Статті в журналах: "Nonzero elements"

1

Pudlák, Pavel. "Cycles of Nonzero Elements in Low Rank Matrices." Combinatorica 22, no. 2 (April 1, 2002): 321–34. http://dx.doi.org/10.1007/s004930200015.

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2

Vukman, Joso, and Irena Kosi-Ulbl. "On dependent elements in rings." International Journal of Mathematics and Mathematical Sciences 2004, no. 54 (2004): 2895–906. http://dx.doi.org/10.1155/s0161171204311221.

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LetRbe an associative ring. An elementa∈Ris said to be dependent on a mappingF:R→Rin caseF(x)a=axholds for allx∈R. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ringR, there are no nonzero elements which are dependent on the mappingα+β, whereαandβare automorphisms ofR.

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3

Hassani, Mehdi. "Wilson's theorem for finite fields." Publikacije Elektrotehnickog fakulteta - serija: matematika, no. 17 (2006): 110–11. http://dx.doi.org/10.2298/petf0617110h.

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In this short note, we introduce an analogue of Wilson's theorem for all nonzero elements of a finite filed, which reproves Wilson's theorem and yields some Wilson type identities. Finally, we obtain an analogue of Wolstenholme's theorem for nonzero elements of a finite filed.

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4

GANCHEV, HRISTO, and ANDREA SORBI. "INITIAL SEGMENTS OF THE ENUMERATION DEGREES." Journal of Symbolic Logic 81, no. 1 (March 2016): 316–25. http://dx.doi.org/10.1017/jsl.2014.84.

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AbstractUsing properties of${\cal K}$-pairs of sets, we show that every nonzero enumeration degreeabounds a nontrivial initial segment of enumeration degrees whose nonzero elements have all the same jump asa. Some consequences of this fact are derived, that hold in the local structure of the enumeration degrees, including: There is an initial segment of enumeration degrees, whose nonzero elements are all high; there is a nonsplitting high enumeration degree; every noncappable enumeration degree is high; every nonzero low enumeration degree can be capped by degrees of any possible local jump (i.e., any jump that can be realized by enumeration degrees of the local structure); every enumeration degree that bounds a nonzero element of strictly smaller jump, is bounding; every low enumeration degree below a non low enumeration degreeacan be capped belowa.

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5

Middendorf, Martin, Hartmut Schmeck, Heiko Schröder, and Gavin Turner. "Multiplication of Matrices With Different Sparseness Properties on Dynamically Reconfigurable Meshes." VLSI Design 9, no. 1 (January 1, 1999): 69–81. http://dx.doi.org/10.1155/1999/32697.

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Algorithms for multiplying several types of sparse n x n-matrices on dynamically reconfigurable n x n-arrays are presented. For some classes of sparse matrices constant time algorithms are given, e.g., when the first matrix has at most kn elements in each column or in each row and the second matrix has at most kn nonzero elements in each row, where k is a constant. Moreover, O(kn ) algorithms are obtained for the case that one matrix is a general sparse matrix with at most kn nonzero elements and the other matrix has at most k nonzero elements in every row or in every column. Also a lower bound of Ω(Kn ) is proved for this and other cases which shows that the algorithms are close to the optimum.

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6

Colliot-Thélène, Jean-Louis, and Bjorn Poonen. "Algebraic families of nonzero elements of Shafarevich-Tate groups." Journal of the American Mathematical Society 13, no. 1 (August 20, 1999): 83–99. http://dx.doi.org/10.1090/s0894-0347-99-00315-x.

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7

Gol'dshte�n, V. M., V. I. Kuz'minov, and I. A. Shvedov. "Nonzero elements in theL p -cohomologies of warped products." Siberian Mathematical Journal 33, no. 6 (1992): 950–65. http://dx.doi.org/10.1007/bf00971018.

