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Journal articles on the topic 'Non-Closed fields'

Author: Grafiati

Published: 8 March 2025

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1

Abramovich, Dan, Jan Denef, and Kalle Karu. "Weak toroidalization over non-closed fields." Manuscripta Mathematica 142, no. 1-2 (April 10, 2013): 257–71. http://dx.doi.org/10.1007/s00229-013-0610-5.

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2

Ballico, E. "Line Bundles and Non-Algebraically Closed Fields." Rocky Mountain Journal of Mathematics 23, no. 2 (June 1993): 447–50. http://dx.doi.org/10.1216/rmjm/1181072570.

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3

Sanford, Sean. "Fusion categories over non-algebraically closed fields." Journal of Algebra 663 (February 2025): 316–51. http://dx.doi.org/10.1016/j.jalgebra.2024.09.010.

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4

Wagner, Frank O. "Minimal fields." Journal of Symbolic Logic 65, no. 4 (December 2000): 1833–35. http://dx.doi.org/10.2307/2695078.

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5

Kuznetsov, Alexander, and Yuri Prokhorov. "Rationality of Fano threefolds over non-closed fields." American Journal of Mathematics 145, no. 2 (April 2023): 335–411. http://dx.doi.org/10.1353/ajm.2023.0008.

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6

Gamboa, J. M. "A note on cohomology over non algebraically closed fields." Bulletin of the Australian Mathematical Society 60, no. 1 (August 1999): 67–72. http://dx.doi.org/10.1017/s0004972700033335.

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7

Geyer, Wulf-Dieter, and Moshe Jarden. "Non-pac fields whose Henselian closures are seperably closed." Mathematical Research Letters 8, no. 4 (2001): 509–19. http://dx.doi.org/10.4310/mrl.2001.v8.n4.a10.

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8

Turki, Nasser Bin, Sharief Deshmukh, and Olga Belova. "A note on closed vector fields." AIMS Mathematics 9, no. 1 (2023): 1509–22. http://dx.doi.org/10.3934/math.2024074.

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<abstract><p>Special vector fields, such as conformal vector fields and Killing vector fields, are commonly used in studying the geometry of a Riemannian manifold. Though there are Riemannian manifolds, which do not admit certain conformal vector fields or certain Killing vector fields, respectively. Closed vector fields exist in abundance on each Riemannian manifold. In this paper, we used closed vector fields to study the geometry of the Riemannian manifold. In the first result, we showed that a compact Riemannian manifold $ (M^{n}, g) $ admits a closed vector field $\boldsymbol{\omega }$ with $ \mathrm{div} \boldsymbol{\omega }$ non-constant and an eigenvector of the rough Laplace operator, the integral of the Ricci curvature $ Ric(\boldsymbol{\omega }, \boldsymbol{\omega }) $ has a suitable lower bound that is necessarily isometric to $ S^{n}(c) $ and that the converse holds. In the other result, we found a characterization of an Euclidean space using a closed vector field $\boldsymbol{\omega }$ with non-constant length that annihilates the rough Laplace operator and squared length of its covariant derivative that has a suitable upper bound. Finally, we used the closed vector field provided by the gradient of the non-trivial solution of the Fischer-Marsden equation on a complete and simply connected Riemannian manifold $ (M, g) $ and showed that it is necessary and sufficient for $ (M, g) $ to be isometric to a sphere and that the squared length of the covariant derivative of this closed vector field has a suitable upper bound.</p></abstract>

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9

Evans, David M. "Expansions of fields by angular functions." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (October 2008): 735–50. http://dx.doi.org/10.1017/s1474748008000200.

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AbstractThe notion of an angular function has been introduced by Zilber as one possible way of connecting non-commutative geometry with two ‘counterexamples’ from model theory: the non-classical Zariski curves of Hrushovski and Zilber, and Poizat's field with green points. This article discusses some questions of Zilber relating to existentially closed structures in the class of algebraically closed fields with an angular function.

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10

Cluckers, R., L. Lipshitz, and Z. Robinson. "Real closed fields with non-standard and standard analytic structure." Journal of the London Mathematical Society 78, no. 1 (May 13, 2008): 198–212. http://dx.doi.org/10.1112/jlms/jdn024.

