In this paper, we study the compressible viscoelastic flows in three-dimensional whole space. Under the assumption of small initial data, we establish the unique global solution by the energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solution if the initial data belong to (ℝ) additionally.

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on , , , and , we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential is allowed to be sign-changing for the asymptotically linear case.

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- antisymmetric affine tensor fields in -dimensions is bounded by ( + 1)!/!( - )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

In this paper, we study the following linearly coupled system [Formula: see text], where ε > 0 is a small parameter, () are positive potentials, and = > 0 ( ≠ ) are coupling constants for , = 1, …, . We investigate the effect of potentials to the structure of the solutions. More precisely, we construct multi-spikes solutions concentrating near the local maximum point [Formula: see text] of (). When [Formula: see text], [Formula: see text], the components have spikes clustering at the same point as ε → 0. When [Formula: see text], the components have spikes clustering at the different points as ε → 0.

We prove results about the Hölder continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip, and Lenz ["Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity," Commun. Math. Phys.55, 191-204 (2000)] about the spectral measure of the discrete Schrödinger operator.

Let (, , α) be a monoidal Hom-Hopf algebra and [Formula: see text] the Hom-Yetter-Drinfeld category over (, α). Then in this paper, we first find sufficient and necessary conditions for [Formula: see text] to be symmetric and pseudosymmetric, respectively. Second, we study the -condition in [Formula: see text] and show that the Hom-Yetter-Drinfeld module (, adjoint, Δ, α) (resp., (, , coadjoint, α)) satisfies the -condition if and only if = . Finally, we prove that [Formula: see text] over a triangular (resp., cotriangular) Hom-Hopf algebra contains a rich symmetric subcategory.

[This corrects the article on p. 022302 in vol. 49.].

Biological systems are often subject to external noise from signal stimuli and environmental perturbations, as well as noises in the intracellular signal transduction pathway. Can different stochastic fluctuations interact to give rise to new emerging behaviors? How can a system reduce noise effects while still being capable of detecting changes in the input signal? Here, we study analytically and computationally the role of nonlinear feedback systems in controlling external noise with the presence of large internal noise. In addition to noise attenuation, we analyze derivatives of Fano factor to study systems' capability of differentiating signal inputs. We find effects of internal noise and external noise may be separated in one slow positive feedback loop system; in particular, the slow loop can decrease external noise and increase robustness of signaling with respect to fluctuations in rate constants, while maintaining the signal output specific to the input. For two feedback loops, we demonstrate that the influence of external noise mainly depends on how the fast loop responds to fluctuations in the input and the slow loop plays a limited role in determining the signal precision. Furthermore, in a dual loop system of one positive feedback and one negative feedback, a slower positive feedback always leads to better noise attenuation; in contrast, a slower negative feedback may not be more beneficial. Our results reveal interesting stochastic effects for systems containing both extrinsic and intrinsic noises, suggesting novel noise filtering strategies in inherently stochastic systems.

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of time scales and OPs which is practical when only a few, widely separated scales exist. The existence of a gap in the spectrum of time scales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component OPs. A continuum of spatially nonlocal Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.

The alpha-stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study sequences of long-range dependent random variables whose distributions have asymptotic power-law decay, and which are called (q,alpha)-stable distributions. These sequences are generalizations of independent and identically distributed alpha-stable distributions and have not been previously studied. Long-range dependent (q,alpha)-stable distributions might arise in the description of anomalous processes in nonextensive statistical mechanics, cell biology, finance. The parameter q controls dependence. If q=1 then they are classical independent and identically distributed with alpha-stable Lévy distributions. In the present paper we establish basic properties of (q,alpha)-stable distributions and generalize the result of Umarov et al. [Milan J. Math. 76, 307 (2008)], where the particular case alpha=2,q[1,3) was considered, to the whole range of stability and nonextensivity parameters alpha(0,2] and q[1,3), respectively. We also discuss possible further extensions of the results that we obtain and formulate some conjectures.

Various real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution , where the degree exponent describes the extent of heterogeneity. In this paper, we study analytically the average path length (APL) of and random walks (RWs) on a family of deterministic networks, recursive scale-free trees (RSFTs), with negative degree correlations and various , with an aim to explore the impacts of structure heterogeneity on the APL and RWs. We show that the degree exponent has no effect on the APL of RSFTs: In the full range of , behaves as a logarithmic scaling with the number of network nodes (i.e., ), which is in sharp contrast to the well-known double logarithmic scaling previously obtained for uncorrelated scale-free networks with . In addition, we present that some scaling efficiency exponents of random walks are reliant on the degree exponent .

We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach presented here is new and leads to a rigorous analysis of Wood's anomalies. These arise when illuminating a grating at specific combinations of the angle of incidence and the frequency of the wave, for which the lattice sums diverge. They were discovered by Wood in 1902 as singularities in the spectral response. The primary tools in our approach are the Euler-Maclaurin formula and a steepest descent argument. The resulting algorithm has super-algebraic convergence and requires only milliseconds of CPU time.

If a measurement is made on one half of a bipartite system, then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation-that is, if shared randomness cannot produce these reduced states for all possible measurements-the bipartite state is said to be . Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for -states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of -a special class of local hidden state models. When the measurements made correspond to real projectors, these allow us to study steerability beyond -states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels.