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Journal articles on the topic 'Asymptotic equivalents'

Author: Grafiati

Published: 19 April 2025

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1

Bhattacharyya, Jishnu, and David Mattingly. "Universal horizons in maximally symmetric spaces." International Journal of Modern Physics D 23, no. 13 (November 2014): 1443005. http://dx.doi.org/10.1142/s0218271814430056.

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Universal horizons in Hořava–Lifshitz gravity and Einstein-æther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared (IR) solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four-dimensional static and spherically symmetric universal horizon solutions with maximally symmetric asymptotics — the equivalents of the Schwarzschild, Schwarzschild–de Sitter or Schwarzschild–anti-de Sitter spacetimes. Additionally, we derive the associated first laws for the universal horizon solutions. Finally, we prove that independent of asymptotic boundary conditions, any spherically symmetric solution in Hořava–Lifshitz gravity with a universal horizon is also a solution of Einstein-æther theory, thereby broadening and complementing the known equivalence region of the solution spaces.

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2

SPEICHER, ROLAND, and CARLOS VARGAS. "FREE DETERMINISTIC EQUIVALENTS, RECTANGULAR RANDOM MATRIX MODELS, AND OPERATOR-VALUED FREE PROBABILITY THEORY." Random Matrices: Theory and Applications 01, no. 02 (April 2012): 1150008. http://dx.doi.org/10.1142/s2010326311500080.

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Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators satisfying certain freeness relations. We comment on the relation between our free deterministic equivalent and deterministic equivalents considered in the engineering literature. We do not only consider the case of square matrices, but also show how rectangular matrices can be treated. Furthermore, we emphasize how operator-valued free probability techniques can be used to solve our free deterministic equivalents. As an illustration of our methods we show how the free deterministic equivalent of a random matrix model from [6] can be treated and we thus recover in a conceptual way the results from [6]. On a technical level, we generalize a result from scalar-valued free probability, by showing that randomly rotated deterministic matrices of different sizes are asymptotically free from deterministic rectangular matrices, with amalgamation over a certain algebra of projections. In Appendix A, we show how estimates for differences between Cauchy transforms can be extended from a neighborhood of infinity to a region close to the real axis. This is of some relevance if one wants to compare the original random matrix problem with its free deterministic equivalent.

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3

Li, Jian, Yong Liu, and Weiping Wang. "High-Dimensional Analysis for Generalized Nonlinear Regression: From Asymptotics to Algorithm." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 12 (March 24, 2024): 13500–13508. http://dx.doi.org/10.1609/aaai.v38i12.29253.

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Overparameterization often leads to benign overfitting, where deep neural networks can be trained to overfit the training data but still generalize well on unseen data. However, it lacks a generalized asymptotic framework for nonlinear regressions and connections to conventional complexity notions. In this paper, we propose a generalized high-dimensional analysis for nonlinear regression models, including various nonlinear feature mapping methods and subsampling. Specifically, we first provide an implicit regularization parameter and asymptotic equivalents related to a classical complexity notion, i.e., effective dimension. We then present a high-dimensional analysis for nonlinear ridge regression and extend it to ridgeless regression in the under-parameterized and over-parameterized regimes, respectively. We find that the limiting risks decrease with the effective dimension. Motivated by these theoretical findings, we propose an algorithm, namely RFRed, to improve generalization ability. Finally, we validate our theoretical findings and the proposed algorithm through several experiments.

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4

Pham, Kim, Agnès Maurel, and Jean-Jacques Marigo. "Revisiting imperfect interface laws for two-dimensional elastodynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (January 2021): 20200519. http://dx.doi.org/10.1098/rspa.2020.0519.

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We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.

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5

van Oosterom, A., and G. J. H. Uijen. "The Relationship Between the MAXABS and the RMS Error." Methods of Information in Medicine 27, no. 04 (October 1988): 161–66. http://dx.doi.org/10.1055/s-0038-1635540.