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11

Isenberg, J., and V. Moncrief. "On spacetimes containing Killing vector fields with non-closed orbits." Classical and Quantum Gravity 9, no. 7 (July 1, 1992): 1683–91. http://dx.doi.org/10.1088/0264-9381/9/7/004.

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12

Konitopoulos, Spyros. "Closed algebras for higher rank, non-Abelian tensor gauge fields." Nuclear Physics B 963 (February 2021): 115285. http://dx.doi.org/10.1016/j.nuclphysb.2020.115285.

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13

Bouscaren, E., and F. Delon. "Minimal groups in separably closed fields." Journal of Symbolic Logic 67, no. 1 (March 2002): 239–59. http://dx.doi.org/10.2178/jsl/1190150042.

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AbstractWe give a complete description of minimal groups infinitely definable in separably closed fields of finite degree of imperfection. In particular we answer positively the question of the existence of such a group with infinite transcendence degree (i.e., a minimal group with non thin generic).

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14

Bhaskaran, R., and V. Karunakaran. "Analytic functions over valued fields." International Journal of Mathematics and Mathematical Sciences 13, no. 2 (1990): 247–52. http://dx.doi.org/10.1155/s0161171290000370.

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LetKbe a non-archimedean, non-trivially (rank 1) valued complete field.B,B0denote the closed and open unit ball ofKrespectively. Necessary and sufficient conditions for analytic functions defined onB,B0with values inKto be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.

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15

Point, Françoise. "Asymptotic theory of modules of separably closed fields." Journal of Symbolic Logic 70, no. 2 (June 2005): 573–92. http://dx.doi.org/10.2178/jsl/1120224729.

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AbstractWe consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.

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16

Castellani, Leonardo. "Non-abelian gauge fields from 10 → 4 compactification of closed superstrings." Physics Letters B 166, no. 1 (January 1986): 54–58. http://dx.doi.org/10.1016/0370-2693(86)91154-8.

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17

Skryabin, S. M. "Modular lie algebras of cartan type over algebraically non-closed fields. II." Communications in Algebra 23, no. 4 (January 1995): 1403–53. http://dx.doi.org/10.1080/00927879508825286.

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18

Avilov, A. A. "Existence of standard models of conic fibrations over non-algebraically-closed fields." Sbornik: Mathematics 205, no. 12 (December 31, 2014): 1683–95. http://dx.doi.org/10.1070/sm2014v205n12abeh004434.

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19

Weitzner, Harold, and Wrick Sengupta. "Exact non-symmetric closed line vacuum magnetic fields in a topological torus." Physics of Plasmas 27, no. 2 (February 2020): 022509. http://dx.doi.org/10.1063/1.5126688.

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20

Skryabin, S. M. "Modular lie algebras of cartan type over algebraically non-closed fields.1." Communications in Algebra 19, no. 6 (January 1991): 1629–741. http://dx.doi.org/10.1080/00927879108824226.

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21

Jakelić, Dijana, and Adriano Moura. "Finite-Dimensional Representations of Hyper Loop Algebras over Non-algebraically Closed Fields." Algebras and Representation Theory 13, no. 3 (February 13, 2009): 271–301. http://dx.doi.org/10.1007/s10468-008-9122-5.

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22

Heyman, E., and L. B. Felsen. "Non-dispersive closed form approximations for transient propagation and scattering of ray fields." Wave Motion 7, no. 4 (July 1985): 335–58. http://dx.doi.org/10.1016/0165-2125(85)90004-6.

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23

Aranson, S. Kh. "On the non-denseness of fields of finite degree of non-robustness in the space of non-robust vector fields on closed two-dimensional manifolds." Russian Mathematical Surveys 43, no. 1 (February 28, 1988): 231–32. http://dx.doi.org/10.1070/rm1988v043n01abeh001537.

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24

Ahmad, Hamza. "The algebraic closure in function fields of quadratic forms in characteristic 2." Bulletin of the Australian Mathematical Society 55, no. 2 (April 1997): 293–97. http://dx.doi.org/10.1017/s0004972700033955.

