A single machine batch scheduling problem with bounded batch size

We address a single-machine batch scheduling problem to minimize total flow time. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. As in many practical situations, batch sizes may be bounded. In the first setting studied in this paper, all batch sizes cannot exceed a common upper bound. In the second setting, all batch sizes share a common lower bound. An optimal solution consists of the number of batches and their (integer) size. We introduce an efficient solution for both problems.     

Communication: phase space approach to laser-driven electronic wavepacket propagation

We propose a phase space method to propagate a quantum wavepacket driven by a strong external field. The method employs the periodic von Neumann basis with biorthogonal exchange recently introduced for the calculation of the energy eigenstates of time-independent quantum systems [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. (in press) [e-print arXiv:1201.2299v1]]. While the individual elements in this basis set are time-independent, a small subset is chosen in a time-dependent manner to adapt to the evolution of the wavepacket in phase space. We demonstrate the accuracy and efficiency of the present propagation method by calculating the electronic wavepacket in a one-dimensional soft-core atom interacting with a superposition of an intense, few-cycle, near-infrared laser pulse and an attosecond extreme-ultraviolet laser pulse.     

Deterministic vs non-deterministic graph property testing

A graph property \(\mathcal{P}\) is said to be testable if one can check whether a graph is close or far from satisfying \(\mathcal{P}\) using few random local inspections. Property \(\mathcal{P}\) is said to be non-deterministically testable if one can supply a “certificate” to the fact that a graph satisfies \(\mathcal{P}\) so that once the certificate is given its correctness can be tested. The notion of non-deterministic testing of graph properties was recently introduced by Lovász and Vesztergombi [9], who proved that (somewhat surprisingly) a graph property is testable if and only if it is non-deterministically testable. Their proof used graph limits, and so it did not supply any explicit bounds. They thus asked if one can obtain a proof of their result which will supply such bounds. We answer their question positively by proving their result using Szemerédi’s regularity lemma. An interesting aspect of our proof is that it highlights the fact that the regularity lemma can be interpreted as saying that all graphs can be approximated by finitely many “template” graphs.     

Semiconductor quantum dot-inorganic nanotube hybrids

A synthetic route for preparation of inorganic WS(2) nanotube (INT)-colloidal semiconductor quantum dot (QD) hybrid structures is developed, and transient carrier dynamics on these hybrids are studied via transient photoluminescence spectroscopy utilizing several different types of QDs. Measurements reveal efficient resonant energy transfer from the QDs to the INT upon photoexcitation, provided that the QD emission is at a higher energy than the INT direct gap. Charge transfer in the hybrid system, characterized using QDs with band gaps below the INT direct gap, is found to be absent. This is attributed to the presence of an organic barrier layer due to the relatively long-chain organic ligands of the QDs under study. This system, analogous to carbon nanotube-QD hybrids, holds potential for a variety of applications, including photovoltaics, luminescence tagging and optoelectronics.     

On almost precipitous ideals

With less than 0^# two generic extensions ofL are identified: one in which ${\aleph_1}With less than 0^# two generic extensions ofL are identified: one in which à₁{\aleph_1}, and the other à₂{\aleph_2}, is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it is shown that if δ is a Woodin cardinal and there is an f:w₁ ? w₁{f:\omega_1 \to \omega_1} with ||f||=w₂{\|f\|=\omega_2}, then after Col(à₂,d){Col(\aleph_2,\delta)} there is a normal precipitous ideal over à₁{\aleph_1}. The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal.     

Generation of a dark nonlinear focus by spatio-temporal coherent control

The transition probability of a two-photon absorption (TPA) process in atomic Cesium, excited by phase-controlled temporally focused ultrashort pulses is shown to be spatially modulated in a controlled manner. In particular, we demonstrate the generation of a dark nonlinear focus. By controlling the excitation pulse shape along the propagation coordinate we create a region in space where the TPA rate vanishes which is flanked by bright regions.     

Generating random graphs in biased Maker‐Breaker games

We present a general approach connecting biased Maker‐Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker‐Breaker games. In particular, we show that for , Maker can build a pancyclic graph (that is, a graph that contains cycles of every possible length) while playing a game on . As another application, we show that for , playing a game on , Maker can build a graph which contains copies of all spanning trees having maximum degree with a bare path of linear length (a bare path in a tree T is a path with all interior vertices of degree exactly two in T). © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 47, 615–634, 2015     

Crystals of Benzamide,the First Polymorphous Molecular Compound,Are Helicoidal

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II ) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X‐ray diffraction reveal a complex lamellar structure of benzamide form II needle‐like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non‐classical morphologies.     

Crystals of Benzamide,the First Polymorphous Molecular Compound,Are Helicoidal

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II ) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X-ray diffraction reveal a complex lamellar structure of benzamide form II needle-like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non-classical morphologies.