Journal articles: 'S-expansion'

1

Harris, Frank E. "Expansion(s) ofr?212." International Journal of Quantum Chemistry 97, no. 5 (2004): 908–13. http://dx.doi.org/10.1002/qua.10792.

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2

Stankovic, Bogoljub. "S-asymptotic expansion of distributions." International Journal of Mathematics and Mathematical Sciences 11, no. 3 (1988): 449–56. http://dx.doi.org/10.1155/s0161171288000523.

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This paper contains first a definition of the asymptotic expansion at infinity of distributions belonging toG′Rn, namedS-asymptotic expansion, as also its properties and application to partial differential equations.

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3

Giovannini, Massimo. "Gradient expansion(s) and dark energy." Journal of Cosmology and Astroparticle Physics 2005, no. 09 (September 9, 2005): 009. http://dx.doi.org/10.1088/1475-7516/2005/09/009.

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4

PILTZ-KIRKBY, MARGARET. "Nursing??s Involvement Enhances Rehab Expansion." Nursing Management (Springhouse) 20, no. 5 (May 1989): 38???43. http://dx.doi.org/10.1097/00006247-198905000-00015.

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5

Nemes, G. "Error bounds for the asymptotic expansion of the Hurwitz zeta function." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2203 (July 2017): 20170363. http://dx.doi.org/10.1098/rspa.2017.0363.

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In this paper, we reconsider the large- a asymptotic expansion of the Hurwitz zeta function ζ ( s , a ). New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes G -function and the s -derivative of the Hurwitz zeta function ζ ( s , a ) are provided. A detailed discussion on the sharpness of our error bounds is also given.

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Lima, Rodrigo A., Clemens Drenowatz, and Karin A. Pfeiffer. "Expansion of Stodden et al.’s Model." Sports Medicine 52, no. 4 (February 7, 2022): 679–83. http://dx.doi.org/10.1007/s40279-021-01632-5.

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7

Kobayashi, T., and A. Leontiev. "Double Gegenbauer expansion of |s–t|α." Integral Transforms and Special Functions 30, no. 7 (March 26, 2019): 512–25. http://dx.doi.org/10.1080/10652469.2019.1585433.

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8

Marker, David. "A strongly minimal expansion of (ω, s)." Journal of Symbolic Logic 52, no. 1 (March 1987): 205–7. http://dx.doi.org/10.2307/2273874.

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We will show that there is a nontrivial strongly minimal expansion of (ω, s), the natural numbers with successor. Pillay and Steinhorn [1] proved that there is no -minimal expansion of (ω, ≤). This result provides an interesting contrast.The strongly minimal expansion of (ω, s) is very easy to describe. Consider the order-two permutation of ω, π recursively defined byLet T be Th(ω, s, π, 0).

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9

Caroca, R., N. Merino, and P. Salgado. "S expansion of higher-order Lie algebras." Journal of Mathematical Physics 50, no. 1 (January 2009): 013503. http://dx.doi.org/10.1063/1.3036177.

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10

Zhao, Xiaonan, Huiyan Lu, and Karen Usdin. "FAN1’s protection against CGG repeat expansion requires its nuclease activity and is FANCD2-independent." Nucleic Acids Research 49, no. 20 (October 28, 2021): 11643–52. http://dx.doi.org/10.1093/nar/gkab899.

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Abstract The Repeat Expansion Diseases, a large group of human diseases that includes the fragile X-related disorders (FXDs) and Huntington's disease (HD), all result from expansion of a disease-specific microsatellite via a mechanism that is not fully understood. We have previously shown that mismatch repair (MMR) proteins are required for expansion in a mouse model of the FXDs, but that the FANCD2 and FANCI associated nuclease 1 (FAN1), a component of the Fanconi anemia (FA) DNA repair pathway, is protective. FAN1’s nuclease activity has been reported to be dispensable for protection against expansion in an HD cell model. However, we show here that in a FXD mouse model a point mutation in the nuclease domain of FAN1 has the same effect on expansion as a null mutation. Furthermore, we show that FAN1 and another nuclease, EXO1, have an additive effect in protecting against MSH3-dependent expansions. Lastly, we show that the loss of FANCD2, a vital component of the Fanconi anemia DNA repair pathway, has no effect on expansions. Thus, FAN1 protects against MSH3-dependent expansions without diverting the expansion intermediates into the canonical FA pathway and this protection depends on FAN1 having an intact nuclease domain.

