Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model by Boutet de Monvel, Anne, Zielinski, Lech

“…We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences $(E_m^+)_{m=0}^\infty $, $(E_m^-)_{m=0}^\infty $ satisfying a three-term asymptotic formula with the remainder estimate $O(m^{-1}\ln m)$ when $m$ tends to infinity. By analogy to the one-photon quantum Rabi model, the leading three terms of this asymptotic formula, describe a generalized rotating-wave approximation for large eigenvalues of the two-photon quantum Rabi model.…”
Get full text

Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases by Dorothee D. Haroske, Leszek Skrzypczak

“…This extends our previous results [25] to more general weights of logarithmically disturbed polynomial growth, both near some singular point and at infinity. We obtain sharp asymptotic estimates for the entropy numbers of this embedding. …”
Get full text

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.…”
Get full text

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. …”
Get full text

THE PRIMARY MOVER AND THE PROBLEM OF UNIVERSAL UNANIMITY by Vytautas Rimvydas Rimvydas Litvinas

“…Material and form are the specific aspects of Primary mover's activity, Universal components unifiedin actual infinity (this way the Primary mover can be called). …”
Get full text

THE PRIMARY MOVER AND THE PROBLEM OF UNIVERSAL UNANIMITY by Vytautas Rimvydas Rimvydas Litvinas

“…Material and form are the specific aspects of Primary mover's activity, Universal components unifiedin actual infinity (this way the Primary mover can be called). …”
Get full text

Spectral Analysis for a Wave/Plate Transmission System by Chengqiang Wang

“…Our result reads as follows: the spectrum of the infinitesimal generator of the semigroup associated with the system in question consists merely of an infinite sequence of eigenvalues which are all located in the open left half of the complex plane; the sequence of eigenvalues has the imaginary axis and another vertical line to the left of the imaginary axis as its asymptote lines; the energy of the system under consideration decreases to zero as time goes to infinity.…”
Get full text

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. …”
Get full text

The Diagonally Dominant Degree and Disc Separation for the Schur Complement of Ostrowski Matrix by Jianxing Zhao, Feng Wang, Yaotang Li

“…In addition, a new upper bound for the infinity norm on the inverse of the Schur complement of Ostrowski matrix is given. …”
Get full text

Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation by Jamel Benameur, Mongi Blel

“…We study the behavior at infinity in time of any global solution θ∈C(R+,Ḣ2-2α(R2)) of the surface quasigeostrophic equation with subcritical exponent 2/3≤α≤1. …”
Get full text

The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory by Huafeng Xiao

“…When the system is 2π-resonant at infinity, by making use a second disturbing of the original functional, some sufficient conditions are obtained to guarantee the existence of periodic solutions to DDEs.…”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

Sulla stima di macro, micro e nano-durezza di materiali metallici mediante analisi elasto-plastiche agli elementi finiti by Luca Susmel, David Taylor

“…Il lavoro sintetizzato nel presente articolo si pone come obiettivo primario quello di investigare lapossibilita di stimare, mediante un approccio elasto-plastico agli elementi finiti, la durezza dei materiali metalliciconvenzionali, e questo sia a livello macroscopico, che a livello microscopico, che, infine, a livello nanoscopico.Per verificare validita e accuratezza della metodologia FEM sviluppata, sono state condotte una serie di analisisperimentali su tre materiali metallici aventi caratteristiche metallurgiche estremamente diverse: una legadfalluminio (Al 7075-T6), un acciaio a basso tenore di carbonio (BS970-En3B) e, infine, un acciaio austenitico(AISI 316L). …”
Get full text

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source by Pan Zheng, Chunlai Mu, Dengming Liu, Xianzhong Yao, Shouming Zhou

“…We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq,  (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. …”
Get full text

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.…”
Get full text

Человеческая жизнь на фоне временного пространства. Романы М.А. Осоргина „Свидетель истории” и „Книга о концах”... by Antoni Murawski

“…Osorgin explains that people should build their own happiness instead of sacrifying their lives for abstract goals, which means nothing in the face of the universe and infinity. These ideas are connected with cosmological ideology of Osorgin.…”
Get full text

Gravitational corner conditions in holography by Gary T. Horowitz, Diandian Wang

“…Abstract Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the timelike boundary at infinity. There are an infinite number of corner conditions that also must be satisfied where the initial data surface hits the boundary. …”
Get full text

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. …”
Get full text