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Journal articles on the topic 'Bloch's theorem'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Poletskii, E. A. "On Bloch's theorem." Russian Mathematical Surveys 41, no. 2 (April 30, 1986): 215–16. http://dx.doi.org/10.1070/rm1986v041n02abeh003287.

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2

MATTIS, D. C., and T. SJOSTROM. "BLOCH'S THEOREM IN NANOARCHITECTURES." Modern Physics Letters B 20, no. 09 (April 10, 2006): 501–13. http://dx.doi.org/10.1142/s0217984906011074.

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We identify and characterize mini-Bloch-sub-bands that condense out of the low-lying states in a semiconductor's conduction band due to repetitive patterns (as in an "antidot lattice"). We discuss limits on the validity of the tight-binding approximation. One appendix touches upon the complications (actually, simplification, in the case of silicon) when the dispersion is given by a set of anisotropic mass tensors, another treats the effects of cross-sectional shape on threshhold energy level of a conduit.
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3

Guillot, Dominique, and Thomas Ransford. "Bloch's Theorem for Algebroid Multifunctions II." Mathematical Proceedings of the Royal Irish Academy 105, no. 2 (January 1, 2005): 103–9. http://dx.doi.org/10.3318/pria.2005.105.2.103.

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4

Kaijia, Cheng. "Comment on Bloch's theorem on theories of superconductivity." Chinese Physics Letters 5, no. 6 (June 1988): 285–88. http://dx.doi.org/10.1088/0256-307x/5/6/013.

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5

KOBAYASHI, RYOICHI. "HOLOMORPHIC CURVES INTO ALGEBRAIC SUBVARIETIES OF AN ABELIAN VARIETY." International Journal of Mathematics 02, no. 06 (December 1991): 711–24. http://dx.doi.org/10.1142/s0129167x91000399.

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We apply a technique introduced in [7] to holomorphic curves into an algebraic variety whose irregularity is greater than its dimension and establish the Second Main Theorem. This gives a new geometric proof of Bloch's conjecture proved by Ochiai, Kawamata, Green-Griffiths in the late 70's.
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6

Fan, Y., and B. Goodman. "Thermal averages for the harmonic oscillator: an extension of Bloch's 'second' theorem." Journal of Physics A: Mathematical and General 20, no. 1 (January 11, 1987): 143–51. http://dx.doi.org/10.1088/0305-4470/20/1/023.

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7

MCCOLLUM, GIN, and PATRICK D. ROBERTS. "DYNAMICS OF EVERYDAY LIFE: RIGOROUS MODULAR MODELING IN NEUROBIOLOGY BASED ON BLOCH'S DYNAMICAL THEOREM." Journal of Integrative Neuroscience 03, no. 04 (December 2004): 397–413. http://dx.doi.org/10.1142/s0219635204000622.

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8

de Jeu, Rob, and James D. Lewis. "Beilinson's Hodge Conjecture for Smooth Varieties." Journal of K-Theory 11, no. 2 (March 6, 2013): 243–82. http://dx.doi.org/10.1017/is013001030jkt212.

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AbstractLet U/ℂ be a smooth quasi-projective variety of dimension d, CHr (U,m) Bloch's higher Chow group, andclr,m: CHr (U,m) ⊗ ℚ → homMHS (ℚ(0), H2r−m (U, ℚ(r)))the cycle class map. Beilinson once conjectured clr,m to be surjective [Be]; however, Jannsen was the first to find a counterexample in the case m = 1 [Ja1]. In this paper we study the image of clr,m in more detail (as well as at the “generic point” of U) in terms of kernels of Abel-Jacobi mappings. When r = m, we deduce from the Bloch-Kato conjecture (now a theorem) various results, in particular that the cokernel of clm,m at the generic point is the same for integral or rational coefficients.
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9

Chen, Shaolin, Saminathan Ponnusamy, and Xiantao Wang. "WEIGHTED LIPSCHITZ CONTINUITY, SCHWARZ–PICK'S LEMMA AND LANDAU–BLOCH'S THEOREM FOR HYPERBOLIC-HARMONIC MAPPINGS IN ℂN." Mathematical Modelling and Analysis 18, no. 1 (February 1, 2013): 66–79. http://dx.doi.org/10.3846/13926292.2013.756834.