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11

Miller, Chris, and Patrick Speissegger. "Expansions of the Real Field by Canonical Products." Canadian Mathematical Bulletin 63, no. 3 (October 4, 2019): 506–21. http://dx.doi.org/10.4153/s0008439519000572.

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AbstractWe consider expansions of o-minimal structures on the real field by collections of restrictions to the positive real line of the canonical Weierstrass products associated with sequences such as $(-n^{s})_{n>0}$ (for $s>0$) and $(-s^{n})_{n>0}$ (for $s>1$), and also expansions by associated functions such as logarithmic derivatives. There are only three possible outcomes known so far: (i) the expansion is o-minimal (that is, definable sets have only finitely many connected components); (ii) every Borel subset of each $\mathbb{R}^{n}$ is definable; (iii) the expansion is interdefinable with a structure of the form $(\mathfrak{R}^{\prime },\unicode[STIX]{x1D6FC}^{\mathbb{Z}})$ where $\unicode[STIX]{x1D6FC}>1$, $\unicode[STIX]{x1D6FC}^{\mathbb{Z}}$ is the set of all integer powers of $\unicode[STIX]{x1D6FC}$, and $\mathfrak{R}^{\prime }$ is o-minimal and defines no irrational power functions.

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12

Iriarte, José, Richard J. Smith, Jonas Gregorio de Souza, Francis Edward Mayle, Bronwen S. Whitney, Macarena Lucia Cárdenas, Joy Singarayer, John F. Carson, Shovonlal Roy, and Paul Valdes. "Out of Amazonia: Late-Holocene climate change and the Tupi–Guarani trans-continental expansion." Holocene 27, no. 7 (November 26, 2016): 967–75. http://dx.doi.org/10.1177/0959683616678461.

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The late-Holocene expansion of the Tupi–Guarani languages from southern Amazonia to SE South America constitutes one of the largest expansions of any linguistic family in the world, spanning ~4000 km between latitudes 0°S and 35°S at about 2.5k cal. yr BP. However, the underlying reasons for this expansion are a matter of debate. Here, we compare continental-scale palaeoecological, palaeoclimate and archaeological datasets, to examine the role of climate change in facilitating the expansion of this forest-farming culture. Because this expansion lies within the path of the South American Low-Level Jet, the key mechanism for moisture transport across lowland South America, we were able to explore the relationship between climate change, forest expansion and the Tupi–Guarani. Our data synthesis shows broad synchrony between late-Holocene increasing precipitation and southerly expansion of both tropical forest and Guarani archaeological sites – the southernmost branch of the Tupi–Guarani. We conclude that climate change likely facilitated the agricultural expansion of the Guarani forest-farming culture by increasing the area of forested landscape that they could exploit, showing a prime example of ecological opportunism.

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13

Sahu, Manjulata, K. Krishnan, B. K. Nagar, M. K. Saxena, and Smruti Dash. "Heat capacity and thermal expansion coefficient of SrCeO3(s) and Sr2CeO4(s)." Thermochimica Acta 525, no. 1-2 (October 2011): 167–76. http://dx.doi.org/10.1016/j.tca.2011.08.007.

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14

Truszczynski, Mirosław. "Modal Nonmonotonic Logic with Restricted Application of the Negation as Failure to Prove Rule1." Fundamenta Informaticae 14, no. 3 (March 1, 1991): 355–66. http://dx.doi.org/10.3233/fi-1991-14309.

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In the paper we study a family of modal nonmonotonic logics closely related to the family of modal nonmonotonic logics proposed by McDermott and Doyle. For a modal logic S and a fixed collection of formulas X we introduce the notion of an ( S, X)-expansion. We restrict to modal logics which have a complete Kripke semantics. We study the properties of ( S, X)-expansions and show that in many respects they are analogous to the properties of S-expansions in nonmonotonic modal logics of McDermott and Doyle.