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8

Yang, Jikun, Zhanmiao Li, Xudong Xin, Xiangyu Gao, Xiaoting Yuan, Zehuan Wang, Zhonghui Yu, Xiaohui Wang, Ji Zhou, and Shuxiang Dong. "Designing electromechanical metamaterial with full nonzero piezoelectric coefficients." Science Advances 5, no. 11 (November 2019): eaax1782. http://dx.doi.org/10.1126/sciadv.aax1782.

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Designing topological and geometrical structures with extended unnatural parameters (negative, near-zero, ultrahigh, or tunable) and counterintuitive properties is a big challenge in the field of metamaterials, especially for relatively unexplored materials with multiphysics coupling effects. For natural piezoelectric ceramics, only five nonzero elements in the piezoelectric matrix exist, which has impeded the design and application of piezoelectric devices for decades. Here, we introduce a methodology, inspired by quasi-symmetry breaking, realizing artificial anisotropy by metamaterial design to excite all the nonzero elements in contrast to zero values in natural materials. By elaborately programming topological structures and geometrical dimensions of the unit elements, we demonstrate, theoretically and experimentally, that tunable nonzero or ultrahigh values of overall effective piezoelectric coefficients can be obtained. While this work focuses on generating piezoelectric parameters of ceramics, the design principle should be inspirational to create unnatural apparent properties of other multiphysics coupling metamaterials.

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9

Chu, Xiaobing, and Feng Gao. "Kinematic coupling complexity of heavy-payload forging manipulator." Robotica 30, no. 4 (August 26, 2011): 551–58. http://dx.doi.org/10.1017/s0263574711000968.

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SUMMARYThere exist several kinds of definitions for complexity in different areas. In mechanical engineering area, some formulations capable of measuring the complexity of robotic architectures have been proposed at the conceptual-design stage. This paper presents the definition of Kinematic Coupling Complexity to measure the kinematic coupling degree of a manipulator based on the input/output velocity matrix. In order to distinguish the differences among many matrixes, three factors will be considered including the proportion of nonzero elements in matrix J, the difference of nonzero elements' numbers in every row among many matrixes, and the difference of nonzero elements' positions among many matrixes. To illustrate the methods introduced in this paper, four types of heavy-payload forging manipulators are analyzed and the type of forging manipulator with the smallest Kinematic Coupling Complexity is chosen as our prototype.

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10

WEI, FENG, та DA BIAN. "NORMAL ELEMENTS OF COMPLETED GROUP ALGEBRAS OVER SLn(ℤp)". International Journal of Algebra and Computation 20, № 08 (грудень 2010): 1021–39. http://dx.doi.org/10.1142/s0218196710006011.

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11

SUPRUNENKO, IRINA D., and ALEXANDRE E. ZALESSKI. "FIXED VECTORS FOR ELEMENTS IN MODULES FOR ALGEBRAIC GROUPS." International Journal of Algebra and Computation 17, no. 05n06 (August 2007): 1249–61. http://dx.doi.org/10.1142/s0218196707004001.

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12

Khemphet, Anchalee, and Justin R. Peters. "Semicrossed Products of the Disk Algebra and the Jacobson Radical." Canadian Mathematical Bulletin 57, no. 1 (March 14, 2014): 80–89. http://dx.doi.org/10.4153/cmb-2012-018-8.

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Abstract We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical of these operator algebras. Furthermore, in the case that the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step, the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.

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13

Lim, Ming–Huat. "Linear Transformations on Symmetric Spaces II." Canadian Journal of Mathematics 45, no. 2 (April 1, 1993): 357–68. http://dx.doi.org/10.4153/cjm-1993-017-2.

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AbstractLet U be a finite dimensional vector space over an infinite field F. Let U(r) denote the r–th symmetric product space over U. Let T: U(r) → U(s) be a linear transformation which sends nonzero decomposable elements to nonzero decomposable elements. Let dim U ≥ s + 1. Then we obtain the structure of T for the following cases: (I) F is algebraically closed, (II) F is the real field, and (III) T is injective.

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14

Farzi-safarabadi, A., and R. Beyranvand. "The set of strong torsion elements of a module over a noncommutative ring." Journal of Algebra and Its Applications 19, no. 07 (July 3, 2019): 2050123. http://dx.doi.org/10.1142/s0219498820501236.