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In this paper, we discuss some properties on hyperbolic-harmonic functions in the unit ball of ℂ n . First, we investigate the relationship between the weighted Lipschitz functions and the hyperbolic-harmonic Bloch spaces. Then we establish the Schwarz–Pick type theorem for hyperbolic-harmonic functions and apply it to prove the existence of Landau-Bloch constant for functions in α-Bloch spaces.
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10

Hoddeson, Lillian. "John Bardeen and the BCS Theory of Superconductivity." MRS Bulletin 24, no. 1 (January 1999): 50–55. http://dx.doi.org/10.1557/s0883769400051745.

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Every theory of superconductivity can be disproved! This tongue-in-cheek theorem struck a chord when Felix Bloch announced it in the early 1930s. Virtually every major physicist then working on theory—including Bloch, Niels Bohr, Wolfgang Pauli, Werner Heisenberg, Lev Landau, Leon Brillouin, W. Elsasser, Yakov Frenkel, and Ralph Kronig—had tried and failed to explain the mysterious phenomenon in which below a few degrees kelvin certain metals and alloys lose all their electrical resistance. The frequency with which Bloch's theorem was quoted suggests the frustration of the many physicists who were struggling to explain superconductivity.Neither the tools nor the evidence were yet adequate for solving the problem. These would gradually be created during the 1940s and 1950s, but bringing them to bear on superconductivity and solving the long-standing riddle required a special set of talents and abilities: a deep understanding of quantum mechanics and solid-state physics, confidence in the solubility of the problem, intuition about the phenomenon, a practical approach to problem-solving, patience, teamwork, and above all refusal to give up in the face of repeated failures. When John Bardeen took on the problem of superconductivity in the late 1930s, he held it like a bulldog holds a piece of meat, until he, his student J. Robert Schrieffer, and postdoctoral candidate Leon Cooper solved it in 1957.
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11

CHOU, TOM. "Band structure of surface flexural–gravity waves along periodic interfaces." Journal of Fluid Mechanics 369 (August 25, 1998): 333–50. http://dx.doi.org/10.1017/s002211209800192x.

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We extend Floquet's Theorem, similar to that used in calculating electronic and optical band gaps in solid state physics (Bloch's Theorem), to derive dispersion relations for small-amplitude water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one-dimensional periodicity (stripes), we find band gaps for wavevectors in the direction of periodicity corresponding to frequency ranges which support only non-propagating standing waves, as a consequence of multiple Bragg scattering. The dependence of these gaps on scatterer strength, density, and water depth is analysed. In contrast to band gap behaviour in electronic, photonic, and acoustic systems, we find that the gaps here can increase with excitation frequency ω. Thus, higher-order Bragg scattering can play an important role in suppressing wave propagation. In simple two-dimensional periodic geometries no complete band gaps are found, implying that there are always certain directions which support propagating waves. Evanescent modes offer one qualitative reason for this finding.
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12

Siu, Yum-Tong, and Sai-Kee Yeung. "A generalized Bloch's theorem and the hyperbolicity of the complement of an ample divisor in an Abelian variety." Mathematische Annalen 306, no. 1 (September 1996): 743–58. http://dx.doi.org/10.1007/bf01445275.

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13

Siu, Yum-Tong, and Sai-Kee Yeung. "A generalized Bloch's theorem and the hyperbolicity of the complement of an ample divisor in an Abelian variety." Mathematische Annalen 326, no. 1 (April 1, 2003): 205–7. http://dx.doi.org/10.1007/s00208-003-0410-4.

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14

Frazier, Michael J., and Mahmoud I. Hussein. "Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex." Comptes Rendus Physique 17, no. 5 (May 2016): 565–77. http://dx.doi.org/10.1016/j.crhy.2016.02.009.

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15

Zhang, Yan, Zhi-Qiang Ni, Lin-Hua Jiang, Lin Han, and Xue-Wei Kang. "Study of the bending vibration characteristic of phononic crystals beam-foundation structures by Timoshenko beam theory." International Journal of Modern Physics B 29, no. 20 (August 5, 2015): 1550136. http://dx.doi.org/10.1142/s0217979215501362.

