Correlation between glass transition temperature and chain structure for randomly crosslinked high polymers

The empirical form for the dependence, T_g(n) ≅ T_g(∞)·(1 + α/n), of the glass transition temperature T_g on the average number n of repeat units between crosslinks, is generalized for randomly crosslinked high polymers. The new form, T_g(n) ≅ T_g(∞) · [1 + c/(n·N_rot)], is based on a correlation study of data for 77 samples of 10 different sets of resins. The fitting parameter α is resolved into composition-dependent N_rot and composition-independent c terms. N_rot summarizes the average number of rotational degrees of freedom per repeat unit, and is estimated in a straightforward manner from the structure and mol fraction of each repeat unit. The value of c is found from data analysis to be 5 ± 2. The results of this work are consistent with expectations based on the entropy theory of glasses, and provide improved understanding and predictive ability for the properties of crosslinked polymers. © 1996 John Wiley & Sons, Inc.     

Calculation of the critical currents of Bi(2223)/Ag tapes and coils with reduced anisotropy in Ic(B) characteristic — effect of different proportional representations of the filaments oriented parallel and perpendicularly to the tape surface

A mathematical model was developed to allow for the prediction of critical currents in Bi(2223)/Ag-sheathed tapes that consist of two groups of filaments, having crystalline texture (c-axis) predominantly in two directions orthogonal to each other and to the length of the conductor (filaments oriented parallel and perpendicular to the tape surface). Using the theory presented, it is possible to estimate the upper limit of critical currents in the tapes prepared with a two-axial rolling technique. Magnetic field and angular dependencies of critical currents were obtained at 77 K measuring tapes with various proportional representations of filaments oriented in both preferred directions, i.e., the parallel and perpendicular directions. The results of calculation indicate that the anisotropy in the I_c(B) characteristic should be reduced considerably using the two-axial rolling. Unfortunately, the effect of anisotropy reduction is accompanied by simultaneous decrease in the current-carrying capacity of the tapes. The data obtained for short tape samples were utilised to estimate the critical currents of the individual turns of a small cylindrical magnet, assembled of eight pancake coils. It is shown that only a slight increase in the critical current of the magnet can be expected if the winding should be made of the tape with reduced anisotropy in the I_c(B) characteristic. The factors that limit the increase of the magnet critical current are discussed in detail.     

Tail Behavior and Breakdown Properties of Equivariant Estimators of Location

For translation and scale equivariant estimators of location, inequalities connecting tail behavior and the finite-sample breakdown point are proved, analogous to those established by He et al. (1990, Econometrika, 58, 1195–1214) for monotone and translation equivariant estimators. Some other inequalities are given as well, enabling to establish refined bounds and in some cases exact values for the tail behavior under heavy- and light-tailed distributions. The inequalities cover translation and scale equivariant estimators in great generality, and they involve new breakdown-related quantities, whose relations to the breakdown point are discussed. The worth of tail-behavior considerations in robustness theory is demonstrated on examples, showing the impact of the basic two techniques in robust estimation: trimming and averaging. The mathematical language employs notions from regular variation theory.     

Trading crossings for handles and crosscaps

Let c_k = cr_k (G) denote the minimum number of edge crossings when a graph G is drawn on an orientable surface of genus k. The (orientable) crossing sequence c_o, c₁,c₂…encodes the trade‐off between adding handles and decreasing crossings. We focus on sequences of the type c_o > c₁ > c₂ = 0; equivalently, we study the planar and toroidal crossing number of doubly‐toroidal graphs. For every ? > 0 we construct graphs whose orientable crossing sequence satisfies c₁/c_o > 5/6??. In other words, we construct graphs where the addition of one handle can save roughly 1/6th of the crossings, but the addition of a second handle can save five times more crossings. We similarly define the non‐orientable crossing sequence ?₀,?₁,?₂, ··· for drawings on non‐orientable surfaces. We show that for every ?₀ > ?₁ > 0 there exists a graph with non‐orientable crossing sequence ?₀, ?₁, 0. We conjecture that every strictly‐decreasing sequence of non‐negative integers can be both an orientable crossing sequence and a non‐orientable crossing sequence (with different graphs). © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 230–243, 2001     

Determination of organic acids in tobacco by capillary isotachophoresis

Nine organic acids and phosphate have been separated and quantified in tobacco by capillary isotachophoresis. Two operating systems for the separation were found: hydrochloric acid (10 mmol l(-1)) adjusted with beta-alanine to pH 2.9 plus 0.1% poly(vinylpyrrolidone) was used as the leading electrolyte and 10 mmol l(-1) nicotinic acid as the terminating electrolyte and hydrochloric acid (10 mmol l(-1)) including 5.5 mmol l(-1) 1,3-bis[tris(hydroxymethyl)methylamino]propane plus 0.1% poly(vinylpyrrolidone) was used as the leading electrolyte and 5 mmol l(-1) 2-morpholinoethanesulfonic acid as the terminating electrolyte. Linearity was observed from 0.008 to 0.100 mmol l(-1) with a coefficient of determination (r2) of 0.999. The separation of anions was achieved in less than 16 min. The minimal sample pretreatment and relatively low running cost make isotachophoresis a good alternative to existing methods.     

Roothaan INDO CI spin density calculation

Spin densities have been calculated by the Roothaan INDO CI method in the parametrization of Pople and Kaufman. The dependence of the spin densities on both the type and the number of configurations in CI has been followed. Results have been compared with the UHF and spin-projected UHF methods.     

Transition probabilities of forbidden lines within the electronic configurations 6p 2 and 6p 7p of Pb I

The least squares fit of radial parameters involving radial functions of the 6p ²- and 6p 7p-configurations of Pb I has been carried out. The wave functions of the 9 lowest even levels of Pb I have been found in the basis of LSJ-states belonging to two configurations. On the base of the wave functions the transition probabilities for magnetic dipole (M1) and electric quadrupole (E2) radiation have been calculated. Comparison of experimental data and theoretical results is discussed.     

The shape of dilepton spectra in heavy ion collisions as a signature of quark-gluon plasma

The formation of quark-gluon plasma in heavy ion collisions should manifest itself by the increase of the ratio of medium to large mass dileptons, the former being produced predominantly in the QGP and the mixed phase whereas the latter are produced mostly by the Drell-Yan process. The increase of this ratio should be visible either when comparing collisions of lighter with heavier ions, e.g. O+O with Pb+Pb or when comparing low and large transverse energy events in heavy ion e.g. Pb+Pb collisions.