Measuring Chern–Simons level k by braiding $$SU(2)_k$$ S U ( 2 ) k anyons by Artem Belov, Andrey Morozov

“…For this purpose, we use the previously derived braiding rules for Chern–Simons $$SU(2)_k$$ S U ( 2 ) k anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. …”
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Chromatin Structure and U2AF1-RS1 Gene Expression in Embryonic Stem Cells following RA-Induced Apoptosis by N. Andollo, M.D. Boyano, M. Garcia-Sanz, A. Asumendi, M.M. Zalduendo, J. Arechaga

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lncRNA ZFAS1 Promotes HMGCR mRNA Stabilization via Binding U2AF2 to Modulate Pancreatic Carcinoma Lipometabolism by Luoluo Wang, Yi Ruan, Xiang Wu, Xinhua Zhou

“…RNA pulldown and RIP assays analyzed the interaction of ZFAS1 with U2AF2 and HMGCR in BxPC-3 cells. Finally, the impacts of U2AF2 and HMGCR on the biological behavior of BxPC-3 were observed. …”
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Nonresonance conditions for fourth order nonlinear boundary value problems by C. De Coster, C. Fabry, F. Munyamarere

“…This paper is devoted to the study of the problemu(4)=f(t,u,u′,u″,u‴),u(0)=u(2π),   u′(0)=u′(2π),   u″(0)=u″(2π),   u‴(0)=u‴(2π).We assume that f can be written under the formf(t,u,u′,u″,u‴)=f2(t,u,u′,u″,u‴)u″+f1(t,u,u′,u″,u‴)u′+f0(t,u,u′,u″,u‴)u+r(t,u,u′,u″,u‴)where r is a bounded function. …”
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Predictors of Functional and Quality of Life Outcomes following Deep Brain Stimulation Surgery in Parkinson’s Disease Patients: Disease, Patient, and Surgical Factors by Hesham Abboud, Gencer Genc, Nicolas R. Thompson, Srivadee Oravivattanakul, Faisal Alsallom, Dennys Reyes, Kathy Wilson, Russell Cerejo, Xin Xin Yu, Darlene Floden, Anwar Ahmed, Michal Gostkowski, Ayman Ezzeldin, Hazem Marouf, Ossama Y. Mansour, Andre Machado, Hubert H. Fernandez

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Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control by Xiu Fang Liu, Gen Qi Xu

“…Suppose that the controller outputs are of the form α1u1(t)+β1u1(t-τ)+∫-τ0‍g1(η)u1(t+η)dη and α2u2(t)+β2u2(t-τ)+∫-τ0‍g2(η)u2(t+η)dη; where u1(t) and u2(t) are the inputs of boundary controllers. …”
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Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales by Gang Wu, Longsuo Li, Xinrong Cong, Xiufeng Miao

“…We study a system of second-order dynamic equations on time scales (p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t), u2(t))=0, satisfying four kinds of different multipoint boundary value conditions, fi is continuous and semipositone. …”
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Existence of nodal solutions of nonlinear Lidstone boundary value problems by Meng Yan, Tingting Zhang

“…We investigate the existence of nodal solutions for the nonlinear Lidstone boundary value problem \begin{document}$ \begin{align} \left\{\begin{array}{ll} (-1)^m (u^{(2m)}(t)+c u^{(2m-2)}(t)) = \lambda a(t)f(u), \; \; \ \ \ t\in (0, r), \\ u^{(2i)}(0) = u^{(2i)}(r) = 0, \ \ i = 0, 1, \cdots, m-1, \end{array} \right.…”
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О разрушении периодических решений одной системы нелинейных уравнений Шредингера by Gintaras Puriuškis

“… Рассматривается система двух нелинейных уравнений Шредингера с нелинейными членами четвертой степени ∂u1∕∂t = iD2и1 + i2|u1|2|u2|2u1 ∂u2∕∂t = iD2и2+ i|u1|4u2 с начальным условием и](0, х) = и0j(х), t > 0, х ∈ (-2,2), D = ∂/∂x . …”
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Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model by Shengmao Fu, Fei Qu

