Fairness in Scheduling

On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long-lived processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion ofdesiredload of a process, which is a function of the tasks it participates in. Theunfairnessof a system is the maximum, taken over all processes, of the difference between the desired load and the actual load.An example of such a setting is thecarpool problemsuggested by Fagin and Williams [IBM Journal of Research and Development27(2) (1983), 133–139]. In this problem, a set ofnpeople form a carpool. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a “fair” way.We investigate this problem under various assumptions on the input distribution. We also show that the carpool problems can capture several other problems of fairness in scheduling.     

Mononuclear Thiolatecobalt Carbonyls

A Partial Statistically Incorporation of Ca²⁺ into the Ba₆Nd₂Al₄O₁₅-Type: Ba₅CaLa₂Fe₄O₁₅ Using high temperature reactions we succeeded in incorporating Ca²⁺ into the Ba₆Nd₂Al₄O₁₅ type. Single crystal X-ray methods reveal a partly ordered alkaline earth distribution. Ba²⁺ and Ca²⁺ occupy face connected MO₆-octahedra as well as a further point position together with La³⁺ ions (space group C−P6₃mc; a = 11.770; c = 7.039 Å; Z = 2).     

Structure and electronic structure of polyacene

It is shown that infinite long polyacene chains may have three energetically close but structurally distinct isomers (a symmetrical, sym, form and two lower symmetry forms: one with double bonds in a trans and another isomer with double bonds in a cis pattern). The energetics is based on solid state MNDO theory. We discuss that the symmetrical form has a substantial energy gap E_g in the Hartree–Fock approach owing to exact exchange terms, which are nonlocal. Broken symmetry Hartree–Fock (HF ) solutions for polyacene are also described. An angularly distorted structure suggested earlier on Jahn–Teller grounds is found to be energetically not favorable.     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

Synthesis,Spectral and Magnetic Properties,and Crystal Structures of Copper(II) Pyridinecarboxylate Adducts with N‐Heterocyclic Ligands

Synthesis and characterization of seven new complexes [Cu(2‐MeSnic)₂(CH₃OH)]₂ (where 2‐MeSnic is 2‐methylthionicotinate), [Cu(2‐MeSnic)₂L₂]₂ (where L is pyridine — py, ethylnicotinate — Etnic and butylnicotinate — Bunic), [Cu(2‐MeSnic)₂L₂(H₂O)₂] (where L is py and nicotinamide — nia) and [Cu(2‐MeSnic)₂(N‐Menia)₂(H₂O)₂]·2H₂O (where N‐Menia is N‐methylnicotinamide) are reported. The characterization were based on elemental analysis, infrared, electronic and EPR spectra, and magnetic susceptibility measurements over a temperature range of 1.8 — 300 K or 70 — 300 K. Three complexes of different type were studied by X‐ray analysis. The molecule of [Cu(2‐MeSnic)₂(CH₃OH)]₂ has dimeric paddle‐wheel cage structure with a tetragonal pyramidal arrangement around Cu^II. The dimer results from the fact that carboxyl groups of four 2‐MeSnic anions function as bridging in a syn‐syn arrangement. On the other hand [Cu(2‐MeSnic)₂(py)₂]₂ forms dimers with hexacoordinated Cu^II atoms in highly distorted coordination octahedra, each with two oxygen atoms of bridging carboxyl groups in an anti‐anti arrangement of two 2‐MeSnic anions, with two oxygen atoms of one asymmetrically chelating 2‐MeSnic anion and with two nitrogen atoms of two pyridine ligands. The temperature independent EPR spectrum for this complex exhibits an axial signal which corresponds to almost isolated S = ¹/₂ magnetic ions. Magnetic data for the dimer show a weak antiferromagnetic interaction between the two metal ions with J = —0.65 cm^—1. The Cu^II atom in complex [Cu(2‐MeSnic)₂(py)₂(H₂O)₂] is hexacoordinated in an elongated centrosymmetrical tetragonal‐bipyramidal arrangement (4 + 2). Based on the molecular structure the electronic, infrared, electron paramagnetic resonance spectra and magnetic properties are discussed and stereochemistry as well as the mode of ligand coordination in new solid complexes under study have been determined.     

On long-term arbitrage opportunities in Markovian models of financial markets

A discrete-time infinite horizon stock market model is considered where the logarithm of the price is assumed to be a Markov chain arising from the time-discretization of a stochastic differential equation. Conditions are given which ensure that there exist investment strategies producing an exponential growth of wealth with a probability converging to 1. The rate of this convergence is studied using large deviation techniques.     

Experimental investigation on the effectiveness of sorption energy recovery wheel in ventilation system

The object of this research was to investigate the effectiveness of sorption energy exchanger and the impact of the operational and thermal environmental conditions on their efficiency under steady-state conditions. To achieve this object, a test facility was installed into the Indoor Air Quality and Thermal Comfort Laboratory of BUTE University. A molecular 3Å sieve sorption wheel with high latent effectiveness is integrated into the experimental setup. In this study, the correlation between the sensible, latent, total effectiveness under different ambient air temperature and humidity values and different rotational speeds of the wheel is investigated in detailed by experimental tests.     

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C₉₆H₂₄Ar₆)₂ (Ar=2,6-dimethylphenyl) ( 1 ₂) was transformed to a triply negatively charged species 1 ₂^3.−, which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 1 ₂^3.− features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp² carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 1 ₂^3.−, which indicates graphene upon reduction doping may behave as a quantum spin liquid.     

The effect of numerical error on the reproducibility of molecular geometry optimizations

Geometry optimization is one of the most often applied techniques in computational drug discovery. Although geometry optimization routines are generally deterministic, the minimization trajectories can be extremely sensitive to initial conditions, especially in case of larger systems such as proteins. Simple manipulations such as coordinate transformations (translations and rotations), file saving and retrieving, and hydrogen addition can introduce small variations ( approximately 0.001 A) in the starting coordinates which can drastically affect the minimization trajectory. With large systems, optimized geometry differences of up to 1 A RMSD and final energy differences of several kcal/mol can be observed when using many commercially available software packages. Differences in computer platforms can also lead to differences in minimization trajectories. Here we demonstrate how routine structure manipulations can introduce small variations in atomic coordinates, which upon geometry optimization, can give rise to unexpectedly large differences in optimized geometries and final energies. We also show how the same minimizations run on different computer platforms can also lead to different results. The implications of these findings on routine computational chemistry procedures are discussed.