Synthesis,characterization and mesomorphic properties of Ag(I) and Pd(II) complexes containing the pyridyl and tetrazoyl rings: crystal structure of [C30H46N10Ag ClO4]

The synthesis of new monodentate heterocyclic ligands 5-(4-pyridyl)-2-alkyltetrazole (L¹a,b) and 4-[5-(2-alkyltetrazole)]aryl-4'-pyridinecarboxylate (L²a,b,c) containing two or three aromatic or heterocyclic rings (tetrazole, pyridine and benzene) and preparation of their corresponding silver(I) and palladium(II) complexes (Ia,b,c and IIa,b,c) are described. The thermal behaviour of the ligands and complexes was characterized by polarizing optical microscopy. The ligands and the complexes Ia,b,c and IIc showed no liquid crystalline phase. The complexes IIa,b showed mesomorphic behaviour, exhibiting smectic A enantiotropic mesomorphism X-ray diffraction measurements for complex Ia showed monodentate coordination of N-pyridine, and no coordination on the nitrogen atoms of the tetrazole ring.     

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.     

Minimal average degree aberration and the state polytope for experimental designs

For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Gröbner bases provide a systematic way of doing this. The algebraic method does not, in general, produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on “aberration” and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase.     

Ein neuer Hitzesammler

Ohne Zusammenfassung     

Single-photon space-like antibunching

We use heralded single photons to perform an antibunching experiment in which the clicks at the detectors are space-like separated events. The idea of such experiment dates back to the 5th Solvay conference, when it was proposed by Einstein as an expression of his concerns about quantum theory.     

An Efficient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines

We give a new and efficient approximation algorithm for scheduling precedence-constrained jobs on machines with different speeds. The problem is as follows. We are given n jobs to be scheduled on a set of m machines. Jobs have processing times and machines have speeds. It takes p_j/s_i units of time for machine i with speed s_i to process job j with processing requirement p_j. Precedence constraints between jobs are given in the form of a partial order. If j k, processing of job k cannot start until job j's execution is completed. The objective is to find a non-preemptive schedule to minimize the makespan of the schedule. Chudak and Shmoys (1997, “Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA),” pp. 581–590) gave an algorithm with an approximation ratio of O(log m), significantly improving the earlier ratio of due to Jaffe (1980, Theoret. Comput. Sci.26, 1–17). Their algorithm is based on solving a linear programming relaxation. Building on some of their ideas, we present a combinatorial algorithm that achieves a similar approximation ratio but runs in O(n³) time. Our algorithm is based on a new and simple lower bound which we believe is of independent interest.     

Über die Umwandlung von Hydrazonen in Oxime

Ohne Zusammenfassung