Resonances are one of the most studied objects in physics, and in quantum mechanics they describe states which in addition to a rest energy have a rate of decay. A mathematical example is given by the zeros of the Riemann zeta function which are the resonances of the quantum Hamiltonian given by the Laplacian on the modular surface. The term "resonance" comes from the analogy with "a bell sound...

We discuss some of the experimental motivation for the need for semigroup decay laws, and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the...

There is a wide class of integrable Hamiltonian systems on finite-dimensional coadjoint orbits of the loop algebra g̃l(r) which are represented by r × r Lax equations with a rational spectral parameter. A reduced complex phase space is foliated with open subsets of Jacobians of regularized spectral curves. Under some generic restrictions on the structure of the Lax matrix, we propose an algebrai...

Baxters's Q-operators for the simplest q-deformed model. Abstract In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be considered as some massless limit of the Lax operator of SG model. We constructed two R op...

The aerial architecture of plants is determined primarily by the pattern of shoot branching. Although shoot apical meristem initiation during embryogenesis has been extensively studied by molecular genetic approaches using Arabidopsis, little is known about the genetic mechanisms controlling axillary meristem initiation, mainly because of the insufficient number of mutants that specifically alt...

Compared the additive benefits of laxative, behavior, and biofeedback treatments for encopresis, while attempting to identify treatment mechanisms and predictors of treatment outcome. 44 encopretic children, ages 6-15 years, were randomly assigned to either laxative therapy (LAX), LAX plus enhanced toilet training (ETT), or LAX + ETT + anal sphincter biofeedback (BF). Daily symptom diaries were...

Descent deceleration using parachutes is widely used in the aerospace field for scenarios such as weather observation descent of high-altitude balloons (radiosondes), re-entry during space sample return, and emergency drone landings. These are to protect aircraft samples, avoid hazards with objects humans on ground. However, it difficult control dropping point parachutes, there have been concer...

We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. This becomes the object part of a 2-functor N : NHom → [∆,Cat], where NHom is a 2-category whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories. The 2-functor N is fully faithful and has a left biadjoint, and we characterize it...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...