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