by perturbing folding despite chaperone engagement. A misfolded mutant capable of oligomerizing with wild-type proteins can dominantly poison oligomer function. We previously found evidence that human-disease-linked mutations in Saccharomyces cerevisiae septin proteins slow folding and attract chaperones, resulting in a kinetic delay in oligomerization that prevents the mutant from interfering with wild-type function. Here we build upon our septin studies to develop a new approach for identifying chaperone interactions in living cells, and use it to expand our understanding of chaperone involvement, kinetic folding delays, and oligomerization in the recessive behavior of tumor-derived mutants of the tumor suppressor p53. We find evidence of increased binding of several cytosolic chaperones to a recessive, misfolding-prone mutant, p53(V272M). Similar to our septin results, chaperone overexpression inhibits the function of p53(V272M) with minimal effect on the wild type. Unlike mutant septins, p53(V272M) is not kinetically delayed under conditions in which it is functional. Instead, it interacts with wild-type p53 but this interaction is temperature sensitive. At high temperatures or upon chaperone overexpression, p53(V272M) is excluded from the nucleus and cannot function or perturb wild-type function. Hsp90 inhibition liberates mutant p53 to enter the nucleus. These findings provide new insights into the effects of missense mutations.

Some results concerning localization property of generalized Herz, Herz-type Besov spaces and Herz-type Triebel-Lizorkin spaces

In this paper, based on generalized Herz-type function spaces $\dot{K}_{q}^{p}(\theta)$ were introduced by Y. Komori and K. Matsuoka in 2009, we define Herz-type Besov spaces $\dot{K}_{q}^{p}B_{\beta }^{s}(\theta)$ and Herz-type Triebel-Lizorkin spaces $\dot{K}_{q}^{p}F_{\beta }^{s}(\theta)$, which cover the Besov spaces and the Triebel-Lizorkin spaces in the homogeneous case, where $\theta=\left\{\theta(k)\right\} _{k\in\mathbb{Z}}$ is a sequence of non-negative numbers $\theta(k)$ such that \begin{equation*} C^{-1}2^{\delta (k-j)}\leq \frac{\theta(k)}{\theta(j)} \leq C2^{\alpha (k-j)},\quad k>j, \end{equation*} for some $C\geq 1$ ($\alpha$ and $\delta $ are numbers in $\mathbb{R}$). Further, under the condition mentioned above on ${\theta }$, we prove that $\dot{K}_{q}^{p}\left({\theta }\right)$ and $\dot{K}_{q}^{p}B_{\beta }^{s}\left({\theta }\right)$ are localizable in the $\ell _{q}$-norm for $p=q$, and $\dot{K}_{q}^{p}F_{\beta }^{s}\left({\theta }\right)$ is localizable in the $\ell _{q}$-norm, i.e. there exists $\varphi \in \mathcal{D}({\mathbb{R}}^{n})$ satisfying $\sum_{k\in \mathbb{Z}^{n}}\varphi \left( x-k\right) =1$, for any $x\in \mathbb{R}^{n}$, such that \begin{equation*} \left\Vert f|E\right\Vert \approx \Big(\underset{k\in \mathbb{Z}^{n}}{\sum }\left\Vert \varphi (\cdot-k)\cdot f|E\right\Vert ^{q}\Big)^{1/q}. \end{equation*} Results presented in this paper improve and generalize some known corresponding results in some function spaces.

The Approximation of Laplace-Stieltjes Transforms Concerning Sun’s Type Function

The main aim of this paper is to establish some theorems concerning the error E n F , β , the Sun’s type function U r , and M u σ , F of entire functions defined by Laplace-Stieltjes transforms with infinite order converge in the whole complex plane. Our results exhibit the growth of Laplace-Stieltjes transforms from the point of view of approximation.

Transverse Momentum and Pseudorapidity Spectrum of the Top Quark, Lepton, and b Jet in Proton-Proton Collisions at LHC

We study the transverse momentum and pseudorapidity spectrum of the top quark and their decay products, the t t ¯ system, and the total number of jets in proton-proton (pp) collisions at 13 TeV by using the Tsallis-Pareto-type function and the three-source Landau hydrodynamic model, respectively. The related parameters, such as the effective temperature of the interacting system ( T ), the nonextensivity of the process ( n ), and the width ( σ ) of pseudorapidity distribution, are extracted.

The Knowledge of Geography Trainee Teachers on the Use of I-Think Thinking Maps in Learning and Facilitation (PdPc) in Schools

This article aims to identify the knowledge of Geography trainee teachers in the use of i-Think thinking maps in Learning and Facilitation (PdPc) in schools during their teaching practice. This study used the in-depth interviews method as a research instrument and primer data collected. Respondents consisted of 25 Geography trainee teachers who are currently studying for the sixth and seventh semesters but have been in the first phase of teaching practice. The data were collected by recording audio of each interview session conducted by the researcher with 25 respondents and transcribed in Microsoft Word and then categorized into sections and reviewed by the researcher to see the answers provided more clearly. The results of this study found that Geography trainee teachers' knowledge of i-Think thinking maps such as the meaning, type, function, and how to apply i-Think thinking maps in PdPc is moderate. This due to the lack of exposure and experience to use i-Think thinking maps either in their learning or in teaching practice. This study implies that there is a growing awareness among Geography teachers in enhancing their knowledge of the use of I-Think thinking maps. This will help the trainee teachers to apply it according to the topics to be taught when they become real teachers in future.

Selective functional inhibition of a tumor-derived p53 mutant by cytosolic chaperones identified using split-YFP in budding yeast

ABSTRACTLife requires the oligomerization of individual proteins into higher-order assemblies. In order to form functional oligomers, monomers must adopt appropriate three-dimensional structures. Molecular chaperones transiently bind nascent or misfolded proteins to promote proper folding. Single missense mutations frequently cause disease by perturbing folding despite chaperone engagement. A misfolded mutant capable of oligomerizing with wild-type proteins can dominantly poison oligomer function. We previously found evidence that human-disease-linked mutations in Saccharomyces cerevisiae septin proteins slow folding and attract chaperones, resulting in a kinetic delay in oligomerization that prevents the mutant from interfering with wild-type function. Here we build upon our septin studies to develop a new approach to identifying chaperone interactions in living cells, and use it to expand our understanding of chaperone involvement, kinetic folding delays, and oligomerization in the recessive behavior of tumor-derived mutants of the tumor suppressor p53. We find evidence of increased binding of several cytosolic chaperones to a recessive, misfolding-prone mutant, p53(V272M). Similar to our septin results, chaperone overexpression inhibits the function of p53(V272M) with minimal effect on the wild type. Unlike mutant septins, p53(V272M) is not kinetically delayed under conditions in which it is functional. Instead, it interacts with wild-type p53 but this interaction is temperature sensitive. At high temperatures or upon chaperone overexpression, p53(V272M) is excluded from the nucleus and cannot function or perturb wild-type function. Chaperone inhibition liberates the mutant to enter the nucleus where it has a slight dominant-negative effect. These findings provide new insights into the effects of missense mutations.

On Stability for Hybrid System under Stochastic Perturbations

The aim of this paper is to find out suitable conditions for almost surely exponential stability of communication protocols, considered for nonlinear hybrid system under stochastic perturbations. By using the Lyapunov-type function, we proved that the almost surely exponential stability remain be guaranteed as long as a bound on the maximum allowable transfer interval (MATI) is satisfied.