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Vibration problems wildly exist in beam-foundation structures. In this paper, finite periodic composites inspired by the concept of ideal phononic crystals (PCs), as well as Timoshenko beam theory (TBT), are proposed to the beam anchored on Winkler foundation. The bending vibration band structure of the PCs Timoshenko beam-foundation structure is derived from the modified transfer matrix method (MTMM) and Bloch's theorem. Then, the frequency response of the finite periodic composite Timoshenko beam-foundation structure by the finite element method (FEM) is performed to verify the above theoretical deduction. Study shows that the Timoshenko beam-foundation structure with periodic composites has wider attenuation zones compared with homogeneous ones. It is concluded that TBT is more available than Euler beam theory (EBT) in the study of the bending vibration characteristic of PCs beam-foundation structures with different length-to-height ratios.
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16

Bahodirovich, Hojiyev Dilmurodjon, Muhammadjonov Akbarshoh Akramjon Og`Li Og`Li, Muzaffarova Dilshoda Botirjon Qizi, Ibrohimjonov Islombek Ilhomjon O`G`Li, and Ahmadjonova Musharrafxon Dilmurod Qizi. "About One Theorem Of 2x2 Jordan Blocks Matrix." American Journal of Applied sciences 03, no. 06 (June 12, 2021): 28–33. http://dx.doi.org/10.37547/tajas/volume03issue06-05.

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In this paper, we have studied one theorem on 2x2 Jordan blocks matrix. There are 4 important statements which is used for proving other theorems such as in the differensial equations. In proving these statements, we have used mathematic induction, norm of matrix, Taylor series of
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17

Andres, Jan. "Randomization of Sharkovsky-type results on the circle." Stochastics and Dynamics 17, no. 03 (March 26, 2017): 1750017. http://dx.doi.org/10.1142/s0219493717500174.

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Two deterministic Sharkovsky-type theorems on the circle due to L. Block [Proc. Amer. Math. Soc. 82 (1981) 481–486] and X. Zhao [Fixed Point Theory Appl., Article ID 194875 (2008)] are randomized. The randomization of Block’s theorem brings an additional information about the forcing alternatives. Some further possibilities of the randomized Zhao’s theorem are discussed for multivalued maps.
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18

CHEN, SH, S. PONNUSAMY, and X. WANG. "LANDAU’S THEOREM AND MARDEN CONSTANT FOR HARMONIC ν-BLOCH MAPPINGS." Bulletin of the Australian Mathematical Society 84, no. 1 (June 10, 2011): 19–32. http://dx.doi.org/10.1017/s0004972711002140.

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AbstractOur main aim is to investigate the properties of harmonic ν-Bloch mappings. Firstly, we establish coefficient estimates and a Landau theorem for harmonic ν-Bloch mappings, which are generalizations of the corresponding results in Bonk et al. [‘Distortion theorems for Bloch functions’, Pacific. J. Math.179 (1997), 241–262] and Chen et al. [‘Bloch constants for planar harmonic mappings’, Proc. Amer. Math. Soc.128 (2000), 3231–3240]. Secondly, we obtain an improved Landau theorem for bounded harmonic mappings. Finally, we obtain a Marden constant for harmonic mappings.
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19

Choe, Boo Rim, and Heungsu Yi. "Representations and interpolations of harmonic Bergman functions on half-spaces." Nagoya Mathematical Journal 151 (June 1998): 51–89. http://dx.doi.org/10.1017/s0027763000025174.

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Abstract.On the setting of the half-space of the euclidean n-space, we prove representation theorems and interpolation theorems for harmonic Bergman functions in a constructive way. We also consider the harmonic (little) Bloch spaces as limiting spaces. Our results show that well-known phenomena for holomorphic cases continue to hold. Our proofs of representation theorems also yield a uniqueness theorem for harmonic Bergman functions. As an application of interpolation theorems, we give a distance estimate to the harmonic little Bloch space. In the course of the proofs, pseudohyperbolic balls are used as substitutes for Bergman metric balls in the holomorphic case.
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20

Lüders, Morten. "DEFORMATION THEORY OF THE CHOW GROUP OF ZERO CYCLES." Quarterly Journal of Mathematics 71, no. 2 (April 13, 2020): 677–76. http://dx.doi.org/10.1093/qmathj/haaa004.

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Abstract We study the deformations of the Chow group of zerocycles of the special fibre of a smooth scheme over a Henselian discrete valuation ring. Our main tools are Bloch’s formula and differential forms. As a corollary we get an algebraization theorem for thickened zero cycles previously obtained using idelic techniques. In the course of the proof we develop moving lemmata and Lefschetz theorems for cohomology groups with coefficients in differential forms.
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21

Zhelyabin, V. N. "Addition to Block's theorem and to Popov's theorem on differentially simple algebras." Sibirskie Elektronnye Matematicheskie Izvestiya 16 (October 7, 2019): 1375–84. http://dx.doi.org/10.33048/semi.2019.16.095.

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22

Morais, João Pedro, and Klaus Gürlebeck. "Bloch’s Theorem in the Context of Quaternion Analysis." Computational Methods and Function Theory 12, no. 2 (August 21, 2012): 541–58. http://dx.doi.org/10.1007/bf03321843.

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23

Stephens, Chris, and Henri Waelbroeck. "Schemata Evolution and Building Blocks." Evolutionary Computation 7, no. 2 (June 1999): 109–24. http://dx.doi.org/10.1162/evco.1999.7.2.109.

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In the light of a recently derived evolution equation for genetic algorithms we consider the schema theorem and the building block hypothesis. We derive a schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The equation makes manifest the content of the building block hypothesis showing how fit schemata are constructed from fit sub-schemata. However, we show that, generically, there is no preference for short, low-order schemata. In the case where schema reconstruction is favored over schema destruction, large schemata tend to be favored. As a corollary of the evolution equation we prove Geiringer's theorem.
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24

Lee, Y. C., and Wei Z. Lee. "Rotational states of a benzenelike ring and Bloch’s theorem." American Journal of Physics 77, no. 12 (December 2009): 1144–46. http://dx.doi.org/10.1119/1.3226564.

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25

Rajala, Kai. "Bloch’s theorem for mappings of bounded and finite distortion." Mathematische Annalen 339, no. 2 (May 26, 2007): 445–60. http://dx.doi.org/10.1007/s00208-007-0124-0.

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26

Tanabe, K., and K. Sugawara-Tanabe. "Bloch-Messiah theorem at finite temperature." Zeitschrift f�r Physik A Hadrons and Nuclei 339, no. 1 (March 1991): 91–95. http://dx.doi.org/10.1007/bf01282937.

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27

Bustamante, Jorge, Raúl Escobedo, and Fernando Macías-Romero. "A fixed point theorem for Whitney blocks." Topology and its Applications 125, no. 2 (November 2002): 315–21. http://dx.doi.org/10.1016/s0166-8641(01)00284-x.

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28

Robinson, Geoffrey R. "The Zp∗-theorem and units in blocks." Journal of Algebra 134, no. 2 (November 1990): 353–55. http://dx.doi.org/10.1016/0021-8693(90)90058-v.

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29

Chen, Huaihui, and Paul M. Gauthier. "The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings." Proceedings of the American Mathematical Society 139, no. 02 (February 1, 2011): 583. http://dx.doi.org/10.1090/s0002-9939-2010-10659-7.

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30

Watanabe, Haruki. "A Proof of the Bloch Theorem for Lattice Models." Journal of Statistical Physics 177, no. 4 (September 17, 2019): 717–26. http://dx.doi.org/10.1007/s10955-019-02386-1.

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Abstract The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium at a finite temperature, irrespective of the details of the Hamiltonian as far as all terms in the Hamiltonian are finite ranged. In this work we present a simple yet rigorous proof for general lattice models. For large but finite systems, we find that both the discussion and the conclusion are sensitive to the boundary condition one assumes: under the periodic boundary condition, one can only prove that the current expectation value is inversely proportional to the linear dimension of the system, while the current expectation value completely vanishes before taking the thermodynamic limit when the open boundary condition is imposed. We also provide simple tight-binding models that clarify the limitation of the theorem in dimensions higher than one.
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31

Cel, J. "Tellegen's Theorem for Subnetworks." Journal of Circuits, Systems and Computers 07, no. 06 (December 1997): 641–42. http://dx.doi.org/10.1142/s0218126697000450.

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Let [Formula: see text] be a directed network and ℳ its subnetwork. It is proved that [Formula: see text] for all vectors of branch voltages uℳ and currents i ℳ in ℳ satisfying Kirchhoff's voltage and current laws in every loop and cutset of [Formula: see text] contained in ℳ if and only if ℳ is a union of blocks of [Formula: see text]. This yields a version of Tellegen's famous theorem for subnetworks.
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32

Kessar, Radha, and Radu Stancu. "A reduction theorem for fusion systems of blocks." Journal of Algebra 319, no. 2 (January 2008): 806–23. http://dx.doi.org/10.1016/j.jalgebra.2006.05.039.

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33

Collins, Michael J. "Blocks, Normal Subgroups, and Brauer's Third Main Theorem." Journal of Algebra 213, no. 1 (March 1999): 69–76. http://dx.doi.org/10.1006/jabr.1998.7662.

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34

FitzGerald, Carl H., and Sheng Gong. "The Bloch theorem in several complex variables." Journal of Geometric Analysis 4, no. 1 (March 1994): 35–58. http://dx.doi.org/10.1007/bf02921592.

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35

Bonk, Mario, David Minda, and Hiroshi Yanagihara. "Distortion theorems for Bloch functions." Pacific Journal of Mathematics 179, no. 2 (June 1, 1997): 241–62. http://dx.doi.org/10.2140/pjm.1997.179.241.

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36

Liu, Xiang Yang, and David Minda. "Distortion theorems for Bloch functions." Transactions of the American Mathematical Society 333, no. 1 (January 1, 1992): 325–38. http://dx.doi.org/10.1090/s0002-9947-1992-1055809-0.

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37

Hawkins, Vincent J. "Applying Pick's Theorem to Randomized Areas." Arithmetic Teacher 36, no. 2 (October 1988): 47–49. http://dx.doi.org/10.5951/at.36.2.0047.

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Elementary school students enjoy working with different shapes. The appeal of these activities is not surprising considering student familiarity with Cuisenaire rods, attribute blocks, geoboards, and other manipulatives that promote concept development.
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38

Chen, Shaolin, Saminathan Ponnusamy, and Xiantao Wang. "Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau–Bloch’s theorem." Monatshefte für Mathematik 177, no. 1 (January 24, 2015): 33–51. http://dx.doi.org/10.1007/s00605-014-0723-2.

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39

Robinson, Geoffrey R. "Central units in blocks and the odd Zp∗-theorem." Journal of Algebra 321, no. 2 (January 2009): 384–93. http://dx.doi.org/10.1016/j.jalgebra.2008.10.017.

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40

Ohashi, Yoji, and Tsutomu Momoi. "On the Bloch Theorem Concerning Spontaneous Electric Current." Journal of the Physical Society of Japan 65, no. 10 (October 15, 1996): 3254–59. http://dx.doi.org/10.1143/jpsj.65.3254.

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41

Zagier, Don. "Partitions, quasimodular forms, and the Bloch–Okounkov theorem." Ramanujan Journal 41, no. 1-3 (November 12, 2015): 345–68. http://dx.doi.org/10.1007/s11139-015-9730-8.

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42

Mirzaii, Behrooz. "Bloch–Wigner theorem over rings with many units." Mathematische Zeitschrift 268, no. 1-2 (January 29, 2010): 329–46. http://dx.doi.org/10.1007/s00209-010-0674-9.

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43

Hamada, Hidetaka. "A distortion theorem and the Bloch constant for Bloch mappings in ℂN." Journal d'Analyse Mathématique 137, no. 2 (March 2019): 663–77. http://dx.doi.org/10.1007/s11854-019-0005-y.

