5,458 research outputs found
Integral operators of certain univalent functions
A function f, analytic in the unit disc Δ, is said to be in the family Rn(α) if Re{(znf(z))(n+1)/(zn−1f(z))(n)}>(n+α)/(n+1) for some α(0≤α<1) and for all z in Δ, where n ϵ No, No={0,1,2,…}. The The class Rn(α) contains the starlike functions of order α for n≥0 and the convex functions of order α for n≥1. We study a class of integral operators defined on Rn(α). Finally an argument theorem is proved
Phase transitions in diluted negative-weight percolation models
We investigate the geometric properties of loops on two-dimensional lattice
graphs, where edge weights are drawn from a distribution that allows for
positive and negative weights. We are interested in the appearance of spanning
loops of total negative weight. The resulting percolation problem is
fundamentally different from conventional percolation, as we have seen in a
previous study of this model for the undiluted case.
Here, we investigate how the percolation transition is affected by additional
dilution. We consider two types of dilution: either a certain fraction of edges
exhibit zero weight, or a fraction of edges is even absent. We study these
systems numerically using exact combinatorial optimization techniques based on
suitable transformations of the graphs and applying matching algorithms. We
perform a finite-size scaling analysis to obtain the phase diagram and
determine the critical properties of the phase boundary.
We find that the first type of dilution does not change the universality
class compared to the undiluted case whereas the second type of dilution leads
to a change of the universality class.Comment: 8 pages, 7 figure
Electronic structure and chemical bonding in Ti2AlC investigated by soft x-ray emission spectroscopy
The electronic structure of the nanolaminated transition metal carbide Ti2AlC
has been investigated by bulk-sensitive soft x-ray emission spectroscopy. The
measured Ti L, C K and Al L emission spectra are compared with calculated
spectra using ab initio density-functional theory including dipole matrix
elements. The detailed investigation of the electronic structure and chemical
bonding provides increased understanding of the physical properties of this
type of nanolaminates. Three different types of bond regions are identified;
the relatively weak Ti 3d - Al 3p hybridization 1 eV below the Fermi level, and
the Ti 3d - C 2p and Ti 3d - C 2s hybridizations which are stronger and deeper
in energy are observed around 2.5 eV and 10 eV below the Fermi level,
respectively. A strongly modified spectral shape of the 3s final states in
comparison to pure Al is detected for the buried Al monolayers indirectly
reflecting the Ti 3d - Al 3p hybridization. The differences between the
electronic and crystal structures of Ti2AlC, Ti3AlC2 and TiC are discussed in
relation to the number of Al layers per Ti layer in the two former systems and
the corresponding change of the unusual materials properties.Comment: 14 pages, 7 figures; PACS:78.70.En, 71.15.Mb, 71.20.-
Electronic structure and chemical bonding in Ti4SiC3 investigated by soft x-ray emission spectroscopy and first principle theory
The electronic structure in the new transition metal carbide Ti4SiC3 has been
investigated by bulk-sensitive soft x-ray emission spectroscopy and compared to
the well-studied Ti3SiC2 and TiC systems. The measured high-resolution Ti L, C
K and Si L x-ray emission spectra are discussed with ab initio calculations
based on density-functional theory including core-to-valence dipole matrix
elements. The detailed investigations of the Ti-C and Ti-Si chemical bonds
provide increased understanding of the physical properties of these
nanolaminates. A strongly modified spectral shape is detected for the buried Si
monolayers due to Si 3p hybridization with the Ti 3d orbitals. As a result of
relaxation of the crystal structure and the charge-transfer from Ti (and Si) to
C, the strength of the Ti-C covalent bond is increased. The differences between
the electronic and crystal structures of Ti4SiC3 and Ti3SiC2 are discussed in
relation to the number of Si layers per Ti layer in the two systems and the
corresponding change of materials properties.Comment: 12 pages, 7 figures, 1 tabl
Electronic structure investigation of Ti3AlC2, Ti3SiC2, and Ti3GeC2 by soft-X-ray emission spectroscopy
The electronic structures of epitaxially grown films of Ti3AlC2, Ti3SiC2 and
Ti3GeC2 have been investigated by bulk-sensitive soft X-ray emission
spectroscopy. The measured high-resolution Ti L, C K, Al L, Si L and Ge M
emission spectra are compared with ab initio density-functional theory
including core-to-valence dipole matrix elements. A qualitative agreement
between experiment and theory is obtained. A weak covalent Ti-Al bond is
manifested by a pronounced shoulder in the Ti L-emission of Ti3AlC2. As Al is
replaced with Si or Ge, the shoulder disappears. For the buried Al and
Si-layers, strongly hybridized spectral shapes are detected in Ti3AlC2 and
Ti3SiC2, respectively. As a result of relaxation of the crystal structure and
the increased charge-transfer from Ti to C, the Ti-C bonding is strengthened.
The differences between the electronic structures are discussed in relation to
the bonding in the nanolaminates and the corresponding change of materials
properties.Comment: 15 pages, 8 figure
Some Properties of Fractional Calculus and Linear Operators Associated with Certain Subclass of Multivalent Functions
We investigate several distortion inequalities involving fractional calculus,
Ruscheweyh derivatives, and some well-known integral operators. In special cases, the results
presented in this paper provide new approaches to several previously known results
Reflectivity Anisotropy Spectra of Cu- and Ag- (110) surfaces from {\it ab initio} theory
We are able to disentagle the effects of the intraband and interband parts of
the bulk dielectric function on the bare dielectric anisotropy of the surface.
We show how the position, sign and amplitude of the structures observed in such
spectra depend on the above quantities. The lineshape of all the calculated
structures agree very well with the ones observed experimentally for samples
treated by suitable surface cleaning. In particular, we reproduce the observed
single peak structure of Ag at high energy, found to represent a state of the
clean surface different from the one giving the originally observed double peak
structure. This results is not reproduced by the 'local field' model.Comment: 4 pages, 3 figures. submitted to Phys. Rev. Let
The maximally entangled symmetric state in terms of the geometric measure
The geometric measure of entanglement is investigated for permutation
symmetric pure states of multipartite qubit systems, in particular the question
of maximum entanglement. This is done with the help of the Majorana
representation, which maps an n qubit symmetric state to n points on the unit
sphere. It is shown how symmetries of the point distribution can be exploited
to simplify the calculation of entanglement and also help find the maximally
entangled symmetric state. Using a combination of analytical and numerical
results, the most entangled symmetric states for up to 12 qubits are explored
and discussed. The optimization problem on the sphere presented here is then
compared with two classical optimization problems on the S^2 sphere, namely
Toth's problem and Thomson's problem, and it is observed that, in general, they
are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and
reference
Elastic and vibrational properties of alpha and beta-PbO
The structure, electronic and dynamic properties of the two layered alpha
(litharge) and beta (massicot) phases of PbO have been studied by density
functional methods. The role of London dispersion interactions as leading
component of the total interaction energy between layers has been addressed by
using the Grimme's approach, in which new parameters for Pb and O atoms have
been developed. Both gradient corrected and hybrid functionals have been
adopted using Gaussian-type basis sets of polarized triple zeta quality for O
atoms and small core pseudo-potential for the Pb atoms. Basis set superposition
error (BSSE) has been accounted for by the Boys-Bernardi correction to compute
the interlayer separation. Cross check with calculations adopting plane waves
that are BSSE free have also been performed for both structures and vibrational
frequencies. With the new set of proposed Grimme's type parameters structures
and dynamical parameters for both PbO phases are in good agreement with
experimental data.Comment: 8 pages, 5 figure
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