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Journal articles on the topic 'Equivalence theorem'

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Published: 4 June 2021
Last updated: 8 February 2022

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1

Wulzer, Andrea. "An Equivalent Gauge and the Equivalence Theorem." Nuclear Physics B 885 (August 2014): 97–126. http://dx.doi.org/10.1016/j.nuclphysb.2014.05.021.

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2

Veltman, H. "The equivalence theorem." Physical Review D 41, no. 7 (April 1, 1990): 2294–311. http://dx.doi.org/10.1103/physrevd.41.2294.

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3

Bagger, Jonathan, and Carl Schmidt. "Equivalence theorem redux." Physical Review D 41, no. 1 (January 1, 1990): 264–70. http://dx.doi.org/10.1103/physrevd.41.264.

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4

Fu, Yaoshun, and Wensheng Yu. "Formalization of the Equivalence among Completeness Theorems of Real Number in Coq." Mathematics 9, no. 1 (December 25, 2020): 38. http://dx.doi.org/10.3390/math9010038.

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The formalization of mathematics based on theorem prover becomes increasingly important in mathematics and computer science, and, particularly, formalizing fundamental mathematical theories becomes especially essential. In this paper, we describe the formalization in Coq of eight very representative completeness theorems of real numbers. These theorems include the Dedekind fundamental theorem, Supremum theorem, Monotone convergence theorem, Nested interval theorem, Finite cover theorem, Accumulation point theorem, Sequential compactness theorem, and Cauchy completeness theorem. We formalize the real number theory strictly following Landau’s Foundations of Analysis where the Dedekind fundamental theorem can be proved. We extend this system and complete the related notions and properties for finiteness and sequence. We prove these theorems in turn from Dedekind fundamental theorem, and finally prove the Dedekind fundamental theorem by the Cauchy completeness theorem. The full details of formal proof are checked by the proof assistant Coq, which embodies the characteristics of reliability and interactivity. This work can lay the foundation for many applications, especially in calculus and topology.
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5

Coskey, Samuel. "Ioana's Superrigidity Theorem and Orbit Equivalence Relations." ISRN Algebra 2013 (December 30, 2013): 1–8. http://dx.doi.org/10.1155/2013/387540.

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We give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups and its applications to ergodic theory and set theory in this expository paper. In addition to a statement and proof of Ioana's theorem, this paper features the following: (i) an introduction to rigidity, including a crash course in Borel cocycles and a summary of some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbit equivalence) and set theory (Borel reducibility); and (iii) a streamlined proof of Simon Thomas's theorem that the classification of torsion-free abelian groups of finite rank is intractable.
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6

James, Daniel F. V., and Emil Wolf. "A spectral equivalence theorem." Optics Communications 72, no. 1-2 (July 1989): 1–6. http://dx.doi.org/10.1016/0030-4018(89)90246-0.

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7

Righetti, Mattia. "On Bohr's equivalence theorem." Journal of Mathematical Analysis and Applications 445, no. 1 (January 2017): 650–54. http://dx.doi.org/10.1016/j.jmaa.2016.08.028.

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8

Lin, F., and Y. Chen. "Discovering Classes of Strongly Equivalent Logic Programs." Journal of Artificial Intelligence Research 28 (April 10, 2007): 431–51. http://dx.doi.org/10.1613/jair.2131.

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In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules.
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9

Pakes, Anthony G. "Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries." Journal of Applied Probability 44, no. 02 (June 2007): 295–305. http://dx.doi.org/10.1017/s0021900200002977.

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Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.
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10

Pakes, Anthony G. "Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries." Journal of Applied Probability 44, no. 02 (June 2007): 295–305. http://dx.doi.org/10.1017/s0021900200117838.

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Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.
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11

Pakes, Anthony G. "Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries." Journal of Applied Probability 44, no. 2 (June 2007): 295–305. http://dx.doi.org/10.1239/jap/1183667402.

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Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.
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12

Torma, Tibor. "Equivalence theorem and infrared divergences." Physical Review D 54, no. 3 (August 1, 1996): 2168–74. http://dx.doi.org/10.1103/physrevd.54.2168.

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13

Noguchi, Mitsunori. "A fuzzy core equivalence theorem." Journal of Mathematical Economics 34, no. 1 (August 2000): 143–58. http://dx.doi.org/10.1016/s0304-4068(99)00036-1.

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14

Booysen, R. "An illustrative equivalence theorem example." IEEE Antennas and Propagation Magazine 42, no. 6 (2000): 132–35. http://dx.doi.org/10.1109/74.894188.