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For a field k of characteristic not two, it is known that k is algebraically closed in the function field of any (non-degenerate) quadratic form in three or more variables. In this note we consider fields of characteristic two and decide when k is algebraically closed in a function field of a quadratic k-form. For quadratic forms in three variables this has recently been done by Ohm.

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25

Delon, Françoise. "Une fonction de Kolchin pour les corps imparfaits de degré d'imperfection fini." Journal of Symbolic Logic 70, no. 2 (June 2005): 664–80. http://dx.doi.org/10.2178/jsl/1120224735.

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AbstractNon-perfect separably closed fields are stable, and not superstable. As a result, not all types can be ranked. We develop here a new tool, a “semi-rank”, which takes values in the non-negative reals, and gives a sufficient condition for forking of types. This semi-rank is built up from a transcendence function, analogous to the one considered by Kolehin in the context of differentially closed fields. It yields some orthogonality and stratification results.

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26

Zappalorto, M. "Strain fields in cracked bodies under antiplane shear for a generalised non-hardening material law." Mathematics and Mechanics of Solids 24, no. 10 (March 19, 2019): 3125–35. http://dx.doi.org/10.1177/1081286519835272.

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An exact, closed form, solution is derived for the non-linear stress distribution in a cracked body under antiplane shear deformation. A generalised, non work-hardening, law is introduced to describe the material behaviour, and the stress and strain fields are derived in closed form. Such a new generalised material law includes the effect of a new parameter, a, which allows the transition from the ideally elastic behaviour (low strain regime) to the pure non-linear behaviour (large strain regime) to be modulated. A discussion is carried out on the features of the new solution and on the behaviour of stresses and strains close to and far away from the crack tip.

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27

DALLEY, S., C. V. JOHNSON, T. R. MORRIS, and A. WÄTTERSTAM. "UNITARY MATRIX MODELS AND 2D QUANTUM GRAVITY." Modern Physics Letters A 07, no. 29 (September 21, 1992): 2753–62. http://dx.doi.org/10.1142/s0217732392002226.

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The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system — open-closed string theory. Non-perturbative solutions of the multicritical unitary matrix models map to non-singular solutions of the 'renormalization group' equation for the string susceptibility, [Formula: see text]. We also demonstrate that the large-N solutions of unitary matrix integrals in external fields, studied by Gross and Newman, equal the non-singular pure closed-string solutions of [Formula: see text].

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28

Shamseddine, Khodr, and Martin Berz. "Intermediate values and inverse functions on non-Archimedean fields." International Journal of Mathematics and Mathematical Sciences 30, no. 3 (2002): 165–76. http://dx.doi.org/10.1155/s0161171202013030.

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Continuity or even differentiability of a function on a closed interval of a non-Archimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness of the field in the order topology. In this paper, we show that differentiability (in the topological sense), together with some additional mild conditions, is indeed sufficient to guarantee that the function assumes all intermediate values and has a differentiable inverse function.

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29

Buzzi, C. A., T. de Carvalho, and P. R. da Silva. "Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane." Journal of Dynamical and Control Systems 19, no. 2 (April 2013): 173–93. http://dx.doi.org/10.1007/s10883-013-9169-4.

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30

Dundas, Bjørn, Michael Hill, Kyle Ormsby, and Paul Østvær. "Hochschild homology of mod-𝑝 motivic cohomology over algebraically closed fields." Communications of the American Mathematical Society 4, no. 13 (September 4, 2024): 578–606. http://dx.doi.org/10.1090/cams/36.

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We perform Hochschild homology calculations in the algebro-geometric setting of motives over algebraically closed fields. The homotopy ring of motivic Hochschild homology contains torsion classes that arise from the mod- p p motivic Steenrod algebra and generating functions defined on the natural numbers with finite non-empty support. Under Betti realization, we recover Bökstedt’s calculation of the topological Hochschild homology of finite prime fields.

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31

Shlyahin, D. A., and V. A. Jurin. "Non-axisymmetric coupled non-stationary problem of thermoelectroelasticity for a long piezoceramic cylinder." Известия Российской академии наук Механика твердого тела, no. 2 (November 12, 2024): 325–44. http://dx.doi.org/10.31857/s1026351924020161.

