Astrophysical insights into magnetic Penrose process around parameterized Konoplya–Rezzolla–Zhidenko black hole by Tursunali Xamidov, Sanjar Shaymatov, Pankaj Sheoran, Bobomurat Ahmedov

“…Our findings indicate that the rotational deformation parameter $$\delta _2$$ δ 2 is crucial for the efficiency of energy extraction from the BH. …”
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Reduction in T gamma delta cell numbers and alteration in subset distribution in systemic lupus erythematosus. by Lunardi, C, Marguerie, C, Bowness, P, Walport, M, So, A

“…There was a marked reduction in the V delta 2+ subset of T gamma delta cells, which resulted in a reversal of the ratio of V delta 2+/V delta 1+ cells from 4.34 to 0.56. …”

Generalized parton distributions of sea quark at zero skewness in the light-cone model by Xiaoyan Luan, Zhun Lu

“…We present the numerical results for $$H^{{\bar{u}}/P}(x,\xi ,\Delta ^2)$$ H u ¯ / P ( x , ξ , Δ 2 ) , $$H^{{\bar{d}}/P}(x,\xi ,\Delta ^2)$$ H d ¯ / P ( x , ξ , Δ 2 ) , $$E^{{\bar{u}}/P}(x,\xi ,\Delta ^2)$$ E u ¯ / P ( x , ξ , Δ 2 ) and $$E^{{\bar{d}}/P}(x,\xi ,\Delta ^2)$$ E d ¯ / P ( x , ξ , Δ 2 ) . …”
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A sharp Remez type inequalities for the functions with asymmetric restrictions on the oldest derivative by V.A. Kofanov, A.V. Zhuravel

“…For odd $r\in \mathbb{N}$; $\alpha, \beta >0$; $p\in [1, \infty]$; $\delta \in (0, 2 \pi)$, any $2\pi$-periodic function $x\in L^r_{\infty}(I_{2\pi})$, $I_{2\pi}:=[0, 2\pi]$, and arbitrary measurable set $B \subset I_{2\pi},$ $\mu B \leqslant \delta/\lambda,$ where $\lambda=$ $\left({\left\|\varphi_{r}^{\alpha, \beta}\right\|_{\infty} \left\| {\alpha^{-1}}{x_+^{(r)}} + {\beta^{-1}}{x_-^{(r)}}\right\|_\infty}{E^{-1}_0(x)_\infty}\right)^{1/r}$, we obtain sharp Remez type inequality $$E_0(x)_\infty \leqslant \frac{\|\varphi_r^{\alpha, \beta}\|_\infty}{E_0(\varphi_r^{\alpha, \beta})^{\gamma}_{L_p(I_{2\pi} \setminus B_\delta)}} \left\|x \right\|^{\gamma}_{{L_p} \left(I_{2\pi} \setminus B \right)}\left\| {\alpha^{-1}}{x_+^{(r)}} + {\beta^{-1}}{x_-^{(r)}}\right\|_\infty^{1-\gamma},$$ where $\gamma=\frac{r}{r+1/p},$ $\varphi_r^{\alpha, \beta}$ is non-symmetric ideal Euler spline of order $r$, $B_\delta:= \left[M- \delta_2, M+ \delta_1 \right]$, $M$ is the point of local maximum of spline $\varphi_r^{\alpha, \beta}$ and $\delta_1 > 0$, $\delta_2 > 0$ are such that $\varphi_r^{\alpha, \beta}(M+ \delta_1) = \varphi_r^{\alpha, \beta}(M- \delta_2), \;\; \delta_1 + \delta_2 = \delta .$ In particular, we prove the sharp inequality of Hörmander-Remez type for the norms of intermediate derivatives of the functions $x\in L^r_{\infty}(I_{2\pi})$.…”
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Estimation of q for ℓ q $\ell _{q}$ -minimization in signal recovery with tight frame by Kaihao Liang, Chaolong Zhang, Wenfeng Zhang

“…We estimated q 0 $q_{0}$ as q 0 = 2 / 3 $q_{0} = 2/3$ in the case of δ 2 s ≤ 1 / 2 $\delta _{2s}\leq 1/2$ and discussed that the value of q 0 $q_{0}$ can be much higher. …”
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A new bound on the block restricted isometry constant in compressed sensing by Yi Gao, Mingde Ma

“…The result improves the bound on the block restricted isometry constant δ 2 s | I $\delta_{2s|\mathcal {I}}$ of Lin and Li (Acta Math. …”
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Existence of solutions for 4p-order PDES by Moradi F., Moradi N., Addam M., Habib S. El

“…\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u\,\,\,in\,\,\Omega ,} \cr {u = \Delta u = \ldots {\Delta ^{2p - 1}}u = 0\,\,\,\,on\,\,\partial \Omega .} …”
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Approximation of the initial value for damped nonlinear hyperbolic equations with random Gaussian white noise on the measurements by Phuong Nguyen Duc, Erkan Nane, Omid Nikan, Nguyen Anh Tuan

“…The main goal of this work is to study a regularization method to reconstruct the solution of the backward non-linear hyperbolic equation $ u_{tt} + \alpha\Delta^2u_t +\beta \Delta ^2u = \mathcal{F}(x, t, u) $ come with the input data are blurred by random Gaussian white noise. …”
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Disparate effects of p24alpha and p24delta on secretory protein transport and processing. by Jeroen R P M Strating, Gerrit Bouw, Theo G M Hafmans, Gerard J M Martens

“…A subset of the p24 proteins (p24alpha(3), -beta(1), -gamma(3) and -delta(2)) is upregulated when Xenopus laevis intermediate pituitary melanotrope cells are physiologically activated to produce vast amounts of their major secretory cargo, the prohormone proopiomelanocortin (POMC). …”
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Existence of solutions for 4p-order PDES with Neumann boundary conditions by Moradi N., Moradi F., Habib S. El, Addam M.

“…\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u\,\,\,in\,\,\,\Omega ,} \cr {{{\partial u} \over {\partial v}} = {{\partial \left( {\Delta u} \right)} \over {\partial v}} = \ldots = {{\partial \left( {{\Delta ^{2p - 1}}u} \right)} \over {\partial v}} = 0\,\,\,on\,\,\,\partial \Omega .} …”
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Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay by Lin Rongrui, Gao Yunlong, She Lianbing

“…We study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t)| }^{m-2}+{\mu }_{2}{u}_{t}\left(x,t-\tau ){| {u}_{t}\left(x,t-\tau )| }^{m-2}=f\left(u), where τ\tau represents the time delay. …”
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Biharmonic system with Hartree-type critical nonlinearity by Anu Rani, Sarika Goyal

“…In this article, we investigate the multiplicity results of the following biharmonic Choquard system involving critical nonlinearities with sign-changing weight function: \begin{align*} \begin{cases} \Delta^{2}u = \lambda F(x) |u|^{r-2}u+ H(x)\left(\displaystyle\int_{\Omega}\frac{H(y)|v(y)|^{2_\alpha^*}}{|x-y|^{\alpha}}dy\right)|u|^{2_\alpha^*-2}u\;& \text{in}\;\Omega,\\ \Delta^{2}v = \mu G(x) |v|^{r-2}v+ H(x)\left(\displaystyle\int_{\Omega}\frac{H(y)|u(y)|^{2_\alpha^*}}{|x-y|^{\alpha}}dy\right)|v|^{2_\alpha^*-2}v\;& \text{in}\;\Omega,\\ u=v=\nabla u =\nabla v= 0\quad \;& \text{on}\;\partial\Omega, \end{cases} \end{align*} where $\Omega$ is a bounded domain in $\mathbb R^N$ with smooth boundary $\partial \Omega$, $N\geq 5$, $1<r <2$, $0<\alpha<N$, $2_\alpha^*=\frac{2N-\alpha}{N-4}$ is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality and $\Delta^2$ denotes the biharmonic operator. …”
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On the canonical solution of $\protect \,\protect \,\protect \overline{\protect \!\partial }$ on polydisks by Jin, Muzhi, Yuan, Yuan

