Solvent effects in dense gases

The effects of perturber gases, partial pressures in the range 0–50 atm, on the absorption spectra of high-n Rydbergs, n ≥ 10, in methyl iodide and benzene have been investigated. The perturbers were rare gases and H₂. It has been shown that the spectroscopic energy shift Δ = Δ(ρ, n) is given by Δ = Δ°ρ, where ρ is the number density of the perturber, for n ≥ 10. The shift data can be interpreted using a Fermi model, and values of scattering lengths for perturbers can be extracted. These scattering lengths are internally consistent, independent of the absorber, and in excellent agreement with electron-swarm results. Given that the Fermi model is nonspecific and microscopic, scattering shifts and lengths for mixtures of perturber gases can be predicted. These predictions, having been verified by experiment for He/Ar mixtures, provide a means of “tailoring” any required scattering length. Finally, it is shown empirically that the determinative scattering parameter is the polarizability of the perturber, and a universal relationship a = ?0.26α + 1.18 between scattering length a, in Bohr radii, and polarizability α is found to exist.     

Interpretation of the curious results of the new quantum formalism of pre- and post-selected systems

The analysis, with the use of two state vectors, of a quantum system, during the time interval between two measurements, leads to some amazing results, which seem to contradict our usual quantum common sense. We explore the questions of compatibility with the conventional quantum theory, uniqueness of pre- and post-selected ensembles, commutativity, simultaneity and reality of strong and weak values in the intermediate time, and the meaning of the weak value. Common criticisms are shown to be unfounded.     

Synthesis of some novel 3,4,5-trisubstituted triazole derivatives bearing quinoline ring and evaluation of their antimicrobial activity

Abstract

Some new 3,4,5-trisubstituted 1,2,4-triazole derivatives were synthesized and studied for their antimicrobial activity. The lead compounds were obtained starting from 8-hydroxyquinoline and ethyl 2-chloroacetate. The obtained ester compound (1) first reacted with hydrazine hydrate (2) then with phenyl isothiocyanate (3). Ring closure by KOH led to 3-mercapto-1,2,4-triazole derivative (4). Lastly, it reacted with 2-chloro-N-(substituted (benzo)/thiazole)acetamide derivatives to obtain the final compounds (5a–j). The structural elucidation of the compounds was performed by ¹H NMR and ¹³C NMR spectroscopy and high resolution mass spectrometry techniques and elemental analysis. The synthesized compounds were investigated for their antimicrobial activities against seven bacteria and four fungi. As a result of the activity studies, it was observed that compounds N-(6-nitrobenzothiazol-2-yl)-2-[[4-phenyl-5-((quinolin-8-yloxy)methyl)-4H-1,2,4-triazol-3-yl]thio]acetamide (5a) and N-(6-fluorobenzothiazol-2-yl)-2-[[4-phenyl-5-((quinolin-8-yloxy)methyl)-4H-1,2,4-triazol-3-yl]thio]acetamide (5d) were the most active molecules. Also, the antifungal activity of the compounds was found to be higher than their antibacterial activity although lower than the standard drug’s potential. Additionally, the physicochemical properties of the compounds were calculated which were evaluated to be at a suitable range for oral administration.     

Quasi-randomness and the distribution of copies of a fixed graph

We show that if a graph G has the property that all subsets of vertices of size n/4 contain the “correct” number of triangles one would expect to find in a random graph G(n, 1/2), then G behaves like a random graph, that is, it is quasi-random in the sense of Chung, Graham, and Wilson [6]. This answers positively an open problem of Simonovits and Sós [10], who showed that in order to deduce that G is quasi-random one needs to assume that all sets of vertices have the correct number of triangles. A similar improvement of [10] is also obtained for any fixed graph other than the triangle, and for any edge density other than 1/2. The proof relies on a theorem of Gottlieb [7] in algebraic combinatorics, concerning the rank of set inclusion matrices.     

Highly efficient doubling of a high-repetition-rate diode-pumped laser with bulk periodically poled KTP

An internal doubling efficiency of 64% at 2 MW/cm(2)was obtained in a single-pass configuration with an uncoated, 1-cm-long, bulk periodically poled KTP crystal placed outside the resonator of a pulsed, diode-pumped Nd:YAG laser. An average of 4.8W of green light was obtained from a 7.5-W pump beam inside the crystal. Doubling efficiency exceeded 50% at levels of 0.75 MW/cm(2). The measured thermal tolerance of the doubling process (FWHM) was 3.3( degrees )C cm, and the measured temperature tuning coefficient was 0.053 nm/( degrees )C .     

Minimizing total completion time on a single machine with step improving jobs

Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions.     

Radiation Reaction of the Classical Off-Shell Relativistic Charged Particle

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed.     

A robust APTAS for the classical bin packing problem

Bin packing is a well studied problem which has many applications. In this paper we design a robust APTAS for the problem. The robust APTAS receives a single input item to be added to the packing at each step. It maintains an approximate solution throughout this process, by slightly adjusting the solution for each new item. At each step, the total size of items which may migrate between bins must be bounded by a constant factor times the size of the new item. We show that such a property cannot be maintained with respect to optimal solutions. A preliminary version of this paper appeared in Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP2006), part I, pp. 214–225.