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44

Freund, Anton. "From Kruskal’s theorem to Friedman’s gap condition." Mathematical Structures in Computer Science 30, no. 8 (September 2020): 952–75. http://dx.doi.org/10.1017/s0960129520000298.

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AbstractHarvey Friedman’s gap condition on embeddings of finite labelled trees plays an important role in combinatorics (proof of the graph minor theorem) and mathematical logic (strong independence results). In the present paper we show that the gap condition can be reconstructed from a small number of well-motivated building blocks: It arises via iterated applications of a uniform Kruskal theorem.
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45

Külshammer, Burkhard. "Central idempotents in p-adic group rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 2 (April 1994): 278–89. http://dx.doi.org/10.1017/s1446788700034881.

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46

TONIEN, DONGVU. "CANCELLATION LAW AND UNIQUE FACTORIZATION THEOREM FOR STRING OPERATIONS." Journal of Algebra and Its Applications 05, no. 02 (April 2006): 231–43. http://dx.doi.org/10.1142/s0219498806001739.

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Recently, Hoit introduced arithmetic on blocks, which extends the binary string operation by Jacobs and Keane. A string of elements from the Abelian additive group of residues modulo m, (Zm, ⊕), is called an m-block. The set of m-blocks together with Hoit's new product operation form an interesting algebraic structure where associative law and cancellation law hold. A weaker form of unique factorization and criteria for two indecomposable blocks to commute are also proved. In this paper, we extend Hoit's results by replacing the Abelian group (Zm, ⊕) by an arbitrary monoid (A, ◦). The set of strings built up from the alphabet A is denoted by String(A). We extend the operation ◦ on the alphabet set A to the string set String(A). We show that (String(A), ◦) is a monoid if and only if (A, ◦) is a monoid. When (A, ◦) is a group, we prove that stronger versions of a cancellation law and unique factorization hold for (String(A), ◦). A general criterion for two irreducible strings to commute is also presented.
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47

Xiao, Jie. "Extension of a Theorem of Zygmund." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 2 (1998): 425–32. http://dx.doi.org/10.1017/s0308210500012865.

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We extend Zygmund's Theorem characterising the Bloch functions via a generalised Libera transform and so we answer an open problem formulated by N. Danikas, S. Ruscheweyh and A. Siskakis. Furthermore, we show some differences between the holomorphic Zygmund class and the class of holomorphic functions whose derivatives are of logarithmic growth on the unit disk.
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48

Hai, Jinke. "The extension of the first main theorem for π-blocks." Science in China Series A 49, no. 5 (April 28, 2006): 620–25. http://dx.doi.org/10.1007/s11425-006-0620-9.

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49

Külshammer, Burkhard, Tetsuro Okuyama, and Atumi Watanabe. "A Lifting Theorem with Applications to Blocks and Source Algebras." Journal of Algebra 232, no. 1 (October 2000): 299–309. http://dx.doi.org/10.1006/jabr.2000.8403.

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50

Lee, Min-Gi. "Asymptotic Stability of Non-Autonomous Systems and a Generalization of Levinson’s Theorem." Mathematics 7, no. 12 (December 10, 2019): 1213. http://dx.doi.org/10.3390/math7121213.

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We study the asymptotic stability of non-autonomous linear systems with time dependent coefficient matrices { A ( t ) } t ∈ R . The classical theorem of Levinson has been an indispensable tool for the study of the asymptotic stability of non-autonomous linear systems. Contrary to constant coefficient system, having all eigenvalues in the left half complex plane does not imply asymptotic stability of the zero solution. Levinson’s theorem assumes that the coefficient matrix is a suitable perturbation of the diagonal matrix. Our objective is to prove a theorem similar to Levinson’s Theorem when the family of matrices merely admits an upper triangular factorization. In fact, in the presence of defective eigenvalues, Levinson’s Theorem does not apply. In our paper, we first investigate the asymptotic behavior of upper triangular systems and use the fixed point theory to draw a few conclusions. Unless stated otherwise, we aim to understand asymptotic behavior dimension by dimension, working with upper triangular with internal blocks adds flexibility to the analysis.
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