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15

EL-MONSEF, M. E. ABD, A. M. KOZAE, and A. A. ABO KHAORA. "ON FILTER EXPANSION OF TOPOLOGIES." Tamkang Journal of Mathematics 25, no. 1 (March 1, 1994): 53–59. http://dx.doi.org/10.5556/j.tkjm.25.1994.4425.

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The lower separation axioms $T_i$, ($i \in \{0, 1, 2\}$) are obviously preserved under topology expansions. This fact is not generally valid for higher separation axioms as well as for recent sorts of separation such as $T_R$, $R_0$, $R_1$ and semi-$R_i$, ($i \in \{0, 1\}$). The purpose of the present work is to investigate preservation of these recent separation properties under filter expansion of topologies. Also, we study the effect of filter expansions on the concept $s$-essentially $T_i$- spaces, ($i \in \{0, 1\}$).

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16

Lewis, Archibald R. "The Medieval Expansion of Europe.J. R. S. Phillips." Speculum 65, no. 2 (April 1990): 483–85. http://dx.doi.org/10.2307/2864356.

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17

Bickers, Kenneth N. "The Programmatic Expansion of the U. S. Government." Western Political Quarterly 44, no. 4 (December 1991): 891. http://dx.doi.org/10.2307/448799.

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18

Sahu, Manjulata, K. Krishnan, M. K. Saxena, and K. L. Ramakumar. "Thermal expansion and heat capacity of Gd6UO12(s)." Journal of Alloys and Compounds 482, no. 1-2 (August 2009): 141–46. http://dx.doi.org/10.1016/j.jallcom.2009.03.104.

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19

Schiedlmeier, B., A. C. Santos, A. Ribeiro, N. Moncaut, D. Lesinski, H. Auer, K. Kornacker, et al. "HOXB4's road map to stem cell expansion." Proceedings of the National Academy of Sciences 104, no. 43 (October 16, 2007): 16952–57. http://dx.doi.org/10.1073/pnas.0703082104.

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20

Kurbanov, M. M., D. D. Bairamov, and N. S. Sardarova. "Thermal expansion of TlInX2 (X = S, Se, Te)." Inorganic Materials 36, no. 2 (February 2000): 132–33. http://dx.doi.org/10.1007/bf02758012.

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21

XU, YE-JUN, JUN SONG, HONG-CHUN YUAN, HONG-YI FAN, and QIU-YU LIU. "QUANTIZATION SCHEME FOR FERMIONIC SYSTEM AND s-ORDERED OPERATOR EXPANSION FORMULA OF FERMIONIC DENSITY OPERATORS." Modern Physics Letters A 26, no. 11 (April 10, 2011): 833–42. http://dx.doi.org/10.1142/s0217732311035213.

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We introduce the generalized fermionic Wigner operator with an s parameter. Based on its remarkable properties, we establish one-to-one mapping between fermion operators and their s-parametrized pseudo-classical correspondence, which may involve fermionic Weyl pseudo-classical correspondence, P-representation and Q-representation in a unified way. Furthermore, starting with the projector of the fermionic coherent state, we obtain the s-ordered operator expansion formula of fermionic density operators, which includes normally ordered, antinormally ordered and Weyl ordered product of operators for different values of s. Applications in calculating some Fermi operators' s-ordered expansions are presented.

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22

Osbaldestin, A. H. "1/s-expansion for generalized dimensions in a hierarchical s-state Potts model." Journal of Physics A: Mathematical and General 28, no. 20 (October 21, 1995): 5951–62. http://dx.doi.org/10.1088/0305-4470/28/20/023.

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23

THOMPSON, WILLIAM R., and KAREN RASLER. "War, the Military Revolution(s) Controversy, and Army Expansion." Comparative Political Studies 32, no. 1 (February 1999): 3–31. http://dx.doi.org/10.1177/0010414099032001001.

