Relevant bibliographies by topics / Theorems

Academic literature on the topic 'Theorems'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Theorems"

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KIKUCHI, MAKOTO, and TAISHI KURAHASHI. "GENERALIZATIONS OF GÖDEL’S INCOMPLETENESS THEOREMS FOR ∑n-DEFINABLE THEORIES OF ARITHMETIC." Review of Symbolic Logic 10, no. 4 (November 7, 2017): 603–16. http://dx.doi.org/10.1017/s1755020317000235.

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AbstractIt is well known that Gödel’s incompleteness theorems hold for ∑1-definable theories containing Peano arithmetic. We generalize Gödel’s incompleteness theorems for arithmetically definable theories. First, we prove that every ∑n+1-definable ∑n-sound theory is incomplete. Secondly, we generalize and improve Jeroslow and Hájek’s results. That is, we prove that every consistent theory having ∏n+1 set of theorems has a true but unprovable ∏n sentence. Lastly, we prove that no ∑n+1-definable ∑n -sound theory can prove its own ∑n-soundness. These three results are generalizations of Rosser’s improvement of the first incompleteness theorem, Gödel’s first incompleteness theorem, and the second incompleteness theorem, respectively.
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LIEBSCHER, VOLKMAR. "NOTE ON ENTANGLED ERGODIC THEOREMS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 02 (June 1999): 301–4. http://dx.doi.org/10.1142/s0219025799000175.

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We prove the entangled ergodic theorem, a notion recently proposed by Accardi, Hashimoto and Obata in connection with central limit theorems1 provided a multidimensional noncommutative analogue of the spectral theorem is valid. This shows at least the possible structure of limit states in such central limit theorems.
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Maran, A. K. "Maran's theorem (New theorem) on Right-angled triangle." Mapana - Journal of Sciences 3, no. 1 (October 6, 2004): 7–10. http://dx.doi.org/10.12723/mjs.5.2.

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In Geometric, right-angled triangle is One Of the two—dimensional plane having three sides With one Of its angle is 9C and whk-h is important to solve problems related to Geometry and sometimes in Other subiect os well. Some fundamental concept 'theorems Of triangles are required to solve such problems and such theorems cre Pythagoras theorern' Pythagoras theorern (ii0 Appollonius theorem Euclids theorem' and (v) Eucli&s 20 theorem (Altitude theorem).3 I n addition to these, the author attempted to develop a new theorem related to right-angled triangle (Maran's theorem of right-angled triangle). The new theorem have been discussed and proved With relevant examples.
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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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Yi, Piljin. "Index Theorems for Gauge Theories." Journal of the Korean Physical Society 73, no. 4 (August 2018): 436–48. http://dx.doi.org/10.3938/jkps.73.436.

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Weinberg, Steven. "Nonrenormalization Theorems in Nonrenormalizable Theories." Physical Review Letters 80, no. 17 (April 27, 1998): 3702–5. http://dx.doi.org/10.1103/physrevlett.80.3702.

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Graczyk, P., and C. R. E. Raja. "Classical theorems of probability on Gelfand pairs—Khinchin’s theorems and Cramér’s theorem." Israel Journal of Mathematics 132, no. 1 (December 2002): 61–107. http://dx.doi.org/10.1007/bf02784506.

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Greene, R. E. "Homotopy finiteness theorems and Helly’s theorem." Journal of Geometric Analysis 4, no. 3 (September 1994): 317–25. http://dx.doi.org/10.1007/bf02921584.

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Chen, Han. "On the Proof of Sylow’s Theorems in Group Theory." Highlights in Science, Engineering and Technology 47 (May 11, 2023): 63–66. http://dx.doi.org/10.54097/hset.v47i.8165.

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The Sylow’s theorems are significant principles for analysis of special subgroups of a finite group, and they are significant theories in finite group research area. It is firmly established that every group owns more than one Sylow group pertaining to every prime factor of . The purpose of this article is to summarize and generalize the existing research progress of Sylow’s theorems. A summary of them will help more people comprehend and apply group theory to analyze problems. In this paper, the basic information of three distinct Sylow’s theorems are introduced, including their definitions and detailed proof procedures. After that, some examples and application that are related to the Sylow’s theorems are shown one by one. After that, the relationship between the Sylow’s theorems to that of the orbit-stabilizer theorem is discussed. This work will potentially stimulate more research efforts on the basis theorems in group theory.
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KO, HWEI-MEI, and KOK-KEONG TAN. "COINCIDENCE THEOREMS AND MATCHING THEOREMS." Tamkang Journal of Mathematics 23, no. 4 (December 1, 1992): 297–309. http://dx.doi.org/10.5556/j.tkjm.23.1992.4553.

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Two coincidence theorems of Ky Fan are first slightly gen­eralized. As applications, new matching theorems are obtained, one of which has several equivalent forms, including the classical Knaster­ Kuratowski-Mazurkiewicz theorem.
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Dissertations / Theses on the topic "Theorems"

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Coloretti, Guglielmo. "On Noether's theorems and gauge theories in hamiltonian formulation." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18723/.

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Nella tesi presente si propone una trattazione esaustiva sui teoremi di Noether, cardine delle più moderne ed avanzate teorie di gauge. In particolare si tenta di fornirne una misura matematica rigorosa senza allontanarsi dalla cruciale intuizione fisica che celano: la ricerca di simmetrie nella natura e la volontà di descrivere le interazioni conosciute con un singolo modello. Più avanti, trovando i caratteri dominanti e l'ispirazione nelle pubblicazioni di Noether, si affrontano i tratti generali della formulazione hamiltoniana delle teorie di gauge, presentando la struttura dell'azione per una particella relativistica, la teoria elettromagnetica e la teoria della relatività generale; si pongono infine alcuni interrogativi sui valori di contorno che emergono dal formalismo adottato. Inoltre, per ottenere un'esposizione più efficace e meno oscura, si accompagna ogni risultato con esempi opportuni.
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Hood, C. "Products and Kunneth theorems in cyclic homology and cohomology theories." Thesis, University of Warwick, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373079.

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Chen, Bin. "Functional limit theorems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ37060.pdf.

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Poutiainen, H. (Hayley). "On Sylow’s theorems." Master's thesis, University of Oulu, 2015. http://urn.fi/URN:NBN:fi:oulu-201512012188.

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Group theory is a mathematical domain where groups and their properties are studied. The evolution of group theory as an area of study is said to be the result of the parallel development of a variety of different studies in mathematics. Sylow’s Theorems were a set of theorems proved around the same time the concept of group theory was being established, in the 1870s. Sylow used permutation groups in his proofs which were then later generalized and shown to hold true for all finite groups. These theorems paved the way for more detailed study of abstract groups and they have had a remarkable impact on the progress of finite group theory. Sylow’s Theorems provide information about the number and nature of the subgroups of a given finite group. The three basic theorems discovered by Sylow are discussed in the paper in detail. Sylow’s Theorems prove the existence of Sylow p-subgroups for any prime p that divides the order of the group. They show that all Sylow p-subgroups are conjugate. And finally they indicate how one can determine the number of Sylow p-subgroups which exist. Due to the power of these theorems in finite group theory they have been proved by a large number of mathematicians in a variety of different ways, as is shown in the final chapter of the paper. The theory necessary to understand the Sylow’s Theorems is covered in the first four chapters of this paper, with Sylow’s Theorems being covered in the final chapter. Lagrange’s Theorem is the first important theorem and is found in Chapter 2. Lagrange’s Theorem links the size of the group and its subgroups. The corollary of Lagrange’s Theorem is not necessarily true and Sylow’s Theorems provided a solution to this particular issue. Cauchy’s Theorem as discussed in Chapter 4, is believed to have been the inspiration for Sylow’s Theorem of existence of the subgroups. Initially Cauchy’s Theorem made use of permutation groups as did Sylow’s Theorem. Cauchy’s Theorem states that if G is a finite group and p is a prime divisor of G then the group contains an element of order p, whilst Sylow’s Theorem generalizes the finding to show that if the group G is divisible by a prime p^n then G contains a subgroup whose order is then ^n. The final section of the paper deals with the consequences that Sylow’s Theorems have in terms of practical application to finite groups. The problem of the corollary to Lagrange’s Theorem and how Sylow’s Theorem provides a solution is also dealt with. The most important references in generating the theory needed for the paper comes from Joseph. J. Rotman: A first course in Abstract Algebra, 2nd ed. (Prentice Hall, Upper Saddle River, 2000) and I. N. Hernstein: Abstract Algebra (Prentice Hall, Upper Saddle River, 1995).
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Davies, Brian E., Graham M. L. Gladwell, Josef Leydold, and Peter F. Stadler. "Discrete Nodal Domain Theorems." Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/976/1/document.pdf.

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Johnson, O. "Entropy and limit theorems." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.605633.