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SummaryResults from mathematical statistics are applied to the analysis of the ratio R between the element having the highest magnitude MAXABS in a sample of size η taken from a Gaussian distribution and the standard deviation RMS of the same sample. Numerically computed . probability density functions of MAXABS are shown for several values of n. For large values of η these density functions are compared with analytical expressions for their asymptotic equivalents. The expectation and variance of MAXABS and RMS are derived and tabulated for different values of n.These results are applied to the analysis of the residual error resulting from an orthogonal expansion of recorded body surface potentials.

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6

Ammar, Hajer, Ahmed E. Kholif, Manel Missaoui, Halimeh Zoabi, Soha Ghzayel, Mario de Haro-Martí, Izabelle Auxiliadora Molina de Almeida Teixeira, et al. "Seasonal Variation in Chemical Composition, Ruminal Fermentation, and Biological Characteristics of Paulownia shan tong: In Vitro Potential Use by Sheep and Goats." Fermentation 9, no. 3 (February 23, 2023): 210. http://dx.doi.org/10.3390/fermentation9030210.

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This study was conducted to determine the seasonal variation (two seasonal harvests during winter and spring) in some chemical and biochemical characteristics of Paulownia shan tong leaves. To achieve this, we analyzed the chemical composition in terms of dry matter (DM), organic matter (OM), crude protein (CP), cell-wall content (neutral detergent fiber (NDF)), acid detergent fiber (ADF), acid detergent lignin (ADL), and lipids. The phenolic compounds (PC) and antioxidant activity (AA) of the leaves were also determined. In vitro gas production (GP) and nutrient degradability were evaluated using two ruminal-content donors (sheep and goats). Higher (p < 0.05) antioxidant activities were observed in the winter harvest of P. shan tong, while higher concentrations of OM (90.5%), lipids (3.02%), NDF (69.7%), ADF (54.8%), ADL (35.4%), total flavonoids (0.45 mg catechin equivalents/mg DM), and total phenolics (2.52 mg gallic acid equivalents/mg DM) were observed in the spring harvest. Higher asymptotic GP and rate of GP (p < 0.05) were observed when the leaves were incubated with rumen liquor of goats compared to sheep; however, higher (p < 0.05) lag time of GP and half-time of GP were observed with rumen liquor from sheep. Moreover, higher asymptotic GP, rate of GP, and half-time of GP were observed with the winter harvest of P. shan tong. Higher (p < 0.001) metabolizable energy, OM degradability, and microbial protein supplies were obtained when the leaves were incubated with rumen fluids from goats and from the winter harvest of P. shan tong compared to the spring harvest. In conclusion, based on the chemical composition and the kinetics of in vitro gas production, P. shan tong leaves seem to be characterized by a good nutritive value and could be considered as an alternative feed resource for ruminants.

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7

Deltas, George. "Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions $\!$." Economic Theory 23, no. 4 (May 1, 2004): 715–38. http://dx.doi.org/10.1007/s00199-003-0390-3.

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8

Hou, Xiang-Dong. "Asymptotic numbers of non-equivalent codes in three notions of equivalence." Linear and Multilinear Algebra 57, no. 2 (March 2009): 111–22. http://dx.doi.org/10.1080/03081080701539023.

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9

Planas, Jaime, Manuel Elices, and Gonzalo Ruiz. "The equivalent elastic crack: 2. X-Y equivalences and asymptotic analysis." International Journal of Fracture 61, no. 3 (June 1993): 231–46. http://dx.doi.org/10.1007/bf00036342.

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10

Bassino, Frédérique, Cyril Nicaud, and Pascal Weil. "Statistics of subgroups of the modular group." International Journal of Algebra and Computation 31, no. 08 (October 12, 2021): 1691–751. http://dx.doi.org/10.1142/s0218196721500624.

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We count the finitely generated subgroups of the modular group [Formula: see text]. More precisely, each such subgroup [Formula: see text] can be represented by its Stallings graph [Formula: see text], we consider the number of vertices of [Formula: see text] to be the size of [Formula: see text] and we count the subgroups of size [Formula: see text]. Since an index [Formula: see text] subgroup has size [Formula: see text], our results generalize the known results on the enumeration of the finite index subgroups of [Formula: see text]. We give asymptotic equivalents for the number of finitely generated subgroups of [Formula: see text], as well as of the number of finite index subgroups, free subgroups and free finite index subgroups. We also give the expected value of the isomorphism type of a size [Formula: see text] subgroup and prove a large deviation statement concerning this value. Similar results are proved for finite index and for free subgroups. Finally, we show how to efficiently generate uniformly at random a size [Formula: see text] subgroup (respectively, finite index subgroup, free subgroup) of [Formula: see text].

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11

Tehrani, Ali Moradi, Evert Slob, and Wim Mulder. "Quasi-analytical method for frequency-to-time conversion in CSEM applications." GEOPHYSICS 77, no. 5 (September 1, 2012): E357—E363. http://dx.doi.org/10.1190/geo2011-0432.1.

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Frequency-to-time transformations are of interest to controlled-source electromagnetic methods when time-domain data are inverted for a subsurface resistivity model by numerical frequency-domain modeling at a selected, small number of frequencies whereas the data misfit is determined in the time domain. We propose an efficient, Prony-type method using frequency-domain diffusive-field basis functions for which the time-domain equivalents are known. Diffusive fields are characterized by an exponential part whose argument is proportional to the square root of frequency and a part that is polynomial in integer powers of the square root of frequency. Data at a limited number of frequencies suffice for the transformation back to the time. In the exponential part, several diffusion-time values must be chosen. Once a suitable range of diffusion-time values are found, the method is quite robust in the number of values used. The highest power in the polynomial part can be determined from the source and receiver type. When the frequency-domain data are accurately approximated by the basis functions, the time-domain result is also accurate. This method is accurate over a wider time range than other methods and has the correct late-time asymptotic behavior. The method works well for data computed for layered and 3D subsurface models.

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12

Astashova, Irina. "On asymptotic equivalence of nth order nonlinear differential equations." Tatra Mountains Mathematical Publications 63, no. 1 (June 1, 2015): 31–38. http://dx.doi.org/10.1515/tmmp-2015-0018.

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Abstract This paper is devoted to the problem of asymptotic equivalence of nth order differential equations with exponentially equivalent right-hand sides. With the help of this result asymptotic behaviour of solutions to nonhomogeneous differential equations is described

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13

Simic, Slavko, and John H. Lindsey. "Equivalent Asymptotics: 11063." American Mathematical Monthly 112, no. 9 (November 1, 2005): 841. http://dx.doi.org/10.2307/30037617.

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14

Yang, Yang, Jun-feng Liu, and Yu-lin Zhang. "A Note on the Tail Behavior of Randomly Weighted Sums with Convolution-Equivalently Distributed Random Variables." Abstract and Applied Analysis 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/273217.

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We investigate the tailed asymptotic behavior of the randomly weighted sums with increments with convolution-equivalent distributions. Our obtained result can be directly applied to a discrete-time insurance risk model with insurance and financial risks and derive the asymptotics for the finite-time probability of the above risk model.

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15

Conrad, Keith. "Partial Euler Products on the Critical Line." Canadian Journal of Mathematics 57, no. 2 (April 1, 2005): 267–97. http://dx.doi.org/10.4153/cjm-2005-012-6.

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AbstractThe initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve L-function at s = 1. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the L-function and that the constant in the asymptotics has an unexpected factor of. We extend Goldfeld's theorem to an analysis of partial Euler products for a typical L-function along its critical line. The general phenomenon is related to second moments, while the asymptotic behavior (over number fields) is proved to be equivalent to a condition that in a precise sense seemsmuch deeper than the Riemann hypothesis. Over function fields, the Euler product asymptotics can sometimes be proved unconditionally.

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16

Radzki, Wiktor. "Contractions of Product Density Operators of Systems of Identical Fermions and Bosons." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–26. http://dx.doi.org/10.1155/2010/890523.

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Recurrence and explicit formulae for contractions (partial traces) of antisymmetric and symmetric products of identical trace class operators are derived. Contractions of product density operators of systems of identical fermions and bosons are proved to be asymptotically equivalent to, respectively, antisymmetric and symmetric products of density operators of a single particle, multiplied by a normalization integer. The asymptotic equivalence relation is defined in terms of the thermodynamic limit of expectation values of observables in the states represented by given density operators. For some weaker relation of asymptotic equivalence, concerning the thermodynamic limit of expectation values of product observables, normalized antisymmetric and symmetric products of density operators of a single particle are shown to be equivalent to tensor products of density operators of a single particle.

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17

Ulusu, Uğur. "Lacunary 𝐈𝝈-Asymptotic Equivalence." Afyon Kocatepe University Journal of Sciences and Engineering 17, no. 3 (December 1, 2017): 899–905. http://dx.doi.org/10.5578/fmbd.66209.

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18

Marouf, Mousa S. "Asymptotic equivalence and summability." International Journal of Mathematics and Mathematical Sciences 16, no. 4 (1993): 755–62. http://dx.doi.org/10.1155/s0161171293000948.

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This paper is a study of the relatioship. between the asymptotic equivalence of two sequences(limnxn/yn=1)and three variatious of this equivalence for a sequence-to-sequence transformationA, the three variations are give by the ratiosRmAx/RmAy.SmAx/SmAy, AndμmAx/μmAy, whereRmAz:=∑n≥m|(Az)n|,SmAz:=∑n≤m|(Az)n|, andμmAz:=supn≥m|(Az)n|.

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19

Matecki, Grzegorz. "Asymptotic Density for Equivalence." Electronic Notes in Theoretical Computer Science 140 (November 2005): 81–91. http://dx.doi.org/10.1016/j.entcs.2005.06.022.

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20

Morel, J. E., J. C. Ragusa, M. L. Adams, and G. Kanschat. "Asymptotic PN-Equivalent SN+1Equations." Transport Theory and Statistical Physics 42, no. 1 (January 2013): 3–20. http://dx.doi.org/10.1080/00411450.2013.771366.

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21

Hazarika, Bipan. "Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/257181.

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An ideal is a family of subsets of positive integers which is closed under taking finite unions and subsets of its elements. In this paper, we introduce a new definition of asymptotically ideal -statistical equivalent sequence in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

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22

Ulusu, Uğur, and Fatih Nuray. "On Asymptotically Lacunary Statistical Equivalent Set Sequences." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/310438.

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This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savaş (2006).

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23

McClure, R. D. "The Role of Binarity in the Evolution of Peculiar Red Giants." International Astronomical Union Colloquium 106 (1989): 196–204. http://dx.doi.org/10.1017/s0252921100062904.

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There are several types of Peculiar Red Giants (PRG's) which have enhanced s-process elements and/or carbon, but which cannot be explained by mixing during helium shell-flashing in the late stages of Asymptotic Giant Branch (AGB) evolution. These are the Ball, CH, sgCH, and the hotter R-type carbon stars. All these PRG's have absolute magnitudes which range down to zero and fainter. The Ball stars (Bidelman & Keenan 1951) are G-K giants whose spectra have strong CN and CH bands, and in extreme cases bands of C2 become noticeable. In addition they have strong lines of s-process elements such as Ball and SrII. The CH stars (Keenan 1942) are Population II equivalents of the Ball stars, and show similar spectral features, but with weaker metal lines, and usually stronger carbon bands. Bond (1974) introduced a new class of late F and G stars named the CH subgiants, which he suggests are fainter than the classical CH and Ball stars. They appear to be of mixed population (Luck & Bond 1982), and they are probably subgiants which will eventually evolve up the giant branch to become classical CH and Ball stars. The R-type carbon stars, at least the hotter (R0-R4) ones, differ from many of the other peculiar red giants in that they do not show enhanced s-process element abundances. The R stars have strong carbon bands, but relative to the N-type carbon stars they have less blue and ultraviolet absorption in their spectra. They range in absolute magnitude from near zero, similar to the Ball stars, up to several magnitudes brighter than this.

