Abstract:
We present a detailed study of the dynamic response of a ring of $N$ equally spaced Josephson junctions to a time-periodic external flux, including screening current effects. The dynamics are described by the resistively shunted Josephson junction model, appropriate for proximity effect junctions, and we include Faraday's law for the flux. We find that the time-averaged $I-V$ characteristics show novel {\em subharmonic giant Shapiro voltage resonances}, which strongly depend on having phase slips or not, on $N$, on the inductance and on the external drive frequency. We include an estimate of the possible experimental parameters needed to observe these quantized voltage spikes.

Abstract:
Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be required, which leads to a large polynomial basis whereas usually only a few of the basis functions are in fact significant. Taking into account the sparse structure of the model, advanced techniques such as sparse PCE (SPCE), have been recently proposed to alleviate the computational issue. In this paper, we propose a novel approach to SPCE, which allows one to exploit the model's hierarchical structure. The proposed approach is based on the adaptive enrichment of the polynomial basis using the so-called principle of heredity. As a result, one can reduce the computational burden related to a large pre-defined candidate set while obtaining higher accuracy with the same computational budget.

Abstract:
Problem statement. The aim of the paper is to describe a method for calculation of cylindrical drilled pier foundation under the action of spatial force system.Results and conclusions. Contact stress contours are taken from results of the experiments. The relations between foundation load bearing capacity and different forms of shearing stress distribu-tion diagrams are obtained. It is established that calculation of load bearing capacity of drilled pier foundations under arbitrary action of inclined force can be reduced to the solution of simpler two-dimensional problems. It is concluded that the force acting on the foundation can be resolved into components located in the plane which goes through the foundation axis.

Abstract:
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from evaluation of finite-dimensional approximations to the time evolution operator. As the scaled hbar is changed from large to small, the statistics of the Quasienergy Eigenvalues (QEE) change from Poisson to circular orthogonal ensemble (COE). Different statistical tests are used to characterize this transition. The transition of the Quasienergy Eigenfunctions (QEF) is also studied using the chi-squared test with nu degrees of freedom, which goes over to the Porter-Thomas distribution for nu=1. We find that the integrable regime is associated with exponentially localized QEF whereas the eigenfunctions are extended in the chaotic, COE regime. We change the representation of the model to one in which the boundary is fixed and the Hamiltonian acquires a quadratic forcing term. We then carry out a successful comparison between specific classical phase space solutions and their corresponding QEFs in the Husimi representation.

Abstract:
The PP-wave/SYM proposal in its original form emphasizes a duality relation between the masses of the string states and the anomalous dimensions of the corresponding BMN operators in gauge theory, the mass--dimension type duality. In this paper, we give evidence in favour of another duality relation of the vertex--correlator type, which relates the coefficients of 3-point correlators of BMN operators in gauge theory to 3-string vertices in lightcone string field theory in the pp-wave background. We verify that all the available field theory results in the literature, as well as the newly obtained ones, for the 3-point functions are successfully reproduced from our proposal.

Abstract:
Agency cost theory is an important branch of capital structural theory. Free cash flow has significant impact on agency cost. The combination of research on these two fields would help to build and extend the theoretical system. Based on agency cost theory, the present study firstly categorized the characteristics of free cash flow as well as the statistical methodologies. Furthermore, the existence of investing free cash flow in agency cost was proved by a model. Then free cash flow was introduced into agency cost theory as restriction, the analysis shows that it will change agency cost, in turn, will have an impact on the relationship between agency cost and capital structure, finally, will influence the optimal capital structure point to maintain the equilibrium. Concretely, with the increasing free cash flow, correspondingly, debt proportion will decrease.

Abstract:
Cyclic voltammetry data in the region 0 to - 0.4V using a static mercury drop electrode indicate a redox active peroxo-molybdate species in solutions obtained by dissolving the metal in 30% v/v H2O2. There was no observable colored species formation in this potential range. Admittance data at different frequencies suggest orientation effects of water molecules at or near the double layer. The admittance maximum near the double layer changeover region exhibits a small anodic shift on lowering the frequencies. Impedance measurements in aqueous H2Mo2O3(O-O)4(H2O)2 suggest spatiotemporal oscillations and the impedance loci observed in four quadrants near 0.1V is a characteristic of the Hopf bifurcation. This unique impedance is exhibited only in a narrow band potential. With increase in surface area the spatiotemporal periodicity becomes more efficient. The negative differential resistance observed, indicative of quantum mechanical resonant tunneling, points to the probable unique role of peroxide and molybdenum enzymes in global coupling to facilitate information transfer in biochemical processes.

Abstract:
MoO42- condenses on increasing acidity in aqueous solution and the extent of condensation depends on the level of pH. Frequency response analysis in the range 1000 Hz to 35 mHz and cyclic voltammetry were used to characterize the admittance, impedance, double layer capacitance, and semiconduction behavior of different protonated mono-, hepta- and octa- isopolyoxomolybdate species in solution. It was found that the dominant species was MoO42- in the pH range 7-12 and the protonated species were of Mo7O246- and of Mo8O264- in the pH range 3-5 and below pH 2 respectively. This observation is consistent with the potentiometric titration data. Frequency as well as potential dependent color oscillations between blue and brown or gold at the mercury electrode were also observed. The results promise a new way of investigating polyoxometalates in solution.