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A new closed solution to the non-axisymmetric coupled non-stationary problem of thermoelectroelasticity was constructed for a long piezoceramic cylinder for the case of satisfaction of the first and the third kind boundary conditions. Cylindrical surfaces were made as electrodes and connected to a measurement device with large input resistance. Limitation of a temperature change “load” rate made it possible to include equations of statics, electrostatics and thermal conductivity in the initial formula. The finite biorthogonal transforms are applying to explore a non-selfadjoint system of differential equations and to develop a closed solution. The obtained relations made it possible to determine the temperature and electric fields, and the stress-strain state in the piezoceramic cylinder, as well as the potential difference between cylindrical surfaces (electrodes) under non-stationary non-axisymmetric temperature impact.

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32

DORBIDI, H. R., R. FALLAH-MOGHADDAM, and M. MAHDAVI-HEZAVEHI. "SOLUBLE MAXIMAL SUBGROUPS IN GLn(D)." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1371–82. http://dx.doi.org/10.1142/s0219498811005233.

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Let D be an F-central non-commutative division ring. Here, it is proved that if GL n(D) contains a non-abelian soluble maximal subgroup, then n = 1, [D : F] < ∞, and D is cyclic of degree p, a prime. Furthermore, a classification of soluble maximal subgroups of GL n(F) for an algebraically closed or real closed field F is also presented. We then determine all soluble maximal subgroups of GL 2(F) for fields F with Char F ≠ 2.

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33

Mushtaq, Q. "Modular group acting on real quadratic fields." Bulletin of the Australian Mathematical Society 37, no. 2 (April 1988): 303–9. http://dx.doi.org/10.1017/s000497270002685x.

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Coset diagrams for the orbit of the modular group G = 〈x, y: x2 = y3 = 1〉 acting on real quadratic fields give some interesting information. By using these coset diagrams, we show that for a fixed value of n, a non-square positive integer, there are only a finite number of real quadratic irrational numbers of the form , where θ and its algebraic conjugate have different signs, and that part of the coset diagram containing such numbers forms a single circuit (closed path) and it is the only circuit in the orbit of θ.

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34

Kaiser, Tobias. "Lebesgue measure and integration theory on non-archimedean real closed fields with archimedean value group." Proceedings of the London Mathematical Society 116, no. 2 (August 31, 2017): 209–47. http://dx.doi.org/10.1112/plms.12070.

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35

Ройтенберг, Владимир Шлеймович. "Planar vector fields with central symmetry: roughness and first degree of non-roughness." Вестник Адыгейского государственного университета, серия «Естественно-математические и технические науки», no. 2(281) (September 28, 2021): 27–40. http://dx.doi.org/10.53598/2410-3225-2021-2-281-27-40.

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Рассматривается пространство гладких векторных полей, заданных в замкнутой области D на плоскости, инвариантных относительно центральной симметрии и трансверсальных границе D. Описано множество векторных полей, грубых относительно этого пространства; показано, что оно открыто и всюду плотно. Во множестве всех негрубых векторных полей выделено открытое всюду плотное подмножество, состоящее из векторных полей первой степени негрубости. We consider the space of smooth vector fields defined in a closed domain D on the plane, invariant under the central symmetry and transversal to the boundary D. The set of vector fields that are rough with respect to this space is described; it is shown that it is open and everywhere dense. In the set of all non-rough vector fields, an open everywhere dense subset consisting of vector fields of the first degree of non-roughness is distinguished.

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36

Freidel, Laurent, Robert G. Leigh, and Djordje Minic. "Manifest non-locality in quantum mechanics, quantum field theory and quantum gravity." International Journal of Modern Physics A 34, no. 28 (October 10, 2019): 1941004. http://dx.doi.org/10.1142/s0217751x19410045.

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We summarize our recent work on the foundational aspects of string theory as a quantum theory of gravity. We emphasize the hidden quantum geometry (modular spacetime) behind the generic representation of quantum theory and then stress that the same geometric structure underlies a manifestly T-duality covariant formulation of string theory, that we call metastring theory. We also discuss an effective non-commutative description of closed strings implied by intrinsic non-commutativity of closed string theory. This fundamental non-commutativity is explicit in the metastring formulation of quantum gravity. Finally we comment on the new concept of metaparticles inherent to such an effective non-commutative description in terms of bi-local quantum fields.