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This thesis uses techniques based on Shannon entropy to prove probabilistic limit theorems. Chapter 1 defines entropy and Fisher information, and reviews previous work. We reformulate the Central Limit Theorem to state that the entropy of sums of independent identically distribution real-value random variables converges to its unique maximum, the normal distribution. This is called convergence in relative entropy, and is proved by Barron. Chapter 2 extends Barron's results to non-identically distributed random variables, extending the Lindeberg-Feller Theorem, under similar conditions. Next, in Chapter 3, we provide a proof for random vectors. In Chapter 4, we discuss convergence to other non-Gaussian stable distributions. Whilst not giving a complete solution to this problem, we provide some suggestions as to how the entropy theoretic method may apply in this case. The next two chapters concern random variables with values on compact groups. Although the situation is different, in that the limit distribution is uniform, again this is a maximum entropy distribution, so some of the same ideas will apply. In Chapter 7 we discuss conditional limit theorems, which relate to the problem in Statistical Physics of 'equivalence of ensembles'. We consider random variables equidistributed on the surface of certain types of manifolds, and show their projections are close to Gibbs densities. Once again, the proof involves convergence in relative entropy, establishing continuity of the projection map with respect to the Kullback-Leibler topology. The bound is sharp and provides a necessary and sufficient condition for convergence in relative entropy. If we consider the manifold as a surface of equal energy for a particular Hamiltonian, this implies that the microcanonical and canonical ensembles are close to one another.
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Rinsma, I. "Existence theorems for floorplans." Thesis, University of Canterbury. Mathematics, 1987. http://hdl.handle.net/10092/8425.

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The existence of floorplans with given areas and adjacencies for the rooms cannot always be guaranteed. Rectangular, isometric and convex floorplans are considered. For each, the areas of the rooms and a graph representing the required internal adjacencies between the rooms is given. This thesis gives existence theorems for a floorplan satisfying these conditions. If the graph is maximal outerplanar, only a convex floorplan can always be guaranteed. Floorplans of each type can be found if the graph is a tree. A branching index is defined for a tree, and used to give the minimum number of vertices of degree 2 in any maximal outerplanar graph, in which the tree can be embedded. If the graph of adjacencies is a tree, and each room in the plan is external, once again only convex floorplans can always be guaranteed. Rectangular floorplans can always be found in some cases, depending on the embedding index of the tree.
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Eriksson, Andreas. "Index Theorems and Supersymmetry." Thesis, Uppsala universitet, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-231033.

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Davies, Brian E., Josef Leydold, and Peter F. Stadler. "Discrete Nodal Domain Theorems." Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/1674/1/document.pdf.

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Preen, James. "Structure theorems for graphs." Thesis, University of Nottingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357965.

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Books on the topic "Theorems"

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Świerczkowski, S. Finite sets and Gödel's incompleteness theorems. Warszawa: Polska Akademia Nauk, Instytut Matematyczny, 2003.

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Gēderu fukanzensei hakken e no michi. Kyōto-shi: Gendai Sūgakusha, 2011.

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Uspenskii, Vladimir Andreevich. Gia to theōrēma mē-plērotētas tou Godel. Athēna: Trochalia, 1998.

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Una guida ai risultati di incompletezza di Kurt Gödel. Pisa: ETS, 2008.

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Uspenskiĭ, V. A. Gödel's incompleteness theorem. Moscow: Mir Publishers, 1987.

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Pianigiani, Duccio. Una guida ai risultati di incompletezza di Kurt Gödel. Pisa: ETS, 2008.

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Sardanashvily, Gennadi. Noether's Theorems. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-171-0.

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Fernández, F. M., and E. A. Castro. Hypervirial Theorems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-93349-3.

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Willem, Michel. Minimax Theorems. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-4146-1.

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Antoine, Brunel, ed. Ergodic theorems. Berlin: W. de Gruyter, 1985.

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Book chapters on the topic "Theorems"

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Louridas, Sotirios E., and Michael Th Rassias. "Theorems." In Problem-Solving and Selected Topics in Euclidean Geometry, 59–78. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7273-5_4.

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Barseghyan, Hakob. "Theorems." In The Laws of Scientific Change, 165–243. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17596-6_5.

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Wasilewska, Anita. "Formal Theories and Gödel Theorems." In Logics for Computer Science, 489–535. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92591-2_11.

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Talagrand, Michel. "Matching Theorems, II: Shor’s Matching Theorem." In Upper and Lower Bounds for Stochastic Processes, 447–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54075-2_14.

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Fernández, F. M., and E. A. Castro. "Hypervirial Theorems and the Variational Theorem." In Lecture Notes in Chemistry, 41–104. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-93349-3_4.

