Global stabilization in nonlinear discrete systems with time-delay

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.     

1,3,2,4-Oxaazaphosphatitanetidine. Structure and Properties

The interaction of 1,3,2,4 -oxaazaphosphatitanetidines with chlorides of aluminium and zirconium, alcohols, piperidine and R₂NBr (R=SiMe₃) has been studied. The reaction routes have been determined with NMR spectra and X-ray structure analyses.     

On the regularization mechanism for the periodic Korteweg–de Vries equation

In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣ^s for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz‐continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in L₂ we also show the Lipschitz‐continuous dependence of these solutions with respect to the initial data as maps from Ḣ^s to Ḣ^s for s ∈(−1,0]. © 2010 Wiley Periodicals, Inc.     

A study of Galerkin method for the heat convection equations

This article investigates the Galerkin method for an initial boundary value problem for heat convection equations. The new error estimates for the approximate solutions and their derivatives in strong norm are obtained.     

Plasmonic properties of silver nanocube monolayers on high refractive index substrates

Extinction spectra of nanocubes supported by a symmetry breaking dielectric substrate are very different from those in solution. In this work, we varied the refractive index of the substrate in order to optimize the refractive index sensitivity (RIS) of supported silver nanocube monolayers. We found that on thin (5?C7?nm) silicon films, the RIS is characterized by the figure of merit (FOM) for the quadrupolar plasmonic mode as high as 5.0, making silicon supported silver nanocube monolayers a promising sensing platform.     

Biochemical and Structural Studies of Conserved Maf Proteins Revealed Nucleotide Pyrophosphatases with a Preference for Modified Nucleotides

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Ferroelectric switching behavior of pulsed laser deposited Ba0.8Sr0.2TiO3 thin films

The effect of pulse amplitude on the ferroelectric and switching properties of pulsed laser deposited Ba_0.8Sr_0.2TiO₃ thin films has been studied. The structural and morphological analysis revealed that the films had a well crystallized perovskite phase and grain size of about 30–40 nm. A well saturated P–E hysteresis loop was observed with a remnant polarization (P_r) ≈ 4.8 μC/cm² and a coercive field ≈ 100 kV/cm at a frequency of 1 kHz. The P_r has been found to be decreased only 4.3% after passing 8.0 × 10⁸ cycles. The analysis of switching response with nucleation limited switching model reveals that characteristic switching time (t₀) variance is due to the random distribution of the local electric fields. The peak value of polarization current and t₀ exhibits exponential dependence on reciprocal of pulse amplitude.     

Patterning silver nanocubes in monolayers using phase separated lipids as templates

Strategies for assembling silver nanocubes (NCs) into distinct 2D patterns on Langmuir–Blodgett (LB) films are demonstrated using two different lipid mixtures as vehicles: (1) raft mixtures containing 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), sphingomyelin (SPM), and cholesterol in different mole ratios (2:2:1 and 1:1:1) and (2) 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) at a 1:3 mol ratio. Atomic force microscopy was employed to unveil the mechanisms of such pattern formation in the LB film. The results demonstrate that aggregation of NCs into round-like pattern is governed by preferential localization of NCs within the liquid condensed (LC) domains of DOPC/SPM/Cholesterol mixture. Cholesterol was found to govern the size and shape of the rounded islands. On the other hand, incorporation of NCs within the liquid expanded (LE) phase of DPPC/DLPC mixture produced linear-branched chains, oriented normal to the Langmuir film transfer direction. The as engineered patterns of silver NCs exhibited characteristic plasmonic signatures. Our results reveal the potential in assembling plasmonic metal nanoparticles into diverse patterns on solid substrates by exploiting their preferential localization either in LC or LE phase of appropriate lipid mixture in Langmuir film.     

Emergent Newtonian dynamics and the geometric origin of mass

We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton’s second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini–Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples.