672 research outputs found
Second harmonic generation and birefringence of some ternary pnictide semiconductors
A first-principles study of the birefringence and the frequency dependent
second harmonic generation (SHG) coefficients of the ternary pnictide
semiconductors with formula ABC (A = Zn, Cd; B = Si, Ge; C = As, P) with
the chalcopyrite structures was carried out. We show that a simple empirical
observation that a smaller value of the gap is correlated with larger value of
SHG is qualitatively true. However, simple inverse power scaling laws between
gaps and SHG were not found. Instead, the real value of the nonlinear response
is a result of a very delicate balance between different intraband and
interband terms.Comment: 13 pages, 12 figure
The Asymptotic distribution of circles in the orbits of Kleinian groups
Let P be a locally finite circle packing in the plane invariant under a
non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When
Gamma is geometrically finite, we construct an explicit Borel measure on the
plane which describes the asymptotic distribution of small circles in P,
assuming that either the critical exponent of Gamma is strictly bigger than 1
or P does not contain an infinite bouquet of tangent circles glued at a
parabolic fixed point of Gamma. Our construction also works for P invariant
under a geometrically infinite group Gamma, provided Gamma admits a finite
Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite.
Some concrete circle packings to which our result applies include Apollonian
circle packings, Sierpinski curves,
Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat
Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros
of cyclotomic polynomials with interlacing zero
An update on the Hirsch conjecture
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to
George Dantzig. It states that the graph of a d-dimensional polytope with n
facets cannot have diameter greater than n - d.
Despite being one of the most fundamental, basic and old problems in polytope
theory, what we know is quite scarce. Most notably, no polynomial upper bound
is known for the diameters that are conjectured to be linear. In contrast, very
few polytopes are known where the bound is attained. This paper collects
known results and remarks both on the positive and on the negative side of the
conjecture. Some proofs are included, but only those that we hope are
accessible to a general mathematical audience without introducing too many
technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2
and put into the appendix arXiv:0912.423
Three-variable Mahler measures and special values of modular and Dirichlet -series
In this paper we prove that the Mahler measures of the Laurent polynomials
, ,
and , for various values of , are of the form , where , is a CM newform of
weight 3, and is a quadratic character. Since it has been proved that
these Maher measures can also be expressed in terms of logarithms and
-hypergeometric series, we obtain several new hypergeometric evaluations
and transformations from these results
Fixed point results for generalized cyclic contraction mappings in partial metric spaces
Rus (Approx. Convexity 3:171â178, 2005) introduced the concept of cyclic contraction
mapping. PËacurar and Rus (Nonlinear Anal. 72:1181â1187, 2010) proved some fixed
point results for cyclic Ï-contraction mappings on a metric space. Karapinar (Appl. Math.
Lett. 24:822â825, 2011) obtained a unique fixed point of cyclic weak Ï- contraction mappings
and studied well-posedness problem for such mappings. On the other hand, Matthews
(Ann. New York Acad. Sci. 728:183â197, 1994) introduced the concept of a partial metric
as a part of the study of denotational semantics of dataflow networks. He gave a modified
version of the Banach contraction principle, more suitable in this context. In this paper, we
initiate the study of fixed points of generalized cyclic contraction in the framework of partial
metric spaces. We also present some examples to validate our results.S. Romaguera acknowledges the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Abbas, M.; Nazir, T.; Romaguera Bonilla, S. (2012). Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 106(2):287-297. https://doi.org/10.1007/s13398-011-0051-5S2872971062Abdeljawad T., Karapinar E., Tas K.: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24(11), 1894â1899 (2011). doi: 10.1016/j.aml.2011.5.014Altun, I., Erduran A.: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. article ID 508730 (2011). doi: 10.1155/2011/508730Altun I., Sadarangani K.: Corrigendum to âGeneralized contractions on partial metric spacesâ [Topology Appl. 157 (2010), 2778â2785]. Topol. Appl. 158, 1738â1740 (2011)Altun I., Simsek H.: Some fixed point theorems on dualistic partial metric spaces. J. Adv. Math. Stud. 1, 1â8 (2008)Altun I., Sola F., Simsek H.: Generalized contractions on partial metric spaces. Topol. Appl. 157, 2778â2785 (2010)Aydi, H.: Some fixed point results in ordered partial metric spaces. arxiv:1103.3680v1 [math.GN](2011)Boyd D.W., Wong J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458â464 (1969)Bukatin M., Kopperman R., Matthews S., Pajoohesh H.: Partial metric spaces. Am. Math. Monthly 116, 708â718 (2009)Bukatin M.A., Shorina S.Yu. et al.: Partial metrics and co-continuous valuations. In: Nivat, M. (eds) Foundations of software science and computation structure Lecture notes in computer science vol 1378., pp. 125â139. Springer, Berlin (1998)Derafshpour M., Rezapour S., Shahzad N.: On the existence of best proximity points of cyclic contractions. Adv. Dyn. Syst. Appl. 6, 33â40 (2011)Heckmann R.: Approximation of metric spaces by partial metric spaces. Appl. Cat. Struct. 