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15

Li, Jun-Li, and Cong-Feng Qiao. "Equivalence theorem of uncertainty relations." Journal of Physics A: Mathematical and Theoretical 50, no. 3 (December 9, 2016): 03LT01. http://dx.doi.org/10.1088/1751-8121/50/3/03lt01.

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16

Qin, Cheng Zhong. "An inner core equivalence theorem." Economic Theory 4, no. 2 (March 1994): 311–17. http://dx.doi.org/10.1007/bf01221208.

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17

Xiong, Siyang, and Charles Zhoucheng Zheng. "Core equivalence theorem with production." Journal of Economic Theory 137, no. 1 (November 2007): 246–70. http://dx.doi.org/10.1016/j.jet.2007.01.009.

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18

Fieldsteel, Adam, Andrés Del Junco, and Daniel J. Rudolph. "α-equivalence: a refinement of Kakutani equivalence." Ergodic Theory and Dynamical Systems 14, no. 1 (March 1994): 69–102. http://dx.doi.org/10.1017/s0143385700007732.

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AbstractFor a fixed irrational α > 0 we say that probability measure-preserving transformationsSandTare α-equivalent if they can be realized as cross-sections in a common flow such that the return time functions on the cross-sections both take values in {1, 1 +α} and have equal integrals. Similarly we call two flowsFandGα-equivalent ifFhas a cross-sectionSandGhas a cross-sectionTisomorphic toSand again both the return time functions take values in {1, 1 + α} and have equal integrals. The integer kα(S), equal to the least positivesuchsuch that exp2πikα-1belongs to the point spectrum ofS, is an invariant of α-equivalence.We obtain a characterization of a-equivalence as a particular type of restricted orbit equivalence and use this to prove that within the class of loosely Bernoulli mapska(S) together with the entropyh(S) are complete invariants of α-equivalence. There is a corresponding a-equivalence theorem for flows which has as a consequence, for example, that up to an obvious entropy restriction, any weakly mixing cross-section of a loosely Bernoulli flow can also be realized as a cross-section with a {1,1 + α}-valued return time function.For the proof of the α-equivalence theorem we develop a relative Kakutani equivalence theorem for compact group extensions which is of interest in its own right. Finally, an example of Fieldsteel and Rudolph is used to show that in generalkα(S) is not a complete invariant of α-equivalence within a given even Kakutani equivalence class.
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19

Cvetkovic, Marija. "On the equivalence between Perov fixed point theorem and Banach contraction principle." Filomat 31, no. 11 (2017): 3137–46. http://dx.doi.org/10.2298/fil1711137c.

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There are many results in the fixed point theory that were presented as generalizations of Banach theorem and other well-known fixed point theorems, but later proved equivalent to these results. In this article we prove that Perov?s existence result follows from Banach theorem by using renormization of normal cone and obtained metric. The observed estimations of approximate point given by Perov, could not be obtained from consequences of Banach theorem on metric spaces.
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20

Jureczko, Joanna. "Strong sequences and partition relations." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (December 1, 2017): 51–59. http://dx.doi.org/10.1515/aupcsm-2017-0004.

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AbstractThe first result in partition relations topic belongs to Ramsey (1930). Since that this topic has been still explored. Probably the most famous partition theorem is Erdös-Rado theorem (1956). On the other hand in 60’s of the last century Efimov introduced strong sequences method, which was used for proving some famous theorems in dyadic spaces. The aim of this paper is to generalize theorem on strong sequences and to show that it is equivalent to generalized version of well-known Erdös-Rado theorem. It will be also shown that this equivalence holds for singulars. Some applications and conclusions will be presented too.
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21

Hjorth, Greg. "A dichotomy theorem for turbulence." Journal of Symbolic Logic 67, no. 4 (December 2002): 1520–40. http://dx.doi.org/10.2178/jsl/1190150297.

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In this note we show:Theorem 1.1. Let G be a Polish group and X a Polish G-space with the induced orbit equivalence relation EG Borel as a subset of X × X. Then exactly one of the following:(I) There is a countable languageℒand a Borel functionsuch that for all x1, x2 ∈ Xor(II) there is a turbulent Polish G-space Y and a continuous G-embeddingThere are various bows and ribbons which can be woven into these statements. We can strengthen (I) by asking that θ also admit a Borel orbit inverse, that is to say some Borel functionfor some Borel set B ⊂ Mod(ℒ), such that for all x ∈ Xand then after having passed to this strengthened version of (I) we still obtain the exact same dichotomy theorem, and hence the conclusion that the two competing versions of (I) are equivalent. Similarly (II) can be relaxed to just asking that τ be a Borel G-embedding, or even simply a Borel reduction of the relevant orbit equivalence relations. It is in fact a consequence of 1.1 that all the plausible weakenings and strengthenings of (I) and (II) are respectively equivalent to one another.I will not closely examine these possible variations here. The equivalences alluded to above follow from our main theorem and the results of [3]. That monograph had previously shown that (I) and (II) are incompatible, and proved a barbaric forerunner of 1.1, and gone on to conjecture the dichotomy result above.
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22

