On the existence for viscoelastodynamic problems with unilateral boundary conditions

This note deals with a damped wave equation and the evolution of a Kelvin–Voigt viscoelastic material, both problems being subject to unilateral boundary conditions. The functional properties of all the traces are precisely identified through Fourier analysis, which implies the existence of a solution satisfying almost everywhere the unilateral boundary conditions. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I

Let X be a Banach lattice and p, p′ be real numbers such that 1 < p, p′<∞ and 1/p + 1/p′ = 1. Then \({\ell_p\hat{\otimes}_FX}\) (respectively, \({\ell_p\tilde{\otimes}_{i}X}\)), the Fremlin projective (respectively, the Wittstock injective) tensor product of ? _p and X, has reflexivity or the Grothendieck property if and only if X has the same property and each positive linear operator from ? _p (respectively, from ? _p′) to X* (respectively, to X**) is compact.     

Classroom mathematical practices in differential equations

This article describes the results of a design experiment conducted in one differential equations classroom. The purpose of the article is to present an analysis of the classroom mathematical practices that were established over the first half of the semester including instruction on first order differential equations. We discuss and illustrate our use of Toulmin’s model of argumentation to develop an analytical technique for documenting the emergence and stability of classroom mathematical practices. This analysis is significant in that it contributes to an emerging body of research on students’ learning in social context, in particular at the undergraduate level where such analyses are lacking. Our analysis also serves as a case to examine the construct of classroom mathematical practices in new light and to extend prior research by documenting two theoretical ideas; that practices can emerge in a non-sequential fashion with regard to both time and structure.     

A Green function for the equilateral triangle

Using the image method, a diffusional Green function has been derived analytically for a triangle, when its three sides, all of equal length, have zero intensity. Because many image sites are involved, computational assistance is employed both to construct the Green function and to use it in solving practical problems. An alternative procedure based on eigenfunctions is also summarized.Received: November 18, 2003; revised: April 6, 2004     

Regulation of prokineticin 2 expression by light and the circadian clock

Background  

The suprachiasmatic nucleus (SCN) contains the master circadian clock that regulates daily rhythms of many physiological and behavioural processes in mammals. Previously we have shown that prokineticin 2 (PK2) is a clock-controlled gene that may function as a critical SCN output molecule responsible for circadian locomotor rhythms. As light is the principal zeitgeber that entrains the circadian oscillator, and PK2 expression is responsive to nocturnal light pulses, we further investigated the effects of light on the molecular rhythm of PK2 in the SCN. In particular, we examined how PK2 responds to shifts of light/dark cycles and changes in photoperiod. We also investigated which photoreceptors are responsible for the light-induced PK2 expression in the SCN. To determine whether light requires an intact functional circadian pacemaker to regulate PK2, we examined PK2 expression in cryptochrome1,2-deficient (Cry1-/-Cry2-/-) mice that lack functional circadian clock under normal light/dark cycles and constant darkness.     

Hybrid magnetic transistor

We report the development of a hybrid semiconductor-metal-semiconductor permeable-base transistor in vertical architecture. This transistor has a p-type silicon collector, a thin tin layer as base and a magnetoresistive conjugated polymer, poly(9,9-dioctyl-1,4-fluorenylenevinylene), as emitter material. The transistor transport characteristics are dependent on the applied magnetic field and the base transport factor for positive charge carriers is nearly ideal, independently of the magnetic field in the investigated range.     

Sexual differentiation of the zebra finch song system: potential roles for sex chromosome genes

Background  

Recent evidence suggests that some sex differences in brain and behavior might result from direct genetic effects, and not solely the result of the organizational effects of steroid hormones. The present study examined the potential role for sex-biased gene expression during development of sexually dimorphic singing behavior and associated song nuclei in juvenile zebra finches.     

Altering protein surface charge with chemical modification modulates protein–gold nanoparticle aggregation

Gold nanoparticles (AuNP) can interact with a wide range of molecules including proteins. Whereas significant attention has focused on modifying the nanoparticle surface to regulate protein–AuNP assembly or influence the formation of the protein “corona,” modification of the protein surface as a mechanism to modulate protein–AuNP interaction has been less explored. Here, we examine this possibility utilizing three small globular proteins—lysozyme with high isoelectric point (pI) and established interactions with AuNP; α-lactalbumin with similar tertiary fold to lysozyme but low pI; and myoglobin with a different globular fold and an intermediate pI. We first chemically modified these proteins to alter their charged surface functionalities, and thereby shift protein pI, and then applied multiple methods to assess protein–AuNP assembly. At pH values lower than the anticipated pI of the modified protein, AuNP exposure elicits changes in the optical absorbance of the protein–NP solutions and other properties due to aggregate formation. Above the expected pI, however, protein–AuNP interaction is minimal, and both components remain isolated, presumably because both species are negatively charged. These data demonstrate that protein modification provides a powerful tool for modulating whether nanoparticle–protein interactions result in material aggregation. The results also underscore that naturally occurring protein modifications found in vivo may be critical in defining nanoparticle–protein corona compositions.     

Optimal design,robustness, and risk aversion

Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an analytic solution for this model which explains the origin of the power laws. We also generalize the model to incorporate risk aversion, which results in truncation of the tails of the power law so that the probability of catastrophically large events is dramatically lowered, giving the system more robustness.     

Two-photon conical emission

A two-photon resonantly enhanced four-wave mixing (FWM) process leading to the conical emission of two new frequency components has been observed in atomic sodium vapor. A dye laser tuned close to the 3s → 3d two-photon allowed transition produces broad-band emission near the frequencies of the 3d → 3p and 3p → 3s transitions. This radiation is emitted in the forward direction in the form of cones surrounding the transmitted laser beam. The dependence of the cone angle on the emission wavelength and atomic number density is in excellent agreement with the predictions of a model that ascribes the origin of the conical emission to a phase-matched four-wave mixing process.