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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Sign-changing solutions for Schrödinger–Kirchhoff-type fourth-order equation with potential vanishing at infinity by Wen Guan, Hua-Bo Zhang

“…Abstract The purpose of this paper is to study the existence of sign-changing solution to the following fourth-order equation: 0.1 Δ 2 u − ( a + b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = K ( x ) f ( u ) in  R N , $$ \Delta ^{2}u- \biggl(a+ b \int _{\mathbb{R}^{N}} \vert \nabla u \vert ^{2}\,dx \biggr) \Delta u+V(x)u=K(x)f(u) \quad\text{in } \mathbb{R}^{N}, $$ where 5 ≤ N ≤ 7 $5\leq N\leq 7$ , Δ 2 $\Delta ^{2}$ denotes the biharmonic operator, K ( x ) , V ( x ) $K(x), V(x)$ are positive continuous functions which vanish at infinity, and f ( u ) $f(u)$ is only a continuous function. …”
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Expression and purification of human cholesterol 7 alpha-hydroxylase in Escherichia coli. by W G Karam, J Y Chiang

“…The translational product of this cDNA would be a truncated protein, P450c7(delta 2-24) with a hydrophilic NH2-terminal sequence, Met-Ala-Arg-Arg-Arg-Gln... …”
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Lower semicontinuity of pullback attractors for a singularly nonautonomous plate equation by Ricardo Parreira da Silva

“…We show the lower semicontinuity of the family of pullback attractors for the singularly nonautonomous plate equation with structural damping $$ u_{tt} + a(t,x)u_{t} + (- Delta) u_{t} + (-Delta)^{2} u + lambda u = f(u), $$ in the energy space $H^2_0(Omega) imes L^2(Omega)$ under small perturbations of the damping term a.…”
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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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Nonexistence of global solutions to the system of semilinear parabolic equations with biharmonic operator and singular potential by Shirmayil Bagirov

“…In the domain $Q_{R}'= \{ x:| x| >R\}\times( 0,+\infty)$ we consider the problem $$\displaylines{ \frac{\partial u_1}{\partial t}+\Delta^2 u_1-\frac{C_1}{|x| ^4}u_1 =| x| ^{\sigma _1}| u_2| ^{q_1}, \quad u_1| _{t=0}=u_{10}( x)\geq0, \cr \frac{\partial u_2}{\partial t}+\Delta^2 u_2-\frac{C_2}{| x| ^4}u_2=| x| ^{\sigma _2}| u_1| ^{q_2},\quad u_2| _{t=0}=u_{20}( x)\geq0, \cr \int_0^\infty \int_{\partial B_{R}} u_i\,ds\,dt\geq 0, \quad \int_0^\infty \int_{\partial B_{R}}\Delta u_i\,ds\,dt\leq 0, }$$ where $\sigma_i\in \mathbb{R} $, $ q_i>1 $, $ 0\leq C_i<( \frac{n( n-4) }{4}) ^2$, $ i=1,2 $. …”
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On the Mints Hierarchy in First-Order Intuitionistic Logic by Aleksy Schubert, Paweł Urzyczyn, Konrad Zdanowski

“…We prove that even the $\Delta_2$ level is undecidable and that $\Sigma_1$ is Expspace-complete. …”
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Refined stability of the additive, quartic and sextic functional equations with counter-examples by Hasanen A. Hammad, Hassen Aydi, Manuel De la Sen

“…In this study, we utilize the direct method (Hyers approach) to examine the refined stability of the additive, quartic, and sextic functional equations in modular spaces with and without the $ \Delta _{2} $-condition. We also use the direct approach to discuss the Ulam stability in $ 2 $-Banach spaces. …”
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On the oscillation of second order nonlinear neutral delay difference equations by A. K. Tripathy

“…In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form $\Delta^2(y(n)+p(n)y(n-m))+q(n)G(y(n-k))=0$ under various ranges of $p(n)$. …”
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Infinitely many solutions for the discrete Schrödinger equations with a nonlocal term by Qilin Xie, Huafeng Xiao

“…Δ u k − 1 = u k − u k − 1 $\Delta u_{k-1}=u_{k}-u_{k-1}$ and Δ 2 = Δ ( Δ ) $\Delta ^{2}=\Delta (\Delta )$ is the one-dimensional discrete Laplacian operator. …”
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Bounded solutions of unilateral problems for strongly nonlinear equations in Orlicz spaces by Ahmed Youssfi, A. Benkirane, Mostafa El Moumni

“…We do not impose the $\Delta_2$-condition on the considered $N$-functions defining the Orlicz-Sobolev functional framework.…”
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Expression of SORL1 and a novel SORL1 splice variant in normal and Alzheimers disease brain by Liu Qiang, Markesbery William R, Schmitt Frederick A, Peterson Shawn L, Simmons Christopher R, Furman Jennifer L, Simpson James F, Ling I-Fang, Grear Karrie E, Crook Julia E, Younkin Steven G, Bu Guojun, Estus Steven

“…In contrast, the expression of the delta-2-SORL1 isoform was similar in AD and non-AD brains. …”
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The Landscape of Compressibility Measures for Two-Dimensional Data by Lorenzo Carfagna, Giovanni Manzini

“…Among other things, we prove that <inline-formula> <tex-math notation="LaTeX">$\delta _{2D}$ </tex-math></inline-formula> is monotone and can be computed in linear time, and we show that, although it is still true that <inline-formula> <tex-math notation="LaTeX">$\delta _{2D}\leq \gamma _{2D}$ </tex-math></inline-formula>, the gap between the two measures can be <inline-formula> <tex-math notation="LaTeX">$\Omega (\sqrt {n})$ </tex-math></inline-formula> and therefore asymptotically larger than the gap between <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula>. …”
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On a fourth order superlinear elliptic problem by M. Ramos, P. Rodrigues

“…We prove the existence of a nonzero solution for the fourth order elliptic equation $$Delta^2u= mu u +a(x)g(u)$$ with boundary conditions $u=Delta u=0$. …”
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Further delineation of the phenotype caused by a novel large homozygous deletion of GRID2 gene in an adult patient by Maryam Taghdiri, Atie Kashef, Golemaryam Abbassi, Azadeh Moshtagh, Neda Sadatian, Majid Fardaei, Kimia Najafi, Roxana Kariminejad

“…Key Clinical Message Different mutations in glutamate receptor ionotropic delta 2 (GRID2) gene cause cerebellar ataxia in human. …”
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Regular tree languages in low levels of the Wadge Hierarchy by Mikołaj Bojańczyk, Filippo Cavallari, Thomas Place, Michał Skrzypczak

“…More precisely we prove decidability for each of the finite levels of the hierarchy; for the class of the Boolean combinations of open sets $BC(\Sigma_1^0)$ (i.e. the union of the first $\omega$ levels); and for the Borel class $\Delta_2^0$ (i.e. for the union of the first $\omega_1$ levels).…”
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