“…We observe that the recent result of Chen–McNeal [6] implies that the canonical solution operator satisfies Sobolev estimates with a loss of $n-2$ derivatives on the polydisk $\Delta ^n$ and particularly is exact regular on $\Delta ^2$.…”
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The infarct-limiting efficacy of deltorphin-II in old rats with diet-induced metabolic syndrome by N. V. Naryzhnaya, A. V. Mukhomedzyanov, B. K. Kurbatov, M. A. Sirotina, M. Kilin, V. N. Azev, L. N. Maslov

“…The obtained results demonstrate the cardioprotective efficacy of the delta-2 opioid receptor agonist deltorphin-II in aging and metabolic syndrome in rats.Conclusions. …”
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Analysis of gamma delta V region usage in normal and diseased human intestinal biopsies and peripheral blood by polymerase chain reaction (PCR) and flow cytometry. by Bucht, A, Söderström, K, Esin, S, Grunewald, J, Hagelberg, S, Magnusson, I, Wigzell, H, Grönberg, A, Kiessling, R

“…In peripheral blood on the other hand, high expression of both V delta 2 and V delta 1 was found. The predominant expression of V delta 1 transcripts in the intestinal mucosa of IBD patients correlated well with protein cell surface expression as analysed by flow cytometry using V delta 1- and V delta 2-specific antibodies. …”

When is the first eigenfunction for the clamped plate equation of fixed sign? by Guido Sweers

“…It is known that the first eigenfunction of the clamped plate equation, $Delta^2 varphi = lambda varphi$ in $Omega$ with $varphi=frac{partial}{partial n}varphi=0$ on $partialOmega$, is not necessarily of fixed sign. …”
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Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent by Sihua Liang, Binlin Zhang

“…More precisely, we consider \begin{equation*} \begin{cases} \Delta^2u - \left(1 + b\int_{\Omega} |\nabla u|^2 dx\right)\Delta u = \lambda f(x,u) + |u|^{2^{\ast\ast}-2}u &\text{in } \Omega,\\ u = \Delta u = 0 & \mbox{on}\ \partial\Omega, \end{cases} \end{equation*} where $\Delta^2$ is the biharmonic operator, $N=\{5, 6, 7\}$, $2^{\ast\ast}=2N/(N-4)$ is the Sobolev critical exponent and $\Omega \subset \mathbb{R}^N$ is an open bounded domain with smooth boundary and $b, \lambda$ are some positive parameters. …”
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Existence of solution for Kirchhoff model problems with singular nonlinearity by Marcelo Montenegro

“…Similar issues are addressed for the equation $(a+b \int_{\Omega} |\nabla u|^2)^\gamma \Delta^2 u - \varrho \Delta u = f(u)$, $\varrho \geq 0$.…”
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The game colouring number of powers of forests by Stephan Dominique Andres, Winfried Hochstättler

“…We prove that the game colouring number of the $m$-th power of a forest of maximum degree $\Delta\ge3$ is bounded from above by \[\frac{(\Delta-1)^m-1}{\Delta-2}+2^m+1,\] which improves the best known bound by an asymptotic factor of 2.…”
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On a class of difference equations involving a linear map with two dimensional kernel by Luís Ferreira, Luis Sanchez Rodrigues

“…We establish necessary and sufficient conditions for the existence of periodic solutions to second-order nonlinear difference equations of the form $\Delta^2x_i+\lambda x_i+\Delta f(x_i)=e_i$, $i\in{\mathbb N}$, and for a simpler equation with difference-free nonlinearity. …”
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