GIORDANO, THIERRY, HIROKI MATUI, IAN F. PUTNAM, and CHRISTIAN F. SKAU. "The absorption theorem for affable equivalence relations." Ergodic Theory and Dynamical Systems 28, no. 5 (October 2008): 1509–31. http://dx.doi.org/10.1017/s0143385707000946.

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AbstractWe prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being ‘small’ in the sense that we modify R on a thin closed subset Y of X. We show that the resulting extended equivalence relation S is orbit equivalent to the original R, and so, in particular, S is affable. Even in the simplest case—when Y is a finite set—this result is highly non-trivial. The result itself—called the absorption theorem—is a powerful and crucial tool for the study of the orbit structure of minimal ℤn-actions on the Cantor set, see Remark 4.8. The absorption theorem is a significant generalization of the main theorem proved in Giordano et al [Affable equivalence relations and orbit structure of Cantor dynamical systems. Ergod. Th. & Dynam. Sys.24 (2004), 441–475] . However, we shall need a few key results from the above paper in order to prove the absorption theorem.
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23

Dobado, A., J. R. Peláez, and M. T. Urdiales. "Applicability constraints of the equivalence theorem." Physical Review D 56, no. 11 (December 1, 1997): 7133–42. http://dx.doi.org/10.1103/physrevd.56.7133.

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24

DUTTA, B., and S. NANDI. "TEST OF GOLDSTONE BOSON EQUIVALENCE THEOREM." Modern Physics Letters A 09, no. 11 (April 10, 1994): 1025–32. http://dx.doi.org/10.1142/s021773239400085x.

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We study the convergence (with energy) of the exact longitudinal gauge boson scattering amplitude to that given by the equivalence theorem. For low Higgs boson masses, this convergence is rather slow, and can have significant effect at the SSC energies. We find that in addition to [Formula: see text] terms, the two amplitudes differ by terms of [Formula: see text]. We incorporate the presence of such terms in the general proof of the equivalence theorem.
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25

Tyutin, I. V. "Once again on the equivalence theorem." Physics of Atomic Nuclei 65, no. 1 (January 2002): 194–202. http://dx.doi.org/10.1134/1.1446571.

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26

Leindler, László. "An addendum of an equivalence theorem." Mathematical Inequalities & Applications, no. 1 (2007): 49–55. http://dx.doi.org/10.7153/mia-10-06.

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27

Pal, Palash B. "Equivalence theorem and dynamical symmetry breaking." Physics Letters B 321, no. 3 (January 1994): 229–33. http://dx.doi.org/10.1016/0370-2693(94)90469-3.

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28

Dobado, Antonio, and JoséRamón Pelaez. "The equivalence theorem for chiral lagrangians." Physics Letters B 329, no. 4 (June 1994): 469–78. http://dx.doi.org/10.1016/0370-2693(94)91092-8.

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29

Donoghue, John F., and Jusak Tandean. "The equivalence theorem and global anomalies." Physics Letters B 301, no. 4 (March 1993): 372–75. http://dx.doi.org/10.1016/0370-2693(93)91165-j.

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30

Kilgore, William B. "Anomalous condensates and the equivalence theorem." Physics Letters B 323, no. 2 (March 1994): 161–68. http://dx.doi.org/10.1016/0370-2693(94)90285-2.

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31

Slavnov, A. A. "Equivalence theorem for spectrum changing transformations." Physics Letters B 258, no. 3-4 (April 1991): 391–94. http://dx.doi.org/10.1016/0370-2693(91)91105-5.

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32

Grosse-Knetter, Carsten, and Ingolf Kuss. "The equivalence theorem and effective Lagrangians." Zeitschrift f�r Physik C Particles and Fields 66, no. 1-2 (March 1995): 95–105. http://dx.doi.org/10.1007/bf01496584.

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33

Lawson, M. V. "An equivalence theorem for inverse semigroups." Semigroup Forum 47, no. 1 (December 1993): 7–14. http://dx.doi.org/10.1007/bf02573736.