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37

STICHEL, P. C., and W. J. ZAKRZEWSKI. "POSSIBLE CONFINEMENT MECHANISMS FOR NONRELATIVISTIC PARTICLES ON A LINE." Modern Physics Letters A 16, no. 29 (September 21, 2001): 1919–32. http://dx.doi.org/10.1142/s0217732301005278.

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The gauge model of nonrelativistic particles on a line interacting with nonstandard gravitational fields5 is supplemented by the addition of a (non)-Abelian gauge interaction. Solving for the gauge fields we obtain equations, in closed form, for a classical two-particle system. The corresponding Schrödinger equation, obtained by the Moyal quantization procedure, is solved analytically. Its solutions exhibit two different confinement mechanisms — dependent on the sign of the coupling λ to the nonstandard gravitational fields. For λ >0 confinement is due to a rising potential, whereas for λ<0 it is due to the dynamical (geometric) bag formation. Numerical results for the corresponding energy spectra are given. For a particular relation between two coupling constants, the model fits into the scheme of supersymmetrical quantum mechanics.

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38

Shlyakhin, D. A., and M. A. Kalmova. "Related dynamic axisymmetric thermoelectroelasticity problem for a long hollow piezoceramic cylinder." Advanced Engineering Research 22, no. 2 (July 9, 2022): 81–90. http://dx.doi.org/10.23947/2687-1653-2022-22-2-81-90.

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Introduction. The article studies the problem of investigation of coupled nonstationary thermoelectroelastic fields in piezoceramic structures. The main approaches related to the construction of a general solution to the initial non-selfadjoint equations describing the process under consideration are briefly outlined. The work aims at constructing a new closed solution to the axisymmetric thermoelectroelasticity problem for a long piezoceramic cylinder.Materials and Methods. A long hollow cylinder whose electrodated surfaces were connected to a measuring device with large input resistance was considered. On the cylindrical surfaces of the plate, a time-varying temperature was given. The hyperbolic theory of Lord–Shulman thermo-electro-elasticity was used. The closed solution is constructed using a generalized method of finite integral transformations.Results. The developed calculation algorithm makes it possible to determine the stress–strain state of the cylinder, its temperature, and electric fields. In addition, it becomes possible to investigate the coupling of fields in a piezoceramic cylinder, as well as to analyze the effect of relaxation of the heat flow on the fields under consideration.Discussion and Conclusion. The use of assumptions about the equality of the components of the temperature stress tensor and the absence of temperature effect on the electric field allowed us to formulate a self-adjoint initial system of equations and construct a closed solution.

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39

HYTTINEN, TAPANI, OLIVIER LESSMANN, and SAHARON SHELAH. "INTERPRETING GROUPS AND FIELDS IN SOME NONELEMENTARY CLASSES." Journal of Mathematical Logic 05, no. 01 (June 2005): 1–47. http://dx.doi.org/10.1142/s0219061305000390.

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This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem: Theorem. Let [Formula: see text] be a large homogeneous model of a stable diagram D. Let p, q ∈ SD(A), where p is quasiminimal and q unbounded. Let [Formula: see text] and [Formula: see text]. Suppose that there exists an integer n < ω such that [Formula: see text] for any independent a1, …, an ∈ P and finite subset C ⊆ Q, but [Formula: see text] for some independent a1, …, an, an+1 ∈ P and some finite subset C ⊆ Q. Then [Formula: see text] interprets a group G which acts on the geometry P′ obtained from P. Furthermore, either [Formula: see text] interprets a non-classical group, or n = 1,2,3 and •If n = 1 then G is abelian and acts regularly on P′. •If n = 2 the action of G on P′ is isomorphic to the affine action of K ⋊ K* on the algebraically closed field K. •If n = 3 the action of G on P′ is isomorphic to the action of PGL2(K) on the projective line ℙ1(K) of the algebraically closed field K. We prove a similar result for excellent classes.

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40

Vidaux, Xavier. "Multiplication complexe et équivalence élémentaire dans le langage des corps (Complex multiplication and elementary equivalence in the language of fields)." Journal of Symbolic Logic 67, no. 2 (June 2002): 635–48. http://dx.doi.org/10.2178/jsl/1190150102.

