A Cut-Invariant Law of Large Numbers for Random Heaps

We consider the framework of Bernoulli measures for heap monoids. We introduce in this framework the notion of asynchronous stopping time, which generalizes the notion of stopping time for classical probabilistic processes. A strong Bernoulli property is proved. A notion of cut-invariance is formulated for convergent ergodic means. Then, a version of the strong law of large numbers is proved for heap monoids with Bernoulli measures. We study a sub-additive version of the law of large numbers in this framework.     

Control of the oscillator strength of the exciton in a single InGaN-GaN quantum dot

We report direct evidence for the control of the oscillator strength of the exciton state in a single quantum dot by the application of a vertical electric field. This is achieved through the study of the radiative lifetime of a single InGaN-GaN quantum dot in a p-i-n diode structure. Our results are in good quantitative agreement with theoretical predictions from an atomistic tight-binding model. Furthermore, the increase of the overlap between the electron and hole wave functions due to the applied field is shown experimentally to increase the attractive Coulomb interaction leading to a change in the sign of the biexcitonic binding energy.     

The characteristic class and ramification of an ℓ-adic étale sheaf

We introduce the characteristic class of an ℓ-adic étale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz–Verdier trace formula, its trace computes the Euler–Poincaré characteristic of the sheaf. We compare the characteristic class to two other invariants arising from ramification theory. One is the Swan class of Kato-Saito [17] and the other is the 0-cycle class defined by Kato for rank 1 sheaves in [16]. Dedicated to Luc Illusie, with admiration     

Stability of Viscoelastic Wave Equation with Structural $\delta$-Evolution in $\mathbb{R}^{n}$

The aim of this paper is to study the Cauchy problem for the viscoelastic wave equation for structural $\delta$-evolution models. By using the energy method in the Fourier spaces, we obtain the decay estimates of the solution to considered problem.     

Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides

We demonstrate all-optical switching in an active two-dimensional photonic crystal waveguide, observing as large as 16 nm blueshifts of a leaky eigenmode at 839 nm and switching ratios of almost 70%. These results are larger than those previously observed in similar experiments performed on passive photonic crystal waveguides; the enhancement is due to resonant photogeneration of carriers by In(0.12)Al(0.2)Ga(0.68)As quantum wells in the core of the waveguide. The effective change in the refractive index of the structure is approximately10(-2), with a rise time of approximately1 ps and a decay time of approximately10 ps, potentially allowing high-speed switching and fast modulation rates.     

A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.     

An efficient one-pot synthesis of N-(substituted phenyl)-1,2,5-thiadiazolidine-2-carboxamide 1,1-dioxide derivatives

1,2,5-Thiadiazolidine-1,1-dioxide carboxamide derivatives 3a-3n are novel heterocyclic compounds synthesized by multicomponent condensation reaction in one pot of aniline, chlorosulfonyl isocyanate, and 2-chloroethylamine hydrochloride which is used as a useful precursor under mild conditions. This reaction is realized with high atom economy, at room temperature and in a short reaction time. Series of these desired products are obtained from good to excellent yields within 2 hours in all cases. All the synthesized compounds are characterized by ¹H, ¹³C NMR, MS, and HMBC/HSQC spectroscopy.     

On countable completions of quotient ordered semigroups

A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect to congruences are two operations that commute with each other. This contrasts with the case of general partially ordered sets.