Weak cosmic censorship, trapped surfaces, and naked singularities for the Einstein vacuum equations by Shlapentokh-Rothman, Yakov

“…The weak cosmic censorship conjecture posits that, generically, all singularities in General Relativity arising from regular asymptotically flat initial data should have a complete future null infinity. While this conjecture remains wide open, it has inspired many mathematical works concerning topics such as trapped surface formation and the construction of naked singularities. …”
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A Survey on the Integral Means Spectrum for Conformal Mappings by I.R. Kayumov

“…Estimates of the integral means spectrum in the class of functions mapping the exterior of the unit disk onto the attraction basins of the infinity of algebraic polynomials are presented.…”
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A Note on the Newman-Unti Group and the BMS Charge Algebra in Terms of Newman-Penrose Coefficients by Glenn Barnich, Pierre-Henry Lambert

“…The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. …”
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Universal Verma Modules and the Misra-Miwa Fock Space by Arun Ram, Peter Tingley

“…Partitions also index the polynomial Weyl modules for Uq(glN) as N tends to infinity. We explain how the powers of v which appear in the Misra-Miwa Fock space also appear naturally in the context of Weyl modules. …”
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A curious property of series involving terms of generalized sequences by Odoardo Brugia, Piero Filipponi

“…The aim of this paper is to find triples (p,q,r) for which the series Un  (p,q)/rn and Vn  (p,q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the factor n. …”
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On Unique Continuation for Navier-Stokes Equations by Zhiwen Duan, Shuxia Han, Peipei Sun

“…We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. …”
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Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters by Yehong Yang, Guohua Cao

“…Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. …”
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The Third Five-Parametric Hypergeometric Quantum-Mechanical Potential by T. A. Ishkhanyan, A. M. Ishkhanyan

“…Depending on an involved parameter, the potential presents either a short-range singular well (which behaves as inverse square root at the origin and vanishes exponentially at infinity) or a smooth asymmetric step-barrier (with variable height and steepness). …”
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CF-RIP: a convergence-free mechanism for RIP protocol by WANG Bin1, ZHANG Jian-hui2, GUO Yun-fei2, LAN Ju-long2

“…In order to solve the problem of distance vector routing protocol converge very slowly to the correct routes when link costs increase,a new convergence-free routing protocol CF-RIP using RIP（routing information protocol） was proposed,which is based on failure-carrying packets and multiple viable next hops per destination.The new protocol eliminated the convergence period altogether and could solve the problem of count to infinity.The CF-RIP provided better stability and availability;meanwhile it was proved that a loop-free path to a destination if one such path exists.Simulations performed show that CF-RIP can dealing with the simultaneous failures of multiple arbitrary links effectively.…”
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Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source by Yingjie Zhu, Fuzhong Cong

“…Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity.…”
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Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 by Ling Ding, Lin Li, Jin-Ling Zhang

“…We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3‍|∇u|2dx)Δu+u=k(x)f(u)+h(x),  x∈R3,  u∈H1(R3),  u>0,  x∈R3, where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.…”
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Breather Positons and Rogue Waves for the Nonlocal Fokas-Lenells Equation by Chun Wang, Rong Fan, Zhao Zhang, Biao Li

“…In this nonlocal optical system, rogue waves can be generated when periods of breather positons go to infinity. In addition, we find two very interesting phenomena: one is that rogue waves sitting on a periodic line wave background are derived; the other is that a hybrid of rogue waves and a periodic kink wave is also constructed. …”
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On-Line Selection of c-Alternating Subsequences from a Random Sample by Robert W. Chen, Larry A. Shepp, Justín Ju-Chen Yang

“…We also give the optimal selection rate when the sample size goes to infinity.…”
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Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model by Yan Li, Guoxin Liu

“…In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. …”
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Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent by Masato Hashizume, Megumi Sano

“…We point out that the decaying speed of q(x) at infinity plays an essential role on the compactness. …”
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Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System by Shengliang Guo, Zhijun Liu, Huili Xiang

“…We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. …”
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Natural Frequencies of a Cracked Beam Coupled with a Compressible Sloshing Fluid by Michele Di Sciuva, Cecilia Surace

“…The coupled system is subject to undisturbed boundary condition at infinity in the fluid domain. A range of different boundary conditions have been analysed such as both incompressible and compressible fluid, with and without sloshing. …”
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De la rage métaphysique au calme scientifique : religion et sciences naturelles chez Flaubert by Juliette Azoulai

“…The study of Nature forces Flaubert’s characters to face an experience of totality that underlines their finitude and opens onto infinity. Thus it offers an experience that belongs to the sacred, so that the natural sciences, far from being opposed to Metaphysics, lead to the understanding of an “immanent surnaturalism”, to use one of Victor Hugo’s expressions, which is a combination of grotesque irrationality and sublime wisdom.…”
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Palmprint Authentication System Based on Local and Global Feature Fusion Using DOST by N. B. Mahesh Kumar, K. Premalatha

“…The global feature is obtained by reducing the scale of discrete orthonormal Stockwell transform to infinity. The local and global matching distances of the two palmprint images are fused to get the final matching distance of the proposed scheme. …”
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Square-free numbers in the intersection of Lehmer set and Piatetski-Shapiro sequence by Zhao Xiaoqing, Yi Yuan

“…By employing additive character properties to transform congruence equations and applying Kloosterman sums and methods of exponential sums, we derive a sharp asymptotic formula as $ q $ approaches infinity, which is significant for understanding the distribution properties of the Lehmer problem.…”
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