Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the $n$-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.Comment: 12 pages, 0 figur

Factorization and Endpoint Singularities in Heavy-to-Light decays

We prove a factorization theorem for heavy-to-light form factors. Our result differs in several important ways from previous proposals. A proper separation of scales gives hard kernels that are free of endpoint singularities. A general procedure is described for including soft effects usually associated with the tail of wavefunctions in hard exclusive processes. We give an operator formulation of these soft effects using the soft-collinear effective theory, and show that they appear at the same order in the power counting as the hard spectator contribution.Comment: 5 pages, Added details on comparison with the literatur

Strong Phases and Factorization for Color Suppressed Decays

We prove a factorization theorem in QCD for the color suppressed decays B0-> D0 M0 and B0-> D*0 M0 where M is a light meson. Both the color-suppressed and W-exchange/annihilation amplitudes contribute at lowest order in LambdaQCD/Q where Q={mb, mc, Epi}, so no power suppression of annihilation contributions is found. A new mechanism is given for generating non-perturbative strong phases in the factorization framework. Model independent predictions that follow from our results include the equality of the B0 -> D0 M0 and B0 -> D*0 M0 rates, and equality of non-perturbative strong phases between isospin amplitudes, delta(DM) = delta(D*M). Relations between amplitudes and phases for M=pi,rho are also derived. These results do not follow from large Nc factorization with heavy quark symmetry.Comment: 38 pages, 6 figs, typos correcte

Gravitational Corrections to the Energy-Levels of a Hydrogen Atom

The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.Comment: 7 page

A Damage Mechanics Approach to Fatigue Assessment in Offshore Structures

This article is intended to describe the development of a fatigue damage model capable of assessing fatigue damage in offshore structures. This is achieved by for mulating a set of damage coupled constitutive and evolution equations which make the for mulation of a unified approach possible under both low and high cycle fatigue damage and consistent with the structural dynamic response of the changing/deteriorating material be haviors. The structural analysis for the whole designed period, say about 30 years, can be carried out with the aid of the proposed analytical procedure, in which the fundamental characteristics of sea wave statistics responsible for the structural dynamic response can be sufficiently considered. An offshore structure subject to complex ocean environment is described by a general stochastic system which embeds a group of stochastic subsystems, each characterizing a duty cycle. An effective analytical method is established by introduc ing the concept of duty strain range with a clear mathematical definition and its analytical solution which covers all possible spectral parameters. The history-dependent damage is also included in the damage model so that the overload effects can be analyzed. It should be pointed out that the whole procedure can be fully computerized such that the practical or engineering significance of varying design variables can be readily highlighted.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67255/2/10.1177_105678959300200405.pd

Experimental study of the flow velocity reduction behind fishing net

A series of physical model experiments is conducted to investigate the flow velocity reduction downstream from fishing net in current. The plane net is fixed on a steel frame, which is 0.3 m in width and 0.3 m in height, and positioned in the center of the flume normal to the flow direction. In the experiments, the acoustic Doppler velocimeter (ADV) is applied to measure the flow velocity behind the plane net. This paper presents the flow velocity reduction behind the plane net(s) with different solidity, spacing distances between two plane nets and plane net numbers. According to the experimental data, there exists an obvious flow velocity reduction downstream from the\ud plane net and the flow velocity reduction increases with increasing net solidity. For two plane nets with different spacing distances, the average value of flow velocity reduction factor is 0.90 between and 0.83 downstream the two plane nets. As the net number increases from 1 to 4, the minimum flow velocity reduction factor downstream from the\ud plane nets decreases from 0.90 to 0.68. It is found that there is a close relationship between the flow velocity reduction and the above parameters of the plane net. These results should help improve understanding of flow around the net cage

On-line distributed hierarchical control and optimisation of large scale systems

This research is concerned with the application of closed-loop coordination techniques for on-line steady state optimisation and control of large scale systems using a micro-computer based system. A two-level hierarchical computer structure consisting of a coordinator at the supremal (upper) level and two local decision units at the infimal (lower) level had been established. Parallel computation were performed at the local decision unit level once the coordination parameters had been received from the supremal level. A steady state system model consisting of two interconnected subprocesses, simulated oy an analogue computer, was used to investigate the coordination methods for closed-loop hierarchical control. First-order time constants were introduced to the interaction inputs and the controls within the simulated subprocesses. Investigations had been carried out to study closed loop control using the Interaction Prediction and Interaction Balance coordination method. Special attention was given to the study of the problems associated with synchronisation of the local decision units for closed-loop control. Stability aspects of both coordination methods when subjected to disturbances in the controls and interconnections had been investigated~ Problems relating to system transient and local. decision asynchronisation, as well as their effects on system stability and convergence of the two tasks, namely the local decision task and the coordinator task had also been investigated. Methods for dealing with these problems had been suggested. The sub-optimality, convergency and robustness properties of each coordination method had been discussed. This research has demonstrated that the Interaction Prediction coordination methods are best suited for on-line distributed optimising control of large scale interconnected systems. Using the local feedback scheme, complete decentralisation at the local decision level operated asynchronou.sly can be achieved with the Interaction Prediction coordination method

What Encourages Purchase of Virtual Gifts in Live Streaming: Cognitive Absorption, Social Experience and Technological Environment

Live streaming has become extraordinarily popular worldwide. As a new form of social media, live streaming enables two levels of real-time interactions (i.e., between viewers and the streamer, and among viewers) and is monetized in a new way-viewers’ purchase of virtual gifts. The new monetization model has achieved a great success, yet there is a lack of understanding about what encourages viewers to purchase virtual gifts in live streaming. To explain such purchase behavior, this study develops a model which investigates the roles of viewers’ holistic experience with the system (i.e., cognitive absorption) and their social experiences (i.e., para-social interaction and virtual crowd experience), as well as how these experiences are developed within the technological environment of live streaming (i.e., interactivity, deep profiling and design aesthetics). The model was validated by using survey data collected from China. We also discuss implications for research and practice emerging out of this study

Revisiting the B {\to} {\pi} {\rho}, {\pi} {\omega} Decays in the Perturbative QCD Approach Beyond the Leading Order

We calculate the branching ratios and CP asymmetries of the $B \to \pi \rho$, $\pi\omega$ decays in the perturbative QCD factorization approach up to the next-to-leading-order contributions. We find that the next-to-leading-order contributions can interfere with the leading-order part constructively or destructively for different decay modes. Our numerical results have a much better agreement with current available data than previous leading-order calculations, e.g., the next-to-leading-order corrections enhance the $B^0\rightarrow \pi^0\rho^0$ branching ratios by a factor 2.5, which is helpful to narrow the gaps between theoretic predictions and experimental data. We also update the direct CP-violation parameters, the mixing-induced CP-violation parameters of these modes, which show a better agreement with experimental data than many of the other approaches.Comment: 23 pages, 4 figures, 4 table