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Let [Formula: see text] be an arbitrary ring and [Formula: see text] be a nonzero right [Formula: see text]-module. In this paper, we introduce the set [Formula: see text], for some nonzero ideal [Formula: see text] of [Formula: see text] of strong torsion elements of [Formula: see text] and the properties of this set are investigated. In particular, we are interested when [Formula: see text] is a submodule of [Formula: see text] and when it is a union of prime submodules of [Formula: see text].

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15

Chen, Charles C. T., and Henry T. Y. Yang. "Flexible Thin Shell Elements under Nonwhite and Nonzero Mean Loads." Journal of Engineering Mechanics 119, no. 8 (August 1993): 1680–97. http://dx.doi.org/10.1061/(asce)0733-9399(1993)119:8(1680).

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16

Koreisha, S. G., and T. M. Pukkila. "Identification of Nonzero Elements in the Polynomial Matrices of MixedVarmaProcesses." Journal of the Royal Statistical Society: Series B (Methodological) 49, no. 1 (September 1987): 112–26. http://dx.doi.org/10.1111/j.2517-6161.1987.tb01432.x.

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17

Coykendall, Jim, and Tiberiu Dumitrescu. "Integral Domains Having Nonzero Elements with Infinitely Many Prime Divisors." Communications in Algebra 35, no. 4 (April 13, 2007): 1333–39. http://dx.doi.org/10.1080/00927870601041474.

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18

Karasev, R. N., and F. V. Petrov. "Partitions of nonzero elements of a finite field into pairs." Israel Journal of Mathematics 192, no. 1 (February 28, 2012): 143–56. http://dx.doi.org/10.1007/s11856-012-0020-5.

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19

Liang, Xiquan, Fuguo Ge, and Xiaopeng Yue. "Some Special Matrices of Real Elements and Their Properties." Formalized Mathematics 14, no. 4 (January 1, 2006): 129–34. http://dx.doi.org/10.2478/v10037-006-0016-x.

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Some Special Matrices of Real Elements and Their Properties This article describes definitions of positive matrix, negative matrix, nonpositive matrix, nonnegative matrix, nonzero matrix, module matrix of real elements and their main properties, and we also give the basic inequalities in matrices of real elements.

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20

Anderson, David F., and Ayman Badawi. "Von Neumann Regular and Related Elements in Commutative Rings." Algebra Colloquium 19, spec01 (October 31, 2012): 1017–40. http://dx.doi.org/10.1142/s1005386712000831.

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Let R be a commutative ring with nonzero identity. In this paper, we study the von Neumann regular elements of R. We also study the idempotent elements, π-regular elements, the von Neumann local elements, and the clean elements of R. Finally, we investigate the subgraphs of the zero-divisor graph Γ(R) of R induced by the above elements.

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21

Hermann, Peter Z. "On the product of all nonzero elements of a finite ring." Glasgow Mathematical Journal 30, no. 3 (September 1988): 325–30. http://dx.doi.org/10.1017/s0017089500007412.

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The aim of the present note is to describe the possible products when taking all the nonzero elements of a finite ring in some sequence. Compared with the analogous situation for finite groups, where the set of products of all elements has been shown in [2] to be a whole coset of the derived group, for rings the set of the above mentioned products will be proved either to be as large as possible or to consist of one or two elements only.

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22

Lei, Tian-Gang, and Bo-Ying Wang. "Indices and nonzero decomposable elements of a symmetry class of tensors." Linear Algebra and its Applications 279, no. 1-3 (August 1998): 21–30. http://dx.doi.org/10.1016/s0024-3795(98)00005-6.

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23

Abe, S., and A. H. Gee. "Global convergence of the Hopfield neural network with nonzero diagonal elements." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 42, no. 1 (1995): 39–45. http://dx.doi.org/10.1109/82.363543.

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24

Lim, M. H. "Linear maps on symmetric spaces: the invariance of nonzero decomposable elements." Linear Algebra and its Applications 148 (April 1991): 89–92. http://dx.doi.org/10.1016/0024-3795(91)90088-e.

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25

Chen, Charles C. T., and Henry T. Y. Yang. "Flexible Beam and Frame Elements under Nonwhite and Nonzero Mean Loads." Journal of Engineering Mechanics 117, no. 6 (June 1991): 1346–64. http://dx.doi.org/10.1061/(asce)0733-9399(1991)117:6(1346).

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26

GERNOTH, K. A., M. SERHAN, and M. L. RISTIG. "STRONGLY CORRELATED BOSONS AT NONZERO TEMPERATURES." International Journal of Modern Physics B 22, no. 25n26 (October 20, 2008): 4315–26. http://dx.doi.org/10.1142/s0217979208050073.

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We investigate the structure of strongly correlated normal Bose liquids and fluids by employing correlated density-matrix (CDM) theory, a generalization of correlated basis functions (CBF) theory to nonzero temperatures. The formalism is applied in a study of structural properties of various correlation functions that characterize the one-body and two-body reduced density matrix elements of a boson system and the associated Fourier transforms such as the static structure function, the exchange structure function, the momentum distribution, and related thermodynamic quantities. We perform a numerical analysis for liquid para-hydrogen, close to the triple point, supercritical 4 He gas at temperatures T ≥ 12 K , and fluid and liquid 4 He in the normal phase below T = 12 K . The results reveal that H 2 and 4 He , at T > 12 K , are typical quantum Boltz-mann systems following classical statistics. In contrast, liquid 4 He exhibits non-classical effects of particle exchange correlations, when the temperature is lowered toward the Bose-Einstein transition regime.

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27

AFKHAMI, MOJGAN, and KAZEM KHASHYARMANESH. "PLANAR, OUTERPLANAR, AND RING GRAPH OF THE COZERO-DIVISOR GRAPH OF A FINITE COMMUTATIVE RING." Journal of Algebra and Its Applications 11, no. 06 (November 14, 2012): 1250103. http://dx.doi.org/10.1142/s0219498812501034.

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Let R be a commutative ring with nonzero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertex-set W*(R), which is the set of all nonzero and non-unit elements of R, and two distinct vertices a and b in W*(R) are adjacent if and only if a ∉ Rb and b ∉ Ra. In this paper, we characterize all finite commutative rings R such that Γ′(R) is planar, outerplanar or ring graph.

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28

Wang, Gaofeng, Bing-Zhong Wang, and Jiechang Hou. "An example of the wavelet impedance matrix with O(N) nonzero elements." Microwave and Optical Technology Letters 14, no. 3 (February 20, 1997): 181–82. http://dx.doi.org/10.1002/(sici)1098-2760(19970220)14:3<181::aid-mop14>3.0.co;2-b.

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29

Koreisha, S. G., and T. M. Pukkila. "Identification of Nonzero Elements in the Polynomial Matrices of Mixed Varma Processes." Journal of the Royal Statistical Society: Series B (Methodological) 50, no. 1 (September 1988): 155. http://dx.doi.org/10.1111/j.2517-6161.1988.tb01720.x.

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30

Mikhalev, Alexander A., and Jie-Tai Yu. "Test Elements, Retracts and Automorphic Orbits of Free Algebras." International Journal of Algebra and Computation 08, no. 03 (June 1998): 295–310. http://dx.doi.org/10.1142/s0218196798000144.

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A nonzero element a of an algebra A is called a test element if for any endomorphism φ of A it follows from φ(a)=a that φ is an automorphism of the algebra A. A subalgebra B of A is a retract if there is an ideal I of A such that A=B ⊕ I. We consider the main types of free algebras with the Nielsen–Schreier property: free nonassociative algebras, free commutative and anti-commutative nonassociative algebras, free Lie algebras and superalgebras, and free Lie p-algebras and p-superalgebras. For any free algebra F of finite rank of such type we prove that an element u is a test element if and only if it does not belong to any proper retract of F. Test elements for monomorphisms of F are exactly elements that are not contained in proper free factors of F. These results give analogs of Turner's results on test elements of free groups. We also characterize retracts of the algebra F. We prove that if some endomorphism φ preserve the automorphic orbit of some nonzero element of F, then φ is a monomorphism. For free Lie algebras and superalgebras over a field of characteristic zero and for free Lie p-(super)algebras over a field of prime characteristic p we show that in this situation φ is an automorphism. We discuss some related topics and formulate open problems.

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31

COYKENDALL, JIM, and RICHARD ERWIN HASENAUER. "FACTORIZATION IN PRÜFER DOMAINS." Glasgow Mathematical Journal 60, no. 2 (October 30, 2017): 401–9. http://dx.doi.org/10.1017/s0017089517000179.

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AbstractWe construct a norm on the nonzero elements of a Prüfer domain and extend this concept to the set of ideals of a Prüfer domain. These norms are used to study factorization properties Prüfer of domains.

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32

SHNEERSON, L. M., and D. EASDOWN. "GROWTH OF FINITELY PRESENTED REES QUOTIENTS OF FREE INVERSE SEMIGROUPS." International Journal of Algebra and Computation 21, no. 01n02 (February 2011): 315–28. http://dx.doi.org/10.1142/s0218196711006182.

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We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial growth if and only if it has bounded height. This occurs if and only if the set of nonzero reduced words has bounded Shirshov height and all nonzero reduced but not cyclically reduced words are nilpotent. This occurs also if and only if the set of nonzero geodesic words have bounded Shirshov height. We also give a simple sufficient graphical condition for polynomial growth, which is necessary when all zero relators are reduced. As a final application of our results, we give an inverse semigroup analogue of a classical result that characterizes polynomial growth of finitely presented Rees quotients of free semigroups in terms of connections between non-nilpotent elements and primitive words that label loops of the Ufnarovsky graph of the presentation.

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33

Турайханов, Д. А., А. В. Шкаликов, А. А. Калачев, И. Р. Имангулова, Н. Н. Лосевский, Е. В. Разуева, С. А. Самагин та С. П. Котова. "Получение однофотонных волновых пакетов инфракрасного диапазона длин волн с орбитальным угловым моментом с использованием фазовых вихревых" пластин-=SUP=-*-=/SUP=-". Журнал технической физики 126, № 1 (2019): 33. http://dx.doi.org/10.21883/os.2019.01.47049.253-18.

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AbstractSpecific features of the construction and recording of axially symmetric vortex fields using diffraction optical elements, which can be used for generating single-photon states with a nonzero orbital angular momentum in the process of spontaneous parametric down-conversion, are considered.

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34

Schrempf, Konrad. "Linearizing the word problem in (some) free fields." International Journal of Algebra and Computation 28, no. 07 (October 15, 2018): 1209–30. http://dx.doi.org/10.1142/s0218196718500546.

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We describe a solution of the word problem in free fields (coming from non-commutative polynomials over a commutative field) using elementary linear algebra, provided that the elements are given by minimal linear representations. It relies on the normal form of Cohn and Reutenauer and can be used more generally to (positively) test rational identities. Moreover, we provide a construction of minimal linear representations for the inverse of nonzero elements.

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35

Liu, Zhouzhou, and Fubao Wang. "WSNs Microseismic Signal Subsection Compression Algorithm Based on Compressed Sensing." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/187095.

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For wireless network microseismic monitoring and the problems of low compression ratio and high energy consumption of communication, this paper proposes a segmentation compression algorithm according to the characteristics of the microseismic signals and the compression perception theory (CS) used in the transmission process. The algorithm will be collected as a number of nonzero elements of data segmented basis, by reducing the number of combinations of nonzero elements within the segment to improve the accuracy of signal reconstruction, while taking advantage of the characteristics of compressive sensing theory to achieve a high compression ratio of the signal. Experimental results show that, in the quantum chaos immune clone refactoring (Q-CSDR) algorithm for reconstruction algorithm, under the condition of signal sparse degree higher than 40, to be more than 0.4 of the compression ratio to compress the signal, the mean square error is less than 0.01, prolonging the network life by 2 times.

