The most general admissible boundary conditions are derived for an idealized AharonovBohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the AharonovBohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the AharonovBohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail.

Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagrange multiplier approach is applied to enforce the global connections of these basis functions. The interface problem on the Lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces, and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem. Our algorithm is shown to give a condition number bound of <i>C</i>(1+log(<i>H</i><i>h</i>))², independent of the two parameters, where <i>H</i><i>h</i> is the number of

We discuss spectral and resonance properties of a Hamiltonian describing motion of an electron moving on a hybrid surface consisting on a halfline attached by its endpoint to a plane under influence of a constant magnetic field which interacts with its spin through a Rashba-type term.

In this paper, we consider the numerical approximation of the three-dimensional poroelastic wave equations in the spherical coordinate system. One difficulty in the design of an efficient numerical scheme is that the problem is singular in the center and the polar axes of the computational domain. Nevertheless, we develop a hybrid finite difference/control volume method for solving this problem. Our method is explicit and is second order accurate in both space and time. Numerical results are shown to confirm the convergence rate of our method and the effectiveness to simulate wave propagation in poroelastic media in the spherical coordinate system.

In this paper, a class of FETI-DP preconditioners is developed for a fast solution of the linear system arising from staggered discontinuous Galerkin discretization of the two-dimensional Stokes equations. The discretization has been recently developed and has the distinctive advantages that it is optimally convergent and has a good local conservation property. In order to efficiently solve the linear system, two kinds of FETI-DP preconditioners, namely, lumped and Dirichlet preconditioners, are considered and analyzed. Scalable bounds C (H/h) and C (1+ log (H/h)) 2 are proved for the lumped and Dirichlet preconditioners, respectively, with the constant C depending on the infsup constant of the discrete spaces but independent of any mesh parameters. Here H/h stands for the number of elements across each subdomain. Numerical results are presented to confirm the theoretical estimates.

The initial decay rate of a mixed state is discussed; is shown to be zero for finite energy states. In the previous paper [1] we investigated a general scheme for description of unstable systems. One of our results concerned the initial decay rate. Generalizing the earlier results of Horwitz and Marchand (see [2] and other references contained in [1]) we proved there, that the initial decay rate of any pure state of the unstable system equals to zero, if this state is so called finite energy state. Here we shall be interested in the same problem, assuming now the state of the decaying system to be in general mixed. Such assumption seems to be reasonable: firstly, from the point of view of an experiment it is too restrictive to treat only pure states of unstable systems. In particular, mixed states are generally considered in the recent studies about the influence of measuring devices on the time evolution of the unstable system [3

We study the relationship between TsT transformations, marginal deformations of string theory on AdS3 backgrounds, and irrelevant deformations of 2d CFTs. We show that TsT transformations of NS-NS backgrounds correspond to instantaneous deformations of the worldsheet action by the antisymmetric product of two Noether currents, holographically mirroring the definition of the TT¯, JT¯, TJ¯, and JJ¯ deformations of 2d CFTs. Applying a TsT transformation to string theory on BTZ ×S^3×M^4 we obtain a general class of rotating black string solutions, including the Horne-Horowitz and the Giveon-Itzhaki-Kutasov ones as special cases, which we show are holographically dual to thermal states in single-trace TT¯-deformed CFTs. We also find a smooth solution interpolating between global AdS3 in the IR and a linear dilaton background in the UV that is interpreted as the NS-NS ground state in the dual TT¯-deformed CFT. This background suggests the existence of an upper bound on the deformation parameter above which the solution becomes complex. We find that the worldsheet spectrum, the thermodynamics of the black strings (in particular their Bekenstein-Hawking entropy), and the critical value of the deformation parameter match the corresponding quantities obtained from single-trace TT¯ deformations.

In this paper, gold ball wire bonding at low temperature using a high frequency transducer was evaluated. The substrates used were FR-4 laminates with two different gold-plated surface finishes: electrolytic and immersion gold-plated. Bonding temperatures of 120/spl deg/C, 80/spl deg/C and 40/spl deg/C were investigated with 1 mil fine pitch gold wire. Prior to wire bonding, the laminates and dice were plasma treated. The surfaces were analyzed prior to and after plasma treatment before wire bonding using XPS and AFM. Bonded areas were also analyzed using SEM. Design of experiment (DOE) techniques have been employed to optimize the bonding parameters at each temperature. The response of the DOE was evaluated by using bond shear and bond pull. The results show that bonding at low temperature is viable with the use of a high frequency transducer wire bonder.

We propose a model for scattering in a flat resonator with a thin antenna. The results are applied to rectangular microwave cavities. We compute the resonance spacing distribution and show that it agrees well with experimental data provided the antenna radius is much smaller than wavelengths of the resonance wavefunctions.

abstract

We generate a class of string backgrounds by a sequence of TsT transformations of the NS1-NS5 system that we argue are holographically dual to states in a single-trace TT¯+JT¯+TJ¯-deformed CFT2. The new string backgrounds include general rotating black hole solutions with two U(1) charges as well as a smooth solution without a horizon that is interpreted as the ground state. As evidence for the correspondence we (i) derive the long string spectrum and relate it to the spectrum of the dual field theory; (ii) show that the black hole thermodynamics can be reproduced from single-trace TT¯+JT¯+TJ¯-deformed CFTs; and (iii) show that the energy of the ground state matches the energy of the vacuum in the dual theory. We also study geometric properties of these new spacetimes and find that for some choices of the parameters the three-dimensional Ricci scalar in the Einstein frame can become positive in a region outside the horizon before reaching closed timelike curves and singularities.

Open quantum walks (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quan- tum information and quantum computation. Quantum Bernoulli noises are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environ- ment of an open quantum system. In this paper, by using quantum Bernoulli noises as the environment, we introduce an open quantum walk on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an open quantum walk. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally we show links between the walk and a unitary quantum walk recently introduced in terms of quantum Bernoulli noises.

Let $f(n)$ be the maximum number of edges in a graph on $n$ vertices in which no two cycles have the same length. P. Erdos raised the problem of determining $f(n)$ (see J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, New York, 1976), p.247, Problem 11). We present the problems, conjectures related to this problems and we summarize the know results. We make the following conjecture: \par \noindent{\bf Conjecture } $$\lim\sb {n \to \infty} {f(n)-n \over \sqrt n} = \sqrt {2 + \frac{4}{9}}.$$

We observe that some self-similar measures defined by finite or infinite iterated function systems with overlaps satisfy certain "bounded measure type condition", which allows us to extract useful measure-theoretic properties of iterates of the measure. We develop a technique to obtain a closed formula for the spectral dimension of the Laplacian defined by self-similar measure satisfying this condition. For Laplacians defined by fractal measures with overlaps, spectral dimension has been obtained earlier only for a small class of one-dimensional self-similar measures satisfying Strichartz second-order self-similar identities. The main technique we use relies on the vector-valued renewal theorem proved by Lau, Wang and Chu.

In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.

We describe an inductive machinery to prove various properties of representations of a category equipped with a generic shift functor. Specifically, we show that if a property (P) of representations of the category behaves well under the generic shift functor, then all finitely generated representations of the category have the property (P). In this way, we obtain simple criteria for properties such as Noetherianity, finiteness of Castelnuovo-Mumford regularity, and polynomial growth of dimension to hold. This gives a systemetic and uniform proof of such properties for representations of the categories $\FI_G$ and $\OI_G$ which appear in representation stability theory.

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