“…Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T),  (u1T,u2T,u3T) such that uiT≤uiT  (i=1,2,3), and the sector {(u1,u2,u3):uiT≤ui≤uiT,  i=1,2,3} is a global attractor of the asymptotically periodic model. …”
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On the solvability of a variational inequality problem and application to a problem of two membranes by A. Addou, E. B. Mermri

“…The purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K={v∈H01(Ω)×H01(Ω):v1≥v2  a.e. in Ω}.…”
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Functional Expression Study of Igf2 Antisense Transcript in Mouse by Carolina Duart-Garcia, Martin H. Braunschweig

“…We conclude that the ΔDMR1-U2 deletion phenotype should be reconsidered in the light of a functional Igf2as gene.…”
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On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN by Zifei Shen, Fashun Gao

“…We study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in ℝN, u∈Hs(RN), with critical exponent 2*s=2N/(N-2s), N>2s, s∈0, 1, where Vx≥0 has a potential well and f:ℝN×ℝ→ℝ is a lower order perturbation of the critical power u2*s-2u. …”
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Ground State Solution for a Fourth Order Elliptic Equation of Kirchhoff Type with Critical Growth in ℝN by Li Zhou, Chuanxi Zhu

“…In this paper, we consider the following fourth order elliptic Kirchhoff-type equation involving the critical growth of the form Δ2u−a+b∫ℝN∇u2dxΔu+Vxu=Iα∗Fufu+λu2∗∗−2u,in ℝN,u∈H2ℝN, where a>0, b≥0, λ is a positive parameter, α∈N−2,N, 5≤N≤8, V:ℝN⟶ℝ is a potential function, and Iα is a Riesz potential of order α. …”
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Unicyclic Graphs with the Fourth Extremal Wiener Indices by Guangfu Wang, Yujun Yang, Yuliang Cao, Shoujun Xu

“…It is shown that, among all unicyclic graphs with n≥8 vertices, C5Sn−4 and C2u1,u2S3,Sn−4 attain the fourth minimum Wiener index, whereas C3u1,u2P3,Pn−4 attains the fourth maximum Wiener index.…”
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Australian compilation of seismic-derived bathymetry by Ulysse Lebrec, Victorien Paumard, Juliette Denudt, Catherine Du Réau, Simon C. Lang, Julien Bailleul

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Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation by Yisheng Huang, Zeng Liu, Yuanze Wu

“…By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)∫ℝ3|∇u|2dx+(1/4)∬ℝ3(|u(x)|2|u(y)|2/|x-y|)dx dy −  (1/p)∫ℝ3|u|pdx:u∈Bρ} can be achieved for p∈(2,3) and ρ>0 small, where Bρ:={u∈H1(ℝ3):∥u∥2=ρ}. …”
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Defect Recognition: Applying Time-Lapse GPR Measurements and Numerical Approaches by Enas Abdelsamei, Diaa Sheishah, Mohamed Aldeep, Csaba Tóth, György Sipos

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Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems by Xiaoling Han, Jia Xu, Guowei Dai

“…We consider the systems of (-1)mu(2m)=λu+λv+uf(t,u,v),  t∈(0,1),  u(2i)(0)=u(2i)(1)=0, and 0≤i≤m-1,  (-1)mv(2m)=μu+μv+vg(t, u,v),  t∈(0,1),  v(2i)(0)=v(2i)(1)=0,  0≤i≤m-1, where λ,μ∈R are real parameters. f,g:[0,1]×R2→R are Ck,k≥3 functions and f(t,0,0)=g(t,0,0)=0,t∈[0,1]. …”
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Global and Local Structures of Bifurcation Curves of ODE with Nonlinear Diffusion by Tetsutaro Shibata

“…We consider the nonlinear eigenvalue problem Duu′′+λfu=0, u(t)>0, t∈I≔(0,1), u(0)=u(1)=0, where D(u)=uk, f(u)=u2n-k-1+sin⁡u, and λ>0 is a bifurcation parameter. …”
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