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36

Leontaris, G. K., and N. D. Vlachos. "A discrete anatomy of the neutrino mass matrix." Modern Physics Letters A 29, no. 33 (October 30, 2014): 1450179. http://dx.doi.org/10.1142/s021773231450179x.

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We investigate the possibility of expressing the charged leptons and neutrino mass matrices as linear combinations of elements of a single finite group. Constraints imposed on the resulting mixing matrix by current data restrict the group types, but allow a nonzero value for the θ13 mixing angle.

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37

Turaykhanov, D. A., A. V. Shkalikov, A. A. Kalachev, I. R. Imangulova, N. N. Losevsky, E. V. Razova, S. A. Samagin, and S. P. Kotova. "Producing single-photon wave packets of the infrared spectrum range with an orbital angular momentum using “vortex” phase plates." EPJ Web of Conferences 190 (2018): 04025. http://dx.doi.org/10.1051/epjconf/201819004025.

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We consider the peculiarities of formation and registration of axially symmetric vortex fields in the context of applying diffractive optical elements such as vortex lenses and vortex axicons for the generation of single-photon states with a nonzero orbital angular momentum in the process of spontaneous parametric down-conversion.

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38

Cronin, Anthony G. "Constructive methods for spectra with three nonzero elements in the nonnegative inverse eigenvalue problem." Linear and Multilinear Algebra 66, no. 3 (March 13, 2017): 435–46. http://dx.doi.org/10.1080/03081087.2017.1301361.

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39

Hatzopoulos, A. A. "Reducing the number of nonzero elements of topological loop (B) and cutset (D) matrices." Electronics Letters 28, no. 17 (1992): 1577. http://dx.doi.org/10.1049/el:19921004.

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40

BAZIAR, M., E. MOMTAHAN, and S. SAFAEEYAN. "A ZERO-DIVISOR GRAPH FOR MODULES WITH RESPECT TO THEIR (FIRST) DUAL." Journal of Algebra and Its Applications 12, no. 02 (December 16, 2012): 1250151. http://dx.doi.org/10.1142/s0219498812501514.

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Let M be an R-module. We associate an undirected graph Γ(M) to M in which nonzero elements x and y of M are adjacent provided that xf(y) = 0 or yg(x) = 0 for some nonzero R-homomorphisms f, g ∈ Hom (M, R). We observe that over a commutative ring R, Γ(M) is connected and diam (Γ(M)) ≤ 3. Moreover, if Γ(M) contains a cycle, then gr (Γ(M)) ≤ 4. Furthermore if ∣Γ(M)∣ ≥ 1, then Γ(M) is finite if and only if M is finite. Also if Γ(M) = ∅, then any nonzero f ∈ Hom (M, R) is monic (the converse is true if R is a domain). For a nonfinitely generated projective module P we observe that Γ(P) is a complete graph. We prove that for a domain R the chromatic number and the clique number of Γ(M) are equal. When R is self-injective, we will also observe that the above adjacency defines a covariant functor between a subcategory of R-MOD and the Category of graphs.

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41

Oldag, Frank, and Dieter H. Sutter. "The Rotational Zeeman Effect in Acetone, its g-Tensor, its Magnetic Susceptibility Anisotropics and its Molecular Electric Quadrupole Moment Tensor; A High Resolution Microwave Fourier Transform Study." Zeitschrift für Naturforschung A 47, no. 3 (March 1, 1992): 527–32. http://dx.doi.org/10.1515/zna-1992-0315.

