One-dimensional global attractor for strongly damped wave equations

We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is a periodic horizontal curve.     

A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations

Navier–Stokes equations (NS) admit transformations which transform a solution to another solution (galilean transformation, scaling transformation, …). They also admit viscosity dependent transformations which transform a solution to a solution of another NS with different viscosity. These particular transformations are called symmetries of NS. Each of them has a physical role (such as conservation laws, …). A consistent turbulence model should then remain invariant under these symmetry transformations. Unfortunately, this is not the case of several models.In this article, a class of subgrid-scale models preserving the symmetries of NS is built. This class is then refined such that the models respect the second law of thermodynamics. One of the simplest models of the class is tested to the flow in a ventilated room. Better results than those provided by Smagorinsky and dynamic models are obtained.     

Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects

This paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones. Easily verifiable sufficient criteria are established. The paper extends some previous results and reports some new results about impulsive functional differential equations.     

The finite steps of convergence of the fast thresholding algorithms with f-feedbacks in compressed sensing

Numerical Algorithms - Iterative algorithms based on thresholding, feedback, and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and efficient, particularly for...     

Invariants for E0-Semigroups on II1 Factors

We introduce four new cocycle conjugacy invariants for E ₀-semigroups on II ₁ factors: a coupling index, a dimension for the gauge group, a super product system and a C*-semiflow. Using noncommutative Itô integrals we show that the dimension of the gauge group can be computed from the structure of the additive cocycles. We do this for the Clifford flows and even Clifford flows on the hyperfinite II ₁ factor, and for the free flows on the free group factor ${L(F_\infty)}$ L ( F ∞ ) . In all cases the index is 0, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the C*-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate E ₀-semigroups.     

The Classical Electron Problem

In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the clock of the source for all observers. The new wave equation contains an additional term (dissipative), which arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a charge on itself but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass so that classical radiation has both a massless and a massive part. Hence, at the local level the theory is one of particles and fields but there is no self-energy divergence (nor any of the other problems). We also show that, for any closed system of particles, there is a global inertial frame and unique (invariant) global proper-time (for each observer) from which to observe the system. This global clock is intrinsically related to the proper clocks of the individual particles and provides a unique definition of simultaneity for all events associated with the system. We suggest that this clock is the historical clock of Horwitz, Piron, and Fanchi. At this level, the theory is of the action-at-a-distance type and the absorption hypothesis of Wheeler and Feynman follows from global conservation of energy.     

Looking for Difference Sets in Groups with Dihedral Images

We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a + 2 for a unique choice of = ±1, and for a = (k – )/2p. If G has an image of order 2p, then and ( – 1)/( – 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D _2m with either (n, m) = 1 or m = p ^t for p an odd prime dividing n, then one of the C ₂ intersection numbers of D is divisible by m. Again, this gives some non-existence results.     

Comparison of performance between rescaled range analysis and rescaled variance analysis in detecting abrupt dynamic change

In the present paper, a comparison of the performance between moving cutting data-rescaled range analysis(MCR/S) and moving cutting data-rescaled variance analysis(MC-V/S) is made. The results clearly indicate that the operating efficiency of the MC-R/S algorithm is higher than that of the MC-V/S algorithm. In our numerical test, the computer time consumed by MC-V/S is approximately 25 times that by MC-R/S for an identical window size in artificial data. Except for the difference in operating efficiency, there are no significant differences in performance between MC-R/S and MC-V/S for the abrupt dynamic change detection. MC-R/S and MC-V/S both display some degree of anti-noise ability. However, it is important to consider the influences of strong noise on the detection results of MC-R/S and MC-V/S in practical application processes.