Determination of the single component and competitive adsorption isotherms of the 1-indanol enantiomers by the inverse method

The inverse method of isotherm determination consists in calculating the numerical values of the coefficients of an isotherm model that give a set of chromatographic profiles in best possible agreement with the set of experimental profiles available. This method was applied to determine the adsorption isotherms of the 1-indanol enantiomers on a cellulose tribenzoate chiral stationary phase. Both single-component and competitive isotherms were determined by using no more than one or two overloaded band profiles. The isotherms determined from the overloaded band profiles agreed extremely well with the isotherms determined by frontal analysis. Several isotherm models were used and tested. The best-fit isotherm was selected by means of statistical evaluation of the results. The results show that the adsorption is best characterized with a model describing heterogeneous adsorption with bimodal adsorption energy distribution.     

On the symmetric travelling salesman problem I: Inequalities

We investigate several classes of inequalities for the symmetric travelling salesman problem with respect to their facet-defining properties for the associated polytope. A new class of inequalities called comb inequalities is derived and their number shown to grow much faster with the number of cities than the exponentially growing number of subtour-elimination constraints. The dimension of the travelling salesman polytope is calculated and several inequalities are shown to define facets of the polytope. In part II (On the travelling salesman problem II: Lifting theorems and facets) we prove that all subtour-elimination and all comb inequalities define facets of the symmetric travelling salesman polytope.     

Four-jet production in e+e−-annihilation

We investigate the four-jet production processes $e^{+}{e}^{?}\to q\overline{q}ggand{e}^{+}{e}^{?}\to q\overline{q}q\overline{q}$ in lowest order QCD perturbation theory. We estimate that four-jet events should be detectable at a rate of about 5% at the highest PETRA energy. The acoplanarity distribution is calculated and compared to nonperturbative effects.     

Atomic and molecular fluorescence with long radiative decay times from laser excited Na2

Na₂ is excited (B¹Π_u←X¹Σ _g ⁺ ) in the presence of noble gases (20–700 Torr). The Na₂ fluorescence decay shows two lifetimes: a short component which corresponds to the well known lifetime of Na₂ in the B¹Π_u state [1], and a long component with a lifetime of about 0,1 μs which depends strongly on the noble gas density [2]. The same long lived radiative decay is also seen via the Na resonance fluorescence Na(3²S)←Na(3²P).     

Radius,perimeter, and density profile for percolation clusters and lattice animals

Monte Carlo simulation and series expansion shows the radius of gyration of large clusters withs sites each to vary ass with0.56 in two and0.47 in three dimensions at the percolation threshold, and with(d=2)0.65 and(d=3)0.53 for random lattice animals (zero concentration). Clusters up tos=100 were used. The perimeter of random animals approaches 2.8s for larges on the simple cubic lattice. Monte Carlo simulation of the Eden process (growing animals) up tos=5,000 indicates a systematic variation of about ±0.05 for the effective exponent=(s) and thus suggests that the true asymptotic exponents may be compatible with the predictions of hyper-scaling.     

Zur Kennzeichnung der Lorentz-Transformationen

Let (V, f) be a real Minkowski space of any, not necessarily finite, dimension, and letd be the corresponding distance function (taking negative values for timelike distances). Then the following statement (among others) is proved: If ? :V →V is a surjective mapping such that $$d(P,Q) = a \Leftrightarrow d(P^\varphi ,Q^\varphi ) = a\forall P,Q \in V$$ is true for some fixeda εR,a<0, then ? is a Lorentz transformation (including a possible translation).     

Infrared bounds,phase transitions and continuous symmetry breaking

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (·) ₃ ² quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function ink space is bounded by 0(k ^–2). When applicable, our results can be fairly accurate numerically. For example, our lower bounds on the critical temperature in the three dimensional Ising (resp. classical Heisenberg) model agrees with that obtained by high temperature expansions to within 14% (resp. a factor of 9%).Research supported by USNSF under grants GP-38048 and MPS-74-13252A. Sloan Fellow; also in the Department of Physics     

Zerlegung total gerichteter Graphen in Kreise

The following statements are valid:The complete directed graph ¯K_n, n1 (mod 2p), is decomposable into directed 2p-cycles.The complete directed bipartite graph ¯K_m,n is decomposable into 2p-cycles if p is a divisor of m and np.If p is a prime, then this condition is necessary, too.The complete directed graph ¯K_n, n12, is decomposable into 6-cycles if and only if 6     

Sign of nuclear electric quadrupole coupling constants in solids fromγ-ray anisotropy measurements after capture of polarized neutrons

An experimental method is presented which allows the determination of the sign of nuclear electric quadrupole interactions in solids. Activated target nuclei with a purely dipolar spin polarization are produced by capture of polarized thermal neutrons. The quadrupole coupling of the nuclei to the electric field gradient tensor in the target crystal converts this (dipolar) polarization partly into a (quadrupolar) alignment, which can be measured by the anisotropy of the-ray emission in a succeeding nuclear transition. The sign of the alignment created in this reorientation process depends on the sign of the electric quadrupole interaction. The reorientation effect can be enhanced by selective induction of nuclear magnetic resonance transitions. The method has been applied to measure the sign of the crystal electric field gradient (efg) in tetragonal MgF₂. Further, the sign of an efg in cubic CaF₂ originating from a¹⁹F interstitial adjacent to the activated²⁰F probe nucleus has been determined. The method is in principle applicable to a considerable number of nuclides.     

Eigenvalues of the Faddeev equation kernel for a system of three spinless particles

For a system of three spinless particles interacting via separable Yamaguchi potential the possibility of the existence of three-particle resonances is studied. To this end, the eigenvaluesλ _i ^L (E ₃) of the Faddeev equation kernel have been calculated in the c.m.-energy region ?30 MeV≦E ₃≦15 MeV for total momentum statesL=0 andL=1. It is shown that in the investigated energy range there are no resonances.