7, 71â83 (1999)Karapinar E.: Fixed point theory for cyclic weak -contraction. App. Math. Lett. 24, 822â825 (2011)Karapinar, E.: Generalizations of Caristi Kirkâs theorem on partial metric spaces. Fixed Point Theory Appl. 2011,4 (2011). doi: 10.1186/1687-1812-2011-4Karapinar E.: Weak -contraction on partial metric spaces and existence of fixed points in partially ordered sets. Math. Aeterna. 1(4), 237â244 (2011)Karapinar E., Erhan I.M.: Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24, 1894â1899 (2011)Karpagam S., Agrawal S.: Best proximity point theorems for cyclic orbital MeirâKeeler contraction maps. Nonlinear Anal. 74, 1040â1046 (2011)Kirk W.A., Srinavasan P.S., Veeramani P.: Fixed points for mapping satisfying cylical contractive conditions. Fixed Point Theory. 4, 79â89 (2003)Kosuru, G.S.R., Veeramani, P.: Cyclic contractions and best proximity pair theorems). arXiv:1012.1434v2 [math.FA] 29 May (2011)Matthews S.G.: Partial metric topology. in: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 728, 183â197 (1994)Neammanee K., Kaewkhao A.: Fixed points and best proximity points for multi-valued mapping satisfying cyclical condition. Int. J. Math. Sci. Appl. 1, 9 (2011)Oltra S., Valero O.: Banachâs fixed theorem for partial metric spaces. Rend. Istit. Mat. Univ. Trieste. 36, 17â26 (2004)PÄcurar M., Rus I.A.: Fixed point theory for cyclic -contractions. Nonlinear Anal. 72, 1181â1187 (2010)Petric M.A.: Best proximity point theorems for weak cyclic Kannan contractions. Filomat. 25, 145â154 (2011)Romaguera, S.: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. (2010, article ID 493298, 6 pages).Romaguera, S.: Fixed point theorems for generalized contractions on partial metric spaces. Topol. Appl. (2011). doi: 10.1016/j.topol.2011.08.026Romaguera S., Valero O.: A quantitative computational model for complete partial metric spaces via formal balls. Math. Struct. Comput. Sci. 19, 541â563 (2009)Rus, I.A.: Cyclic representations and fixed points. Annals of the Tiberiu Popoviciu Seminar of Functional equations. Approx. Convexity 3, 171â178 (2005), ISSN 1584-4536Schellekens M.P.: The correspondence between partial metrics and semivaluations. Theoret. Comput. Sci. 315, 135â149 (2004)Valero O.: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Top. 6, 229â240 (2005)Waszkiewicz P.: Quantitative continuous domains. Appl. Cat. Struct. 11, 41â67 (2003
Hamiltonian Study of Improved Lattice Gauge Theory in Three Dimensions
A comprehensive analysis of the Symanzik improved anisotropic
three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made.
Monte Carlo techniques are used to obtain numerical results for the static
potential, ratio of the renormalized and bare anisotropies, the string tension,
lowest glueball masses and the mass ratio. Evidence that rotational symmetry is
established more accurately for the Symanzik improved anisotropic action is
presented. The discretization errors in the static potential and the
renormalization of the bare anisotropy are found to be only a few percent
compared to errors of about 20-25% for the unimproved gauge action. Evidence of
scaling in the string tension, antisymmetric mass gap and the mass ratio is
observed in the weak coupling region and the behaviour is tested against
analytic and numerical results obtained in various other Hamiltonian studies of
the theory. We find that more accurate determination of the scaling
coefficients of the string tension and the antisymmetric mass gap has been
achieved, and the agreement with various other Hamiltonian studies of the
theory is excellent. The improved action is found to give faster convergence to
the continuum limit. Very clear evidence is obtained that in the continuum
limit the glueball ratio approaches exactly 2, as expected in a
theory of free, massive bosons.Comment: 13 pages, 15 figures, submitted to Phys. Rev.
Electrostatic Potentials in Supernova Remnant Shocks
Recent advances in the understanding of the properties of supernova remnant
shocks have been precipitated by the Chandra and XMM X-ray Observatories, and
the HESS Atmospheric Cerenkov Telescope in the TeV band. A critical problem for
this field is the understanding of the relative degree of dissipative
heating/energization of electrons and ions in the shock layer. This impacts the
interpretation of X-ray observations, and moreover influences the efficiency of
injection into the acceleration process, which in turn feeds back into the
thermal shock layer energetics and dynamics. This paper outlines the first
stages of our exploration of the role of charge separation potentials in
non-relativistic electron-ion shocks where the inertial gyro-scales are widely
disparate, using results from a Monte Carlo simulation. Charge density spatial
profiles were obtained in the linear regime, sampling the inertial scales for
both ions and electrons, for different magnetic field obliquities. These were
readily integrated to acquire electric field profiles in the absence of
self-consistent, spatial readjustments between the electrons and the ions. It
was found that while diffusion plays little role in modulating the linear field
structure in highly oblique and perpendicular shocks, in quasi-parallel shocks,
where charge separations induced by gyrations are small, and shock-layer
electric fields are predominantly generated on diffusive scales.Comment: 7 pages, 2 embedded figures, Accepted for publication in Astrophysics
and Space Science, as part of the HEDLA 2006 conference proceeding
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