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24

SHANKAR, V., and V. KUMARAN. "Stability of fluid flow in a flexible tube to non-axisymmetric disturbances." Journal of Fluid Mechanics 407 (March 25, 2000): 291–314. http://dx.doi.org/10.1017/s0022112099007570.

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The stability of fluid flow in a flexible tube to non-axisymmetric perturbations is analysed in this paper. In the first part of the paper, the equivalents of classical theorems of hydrodynamic stability are derived for inviscid flow in a flexible tube subjected to arbitrary non-axisymmetric disturbances. Perturbations of the form vi = v˜i exp [ik(x − ct) + inθ] are imposed on a steady axisymmetric mean flow U(r) in a flexible tube, and the stability of mean flow velocity profiles and bounds for the phase velocity of the unstable modes are determined for arbitrary values of azimuthal wavenumber n. Here r, θ and x are respectively the radial, azimuthal and axial coordinates, and k and c are the axial wavenumber and phase velocity of disturbances. The flexible wall is represented by a standard constitutive relation which contains inertial, elastic and dissipative terms. The general results indicate that the fluid flow in a flexible tube is stable in the inviscid limit if the quantity Ud[Gscr ]/dr [ges ] 0, and could be unstable for Ud[Gscr ]/dr < 0, where [Gscr ] ≡ rU′/(n2 + k2r2). For the case of Hagen–Poiseuille flow, the general result implies that the flow is stable to axisymmetric disturbances (n = 0), but could be unstable to non-axisymmetric disturbances with any non-zero azimuthal wavenumber (n ≠ 0). This is in marked contrast to plane parallel flows where two-dimensional disturbances are always more unstable than three-dimensional ones (Squire theorem). Some new bounds are derived which place restrictions on the real and imaginary parts of the phase velocity for arbitrary non-axisymmetric disturbances.In the second part of this paper, the stability of the Hagen–Poiseuille flow in a flexible tube to non-axisymmetric disturbances is analysed in the high Reynolds number regime. An asymptotic analysis reveals that the Hagen–Poiseuille flow in a flexible tube is unstable to non-axisymmetric disturbances even in the inviscid limit, and this agrees with the general results derived in this paper. The asymptotic results are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the critical Reynolds number obtained for inviscid instability to non-axisymmetric disturbances is much lower than the critical Reynolds numbers obtained in the previous studies for viscous instability to axisymmetric disturbances when the dimensionless parameter Σ = ρGR2/η2 is large. Here G is the shear modulus of the elastic medium, ρ is the density of the fluid, R is the radius of the tube and η is the viscosity of the fluid. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

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25

Gluskin, Efim, and Yaron Ostrover. "Asymptotic equivalence of symplectic capacities." Commentarii Mathematici Helvetici 91, no. 1 (2016): 131–44. http://dx.doi.org/10.4171/cmh/380.

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26

Pinto, Manuel. "Asymptotic equivalence of difference systems." Journal of Difference Equations and Applications 1, no. 3 (January 1995): 249–62. http://dx.doi.org/10.1080/10236199508808025.

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27

Bali, Valentina, and Matthew Jackson. "Asymptotic Revenue Equivalence in Auctions." Journal of Economic Theory 106, no. 1 (September 2002): 161–76. http://dx.doi.org/10.1006/jeth.2001.2870.