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Jurzak, J. P. "Density Theorems." In Unbounded Non-Commutative Integration, 21–29. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5231-7_3.

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da Silva, Ana Cannas. "Moser Theorems." In Lecture Notes in Mathematics, 49–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-45330-7_7.

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Givant, Steven. "Representation theorems." In Advanced Topics in Relation Algebras, 201–314. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65945-9_4.

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Rataj, Jan, and Martina Zähle. "Characterization Theorems." In Springer Monographs in Mathematics, 159–70. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18183-3_8.

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Greiner, Walter. "Green’s Theorems." In Classical Electrodynamics, 45–69. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0587-6_2.

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Conference papers on the topic "Theorems"

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Wavrik, John J. "Commutativity theorems." In the 1999 international symposium. New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/309831.309851.

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Palmer, R. B. "Acceleration theorems." In The sixth advanced accelerator concepts workshop. AIP, 1995. http://dx.doi.org/10.1063/1.48253.

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Wolkowski, Z. W. "Gödel's Theorems." In First International Symposium. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814536035.

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Kostin, Andrey Viktorovich. "On generalizations of Furman theorem on hyperbolic plane." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-75.

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Furman's theorem is also called Ptolemy's theorem for an inscribed hexagon. The paper considers various analogues of this theorems on the Lobachevsky plane, as well as analogs of a theorem generalizing the Kezi (Casey) theorem for six circles tangent to one circles. "Point" interpretations are built "cyclic" theorems.
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James, Daniel, and Emil Wolf. "Spectral equivalence theorems." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.tuo7.

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Equivalence theorems are known which provide conditions in which sources with different coherence properties will generate fields with the same angular distribution of the radiant intensity.1,2 Another equivalence theorem for partially coherent sources is formulated; it provides conditions which ensure that 3-D primary sources with different coherence properties generate radiation fields that have identical spectra. The results are illustrated by describing sources of different coherence lengths, all of which produce the same far zone spectrum as a spatially completely incoherent source.
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Eastlund, Carl. "DoubleCheck your theorems." In the Eighth International Workshop. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1637837.1637844.

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Wadler, Philip. "Theorems for free!" In the fourth international conference. New York, New York, USA: ACM Press, 1989. http://dx.doi.org/10.1145/99370.99404.

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Ballarin, Clemens, Karsten Homann, and Jacques Calmet. "Theorems and algorithms." In the 1995 international symposium. New York, New York, USA: ACM Press, 1995. http://dx.doi.org/10.1145/220346.220366.

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Galanis, Spyros. "Theorems and unawareness." In the 11th conference. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1324249.1324270.

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Xueqiu Zhan. "Decomposition theorems and representation theorems of lattice interval value fuzzy sets." In 2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2013. http://dx.doi.org/10.1109/fskd.2013.6816165.

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Reports on the topic "Theorems"

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Blum, L. Contact Theorems for Rough Interfaces. Fort Belvoir, VA: Defense Technical Information Center, April 1994. http://dx.doi.org/10.21236/ada282988.

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Glynn, Peter W., and Ward Whitt. Limit Theorems for Cumulative Processes. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada248507.

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Chaganty, Narasinga R., and Jayaram Sethuraman. Multidimensional Strong Large Deviation Theorems. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada256939.

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Wardlaw, William. A Transfer Device for Matrix Theorems. Washington, DC: The MAA Mathematical Sciences Digital Library, February 2010. http://dx.doi.org/10.4169/capsules003375.

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Deffner, Sebastian. Quantum fluctuation theorems in open systems. Office of Scientific and Technical Information (OSTI), March 2015. http://dx.doi.org/10.2172/1209322.

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Glynn, Peter W., and Donald L. Iglehart. Smoothed Limit Theorems for Equilibrium Processes. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada212321.

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Chaganty, Narasinga R. Large Deviation Limit Theorems, with Applications. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada290392.

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Özen, Mehmet, OsamaA Naji, Unsal Tekir, and Kar Ping Shum. Characterization Theorems of S-Artinian Modules. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, April 2021. http://dx.doi.org/10.7546/crabs.2021.04.03.

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Chaganty, Narasinga R., and Jayaram Sethuraman. Strong Large Deviation and Local Limit Theorems. Fort Belvoir, VA: Defense Technical Information Center, August 1989. http://dx.doi.org/10.21236/ada213610.

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Horvath, Lajos, and Emanuel Parzen. Limit Theorems for Fisher-Score Change Processes. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada257278.

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