The Edge Ideals of Complete Multipartite Hypergraphs

We classify all complete uniform multipartite hypergraphs with respect to some algebraic properties, such as being (almost) complete intersection, Gorenstein, level, l-Cohen-Macaulay, l-Buchsbaum, unmixed, and satisfying Serre's condition S _r , via some combinatorial terms. Also, we prove that for a complete s-uniform t-partite hypergraph ?, vertex decomposability, shellability, sequentially S _r , and sequentially Cohen–Macaulay properties coincide with the condition that ? has t ? 1 sides consisting of a single vertex. Moreover, we show that the latter condition occurs if and only if it is a chordal hypergraph.     

Multipliers on homogeneous Banach spaces with respect to Jacobi polynomials

A bounded linear operator is called multiplier with respect to Jacobi polynomials if and only if it commutes with all Jacobi translation operators on $[-1,1]$ . Multipliers on homogeneous Banach spaces on $[-1,1]$ determined by the Jacobi translation operator are introduced and studied. First we prove four equivalent characterizations of a multiplier for an arbitrary homogeneous Banach spaces $B$ on $[-1,1]$ . One of them implies the existence of an algebra isomorphism from the set of all multipliers on $B$ into the set of all pseudomeasures. Further, we study multipliers on specific examples of homogeneous Banach spaces on $[-1,1]$ . Amongst others, multipliers on the Wiener algebra, on the Beurling space and on Sobolev spaces are analyzed. We obtain that the multiplier spaces of the Wiener algebra, the Beurling space and of all Sobolev spaces are isometric isomorphic to each other. Furthermore, these multiplier spaces are all isometric isomorphic to the set of all pseudomeasures.     

Maximal Subgroups of Subnormal Subgroups of GL n (D) with Finite Conjugacy Classes

Let D be an infinite division ring. A famous result due to Herstein says that every noncentral element of D has infinitely many conjugates in D. So, if D* is an FC-group, then D is a field. Now let N be a subnormal subgroup of GL _n (D), where n ≥ 1, and M a maximal subgroup of N. In this article, we prove that if M is an FC-group, then M is contained in the multiplicative group of some subfield of M _n (D).     

Cosmological dynamics with modified induced gravity on the normal DGP branch

In this Letter we investigate cosmological dynamics on the normal branch of a DGP-inspired scenario within a phase space approach where induced gravity is modified in the spirit of f(R)$f(R)$-theories. We apply the dynamical system analysis to achieve the stable solutions of the scenario in the normal DGP branch. Firstly, we consider a general form of the modified induced gravity and we show that there is a standard de Sitter point in phase space of the model. Then we prove that this point is stable attractor only for those f(R)$f(R)$ functions that account for late-time cosmic speed-up.     

Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field

The vibration and instability of a single-walled carbon nanotube (SWCNT) under a general magnetic field are of particular interest to researchers. Using nonlocal Rayleigh beam theory and Maxwell’s equations, the dimensionless governing equations pertinent to the free vibration of a SWCNT due to a general magnetic field were derived. The effects of the longitudinal and transverse magnetic fields on the longitudinal and flexural frequencies as well as their corresponding phase velocities were addressed and are discussed below. The critical transverse magnetic field (CTMF) associated with the lateral buckling of the SWCNT was obtained. The obtained results reveal that the CTMF increases with the longitudinally induced magnetic field. Further, its value decreases as the effect of the small-scale parameter increases.     

Theory and simulation of cavity quantum electro-dynamics in multi-partite quantum complex systems

The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole–dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured.     

Temperature dependence of the optical properties of ion-beam sputtered ZrN films

The reflectivity of sputtered Zirconium nitride films on glass substrate has been investigated in the spectral energy range of 0.8–6.1 eV as a function of deposition temperature varying between 373 and 723 K. Optical constants of the prepared films have been determined using the Drude analysis. Experimental results showed strong dependency of optical properties of the films, such as optical resistivity on the substrate temperature. The temperature increase of the substrate has shown an increase in both the plasmon frequency and electron scattering time. The electrical behavior of the films showed a good agreement between their optical and electrical resistivity.     

Discrete mechanics and mixed integer optimal control of dynamical systems

Mixed integer optimal control problems are a generalization of ordinary optimal control problems that include additional integer valued control functions. The integer control functions are used to switch instantaneously from one system to another. We use a time transformation (similar as in [1]) to get rid of the integer valued functions. This allows to apply gradient based optimization methods to approximate the mixed integer optimal control problem. The time transformation from [1] is adapted such that problems with distinct state domains for each system can be solved and it is combined with the direct discretization method DMOC [2,3] (Discrete Mechanics and Optimal Control) to approximate trajectories of the underlying optimal control problems. Our approach is illustrated with the help of a first example, the hybrid mass oscillator. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An alternative approach for measuring the scattered acoustic pressure field of immersed single and multiple cylinders

The form function of an elastic target can be obtained from the scattered signal through a deconvolution process. The deconvolution process uses the signal measured from an acoustically hard target (reference signal) to compensate for the impulse response of the measurement system. In this paper, it is shown that this approach limits the usable frequency range of the signal and leads to inaccuracies in the final results. An alternative approach is proposed in which the reference signal is replaced by the specular echo. A procedure is described for extracting the specular echo from the measured signal even in cases where it is not completely isolated from the resonant components. Modifications are made to the existing deconvolution formulation and it is further extended to be applicable to multiple scattering measurements. Experimental results show that the new approach provides improved accuracy and wider usable frequency range in both single and multiple scattering experiments.