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28

Stanzhyts’kyi, O. M., and O. O. Misyats’. "Asymptotic equivalence of impulsive systems." Ukrainian Mathematical Journal 59, no. 4 (April 2007): 577–87. http://dx.doi.org/10.1007/s11253-007-0037-9.

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29

Andrianov, Igor V., and Jan Awrejcewicz. "New Trends in Asymptotic Approaches: Summation and Interpolation Methods." Applied Mechanics Reviews 54, no. 1 (January 1, 2001): 69–92. http://dx.doi.org/10.1115/1.3097289.

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In this review article, we present in some detail new trends in application of asymptotic techniques to mechanical problems. First we consider the various methods which allows for the possibility of extending the perturbation series application space and hence omiting their local character. While applying the asymptotic methods very often the following situation appears: an existence of the asymptotics ε → 0 implies an existence of the asymptotics ε → ∞ (or, in a more general sense, ε → a and ε → b). Therefore, an idea of constructing a single solution valid for a whole interval of parameter ε changes is very attractive. In other words, we discuss a problem of asymptotically equivalent function constructions possessing for ε → a and ε → b a known asymptotic behavior. The defined problems are very important from the point of view of both theoretical and applied sciences. In this work, we review the state-of-the-art, by presenting the existing methods and by pointing out their advantages and disadvantages, as well as the fields of their applications. In addition, some new methods are also proposed. The methods are demonstrated on a wide variety of static and dynamic solid mechanics problems and some others involving fluid mechanics. This review article contains 340 references.

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30

Švec, Marko. "Oscillatory properties of a differential inclusion of order $n>1$ and the asymptotic equivalence." Czechoslovak Mathematical Journal 44, no. 3 (1994): 561–69. http://dx.doi.org/10.21136/cmj.1994.128479.

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31

Abate, Joseph, and Ward Whitt. "Limits and Approximations for the Busy-Period Distribution in Single-Server Queues." Probability in the Engineering and Informational Sciences 9, no. 4 (October 1995): 581–602. http://dx.doi.org/10.1017/s0269964800004071.

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Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/l queue, the complementary busy-period c.d.f. is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as p → 1), where the scaling parameters are based on the asymptotics as t → ∞. We call this the asymptotic normal approximation, because it involves the standard normal c.d.f. and density. The asymptotic normal approximation is asymptotically correct as t → ∞ for each fixed p and as p → 1 for each fixed t and yields remarkably good approximations for times not too small, whereas the direct heavy-traffic (p → 1) and asymptotic (t → ∞) limits do not yield such good approximations. Indeed, even the approximation based on three terms of the standard asymptotic expansion does not perform well unless t is very large. As a basis for generating corresponding approximations for the busy-period distribution in more general models, we also establish a more general heavy-traffic limit theorem.

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32

Ando, Shuji. "Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables." Biometrical Letters 58, no. 2 (December 1, 2021): 105–17. http://dx.doi.org/10.2478/bile-2021-0008.

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Summary Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models.

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Hazarika, Bipan, and Ayhan Esi. "On asymptotically Wijsman lacunary statistical convergence of set sequences in ideal context." Filomat 31, no. 9 (2017): 2691–703. http://dx.doi.org/10.2298/fil1709691h.

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In this paper, we introduce some definitions which are natural combination of the notions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, Wijsman convergence and ideal. In addition, we also define the concept of asymptotically equivalent sequences of sets in the sense ofWijsman convergence and prove some interesting results related to these concepts.

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34

MANNERS, FREDDIE. "A note on the polynomial Freĭman–Ruzsa conjecture over ℤ." Mathematical Proceedings of the Cambridge Philosophical Society 166, no. 2 (November 10, 2017): 243–45. http://dx.doi.org/10.1017/s0305004117000809.

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AbstractThe polynomial Freĭman–Ruzsa conjecture over the integers is often phrased in terms of convex progressions. We give an alternative, apparently stronger formulation in terms of the more restrictive “ellipsoid progressions”, and show that these formulations are in fact equivalent. The key input to the equivalence proof comes from strong results in asymptotic convex geometry.

