Milnor numbers, spanning trees, and the Alexander–Conway polynomial

We study relations between the Alexander–Conway polynomial _L and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We give a formula for the first non-vanishing coefficient of _L of an m-component link L all of whose Milnor numbers μ_i1…ip vanish for pn. We express this coefficient as a polynomial in Milnor numbers of L. Depending on whether the parity of n is odd or even, the terms in this polynomial correspond either to spanning trees in certain graphs or to decompositions of certain 3-graphs into pairs of spanning trees. Our results complement determinantal formulas of Traldi and Levine obtained by geometric methods.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

Phase synchronization of chaotic oscillations in terms of periodic orbits

We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization. (c) 1997 American Institute of Physics.     

Syntheses and oxidation of methyloxorhenium(V) complexes with tridentate ligands

Four new methyloxorhenium(V) compounds were synthesized with these tridentate chelating ligands: 2-mercaptoethyl sulfide (abbreviated HSSSH), 2-mercaptoethyl ether (HSOSH), thioldiglycolic acid (HOSOH), and 2-(salicylideneamino)benzoic acid (HONOH). Their reactions with MeReO(3) under suitable conditions led to these products: MeReO(SSS), 1, MeReO(SOS), 2, MeReO(OSO)(PAr(3)), 3, and MeReO(ONO)(PPh(3)), 4. These compounds were characterized spectroscopically and crystallographically. Compounds 1 and 2 have a five-coordinate distorted square pyramidal geometry about rhenium, whereas 3 and 4 are six-coordinate compounds with distorted octahedral structures. The kinetics of oxidation of 2 and 3 in chloroform with pyridine N-oxides follow different patterns. The oxidation of 2 shows first-order dependences on the concentrations of 2 and the ring-substituted pyridine N-oxide. The Hammett analysis of the rate constants gives a remarkably large and negative reaction constant, rho = -4.6. The rate of oxidation of 3 does not depend on the concentration or the identity of the pyridine N-oxide, but it is directly proportional to the concentration of water, both an accidental and then a deliberate cosolvent. The mechanistic differences have been interpreted as reflecting the different steric demands of five- and six-coordinate rhenium compounds.     

Stereoselective preparation of functionalized acyclic alkenylmagnesium reagents using i-PrMgCl.LiCl

Acyclic functionalized alkenyl iodides are converted with high stereoselectivity to the corresponding functionalized alkenylmagnesium derivatives by the reaction with i-PrMgCl.LiCl between -40 and -20 degrees C. Functional groups such as a nitrile, chloride, iodide, and ester are readily tolerated. The conversion of an alkenyl iodide bearing a keto group to the corresponding silylated cyanohydrin allows preparation of the corresponding Grignard reagent affording, after acylation and deprotection, unsaturated 1,4-diketones.     

Selection of internal standards for quantitative analysis by matrix-assisted laser desorption-ionization (MALDI) time-of-flight mass spectrometry

The selection of an appropriate internal standard (IS) for quantification by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry is critical for the successful application of quantitative MALDI. Selection of the IS depends on the chemical similarity of the analyte and IS and the mass separation of the analyte and IS as a function of instrumental peak resolution. For the quantification of bovine insulin, a series of internal standards including horse heart cytochrome C, bovine insulin chain B, des-pentapeptide human insulin, and des-octapeptide porcine insulin was investigated. Des-pentapeptide human insulin was found to be the most appropriate internal standard (relative standard deviation of the standard curve slope = 2.99%, correlation coefficient = 0.988 in the range of 0.5-0.4 μmol/L). Two methods for measuring of the MALDI signal intensity were evaluated, direct peak integration following subtraction of a linear background and non-linear least squares curve fitting. The results obtained with these methods were equivalent.     

International symposium on fundamental problems in quantum physics

Announcement

International symposium on fundamental problems in quantum physics     

Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].