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Abstract Acetone is a molecule with an intermediate barrier for methyl- top internal rotation, and only molecules in the A1A1 - state of the tunneling motion exhibit a rigid rotor spectrum. For this state we report the results of a rotational Zeeman effect study of acetone in exterior fields up to 20 kGauss (2 Tesla). From an analysis of the observed Zeeman splittings within the asymmetric top approximation the nonzero elements of the g-tensor and the magnetic susceptibility anisotropies were obtained as follows: gaa= -0.04379 (8), gbb = - 0.06611 (5), gcc=-O.O1481 (7), 2ξaa -ξbb - ξcc = - 9.53 (21) 10-6 erg G -2 mole-1 and 2 ξbb - ξcc - ξaa = 25.57 (18) 10-6 erg G -2 mole-1 . The nonzero elements of the molecular electric quadrupole moment tensor were derived as Qaa- 2-77 (13) DÅ, Qbb= -4.59 (10) DÅ and Qcc= 1.82 (15) DÅ. Zeeman spectra were also recorded for seveal low-J transitions of molecules in the EE-state of methyl top tunneling (one top tunneling), and so far the same splittings have been found as for the A1 A1-species

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42

Zhao, Ya. "Obtaining nonvanishing 𝜃13 with constrained neutrino Yukawa matrix and implications for flavor model buildings". Modern Physics Letters A 32, № 16 (25 квітня 2017): 1750080. http://dx.doi.org/10.1142/s0217732317500808.

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Assuming a diagonal Majorana neutrino mass matrix, we investigate the neutrino Yukawa textures which lead to a nonzero reactor mixing angle [Formula: see text]. The neutrino effective coupling matrix [Formula: see text] is pre-diagonalized by a constant mixing pattern [Formula: see text] with a vanishing [Formula: see text]. The resulting pre-diagonal symmetrical matrix [Formula: see text] is set to be four texture zeros with two types of off-diagonal elements nonzero, which are [Formula: see text] and [Formula: see text], respectively. With the expectation of simple textures, we thoroughly classify the linear combinations, [Formula: see text], [Formula: see text] and [Formula: see text] of Yukawa elements [Formula: see text] in the same row, according to the values, vanishing or not. Each set of the classifications can lead to a Yukawa texture which may have implications for the discrete flavor model buildings. We also present a model based on [Formula: see text] according to one set of the constraints on the three combinations with a specific choice of a coefficient in Yukawa texture.

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43

GILL, P. S., and MANMOHAN GUPTA. "FRITZSCH-LIKE QUARK MASS MATRICES WITH DECOUPLED u QUARK." Modern Physics Letters A 09, no. 26 (August 30, 1994): 2461–67. http://dx.doi.org/10.1142/s0217732394002331.

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Fritzsch-like Hermitian quark mass matrices with decoupled u quark as well as nonzero 22-elements, both in ‘U’ and ‘D’ sectors, have been considered to reconcile the data regarding [Formula: see text] and CKM matrix elements. Exploiting the idea of maximality of CP-violation, we find two interesting relations between CKM matrix elements, viz. |Vtd|≅ |Vus||Vcb|, |Vub|≅ ½(ms/ mb)|Vus|. Apart from obtaining 0.05≤|Vub/Vcb|≤0.12 and [Formula: see text], we find CP-violating rephasing invariant parameter |J|≅(3–5)×10−5. The predicted |Vtd| value implies almost maximal mixing in [Formula: see text] system.

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44

Nagy, Gergő. "Preservers for thep-Norm of Linear Combinations of Positive Operators." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/434121.

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We describe the structure of those transformations on certain sets of positive operators which preserve thep-norm of linear combinations with given nonzero real coefficients. These sets are the collection of all positivepth Schatten-class operators and the set of its normalized elements. The results of the work generalize, extend, and unify several former theorems.

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45

Klep, Igor, and Primož Moravec. "Lie Algebras with Abelian Centralizers." Algebra Colloquium 17, no. 04 (December 2010): 629–36. http://dx.doi.org/10.1142/s100538671000060x.

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We classify all finite-dimensional Lie algebras over an algebraically closed field of characteristic 0, whose nonzero elements have abelian centralizers. These algebras are either simple or solvable, where the only simple such Lie algebra is [Formula: see text]. In the solvable case, they are either abelian or a one-dimensional split extension of an abelian Lie algebra.

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46

Карпиловский, Виктор. "FINITE ELEMENTS OF THE PLANE PROBLEM OF THE THEORY OF ELASTICITY WITH DRILLING DEGREES OF FREEDOM." International Journal for Computational Civil and Structural Engineering 16, no. 1 (May 20, 2020): 48–72. http://dx.doi.org/10.22337/2587-9618-2020-16-1-48-72.

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Twelve new finite elements with drilling degrees of freedom have been developed: triangular and quadrangular elements based on a modified hypothesis about the value of approximating functions on the sides of the element, which made it possible to avoid dimensional instability when all rotation angles are zero; incompatible and compatible triangular and quadrangular elements which can have additional nodes on the sides. Approximating functions satisfy the following condition: the value of the rotational degree of freedom of a node is nonzero and equal to one only for one of them. Numerical examples illustrate estimated minimum orders of convergence for displacements and stresses. All created elements retain the existing symmetry of the design models.

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47

Han, Dong, та Feng Wei. "Normal elements of noncommutative Iwasawa algebras over SL3(ℤ_ p )". Forum Mathematicum 31, № 1 (1 січня 2019): 111–47. http://dx.doi.org/10.1515/forum-2018-0034.

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Abstract Let p be a prime integer and let {\mathbb{Z}_{p}} be the ring of p-adic integers. By a purely computational approach we prove that each nonzero normal element of a noncommutative Iwasawa algebra over the special linear group {\mathrm{SL}_{3}(\mathbb{Z}_{p})} is a unit. This gives a positive answer to an open question in [F. Wei and D. Bian, Erratum: Normal elements of completed group algebras over \mathrm{SL}_{n}(\mathbb{Z}_{p}) [mr2747414], Internat. J. Algebra Comput. 23 2013, 1, 215] and makes up for an earlier mistake in [F. Wei and D. Bian, Normal elements of completed group algebras over \mathrm{SL}_{n}(\mathbb{Z}_{p}) , Internat. J. Algebra Comput. 20 2010, 8, 1021–1039] simultaneously.

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48

Britten, D. J., and F. W. Lemire. "On Level 0 Affine Lie Modules." Canadian Mathematical Bulletin 37, no. 3 (September 1, 1994): 310–14. http://dx.doi.org/10.4153/cmb-1994-047-9.

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AbstractIt is proven that the dimensions of the homogeneous summands of a nontrivial Z graded module for an infinité dimensional Heisenberg algebra on which a central element acts as nonzero scalar are unbounded. This result is then applied to show that the central elements of an affine Lie algebra act trivially on any indecomposable diagonalizable module whose weight spaces are of bounded dimension.

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49

ZHAO, MEISHAN. "SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS." International Journal of Modern Physics C 06, no. 01 (February 1995): 105–21. http://dx.doi.org/10.1142/s0129183195000095.

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This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

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50

Siriwong, Pinkaew, and Ratinan Boonklurb. "k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings." Symmetry 13, no. 11 (October 20, 2021): 1980. http://dx.doi.org/10.3390/sym13111980.

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Let R be a commutative ring with nonzero identity and k≥2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R,k), the set of all k-zero-divisors of R, and the hyperedges of the form {a1,a2,a3,…,ak}, where a1,a2,a3,…,ak are k distinct elements in Z(R,k), which means (i) a1a2a3⋯ak=0 and (ii) the products of all elements of any (k−1) subsets of {a1,a2,a3,…,ak} are nonzero. This paper provides two commutative rings so that one of them induces a family of complete k-zero-divisor hypergraphs, while another induces a family of k-partite σ-zero-divisor hypergraphs, which illustrates unbalanced or asymmetric structure. Moreover, the diameter and the minimum length of all cycles or girth of the family of k-partite σ-zero-divisor hypergraphs are determined. In addition to a k-zero-divisor hypergraph, we provide the definition of an ideal-based k-zero-divisor hypergraph and some basic results on these hypergraphs concerning a complete k-partite k-uniform hypergraph, a complete k-uniform hypergraph, and a clique.

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