On the Motion of a Dynamic System with Minimal Dissipation

The motion of a holonomic scleronomic non-conservative mechanicalsystem with minimal dissipation is considered. As applicationsof the theory several problems are studied in detail.     

Electron-transfer polymers. XXVIII. Synthesis of vinyl hydroquinone derivatives by means of the wittig reaction

The Wittig reaction has been applied to unsubstituted, monomethyl-, 3,6-dimethyl-, and trimethyl-2,5-dimethoxybenzyl chlorides to produce in quantitative to good yields the corresponding vinyl monomers, unsubstituted, monomethyl-, 3,6-dimethyl-, and trimethyl-2,5-dimethoxystyrenes. The reaction is applicable also to 2,5-dimethoxy-4-methylbenzaldehyde, and to O,O′-bis-(methoxymethyl)resorcinol-4-aldehyde to yield the corresponding vinyl monomers. The reaction is particularly suitable with all these compounds because it is run at room temperature or below and gives good to quantitative yields.     

Coalition behaviour in n‐person conflicts†

This paper presents a theory of behaviour in n‐person conflicts. The theory and its solution are predicated on the inter‐dependency of coalition formation and pay‐off determination in an n‐person conflict. The solution, therefore, involves not only pay‐off determination but also coalition formation in the game. The theory is developed using mathematical notions of fixed points together with some behavioural theories about choice behaviour and interdependency of persons in competitive situations. It predicts not only the final state of coalition formation but also transient choices and coalitions in the games. Finally, the model is tested on some experimental games of W. Riker.     

Quotients of Koszul Algebras and 2-d-Determined Algebras

Vatne [13 Vatne , J. E. ( 2012 ). Quotients of Koszul algebras with almost linear resolution. Preprint, arXiv:1103.3572 . [Google Scholar]] and Green and Marcos [9 Green , E. L. , Marcos , E. N. (2011). d-Koszul algebras, 2-d-determined algebras and 2-d-Koszul algebras. J. Pure Appl. Algebra 215(4):439–449.[Crossref], [Web of Science ®] , [Google Scholar]] have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees.     

On the Computation of Eigenvalues of the Anharmonic Coulombic Potential

In this work, we propose a method combining the Sinc collocation method with the double exponential transformation for computing the eigenvalues of the anharmonic Coulombic potential. We introduce a scaling factor that improves the convergence speed and the stability of the method. Further, we apply this method to Coulombic potentials leading to a highly efficient and accurate computation of the eigenvalues.     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

Capillary electrophoresis with end-capillary potentiometric detection using a copper electrode.

Potentiometric end-capillary detection in capillary electrophoresis has the advantage of relatively easy miniaturisation without having to compromise the concentration sensitivity. Potentiometric end-capillary detection using a copper electrode is also attractive because of the sensitive detection of many inorganic and organic UV-transparent ions and the ability to work in both direct and indirect mode. In this work, detection of a number of common anions in a tartrate electrolyte at pH 3 was studied. The influence of the end-capillary detection geometry on the detection performance was investigated. An end-capillary detection cell allowing the separation capillary to be changed without the need to realign the detection electrode was constructed and fitted into a commercial CE apparatus. Under the optimal configuration, which was a 25 microm diameter copper electrode aligned coaxially with a 25 microm capillary and positioned at a distance of about 25 microm from the capillary end, excellent peak shapes were achieved and comparison with simultaneous on-capillary photometric detection showed no additional peak broadening. Good sensitivity was obtained, resulting in concentration limits of detection (LODs) in the low microM range and mass LODs in the low amol range. Examples of separations of inorganic and organic anions are presented and the analytical potential of the detection method is assessed.     

Synthesis of novel polyxanthenes from poly(arylene ether)s containing benzoyl groups

Poly(arylene ether)s ( 3 ), ( 4 ) containing pendant benzoyl groups as precursors for novel polyxanthenes ( 7 ), ( 8 ) were prepared by nucleophilic substitution reaction of 2,5-difluoro-4-benzoylbenzophenone ( 1 ) or 2,5-difluoro-4-(4-dodecylbenzoyl)-4′-dodecylbenzophenone ( 2 ) with hydroquinone derivatives in the presence of potassium carbonate in N,N-dimethylacetamide. The polycondensation proceeded smoothly at 165°C and produced poly(arylene ether)s with inherent viscosities up to 0.80 dL/g. The novel polyxanthenes were synthesized via the reduction of poly(arylene ether)s followed by the Friedel-Crafts cyclization of diol polymers. The structure of the polyxanthenes was characterized by ¹H-NMR and IR spectroscopies. Polyxanthene 8 was quite soluble in chloroform and THF. The 10% weight loss temperature of polyxanthene 7 was 510°C in nitrogen and it was 90°C higher than the corresponding poly(arylene ether) 3 . © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2267–2272, 1997