On the maximum number of Hamiltonian paths in tournaments

By using the probabilistic method, we show that the maximum number of directed Hamiltonian paths in a complete directed graph with n vertices is at least (e?o(1)) (n!/2^n?1). © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 291–296, 2001     

Large Eddy Simulation and Thermodynamic Design of the Organic Rankine Cycle Based on Butane Working Fluid and the High-Boiling-Point Phenyl Naphthalene Liquid Heating System

Large Eddy Simulation (LES) and Thermodynamic study have been performed on Organic Rankine Cycle (ORC) components (boiler, evaporator, turbine, pump, and condenser). The petroleum Coke burner provided the heat flux needed for the butane evaporator. High boiling point fluid (called phenyl-naphthalene) has been applied in the ORC. The high boiling liquid is safer (steam explosion hazard may be prevented) for heating the butane stream. It has best exergy efficiency. It is non-corrosive, highly stable, and flammable. Fire Dynamics Simulator software (FDS) has been applied in order to simulate the pet-coke combustion and calculate the Heat Release Rate (HRR). The maximal temperature of the 2-Phenylnaphthalene flowing in the boiler is much less than its boiling temperature (600 K). Enthalpy, entropy and specific volume required for evaluating the heat rates and the power have been computed by employing the THERMOPTIM thermodynamic code. The proposed design ORC is safer. This is because the flammable butane is separated from the flame produced in the petroleum coke burner. The proposed ORC obeys the two fundamental laws of thermodynamics. The calculated net power is 3260 kW. It is in good agreement with net power is reported in the literature. The thermal efficiency of the ORC is 18.0%.     

Random Cayley graphs and expanders

For every 1 > δ > 0 there exists a c = c(δ) > 0 such that for every group G of order n, and for a set S of c(δ) log n random elements in the group, the expected value of the second largest eigenvalue of the normalized adjacency matrix of the Cayley graph X(G, S) is at most (1 - δ). This implies that almost every such a graph is an ?(δ)-expander. For Abelian groups this is essentially tight, and explicit constructions can be given in some cases. © 1994 John Wiley & Sons, Inc.     

Hypergraph list coloring and Euclidean Ramsey theory

A hypergraph is simple if it has no two edges sharing more than a single vertex. It is s‐list colorable (or s‐choosable) if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. We prove that for every positive integer r, there is a function d_r(s) such that no r‐uniform simple hypergraph with average degree at least d_r(s) is s‐list‐colorable. This extends a similar result for graphs, due to the first author, but does not give as good estimates of d_r(s) as are known for d₂(s), since our proof only shows that for each fixed r ≥ 2, d_r(s) ≤ 2 We use the result to prove that for any finite set of points X in the plane, and for any finite integer s, one can assign a list of s distinct colors to each point of the plane so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of X. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

Study of elastic and inelastic scattering of protons from 74Ge at isobaric analogue resonances

Excitation functions of the elastic and the inelastic proton scattering leading to the ground state and to the 2⁺ (0.596 MeV) state in ⁷⁴Ge were measured at 90°, 125°, 140° and 165° at bombarding energies from 3.34 to 5.4 MeV. Ten isobaric analogue resonances in ⁷⁵As were identified. Five of these resonances decay to the 2⁺ excited state in ⁷⁴Ge. Angular distributions of the inelastically scattered protons were measured at bombarding energies corresponding to these resonances. The partial widths of the isobaric analogue states for decay to the ground state and to the 2⁺ excited state in ⁷⁴Ge were determined as well as the l-values of the captured protons and the spins of the resonances. The Coulomb displacement energy for the pair ⁷⁵As-⁷⁵Ge was found to be 10.01 MeV. A comparison is made with the parent analogue states in ⁷⁵Ge. The results indicate that several levels of ⁷⁵Ge may be described as having a large component of a single particle state coupled to the first 2⁺ excited state in ⁷⁴Ge, and that the 2⁺ state has a configuration with a large 2p-2h component.     

A simple and inexpensive "solvent in silicone tube extraction" approach and its evaluation in the gas chromatographic analysis of pesticides in fruits and vegetables

A novel, simple, and inexpensive approach to sorptive extraction, which we call solvent in silicone tube extraction (SiSTEx), was applied to pesticide residue analysis and its effectiveness and efficiency were evaluated. In SiSTEx, which is a form of open tubular sorptive extraction, a piece of silicone tubing (4 cm long, 1.47 mm ID, 1.96 mm OD in this study) is attached to the cap of a 20 mL glass vial that contains the aqueous sample. The tubing is plugged at the end dangling in the sample solution, and MeCN (e.g., 40 microL) added by syringe to the inner tube volume through a septum in the cap. A stir-bar is used to mix the sample for a certain time (e.g., 60 min), which allows chemicals to partition into the tubing where they diffuse across the silicone and partition into the MeCN. The final MeCN extract is then analyzed for the concentrated analytes. In this study, the SiSTEx approach was evaluated for the analysis of organophosphorus (OP) and organochlorine (OC) pesticides in fruits and vegetables using GC/pulsed flame photometric (PFPD) and halogen specific (XSD) detectors for analysis. The produced samples were initially extracted by a rapid MeCN procedure, and 5 mL of the initial extract was diluted four-fold with water to undergo sorptive extraction for 60 min. The final extract was analyzed by GC/PFPD + XSD for 14 OP and 22 OC pesticides. This simple approach was able to detect 26 of the 36 pesticides at 10 ng/g or less original equivalent sample concentration with average reproducibility of 11% RSD. For those 26 pesticides, a 44-fold lower detection limit on average was achieved in matrix extracts using SiSTEx despite the four-fold dilution with water.     

Semicharacters of Groups

We define the notion of a semicharacter of a group G: A function from the group to ?*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is divisible by the order of the group. We prove that the conjecture holds for some important families of groups, including the Symmetric groups and the groups GL(2, q).