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34

Sepulcre, J. M., and T. Vidal. "A Generalization of Bohr’s Equivalence Theorem." Complex Analysis and Operator Theory 13, no. 4 (February 19, 2019): 1975–88. http://dx.doi.org/10.1007/s11785-019-00900-7.

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35

Naraynan, H. "On the equivalence of Minty's painting theorem and Tellegen's theorem." International Journal of Circuit Theory and Applications 13, no. 4 (October 1985): 353–57. http://dx.doi.org/10.1002/cta.4490130407.

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36

Berkani, M. "On the Equivalence of Weyl Theorem and Generalized Weyl Theorem." Acta Mathematica Sinica, English Series 23, no. 1 (March 30, 2006): 103–10. http://dx.doi.org/10.1007/s10114-005-0720-4.

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37

Simpson, Stephen G. "Ordinal numbers and the Hilbert basis theorem." Journal of Symbolic Logic 53, no. 3 (September 1988): 961–74. http://dx.doi.org/10.2307/2274585.

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In [5] and [21] we studied countable algebra in the context of “reverse mathematics”. We considered set existence axioms formulated in the language of second order arithmetic. We showed that many well-known theorems about countable fields, countable rings, countable abelian groups, etc. are equivalent to the respective set existence axioms which are needed to prove them.One classical algebraic theorem which we did not consider in [5] and [21] is the Hilbert basis theorem. Let K be a field. For any natural number m, let K[x1,…,xm] be the ring of polynomials over K in m commuting indeterminates x1,…,xm. The Hilbert basis theorem asserts that for all K and m, every ideal in the ring K[x1,…,xm] is finitely generated. This theorem is of fundamental importance for invariant theory and for algebraic geometry. There is also a generalization, the Robson basis theorem [11], which makes a similar but more restrictive assertion about the ring K〈x1,…,xm〉 of polynomials over K in mnoncommuting indeterminates.In this paper we study a certain formal version of the Hilbert basis theorem within the language of second order arithmetic. Our main result is that, for any or all countable fields K, our version of the Hilbert basis theorem is equivalent to the assertion that the ordinal number ωω is well ordered. (The equivalence is provable in the weak base theory RCA0.) Thus the ordinal number ωω is a measure of the “intrinsic logical strength” of the Hilbert basis theorem. Such a measure is of interest in reference to the historic controversy surrounding the Hilbert basis theorem's apparent lack of constructive or computational content.
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38

Raeburn, Iain, and Dana P. Williams. "Dixmier-Douady Classes of Dynamical Systems and Crossed Products." Canadian Journal of Mathematics 45, no. 5 (October 1, 1993): 1032–66. http://dx.doi.org/10.4153/cjm-1993-057-8.

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AbstractContinuous-trace C*-algebras A with spectrum T can be characterized as those algebras which are locally Monta equivalent to C0(T). The Dixmier-Douady class δ(A) is an element of the Čech cohomology group Ȟ3(T, ℤ) and is the obstruction to building a global equivalence from the local equivalences. Here we shall be concerned with systems (A, G, α) which are locally Monta equivalent to their spectral system (C0(T),G, τ), in which G acts on the spectrum T of A via the action induced by α. Such systems include locally unitary actions as well as N-principal systems. Our new Dixmier-Douady class δ (A, G, α) will be the obstruction to piecing the local equivalences together to form a Monta equivalence of (A, G, α) with its spectral system. Our first main theorem is that two systems (A, G, α) and (B, G, β) are Monta equivalent if and only if δ (A, G, α) = δ (B, G, β). In our second main theorem, we give a detailed formula for δ (A ⋊α G) when (A, G, α) is N-principal.
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39

Du, Wei-Shih. "The Existence of Cone Critical Point and Common Fixed Point with Applications." Journal of Applied Mathematics 2011 (2011): 1–22. http://dx.doi.org/10.1155/2011/985797.

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We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.
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40

Du, Wei-Shih. "Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems." Abstract and Applied Analysis 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/247236.

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By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium problem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem is also given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed point theorem, and maximal element theorem.
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41

Nguyen, Dinh, and Mo Hong Tran. "An approximate Hahn-Banach-Lagrange theorem." Science and Technology Development Journal 19, no. 4 (December 31, 2016): 169–77. http://dx.doi.org/10.32508/stdj.v19i4.639.

