A standard rule of thumb about whether a quantum Hamiltonian H = -A + V(x) has purely discrete spectrum or some continuous spectrum is the following. Look at the volume {(p, q) Ip* + V(q) <E} in R*“. If this volume is finite for all E, the standard wisdom is that H has only discrete spectrum. This standard wisdom also says that if this volume is infinite for some E < oo, then the spectrum is no...

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation...

Viscoelastic effects of the matrix polymer on molecular dynamics dielectric probes were examined using generalized Langevin equation, which was derived to include retardation effect viscous force. By solving we successfully obtained universal relationship between complex relaxation modulus and spectrum probe. When viscoelastic properties are assumed be viscous, is described with Debye function....

This article proposes a novel framework of resource allocation in multi-cell intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) networks, where an IRS is deployed to enhance the wireless service. The problem joint user association, subchannel assignment, power allocation, phase shifts design, and decoding order determination formulated for maximizing achievable sum...

We prove that in the weak topology of measure preserving transformations , a dense G has purely singular continuous spectrum in the orthocomplement of the constant functions. In the uniform topology, a dense G of aperiodic transformations has singular continuous spectrum. We show that a dense G of shift-invariant measures has purely singular continuous spectrum. These results stay true for Z d ...

The concept of M-convexity for functions in integer variables, introduced by Murota (1995), plays a primary role in the theory of discrete convex analysis. In this paper, we consider the problem of minimizing an M-convex function, which is a natural generalization of the separable convex resource allocation problem under a submodular constraint and contains some classes of nonseparable convex f...

In this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as Poincar'e mapping, power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.

As a liquid is progressively supercooled toward its glass transition temperature, an intriguing weakening of the wavenumber (q) dependence of the structural relaxation time tau(q) in the intermediate-to-large q limit is observed both in experiments and simulation studies. Neither continuous Brownian diffusive dynamics nor discontinuous activated events can alone explain the anomalous wavenumber...