Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws

We study the large-time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system. The initial data considered here is a perturbation of a constant state. It is shown that the solutions converge to single-mode diffusion waves in directions of strictly hyperbolic fields, and to multiple-mode diffusion waves in directions of nonstrictly hyperbolic fields. The multiple-mode diffusion waves, which are the new elements here, are the self-similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields, with the nonlinear fluxes replaced by their quadratic parts. The convergence rate to these diffusion waves isO(t ^–3/4+1/2p+) inL ^p , 1p, with >0 being arbitrarily small.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38     

Design and Synthesis of 3‐Aryl‐5‐Alicylic‐[1,2,4]‐oxadiazoles as Novel Platelet Aggregation Inhibitors

A series of 4‐[2‐(alicyclic‐[1,2,4]oxadiazol‐3‐yl)phenoxy]‐butyric acids were synthesized from N‐hydroxy‐2‐isopropoxy benzamidine in 4 steps with good yields. These [1,2,4]oxadiazoles are novel platelet aggregation inhibitors preventing human platelet aggregation induced by thromboxane derivative U44,619 and adenosine diphosphate. A structure‐activity‐relationship study revealed that the potency for these 5‐oxadiazoles increases with the increase in the ring size of the alicylic rings. Derivative 8f may be useful as a template for the design of more potent anti‐platelet agents.     

On the solutions to a Liouville-type system involving singularity

In this paper, we consider a Liouville-type system with singularity in the plane. The existence and uniqueness of solutions to the Dirichlet problem are proved. In addition, the structure of solutions in terms of analogues of the so-called total curvature in geometry or total mass in physics will be offered as well.     

New family of models for incompressible quantum liquids in d>/=2

Through Haldane's construction, the fractional quantum Hall states on a two-sphere were shown to be the ground states of one-dimensional SU(2) spin Hamiltonians. In this Letter we generalize this construction to obtain a new class of SU(N) spin Hamiltonians. These Hamiltonians describe center-of-mass-position conserving pair hopping fermions in space dimension d>/=2.     

The inhibition profiles of 4'-acylpyrrole–5-fluoroindolin-2-ones with a C-3' side chain for VEGFR2, PDGFR-β, and FGFR-1 protein kinases

In this study, we reported the inhibition profiles of 4′-acylpyrrole–5-fluoroindolin-2-one 3 with a C-3′ side chain for VEGFR2, PDGFR-β, and FGFR-1 protein kinases. The pyrrole-fused cyclohexanone moiety provided 3 with the best potency to inhibit the three kinases, and the C-3′ side chains contributed to the different inhibition profiles of 3 . Compound 3b with a C-3′ 2-carboxylethyl side chain showed good potency for the three kinase (IC₅₀: 25–260 nM), and compound 3g with a N,N-dialkyl-2-carbamoylethyl side chain was more active for VEGFR2 (IC₅₀: 59 nM) and PDGFR-β (IC₅₀: 16 nM) than FGFR-1 (IC₅₀: 1.7 μM). The C-3′ 3-(dialkylamino)propyl side chain accomplished 3h – j as selective PDGFR-β inhibitors (IC₅₀: 7.8–13 nM). Compound 3b was further investigated and found potent to inhibit VEGF- and FGF-dependent cell proliferation with moderate in vivo anticancer activity. Results from docking simulations revealed that the interactions of 3b with VEGFR2 and FGFR-1 which could account for the different inhibition profiles of 3 .     

Relative intensity fluctuations of single-mode class B lasers

Relative intensity fluctuations in single-mode class B lasers, i.e., a laser diode (LD) and a microchip Nd YVO(4) solid-state laser (SSL), were examined. Experimental observations revealed significant difference in the characteristics of the LD and the SSL. A stochastic laser model and the Fokker-Planck equation approach were used, and reduced moment equations were developed. A close agreement was achieved between the theoretical and experimental results. As indicated by the theoretical analysis, the intrinsic parameter of the lasers; i.e., the time ratio between the lifetimes of the carrier density (population inversion) and the photons, is crucial to fluctuation dynamics.     

Fractional vortices and composite domain walls in flat nanomagnets

We provide a simple explanation of complex magnetic patterns observed in ferromagnetic nanostructures. To this end we identify elementary topological defects in the field of magnetization: ordinary vortices in the bulk and vortices with half-integer winding numbers confined to the edge. Domain walls found in experiments and numerical simulations in strips and rings are composite objects containing two or more of the elementary defects.     

Characterization of the signature of subwavelength variation from far-field irradiance

The dynamic signature of the subwavelength variation of a slit is shown to be determinable from far-field irradiance with a precision of better than 1 nm. One can increase the efficiency of measurement of the subwavelength's signature by adjusting the detection width over which the subwavelength variation is detected. The subwavelength variation of a rectangular aperture was also examined to show the general feasibility.     

1.5-mum emissions from laser-diode-pumped Nd-doped microchip solid-state lasers

1.5-mum emissions from Nd:YAG, Nd:YVO(4), and LiNdP(4) O>(12) microchip lasers pumped by laser diodes have been observed. These coherent emissions are attributed to the effect of high-energy modified lattice vibration owing to the existence of Nd ions as well as to stimulated intracavity Raman scattering enhanced by the microchip configuration. A four-wave mixing process involving two lasing fields and a Stokes field was identified as the generator of new adjacent 1.5-mu;m emission.