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One school of thought on European state making argues that discontinuous change in weapons and tactics led to the expansion of armies, and, therefore, states. Others argue that decision makers expanded state organizations to make war for its own sake, not simply because the tools of war changed. Although this controversy is not easily resolved, the empirical evidence indicates that major expansions in army sizes over the past 500 years were almost exclusively related to major wars fought over regional and global primacy. Moreover, the leaders in expanding armies were usually the states aspiring to regional hegemony and their principal opponent. This evidence buttresses the argument for drawing a direct relationship between war and state making—instead of emphasizing an indirect relationship between weapons/tactics and army size.

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24

Artebani, M., R. Caroca, M. C. Ipinza, D. M. Peñafiel, and P. Salgado. "Geometrical aspects of the Lie algebra S-expansion procedure." Journal of Mathematical Physics 57, no. 2 (February 2016): 023516. http://dx.doi.org/10.1063/1.4941135.

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25

Peñafiel, D. M., and L. Ravera. "Infinite S-expansion with ideal subtraction and some applications." Journal of Mathematical Physics 58, no. 8 (August 2017): 081701. http://dx.doi.org/10.1063/1.4991378.

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26

Izaurieta, F., A. Perez, E. Rodriguez, and P. Salgado. "Dual formulation of the Lie algebra S-expansion procedure." Journal of Mathematical Physics 50, no. 7 (July 2009): 073511. http://dx.doi.org/10.1063/1.3171923.

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27

Katsube, Y., K. Horiguchi, and N. Hamada. "System reduction by continued-fraction expansion about s=jωi." Electronics Letters 21, no. 16 (1985): 678. http://dx.doi.org/10.1049/el:19850480.

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28

Lopuhaä, H. P. "Asymptotic expansion of S‐estimators of location and covariance." Statistica Neerlandica 51, no. 2 (July 1997): 220–37. http://dx.doi.org/10.1111/1467-9574.00051.

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29

Abbas, Shawki A. M. "Some Notes on Taylors Series Expansion with ODE´S." Journal of Al-Nahrain University-Science 18, no. 2 (June 2015): 149–56. http://dx.doi.org/10.22401/jnus.18.2.19.

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30

Kalasin, Kiattichai, Alvaro Cuervo‐Cazurra, and Ravi Ramamurti. "State ownership and international expansion: The S‐curve relationship." Global Strategy Journal 10, no. 2 (April 2019): 386–418. http://dx.doi.org/10.1002/gsj.1339.

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31

Hussein, T. S., A. N. Filby, R. B. Gilchrist, and M. Lane. "114. HUMAN CUMULUS - OOCYTE COMPLEXES SECRETE CUMULUS EXPANSION ENABLING FACTOR(S)." Reproduction, Fertility and Development 21, no. 9 (2009): 33. http://dx.doi.org/10.1071/srb09abs114.

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Interactions between the oocyte and its companion somatic cells are crucial to establish and maintain a highly specialized microenvironment required for oocyte viability. Specifically, cumulus cell expansion in the mouse is reliant on oocyte-secreted factors (OSF). Little is know about factors secreted by the human oocyte and how they may interact with cumulus cells. Therefore, the aim of this study was to establish whether human cumulus oocyte complexes (COC) produce OSF that induces cumulus expansion. COC of patients undergoing routine clinical IVF were cultured individually for 6h following oocyte retrieval. The human oocyte conditioned medium (HOCM) was collected. The bioactivity of OSF in the HOCM was assessed using an established assay of cumulus expansion of mouse oocytectomized complexes (OOX). Cumulus expansion was assessed blinded using the scoring system; 1 (no expansion) to 4 (maximally expanded) and gene expression was assessed by real time RT-PCR. Culture of OOX in control media with or without FSH did not induce expansion. Similarly, OOX cultured in HOCM without FSH did not expand. However, culture of OOX in HOCM with FSH significantly induced expansion (2.4±0.1 compared with control 1.1±0.04, P<0.05). Furthermore, this expansion was not different to OOX co-cultured with human (2.9±0.1) or mouse (2.6±0.1) denuded oocytes. Cumulus/OOX gene expression of hyaluronan synthase-2 and cyclooxygenase-2 was significantly up-regulated 4-5 fold when OOX were cultured in HOCM compared to control (P<0.05). Interestingly, different patients produced HOCM which resulted in different levels of expansion (range from 1.5-3.7). This study has established that human COC secrete paracrine factor(s) that enable cumulus expansion. This expansion was dependent on the presence of FSH. The identity of these factor(s) are currently unknown however it appears that COC from different patients produce differing levels of these cumulus expansion enabling factor(s).