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In this paper, we proved a new extended version of the Hahn-Banach-Lagrange theorem that is valid in the absence of a qualification condition and is called an approximate Hahn-Banach-Lagrange theorem. This result, in special cases, gives rise to approximate sandwich and approximate Hahn-Banach theorems. These results extend the Hahn-Banach-Lagrange theorem, the sandwich theorem in [18], and the celebrated Hahn-Banach theorem. The mentioned results extend the original ones into two features: Firstly, they extend the original versions to the case with extended sublinear functions (i.e., the sublinear functions that possibly possess extended real values). Secondly, they are topological versions which held without any qualification condition. Next, we showed that our approximate Hahn-Banach-Lagrange theorem was actually equivalent to the asymptotic Farkas-type results that were established recently [10]. This result, together with the results [5, 16], give us a general picture on the equivalence of the Farkas lemma and the Hahn-Banach theorem, from the original version to their corresponding extensions and in either non-asymptotic or asymptotic forms.
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42

KRUPIŃSKI, KRZYSZTOF, and TOMASZ RZEPECKI. "SMOOTHNESS OF BOUNDED INVARIANT EQUIVALENCE RELATIONS." Journal of Symbolic Logic 81, no. 1 (March 2016): 326–56. http://dx.doi.org/10.1017/jsl.2015.44.

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AbstractWe generalise the main theorems from the paper “The Borel cardinality of Lascar strong types” by I. Kaplan, B. Miller and P. Simon to a wider class of bounded invariant equivalence relations. We apply them to describe relationships between fundamental properties of bounded invariant equivalence relations (such as smoothness or type-definability) which also requires finding a series of counterexamples. Finally, we apply the generalisation mentioned above to prove a conjecture from a paper by the first author and J. Gismatullin, showing that the key technical assumption of the main theorem (concerning connected components in definable group extensions) from that paper is not only sufficient but also necessary to obtain the conclusion.
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43

MILLER, BENJAMIN. "INCOMPARABLE TREEABLE EQUIVALENCE RELATIONS." Journal of Mathematical Logic 12, no. 01 (June 2012): 1250004. http://dx.doi.org/10.1142/s0219061312500043.

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We establish Hjorth's theorem that there is a family of continuum-many pairwise strongly incomparable free actions of free groups, and therefore a family of continuum-many pairwise incomparable treeable equivalence relations.
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44

Tanaka, Yasuhito. "Equivalence of the HEX game theorem and the Arrow impossibility theorem." Applied Mathematics and Computation 186, no. 1 (March 2007): 509–15. http://dx.doi.org/10.1016/j.amc.2006.07.115.

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45

Hasfura-Buenaga, J. Roberto. "The equivalence theorem for ℤd-actions of positive entropy." Ergodic Theory and Dynamical Systems 12, no. 4 (December 1992): 725–41. http://dx.doi.org/10.1017/s0143385700007069.

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AbstractFirst, the class of id-finitely fixed actions of ℤdon a Lebesgue space is defined. Then, it is demonstrated that this property is stable under id-Kakutani equivalence and that, conversely, any two id-finitely fixed ℤd-actions of the same (finite) positive entropy are id-Kakutani equivalent. By id-Kakutani equivalence we mean that element in A. del Junco and D. Rudolph's family of relations on ℤd-actions corresponding to the identityd×dmatrix.
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46

Shpilev, P. V. "Equivalence theorem for singular L-optimal designs." Vestnik St. Petersburg University: Mathematics 48, no. 1 (January 2015): 29–34. http://dx.doi.org/10.3103/s1063454115010094.

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47

Hinz, Juri. "A revenue-equivalence theorem for electricity auctions." Journal of Applied Probability 41, no. 02 (June 2004): 299–312. http://dx.doi.org/10.1017/s0021900200014315.

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The purpose of this paper is to analyse the real-time trading of electricity. We address a model for an auction-like trading which captures key features of real-world electricity markets. Our main result establishes that, under certain conditions, the expected total payment for electricity is independent of the particular auction type. This result is analogous to the revenue-equivalence theorem known for classical auctions and could contribute to an improved understanding of different electricity market designs and their comparison.
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48

Bonneau, Guy, and François Delduc. "Non-linear renormalisation and the equivalence theorem." Nuclear Physics B 266, no. 3-4 (March 1986): 536–46. http://dx.doi.org/10.1016/0550-3213(86)90184-7.

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49

Booysen, A. J. "A physical interpretation of the equivalence theorem." IEEE Transactions on Antennas and Propagation 48, no. 8 (2000): 1260–62. http://dx.doi.org/10.1109/8.884497.

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50

Boulier, François, François Lemaire, Adrien Poteaux, and Marc Moreno Maza. "An equivalence theorem for regular differential chains." Journal of Symbolic Computation 93 (July 2019): 34–55. http://dx.doi.org/10.1016/j.jsc.2018.04.011.

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