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35

Choi, Sung-Kyu, Nam-Jip Koo, and Dong-Man Im. "ASYMPTOTIC EQUIVALENCE BETWEEN LINEAR DIFFERENTIAL SYSTEMS." Bulletin of the Korean Mathematical Society 42, no. 4 (November 1, 2005): 691–701. http://dx.doi.org/10.4134/bkms.2005.42.4.691.

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36

Bouten, Luc, and John E. Gough. "Asymptotic equivalence of quantum stochastic models." Journal of Mathematical Physics 60, no. 4 (April 2019): 043501. http://dx.doi.org/10.1063/1.5046189.

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37

Morchalo, J. "Asymptotic equivalence of Volterra difference systems." Publicacions Matemàtiques 39 (July 1, 1995): 301–12. http://dx.doi.org/10.5565/publmat_39295_07.

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Choi, Sung-Kyu, Nam-Jip Koo, and Keon-Hee Lee. "ASYMPTOTIC EQUIVALENCE FOR LINEAR DIFFERENTIAL SYSTEMS." Communications of the Korean Mathematical Society 26, no. 1 (January 31, 2011): 37–49. http://dx.doi.org/10.4134/ckms.2011.26.1.037.

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39

Leiva, Hugo, E. Medina, and N. Merentes. "Relative asymptotic equivalence between difference equations." Journal of Difference Equations and Applications 21, no. 5 (May 4, 2015): 418–36. http://dx.doi.org/10.1080/10236198.2015.1013536.

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Leiva, Hugo, and Hildebrando M. Rodrigues. "Relative asymptotic equivalence of evolution equations." Nonlinear Analysis: Theory, Methods & Applications 47, no. 7 (August 2001): 4579–90. http://dx.doi.org/10.1016/s0362-546x(01)00570-3.

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Lin, H., and Z. Niu. "Asymptotic unitary equivalence in C*-algebras." Russian Journal of Mathematical Physics 22, no. 3 (July 2015): 336–60. http://dx.doi.org/10.1134/s106192081503005x.

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Choi, Sung Kyu, Nam Jip Koo, and Hyun Sook Ryu. "Asymptotic equivalence between two difference systems." Computers & Mathematics with Applications 45, no. 6-9 (March 2003): 1327–37. http://dx.doi.org/10.1016/s0898-1221(03)00106-8.

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Ishkin, Khabir Kabirovich, and Rustem Il'darovich Marvanov. "Equivalence criterion for two asymptotic formulae." Ufimskii Matematicheskii Zhurnal 12, no. 1 (2020): 30–42. http://dx.doi.org/10.13108/2020-12-1-30.

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Dadarlat, Marius, and Søren Eilers. "Asymptotic Unitary Equivalence in KK-Theory." K-Theory 23, no. 4 (August 2001): 303–22. http://dx.doi.org/10.1023/a:1011930304577.

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Li, Jinlu. "Asymptotic equivalence of sequences and summability." International Journal of Mathematics and Mathematical Sciences 20, no. 4 (1997): 749–57. http://dx.doi.org/10.1155/s0161171297001038.

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For a sequence-to-sequence transformationA, letRmAx=∑n≥m|(Ax)n|andμmAx=supn≥m|(Ax)n|. The purpose of this paper is to study the relationship between the asymptotic equivalence of two sequences(limnxn/yn=1)and the variations of asymptotic equivalence based on the ratiosRmAx/RmAyandμmAx/μmAy.

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46

Schwingenschlögl, Udo. "Asymptotic Equivalence of Seat Bias Models." Statistical Papers 49, no. 2 (June 28, 2006): 191–200. http://dx.doi.org/10.1007/s00362-006-0005-8.

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47

Masaki, Satoshi, Jun-ichi Segata, and Kota Uriya. "On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension." Transactions of the American Mathematical Society, Series B 9, no. 18 (June 8, 2022): 517–63. http://dx.doi.org/10.1090/btran/116.

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In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems by the equivalence relation naturally induced by the linear transformation of the unknowns. It is revealed that the equivalence relation is well described by an identification with a matrix. In particular, we characterize some known systems in terms of the matrix and specify all systems equivalent to them. An explicit reduction procedure from a given system in the suitable subset to a model system, i.e., to a representative, is also established. The classification also draws our attention to some model systems which admit solutions with a new kind of asymptotic behavior. Especially, we find new systems which admit a solution of which decay rate is worse than that of a solution to the linear Klein-Gordon equation by logarithmic order.

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Kunakh, O. N., S. S. Kramarenko, A. V. Zhukov, A. S. Kramarenko, and N. V. Yorkina. "Fitting competing models and evaluation of model parameters of the abundance distribution of the land snail Vallonia pulchella (Pulmonata, Valloniidae)." Regulatory Mechanisms in Biosystems 9, no. 2 (April 25, 2018): 198–202. http://dx.doi.org/10.15421/021829.

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This paper summarizes the mechanisms behind the patterning of the intra-population abundance distribution of the land snail Vallonia pulchella (Müller, 1774). The molluscs were collected in recultivated soil formed on red-brown clays (Pokrov, Ukraine). Data obtained in this study reveal that V. pulchella population abundance ranges from 1 to 13 individuals per 100 g of soil sample. To obtain estimates of the mean, three models were used: the model of the arithmetic mean, the Poisson model and a log-normal model. The arithmetic mean of the occurrence of this species during the study period was 1.84 individuals/sample. Estimation of the average number of molluscs in one sample calculated using the Poisson model is lower and equals 1.40 individuals/sample. The distribution of the number of individuals in a population was described by the graphics "rank – abundance". The individual sample plot sites with molluscs may be regarded as equivalents of individual species in the community. For the analysis, the following models were used: broken sticks model, niche preemption model, log-normal model, Zipf model, and Zipf-Mandelbrot model. Applying the log-normal distribution gives a lower estimate of the mean density at 1.28 individuals/sample. Median value and mode is estimated at 1.00 individuals/sample. The Zipf-Mandelbrot model was shown as the most adequate to describe distribution of the V. pulchella population within the study area. The Zipf-Mandelbrot model belongs to the family of so-called non-Gaussian distributions. This means that the sample statistics do not possess asymptotic properties and by increasing the sample size, they tend to infinity, and are not close to the values of the general population. Therefore, the average value of the random variable that describes the non-Gaussian distribution has no statistical meaning. From an environmental point of view, this means that within the study area the capacity of the habitat is large, and for some combination of environmental conditions the rapid growth of the abundance of a given species is possible.

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Corcino, Cristina B., Roberto B. Corcino, and Raylee J. Gasparin. "Equivalent asymptotic formulas of second kindr-Whitney numbers." Integral Transforms and Special Functions 26, no. 3 (November 10, 2014): 192–202. http://dx.doi.org/10.1080/10652469.2014.979410.

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Hazarika, Bipan, and Ayhan Esi. "ON λ-ASYMPTOTICALLY WIJSMAN GENERALIZED STATISTICAL CONVERGENCE OF SEQUENCES OF SETS." Tatra Mountains Mathematical Publications 56, no. 1 (November 1, 2013): 67–77. http://dx.doi.org/10.2478/tmmp-2013-0025.

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ABSTRACT The concept of Wijsman statistical convergence was defined by [Nuray, F.-Rhoades, B. E.: Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 1-9]. In this paper we present three definitions which are a natural combination of the definition of asymptotic equivalence, statistical convergence, generalized statistical convergence and Wijsman convergence. In addition, we also present asymptotically equivalent sequences of sets in sense of Wijsman and study some properties of this concept.

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