On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Characterization and linear-time detection of minimal obstructions to concave-round graphs and the circular-ones property

A graph is concave-round if its vertices can be circularly enumerated so that the closed neighborhood of each vertex is an interval in the enumeration. In this study, we give a minimal forbidden induced subgraph characterization for the class of concave-round graphs, solving a problem posed by Bang-Jensen, Huang, and Yeo [SIAM J. Discrete Math., 13 (2000), pp. 179–193]. In addition, we show that it is possible to find one such forbidden induced subgraph in linear time in any given graph that is not concave-round. As part of the analysis, we obtain characterizations by minimal forbidden submatrices for the circular-ones property for rows and for the circular-ones property for rows and columns and show that, also for both variants of the property, one of the corresponding forbidden submatrices can be found (if present) in any given matrix in linear time. We make some final remarks regarding connections to some classes of circular-arc graphs.     

Effect of high intensity ultrasound on gelation properties of silver carp surimi with different salt contents

Surimi from silver carp with different salt contents (0–5%) was obtained treated by high intensity ultrasound (HIU, 100 kHz 91 W·cm⁻²). The gelation properties of samples were evaluated by puncture properties, microstructures, water-holding capacity, dynamic rheological properties and intermolecular interactions. As the salt content increased from 0 to 5%, gel properties of surimi without HIU significantly improved. For samples with low-salt (0–2% NaCl) content, HIU induced obvious enhancement in breaking force and deformation. HIU promoted the protein aggregation linked by SS bonds, hydrophobic interactions and non-disulfide covalent bonds in surimi gels with low-salt content. Moreover, microstructures of HIU surimi gels with low-salt content were more compact than those of the corresponding control samples. HIU also improved the gelation properties of surimi with 3% NaCl to an extent. However, for high-salt (4–5% NaCl) samples, HIU decreased the breaking force and deformation of surimi gels due to the degradation of proteins suggested by increased TCA-soluble peptides. In conclusion, HIU effectively improved the gelation properties of surimi with low-salt content (0–2% NaCl), but was harmful for high-salt (4–5% NaCl) surimi. This might provide the theoretical basis for the production of low-salt surimi gels.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

FINITE GROUPS WHOSE AUTOMORPHISM GROUP HAS ORDER CUBEFREE

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Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.     

Carathéodory's method for a class of dynamic games

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate feedback Nash equilibria for a class of n-person differential games. Both the finite-horizon and infinite-horizon cases are considered. Examples are given to illustrate the presented results.     

An optical measurement of vortex shape at a free surface

We have proposed an optical method of vortex shape measurement based on Fourier transform profilometry (FTP) and verified it by experiment. The results of our experiment proposed in this paper show that FTP can efficiently reconstruct the vortex shape at a free surface and this method is suitable for wide use in studying such problems as liquid shear flow, wake of an object, flow behind a bluff body, and wetting angle.