2<Emphasis Type="Italic">T</Emphasis>-periodic solution for<Emphasis Type="Italic">m</Emphasis> order neutral type differential equations with time delays

Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1), the better result cannot be found by using the same method. Foundation item: the Natural Science Foundation of Yunnan Education Committee (990002) Biography: ZHANG Bao-sheng (1962-)     

An experimental—Numerical evaluation of the<Emphasis Type="Italic">T</Emphasis><Stack><Subscript>ε</Subscript><Superscript>*</Superscript></Stack> integral for a three-dimensional crack front

TheT _ε ^* integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained displacements. Comparison was made withT _ε ^* calculated with the measured surface displacements andT _ε ^* calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison was found between the surfaceT _ε ^* calculated from displacements extracted from the FE model and the surfaceT _ε ^* calculated from experimentally obtained displacements. The computedT _ε ^* integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen. Mid-planeT _ε ^* values tend to be approximately 10% of the surface values.     

<Emphasis Type="Italic">T</Emphasis>-stress estimation by the two-parameter approach for a specimen with a V-shaped notch

In the present research, T-stress solutions are provided for a V-shaped notch in the case of surface defects in a pressurised pipeline. The V-shaped notch is analyzed with the use of the finite element method by the Castem2000 commercial software to determine the stress distribution ahead of the notch tip. The notch aspect ratio is varied. In contrast to a crack, it is found that the T-stress is not constant and depends on the distance from the notch tip. To estimate the T-stress in the case of a notch, a novel method is developed, inspired by the volumetric method approach proposed by Pluvinage. The method is based on averaging the T-stress over the effective distance ahead of the notch tip. The effective distance is determined by the point with the minimum stress gradient in the fracture process zone. This approach is successfully used to quantify the constraints of the notch-tip fields for various geometries and loading conditions. Moreover, the proposed T-stress estimation creates a basis for analyzing the crack path under mixed-mode loading from the viewpoint of the two-parameter fracture mechanics.     

Green’s function for T-stress of semi-infinite plane crack

Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Gre...     

A parametric type of KKM theorem in <Emphasis Type="Italic">FC</Emphasis>-spaces with applications

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.     

Holographic microrheology of polysaccharides from <Emphasis Type="Italic">Streptococcus mutans</Emphasis> biofilms

We use three-dimensional holographic particle tracking to perform microrheological measurements of model gelled media, including the polysaccharide pellicle of dental biofilms created by the common cariogenic oral pathogen Streptococcus mutans. Nanometer-resolution video-rate holographic tracking of embedded colloidal spheres provides accurate measurements of the gels’ complex viscoelastic moduli, including insights into these properties’ heterogeneity. When applied to polysaccharides of S. mutans biofilms, these techniques promise quantitative microscopic assays for candidate therapeutic agents against cariogenic dental biofilms.     

Strong convergence theorem for a generalized equilibrium problem and a <Emphasis Type="Italic">k</Emphasis>-strict pseudocontraction in Hilbert spaces

The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in the Hilbert space. The presented results extend and improve the corresponding results reported in the lit-erature.     

Solutions for Quasilinear Nonsmooth Evolution Systems in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>

We prove that nonsmooth quasilinear parabolic systems admit a local solution in L ^p strongly differentiable with respect to time over a bounded three-dimensional polyhedral space domain. The proof rests essentially on new elliptic regularity results for polyhedral Laplace interface problems for anisotropic materials. These results are based on sharp pointwise estimates for Greens function, which are also of independent interest. To treat the nonlinear problem, we then apply a classical theorem of Sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results. As applications we have in mind primarily reaction-diffusion systems. The treatment of such equations in an L ^p context seems to be new and allows (by Gauss theorem) the proper definition of the normal component of currents across the boundary.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">1</Emphasis></Superscript> Stability of Multi-Dimensional Discrete-Velocity Boltzmann Equations

We study the L ¹ stability of multi-dimensional discrete-velocity Boltzmann equations. Under suitable smallness assumption on initial data, we show that bounded mild solutions are L ¹ stable. For a stability estimate, we employ Bonys multi-dimensional analysis for total interactions over characteristic planes.     

On the <Emphasis Type="Italic">H</Emphasis><Superscript><Emphasis Type="Italic">s</Emphasis></Superscript> Theory of Hydrostatic Euler Equations

In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence and uniqueness of H ^s solutions under the local Rayleigh condition. This extends Brenier’s (Nonlinearity 12(3):495–512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak–strong uniqueness, mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based on weighted H ^s a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity.     

Levitan Almost Periodic and Almost Automorphic Solutions of <Emphasis Type="Italic">V</Emphasis>-monotone Differential Equations

In the present article we consider a special class of equations

Positive solutions to （n-1,1） m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.     

Three solutions to inequalities of Dirichlet problem driven by p（x）-Laplacian

A class of nonlinear elliptic problems driven by p（x）-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved.     

Torus generated by <Emphasis Type="Italic">Escherichia coli</Emphasis>

The bioluminescence images of unstirred cultures show that lux reporter E. coli (0.10 mg biomass per ml of the broth medium) in 6.4–10 mm diameter circular containers induce center-fluid-rising toroidal convection of ≤1 mm/min. The bioconvective torus is stable in a Teflon vessel and is deformed by 3.2–4.4 mm wavelength azimuthal waves in polystyrene or glass vessels.     

On the <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.     

Mechanical properties and structure of Haliotis discus hannai Ino and Hemifusus tuba conch shells： a comparative study

Haliotis discus hannai Ino （abalone shell） and Hemifusus tuba conch shell have been studied for the purpose to comparatively investigate the mechanisms by which nature designs composites. It is shown that both shells are composed of aragonite and a small amount of proteins while the conch shell shows finer microstructure but lower strength than aba- lone shell. It is also shown that the fresh shells exhibits better property than those after heat-treatments. It is therefore sup- posed that the size of inorganic substance is not a dominant factor to improve strength, while both proteins in shells and the microstructure of inorganic matter also play important roles.     

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.     

Adhesion Energy of <Emphasis Type="Italic">C. elegans</Emphasis>

The surface adhesion between C. elegans and the agar plates on which they are commonly grown has yet to be accurately quantified. C. elegans is a scientifically important species of nematode whose simple structure allowed the first mapping of the complete nervous system in a multicellular organism. One of the current topics of research in the C. elegans community is the investigation of neuronal function in locomotion. Models of locomotion are used in these studies to aid in determination of the functions of specific neurons involved in locomotion. The adhesion force plays a critical role in developing these models. This paper presents the experimental determination of the adhesion energy of a representative sample of C. elegans. Adhesion energy was determined by a direct pull-off technique. In this approach, nematodes are anesthetized to prevent movement and secured to a small load cell before an agar plate is slowly brought into contact with the specimen and then removed. The maximum tensile force is then fit to a JKR-type adhesion model, which assumes that the nematode is a cylinder in order to determine the adhesion energy. Repeated adhesions are also investigated to determine the importance of drying on the measured adhesion force. From these experiments, the adhesion energy was found to be W =?4.94 ± 1.19 mJ/m². Limited experiments on the rol-6 cuticle mutant found a lower adhesion energy W =?2.65 ± 1.16 mJ/m² for these animals.