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AbstractLet K and K′ be two elliptic fields with complex multiplication over an algebraically closed field k of characteristic 0. non k-isomorphic, and let C and C′ be two curves with respectively K and K′ as function fields. We prove that if the endomorphism rings of the curves are not isomorphic then K and K′ are not elementarily equivalent in the language of fields expanded with a constant symbol (the modular invariant). This theorem is an analogue of a theorem from David A. Pierce in the language of k-algebras.

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41

SETARE, M. R., and ALBERTO ROZAS-FERNÁNDEZ. "INTERACTING NON-MINIMALLY COUPLED CANONICAL, PHANTOM AND QUINTOM MODELS OF HOLOGRAPHIC DARK ENERGY IN NON-FLAT UNIVERSE." International Journal of Modern Physics D 19, no. 12 (October 2010): 1987–2002. http://dx.doi.org/10.1142/s0218271810018141.

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Motivated by our recent work,72 we generalize this work to the interacting non-flat case. Therefore in this paper we deal with canonical, phantom and quintom models, with various fields that are non-minimally coupled to gravity, within the framework of interacting holographic dark energy. We employ the holographic model of interacting dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named L.

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42

Nesin, Ali. "On bad groups, bad fields, and pseudoplanes." Journal of Symbolic Logic 56, no. 3 (September 1991): 915–31. http://dx.doi.org/10.2307/2275061.

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Cherlin introduced the concept of bad groups (of finite Morley rank) in [Ch1]. The existence of such groups is an open question. If they exist, they will contradict the Cherlin-Zil'ber conjecture that states that an infinite simple group of finite Morley rank is a Chevalley group over an algebraically closed field. In this paper, we prove that bad groups of finite Morley rank 3 act on a natural geometry Γ (namely on a special pseudoplane; see Corollary 20) sharply flag-transitively.We show that Γ is not very far from being a projective plane and when it is so rk(Γ) = 2 and Γ is not Desarguesian (Theorem 2). Baldwin [Ba] recently discovered non-Desarguesian projective planes of Morley rank 2. This discovery, together with this paper, makes the existence of bad groups (also of bad fields) more plausible. A bad field is a pair (K, A) of finite Morley rank, where K is an algebraically closed field, A <≠K* and A is infinite. There existence is also unknown.In this paper, we define the concept of a sharp-field as a pair (K, A), where K is a field, A < K*and1. K = A − A,2. If a + b − 1 ∈ A, a ∈ A, b ∈ A, then either a = 1 or b = 1.If K is finite this is equivalent to 1 and2.′ ∣K∣ = ∣A∣2 ∣A∣ + 1.Finite sharp-fields are special cases of difference sets [De]

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43

Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.

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44

Ludkovsky, S. V., and B. Diarra. "Profinite and finite groups associated with loop and diffeomorphism groups of non-Archimedean manifolds." International Journal of Mathematics and Mathematical Sciences 2003, no. 42 (2003): 2673–88. http://dx.doi.org/10.1155/s0161171203011499.

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We investigatep-adic completions of clopen (i.e., closed and open at the same time) subgroupsWof loop groups and diffeomorphism groupsGof compact manifolds over non-Archimedean fields. We outline two different compactifications of loop groups and one compactification of diffeomorphism groups, describe associated finite groups in projective limits, and discuss relations with the representation theory.

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Samal, M. K., P. Seshu, U. von Wagner, P. Hagedorn, B. K. Dutta, and H. S. Kushwaha. "A mathematical model in three-dimensional piezoelectric continuum to predict non-linear responses of piezoceramic materials." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 11 (November 1, 2008): 2251–68. http://dx.doi.org/10.1243/09544062jmes1002.

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It has been experimentally observed that the piezoceramic materials exhibit different types of non-linearities under different combinations of electrical and mechanical fields. When excited near resonance in the presence of weak electric fields, they exhibit typical non-linearities similar to a Duffing oscillator such as jump phenomena and the presence of superharmonics in the response spectra. In this work, these non-linearities have been modelled for a generalized three-dimensional piezoelectric continuum using higher-order quadratic and cubic terms in the electric enthalpy density function and the virtual work. The identification of the parameters of the model requires a closed form solution for non-linear response of a simplified geometry. A simple proportional damping formulation has been used in the model. Experiments have been conducted on rectangular and cylindrical geometries of piezoceramic PIC 181 at different magnitudes of applied electric fields and results have been compared with those of simulation.

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DARIESCU, MARINA-AURA, and CIPRIAN DARIESCU. "SCALAR AND ELECTROMAGNETIC CONFIGURATIONS IN k = 1 FRIEDMANN–ROBERTSON–WALKER UNIVERSES." International Journal of Modern Physics A 20, no. 11 (April 30, 2005): 2510–14. http://dx.doi.org/10.1142/s0217751x05024857.

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The present work focuses on the scalar and electromagnetic fields in a spatially closed FRW Universe with incoherent dust. First, as the complex scalar field is under consideration, we derive the general solutions of the Gordon equation, in terms of the positive-frequency-like parity modes, and the corresponding propagator. Secondly, we turn to the source-free Maxwell equations in order to find a (1 + 4)-parametric class of closed form solutions representing a non-propagating fundamental electric field and a burst of electromagnetic radiation.

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BYTSENKO, ANDREI, KLAUS KIRSTEN, and SERGEI ODINTSOV. "SELF-INTERACTING SCALAR FIELDS ON SPACE-TIME WITH COMPACT HYPERBOLIC SPATIAL PART." Modern Physics Letters A 08, no. 21 (July 10, 1993): 2011–21. http://dx.doi.org/10.1142/s0217732393001720.

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We calculate the one-loop effective potential of a self-interacting scalar field on the space-time of the form ℝ2×H2/Γ. The Selberg trace formula associated with a co-compact discrete group Γ in PSL(2, ℝ) (hyperbolic and elliptic elements only) is used. The closed form for the one-loop unrenormalized and renormalized effective potentials is given. The influence of non-trivial topology on curvature induced phase transitions is also discussed.

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Herlemann, H., and M. Koch. "Measurement of the transient shielding effectiveness of enclosures using UWB pulses inside an open TEM waveguide." Advances in Radio Science 5 (June 12, 2007): 75–79. http://dx.doi.org/10.5194/ars-5-75-2007.

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Abstract. Recently, new definitions of shielding effectiveness (SE) for high-frequency and transient electromagnetic fields were introduced by Klinkenbusch (2005). Numerical results were shown for closed as well as for non closed cylindrical shields. In the present work, a measurement procedure is introduced using ultra wideband (UWB) electromagnetic field pulses. The procedure provides a quick way to determine the transient shielding effectiveness of an enclosure without performing time consuming frequency domain measurements. For demonstration, a cylindrical enclosure made of conductive textile is examined. The field pulses are generated inside an open TEM-waveguide. From the measurement of the transient electric and magnetic fields with and without the shield in place, the electric and magnetic shielding effectiveness of the shielding material as well as the transient shielding effectiveness of the enclosure are derived.

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Van Goethem, Nicolas. "Incompatibility-governed singularities in linear elasticity with dislocations." Mathematics and Mechanics of Solids 22, no. 8 (May 19, 2016): 1688–95. http://dx.doi.org/10.1177/1081286516642817.

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The purpose of this paper is to prove the relation [Formula: see text] relating the elastic strain [Formula: see text] and the contortion tensor [Formula: see text], related to the density tensor of mesoscopic dislocations. Here, the dislocations are given by a finite family of closed Lipschitz curves in [Formula: see text]. Moreover the fields are singular at the dislocations, and, in particular, the strain is non square integrable. Moreover, the displacement fields show a constant jump around each isolated dislocation loop. This relation is called after E. Kröner who first derived the same formula for smooth fields at the macroscale.

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Lin, W., C. H. Kuo, and L. M. Keer. "Analysis of a Transversely Isotropic Half Space Under Normal and Tangential Loadings." Journal of Tribology 113, no. 2 (April 1, 1991): 335–38. http://dx.doi.org/10.1115/1.2920625.

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This paper analyzes the response of a transversely isotropic half space subjected to various distributions of normal and tangential contact stresses on its surface. Both the interior displacement and stress fields are given in closed form. Among them, rectangular patch solutions are constructed for application to solutions to non-Hertzian contact problems.

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