295,410 research outputs found
Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs
The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes
Coupled oscillators and Feynman's three papers
According to Richard Feynman, the adventure of our science of physics is a
perpetual attempt to recognize that the different aspects of nature are really
different aspects of the same thing. It is therefore interesting to combine
some, if not all, of Feynman's papers into one. The first of his three papers
is on the ``rest of the universe'' contained in his 1972 book on statistical
mechanics. The second idea is Feynman's parton picture which he presented in
1969 at the Stony Brook conference on high-energy physics. The third idea is
contained in the 1971 paper he published with his students, where they show
that the hadronic spectra on Regge trajectories are manifestations of
harmonic-oscillator degeneracies. In this report, we formulate these three
ideas using the mathematics of two coupled oscillators. It is shown that the
idea of entanglement is contained in his rest of the universe, and can be
extended to a space-time entanglement. It is shown also that his parton model
and the static quark model can be combined into one Lorentz-covariant entity.
Furthermore, Einstein's special relativity, based on the Lorentz group, can
also be formulated within the mathematical framework of two coupled
oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman
Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction
Conductance Oscillations in Transition Metal Superlattices
We present a numerical study of conductance oscillations of transition metal
multilayers as a function of layer thickness. Using a material-specific
tight-binding model, we show that for disorder-free layers with random
thicknesses but clean interfaces, long-period oscillations in the conductance
can occur, which are reminiscent of those found in structures exhibiting GMR.
Using a heuristic effective mass model, we argue that these oscillations arise
from beating between the Fermi wavevector and a class of wavevectors
characteristic of the superlattice structure.Comment: 4 pages, 4 figure
Single-shot layered reflectance separation using a polarized light field camera
We present a novel computational photography technique for single shot separation of diffuse/specular reflectance as well as novel angular domain separation of layered reflectance. Our solution consists of a two-way polarized light field (TPLF) camera which simultaneously captures two orthogonal states of polarization. A single photograph of a subject acquired with the TPLF camera under polarized illumination then enables standard separation of diffuse (depolarizing) and polarization preserving specular reflectance using light field sampling. We further demonstrate that the acquired data also enables novel angular separation of layered reflectance including separation of specular reflectance and single scattering in the polarization preserving component, and separation of shallow scattering from deep scattering in the depolarizing component. We apply our approach for efficient acquisition of facial reflectance including diffuse and specular normal maps, and novel separation of photometric normals into layered reflectance normals for layered facial renderings. We demonstrate our proposed single shot layered reflectance separation to be comparable to an existing multi-shot technique that relies on structured lighting while achieving separation results under a variety of illumination conditions
The (1,2)-Step Competition Graph of a Tournament
The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C1,2(D), as the graph on V(D) where {x,y}∈E(C1,2(D)) if and only if there exists a vertex z≠x,y, such that either dD−y(x,z)=1 and dD−x(y,z)≤2 or dD−x(y,z)=1 and dD−y(x,z)≤2. In this paper, we characterize the (1,2)-step competition graphs of tournaments and extend our results to the (i,k)-step competition graph of a tournament
Elliptical Tempered Stable Distribution and Fractional Calculus
A definition for elliptical tempered stable distribution, based on the
characteristic function, have been explained which involve a unique spectral
measure. This definition provides a framework for creating a connection between
infinite divisible distribution, and particularly elliptical tempered stable
distribution, with fractional calculus. Finally, some analytical approximations
for the probability density function of tempered infinite divisible
distribution, which elliptical tempered stable distributions are a subclass of
them, are considered.Comment: 16 pages, working pape
Enhanced dynamical entanglement transfer with multiple qubits
We present two strategies to enhance the dynamical entanglement transfer from
continuous variable (CV) to finite dimensional systems by employing multiple
qubits. First, we consider the entanglement transfer to a composite finite
dimensional system of many qubits simultaneously interacting with a bipartite
CV field. We show that, considering realistic conditions in the generation of
CV entanglement, a small number of qubits resonantly coupled to the CV system
is sufficient for an almost complete dynamical transfer of the entanglement.
Our analysis also sheds further light on the transition between microscopic and
macroscopic behaviours of composite finite dimensional systems coupled to
bosonic fields (like atomic clouds interacting with light). Furthermore, we
present a protocol based on sequential interactions of the CV system with some
ancillary qubit systems and on subsequent measurements, allowing to
probabilistically convert CV entanglement into `almost perfect' Bell pairs of
two qubits. Our proposals are suited for realizations in various experimental
settings, ranging from cavity-QED to cavity-integrated superconducting devices.Comment: 10 pages, 8 figures, RevTeX4; terminology revised; accepted for
publicatio
Standing waves in the Lorentz-covariant world
When Einstein formulated his special relativity, he developed his dynamics
for point particles. Of course, many valiant efforts have been made to extend
his relativity to rigid bodies, but this subject is forgotten in history. This
is largely because of the emergence of quantum mechanics with wave-particle
duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have
to deal with Lorentz transformations of waves. We now have some understanding
of plane waves or running waves in the covariant picture, but we do not yet
have a clear picture of standing waves. In this report, we show that there is
one set of standing waves which can be Lorentz-transformed while being
consistent with all physical principle of quantum mechanics and relativity. It
is possible to construct a representation of the Poincar\'e group using
harmonic oscillator wave functions satisfying space-time boundary conditions.
This set of wave functions is capable of explaining the quantum bound state for
both slow and fast hadrons. In particular it can explain the quark model for
hadrons at rest, and Feynman's parton model hadrons moving with a speed close
to that of light.Comment: LaTex 20 pages, presented at the 2004 meeting of the International
Association of Relativistic Dynamincs, to be published in the proceeding
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