A finite difference approach to the equations of age-dependent population dynamics

We establish the convergence of the finite difference scheme for the nonlinear equations of population dynamics proposed by Guertin and MacCamy. The applicability of the discrete equations to establish qualitative properties of the solution to the continuous problem is also illustrated.     

Evaluation of a 6.71 kW power tiller for draft and drawbar power on tar roads

A 6.71 kW power tiller was evaluated for draft and drawbar power on tar roads. The effect of mounting 40 kg of wheel ballast was also studied. Polynomial regression analysis was used to establish the relationship between draft and wheel slip, drawbar power and wheel slip, drawbar power and fuel consumption, and drawbar power and specific fuel consumption. The results of the study showed draft values of 2107, 2110 and 2110 N in second low, third low and first high gears at an engine speed of 150o rpm with a 15% wheel slip. The respective draft values at engine speed of 2000 rpm with a 15% wheel slip were 2172, 2189 and 2212 N. With the mounting of 40kg wheel ballast there was an increase in draft of 217, 207 and 291 N at 1500 rpm, and 328, 306 and 344 N at 2000 rpm of the engine with a 15% wheel slip in second low, third low and first high gears, respectively. The increase in drawbar power with 40 kg ballast was 10.88%, 7.83% and 20.13% at 1500 rpm and 18.89%, 16.56% and 14.88% at 2000 rpm of engine over the drawbar power available with zero ballast. The fuel consumption with the use of wheel ballast was slightly more than the fuel consumption without any ballast.     

Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.     

Kinetic evidence of a common mechanism in the oxidations of diethyl sulfide by dichromates and halochromates of heterocyclic bases

The oxidations of diethyl sulfide by potassium dichromate, pyridinium dichromate, quinolinium dichromate, imidazolium dichromate, nicotinium dichromate, isonicotinium dichromate, pyridinium fluorochromate, quinolinium fluorochromate, imidazolium fluorochromate, pyridinium chlorochromate, quinolinium chlorochromate, and pyridinium bromochromate follow identical kinetic orders—first‐order each with respect to the chromium(VI) reagents, sulfide and hydrogen ion, and moderately inhibited by manganese(II) ion. The energy of activation varies linearly with the logarithm of frequency factor and so does the enthalpy of activation with the entropy of activation. Also, the activation free energies do not differ significantly. The dichromates and halochromates of heterocyclic bases oxidize diethyl sulfide via a common mechanism. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 1–8, 2003     

Block copolymer mediated synthesis of amphiphilic gold nanoparticles in water and an aqueous tetrahydrofuran medium: An approach for the preparation of polymer–gold nanocomposites

The synthesis of polymer‐matrix‐compatible amphiphilic gold (Au) nanoparticles with well‐defined triblock polymer poly[2‐(N,N‐dimethylamino)ethyl methacrylate]‐b‐poly(methyl methacrylate)‐b‐poly[2‐(N,N‐dimethylamino)ethyl methacrylate] and diblock polymers poly(methyl methacrylate)‐b‐poly[2‐(N,N‐dimethylamino)ethyl methacrylate], polystyrene‐b‐poly[2‐(N,N‐dimethylamino)ethyl methacrylate], and poly(t‐butyl methacrylate)‐b‐poly[2‐(N,N‐dimethylamino)ethyl methacrylate] in water and in aqueous tetrahydrofuran (tetrahydrofuran/H₂O = 20:1 v/v) at room temperature is reported. All these amphiphilic block copolymers were synthesized with atom transfer radical polymerization. The variations of the position of the plasmon resonance band and the core diameter of such block copolymer functionalized Au particles with the variation of the surface functionality, solvent, and molecular weight of the hydrophobic and hydrophilic parts of the block copolymers were systematically studied. Different types of polymer–Au nanocomposite films [poly(methyl methacrylate)–Au, poly(t‐butyl methacrylate)–Au, polystyrene–Au, poly(vinyl alcohol)–Au, and poly(vinyl pyrrolidone)–Au] were prepared through the blending of appropriate functionalized Au nanoparticles with the respective polymer matrices {e.g., blending poly[2‐(N,N‐dimethylamino)ethyl methacrylate]‐b‐poly(methyl methacrylate)‐b‐poly[2‐(N,N‐dimethylamino)ethyl methacrylate‐stabilized Au with the poly(methyl methacrylate)matrix only}. The compatibility of specific block copolymer modified Au nanoparticles with a specific homopolymer matrix was determined by a combination of ultraviolet–visible spectroscopy, transmission electron microscopy, and differential scanning calorimetry analyses. The facile formation of polymer–Au nanocomposites with a specific block copolymer stabilized Au particle was attributed to the good compatibility of block copolymer coated Au particles with a specific polymer matrix. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1841–1854, 2006     

Proton and alpha evaporation spectra in low energy 12C and 16O induced reactions

Proton and alpha particle spectra have been measured in the ¹²C+⁹³Nb and ¹²C+⁵⁸Ni reactions at E(¹²C)=40 and 50 MeV and in the ¹⁶O + ⁹³Nb reaction at E(¹⁶O) =75 MeV. The spectra are compared with the statistical model calculations. The shapes of the calculated spectra are in agreement with experimental data except for the alpha spectrum in the ¹²C + ⁹³Nb reaction at 40 MeV. The observed evaporation bump is at ∼2 MeV lower energy compared to the calculated one. This discrepancy could imply alpha particle emission from a deformed configuration before compound nucleus formation at this near Coulomb barrier beam energy.     

Chvátal closures for mixed integer programming problems

Chvátal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that for a polyhedronP and integral vectorw, if max(wx|x P, wx integer} =t, thenwx t is valid for all integral vectors inP. We consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that be integer for some other integral vector . The cutting-plane proofs thus obtained may be seen either as an abstraction of Gomory's mixed integer cutting-plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by Balas and Jeroslow. Our main result is that for a given polyhedronP, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again a polyhedron. This allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron, analogous to the process of repeatedly taking Chvátal closures in the integer programming case. These results are illustrated with a number of examples from combinatorial optimization. Our work can be seen as a continuation of that of Nemhauser and Wolsey on mixed integer cutting planes.Supported by Sonderforschungsbereich 303 (DFG) and by NSF Grant Number ECS-8611841.Supported by NSF Grant Number ECS-8418392 and Sonderforschungsbereich 303 (DFG), Institut für Ökonometrie und Operations Research, Universität Bonn, FR Germany.     

Synthesis and characterization of liquid‐crystalline polyphosphonates containing disubstituted ferrocene esters as mesogens

A series of ferrocene‐containing liquid‐crystalline polyphosphonates with an even number of methylene groups are reported. All the polymers gave birefringent melts. The mesophase was identified as transparent with an increase in the spacer. The effects of pendant substitution and the spacer were studied with thermogravimetric analysis and differential scanning calorimetry. The effects of the phosphonate group in the spacer and the ferrocene ester group in the mesogen were examined. The presence of a steplike mesogenic structure and a pendant phenyl group in the spacer led to reductions in the glass‐transition and melting temperatures. The ferrocene moiety in the mesogen might be one of the reasons for the increased thermal stability and decreased liquid crystallinity. An energy‐minimized structure for the mesogenic and spacer segments was created with computer‐modeling programs, and it suggested the reason for the reductions in the glass‐transition and melting temperatures. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2256–2263, 2002