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32

ARNETTE, STEPHEN A., MO SAMIMY, and GREGORY S. ELLIOTT. "The effects of expansion on the turbulence structure of compressible boundary layers." Journal of Fluid Mechanics 367 (July 25, 1998): 67–105. http://dx.doi.org/10.1017/s0022112098001475.

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A fully developed Mach 3 turbulent boundary layer subjected to four expansion regions (centred and gradual expansions of 7° and 14°) was investigated with laser Doppler velocimetry. Measurements were acquired in the incoming flat-plate boundary layer and to s/δ≃20 downstream of the expansions. While mean velocity profiles exhibit significant progress towards recovery by the most downstream measurements, the turbulence structure remains far from equilibrium. Comparisons of computed (method of characteristics) and measured velocity profiles indicate that the post-expansion flow evolution is largely inviscid for approximately 10δ. Turbulence levels decrease across the expansion, and the reductions increase in severity as the wall is approached. Downstream of the 14° expansions, the reductions are more severe and reverse transition is indicated by sharp reductions in turbulent kinetic energy levels and a change in sign of the Reynolds shear stress. Dimensionless parameters such as anisotropy and shear stress correlation coefficient highlight the complex evolution of the post-expansion boundary layer. An examination of the compressible vorticity transport equation and estimates of the perturbation impulses attributable to streamline curvature, acceleration, and dilatation both confirm dilatation to be the primary stabilizer. However, the dilatation impulse increases only slightly for the 14° expansions, so the dramatic differences downstream of the 7° and 14° expansions indicate nonlinear boundary layer response. Differences attributable to the varied radii of surface curvature are fleeting for the 7° expansions, but persist through the spatial extent of the measurements for the 14° expansions.

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33

PILIPOVIĆ, STEVAN, and DORA SELEŠI. "EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, no. 01 (March 2007): 79–110. http://dx.doi.org/10.1142/s0219025707002634.

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A new Gel'fand triple exp (S)1 ⊆ (L)2 ⊆ exp (S)-1 is constructed as extension of the known Kondratiev one (S)1 ⊆ (L)2 ⊆ (S)-1. Expansion theorems for generalized stochastic processes considered as elements of the spaces [Formula: see text] and [Formula: see text] are derived. This series expansion is used for solving a class of evolution stochastic differential equations. The Wick product is developed on the spaces exp (S)-1, [Formula: see text] and [Formula: see text]. The series expansion of generalized stochastic processes is used for solving a class of nonlinear stochastic differential equations by means of Wick products.

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34

Gao, Ruipeng, and Yefei Li. "Theoretical study on the electronic structure, mechanical property, and thermal expansion of yttrium oxysulfide." International Journal of Computational Materials Science and Engineering 04, no. 01 (March 2015): 1550004. http://dx.doi.org/10.1142/s2047684115500049.

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The electronic structure, mechanical property and thermal expansion of yttrium oxysulfide are calculated from first-principles using the theory of density functional. The calculated cohesive energy indicates its thermodynamic stable nature. From bond structure, the calculated bandgap is obtained as 2.7 eV; and strong covalent bonds exist between Y and O atoms intra 2D [ Y – O ] layer in material, while relatively weak covalent bonds also exist inter 2D [ Y – O ] layer and S atoms. From simulation, it is found that the bulk modulus is about 119.4 GPa for the elastic constants, and the bulk modulus shows weak anisotropy because the surface contours of them are close to a spherical shape. The calculated B/G clearly implies its ductile nature, and the Y 2 O 2 S phase can also be compressed easily. The temperature dependence of thermal expansions is mainly caused by the restoration of thermal energy due to lattice excitations at low temperature. When the temperature is very high, the thermal expansion coefficient increases linearly with temperature increasing. Meanwhile, the heat capacities are also calculated and discussed by thermal expansion and elasticity.

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35

Benaissa, A., and C. Roger. "Asymptotic expansion of multiple oscillatory integrals with a hypersurface of stationary points of the phase." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2155 (July 8, 2013): 20130109. http://dx.doi.org/10.1098/rspa.2013.0109.

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In this paper, we present a method solving the problem of the asymptotic expansion of the integral , in the case when D is a bounded domain in ( n ≥2), and the set S of stationary points of the phase f is a hypersurface. This problem was considered in the literature, in the two-dimensional case, where it is required that the Laplacian △ f of the phase f does not vanish on S , and the curve S cuts transversely ∂ D . It will be seen that the order of degeneracy of normal derivatives of f , with respect to the surface S , plays a key role in solving the problem. We shall develop complete asymptotic expansions when this order is constant along S , and show that the problem leads to the use of special functions in the other case.

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36

Efthimiou, C. A., M. E. Grypeos, C, G. Koutroulos, W. J. Oyewumi, and Th Petridou. "A renormalized HVT approach for a class of central potential wells." HNPS Proceedings 16 (January 1, 2020): 107. http://dx.doi.org/10.12681/hnps.2587.

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An investigation is carried out to consider a renormalized HVT approach in the context of s-power series expansions for the energy eigenvalues of a particle moving non-relativistically in a central potential well belonging to the class V(r)=−Df(rR), D>0 where f is an appropriate even function of x=r/R and the dimensionless quantity s = (h^2/2μDR)^{1/2} is assumed to be sufficiently small. Previously, the more general class of central potentials of even power series in r is considered and the renormalized recurrence relations from which the expansions of the energy eigenvalues follow, are derived. The s-power series of the renormalized expansion are then given for the initial class of potentials up to third order in s (included) for each energy-level Enl . It is shown that the renormalization parameter Κ enters the coefficients of the renormalized expansion through the state-dependent quantity a_{nl}χ^{1/2} =a_{nl}(1+K ((−d_1D)R^2))^{½}, a_{nl}=(2n+l+32). The question of determining χ is discussed. Our first numerical results are also given and the utility of potentials of the class considered (to which belong the well-known Gaussian and reduced Poschl- Teller potentials) in the study of single–particle states of a Λ in hypernuclei is pointed out.

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37

Xu, F., G. Morard, N. Guignot, A. Rivoldini, G. Manthilake, J. Chantel, L. Xie, et al. "Thermal expansion of liquid Fe-S alloy at high pressure." Earth and Planetary Science Letters 563 (June 2021): 116884. http://dx.doi.org/10.1016/j.epsl.2021.116884.

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38

sci, Jing Chen. "Coulomb divergence in S-matrix expansion of above- threshold ionization." Journal of Atomic and Molecular Sciences 8, no. 1 (June 2017): 5–9. http://dx.doi.org/10.4208/jams.050517.072017a.

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39

Gomis, Jaume, and Takuya Okuda. "S-duality, 't Hooft operators and the operator product expansion." Journal of High Energy Physics 2009, no. 09 (September 15, 2009): 072. http://dx.doi.org/10.1088/1126-6708/2009/09/072.

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40

Enserink, M. "EUROPEAN EXPANSION: Outwitting TB on the E.U.'s Eastern Frontier." Science 304, no. 5668 (April 9, 2004): 199. http://dx.doi.org/10.1126/science.304.5668.199.

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41

Lai, K. F. "On Arthur?s class expansion of the relative trace formula." Duke Mathematical Journal 64, no. 1 (October 1991): 111–17. http://dx.doi.org/10.1215/s0012-7094-91-06405-7.

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42

Galvan, J. B., and J. Sesma. "Ambiguities in the Debye expansion of the elastic S matrix." Journal of Mathematical Physics 28, no. 10 (October 1987): 2420–26. http://dx.doi.org/10.1063/1.527781.

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43

Chubukov, A. V., S. Sachdev, and T. Senthil. "Large-S expansion for quantum antiferromagnets on a triangular lattice." Journal of Physics: Condensed Matter 6, no. 42 (October 17, 1994): 8891–902. http://dx.doi.org/10.1088/0953-8984/6/42/019.

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44

Carini, Luisa, and J. B. Remmel. "Formulas for the expansion of the plethysms s2[S(a,b)] and S2[S(nk)]." Discrete Mathematics 193, no. 1-3 (November 1998): 147–77. http://dx.doi.org/10.1016/s0012-365x(98)00139-3.

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45

d’Elbée, Christian. "Expansions and Neostability in Model Theory." Bulletin of Symbolic Logic 27, no. 2 (June 2021): 216–17. http://dx.doi.org/10.1017/bsl.2021.26.

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AbstractThis thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$ . Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$ , for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ -theory that axiomatises the following structures: $(\mathscr {M},\mathscr {M}_0)$ consist of a model $\mathscr {M}$ of T and S is a predicate for a model $\mathscr {M}_0$ of $T_0$ which is a substructure of $\mathscr {M}$ . We present a setting for the existence of a model-companion $TS$ of $T_S$ . As a consequence, we obtain the existence of the model-companion of the following theories, for $p>0$ a prime number: • $\mathrm {ACF}_p$ , $\mathrm {SCF}_{e,p}$ , $\mathrm {Psf}_p$ , $\mathrm {ACFA}_p$ , $\mathrm {ACVF}_{p,p}$ in appropriate languages expanded by arbitrarily many predicates for additive subgroups;• $\mathrm {ACF}_p$ , $\mathrm {ACF}_0$ in the language of rings expanded by a single predicate for a multiplicative subgroup;• $\mathrm {PAC}_p$ -fields, in an appropriate language expanded by arbitrarily many predicates for additive subgroups.From an independence relation in T, we define independence relations in $TS$ and identify which properties of are transferred to those new independence relations in $TS$ , and under which conditions. This allows us to exhibit hypotheses under which the expansion from T to $TS$ preserves $\mathrm {NSOP}_{1}$ , simplicity, or stability. In particular, under some technical hypothesis on T, we may draw the following picture (the left column implies the right column): Configuration $T_0\subseteq T$ Generic expansion $TS$ $T_0 = T$ Preserves stability $T_0\subseteq T$ Preserves $\mathrm {NSOP}_{1}$ $T_0 = \emptyset $ Preserves simplicityIn particular, this construction produces new examples of $\mathrm {NSOP}_{1}$ not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. We give a full description of imaginaries, forking, and Kim-forking in this example.The second part studies expansions of the group of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of independent p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to “reconstruct” the valuation using only the group operation.Abstract prepared by Christian d’Elbée.E-mail: delbee@math.univ-lyon1.frURL: https://choum.net/~chris/page_perso

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46

Masuda, Takuya, and Toshio Tagawa. "Effect of Asymmetry of Channels on Flows in Parallel Plates with a Sudden Expansion." Symmetry 13, no. 10 (October 3, 2021): 1857. http://dx.doi.org/10.3390/sym13101857.

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In order to quantitatively grasp the influence of asymmetry of a channel, flow in an eccentric sudden expansion channel, in which the channel centers are different on the upstream and downstream sides, was calculated to be less than the Reynolds number of 400, where the expansion rate was 2. The asymmetry of a channel is expressed by an eccentricity S, where a symmetric expansion channel is S = 0 and a channel with one side step is S = 1. Both flows firstly reattached on the wall located on the short and long side of a sudden expansion and were observed in the range of S ≤ 0.2, although only the former was seen in the range of S > 0.2. The critical Reynolds number of the multiple solutions increases parabolically to S. At least two separation vortices occur, and the third separation vortex is generated in both solutions above the critical Reynolds number of the third vortex. The length of an entrance region increases linearly to the Reynolds number and slightly with the increase in S. The pressure drop coefficient is proportional to the power of the Reynolds number and increases with S.

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47

Remmel, Jeffrey B. "Formulas for the expansion of the Kronecker products S(m, n) ⊗ S(1p−r, r) and S(1k2l) ⊗ S(1p−r, r)." Discrete Mathematics 99, no. 1-3 (April 1992): 265–87. http://dx.doi.org/10.1016/0012-365x(92)90376-q.

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Billhardt, B. "Expansions of completely simple semigroups." Studia Scientiarum Mathematicarum Hungarica 41, no. 1 (March 2004): 39–58. http://dx.doi.org/10.1556/012.2004.41.1.3.

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For any completely simple semigroup C a regular expansion S(C) is constructed which is the Birget-Rhodes prefix expansion CPr if C is a group [6]. We show that our construction generalizes two important features of CPr. Moreover we embed S (C) into a restricted semidirect product of a semilattice by C and investigate the relationship to the expansion P(C), introduced by Meakin [14].

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Hyun, Youngbin, Jeong-Bong Lee, Sangkug Chung, and Daeyoung Kim. "Acoustic Wave-Driven Liquid Metal Expansion." Micromachines 13, no. 5 (April 28, 2022): 685. http://dx.doi.org/10.3390/mi13050685.

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In this paper, we report a volume expansion phenomenon of a liquid metal droplet naturally oxidized in an ambient environment by applying an acoustic wave. An oxidized gallium-based liquid metal droplet was placed on a paper towel, and a piezo-actuator was attached underneath it. When a liquid metal droplet was excited by acoustic wave, the volume of liquid metal was expanded due to the inflow of air throughout the oxide crack. The liquid metal without the oxide layer cannot be expanded with an applied acoustic wave. To confirm the effect of the expansion of the oxidized liquid metal droplet, we measured an expansion ratio, which was calculated by comparing the expanded size in the x (horizontal), y (vertical) axis to the initial size of the liquid metal droplet, using a high-speed camera. For various volumes of the droplet, when we applied various voltages in the range of 5~8 Vrms with 18.5~24.5 kHz using the piezo-actuator, we obtained a maximum expansion ratio of 2.4 in the x axis and 3.8 in the y axis, respectively. In addition, we investigated that the time to reach the maximum expansion in proportion to the volume size of liquid metal differed by five times from 4 s to 20 s, and that the time to maintain the maximum expansion differed from 23 s to 2.5 s, which was inversely proportional to the volume size. We also investigated the expansion ratios depending on the exposure time to the atmosphere. Finally, a circuit containing LED, which can be turned on by expanded liquid metal droplet, was demonstrated.

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De Maré, George R., Yurii N. Panchenko, Alexander V. Abramenkov, and Charles W. Bock. "An empirically corrected quantum mechanical potential energy curve of internal rotation of acryloyl fluoride, CH2=CH-CF=O." Canadian Journal of Chemistry 71, no. 5 (May 1, 1993): 656–62. http://dx.doi.org/10.1139/v93-088.

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The geometrical parameters of acryloyl fluoride were optimized completely at the MP2/6-31G* computational level for 17 points on the internal rotation potential energy (IRPE) curve for rotation around the formal single carbon–carbon bond. The expansion coefficients of the reduced rotational constant function F(φ) and the four, five, and six-term expansions of the IRPE function,[Formula: see text]were obtained from these data. The theoretical IRPE functions were then refined using only the experimental torsional transition frequencies in both the s-trans and s-cis wells. The IRPE functions obtained are compared with those in the literature, calculated at lower levels of theory in both the rigid and nonrigid rotation approximations. The best representation of the refined IRPE function is given by the six-term expansion with V1 = 71.7, V2 = 1944.8, V3 = 113.0, V4 = −122.8, V5 = −8.7, and V6 = 12.5 cm−1, respectively. From this IRPE function, one correctly predicts the s-trans conformer to be more stable with ΔH0 = 168 cm−1. The barrier to rotation from the s-trans to the s-cis positions, ΔH#, is 2048 cm−1 at 88° from the s-trans well. The advantages of using the nonrigid rotation approximation, based on high-quality quantum mechanical calculations that include correlation effects, to construct the effective IRPE function for molecules are emphasized.

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Journal articles on the topic 'S-expansion'

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