Simultaneous K plus L shell ionized atoms during heavy-ion collision process

The fraction of simultaneous K plus L shell ionized atoms is estimated in Fe, Co and Cu elements using carbon ions at different projectile energies. The present results indicate that the fraction of simultaneous K plus L shell ionization probability decreases with increase in projectile energy as well as with increase in the atomic number of the targets atoms.     

On the suitability of Peltier cooled Si-PIN detectors in transmission experiments

The performance of a Peltier cooled Si-PIN detector is compared with that for a Freolectric cooled Si(Li) detector, references being made to transmission experiments that evaluate total cross sections at low photon energies. The results of these measurements are discussed.     

Crystallization kinetics study on higher homologues of benzylidene aniline compounds: impact of phase variant on nucleation process

A systematic kinetic study leading to the crystallization process from the kinetophases (which occur prior to crystal phase) smectic B, crystal G and smectic F is performed on representative compounds of the homologous series p-phenylbenzylidene-p'-alkylanilines (PBnA) and p-n-alkoxybenzylidene-p'-alkylanilines (nO.m) these compounds are p-phenylbenzylidene-p'-nonylaniline (PB9A), p-phenylbenzylidene-p'-tetradecylaniline (PB14A), p-n-pentadecyloxybenzylidene p'-tetradecylaniline (15O.14) and p-n-octadecyloxybenzylidene-p'-nonylaniline (18O.9). The molecular mechanism and dimensionality in crystal growth from the kineto phases are computed from the Avrami equation, while the characteristic crystalline time (t*) at each crystallization temperature is deduced from the individual plots of log t vs. ΔH. The low magnitudes of the dimensionality parameter n infers the occurrence of diffusion-controlled transformations leading to the formation of plates or needles of finite size possessing impinged edges. The degree of variation in the value of n at each crystallization temperature also reveals the existence of an independent nucleation mechanism for any individual member of the series. The influence of the terminal alkyl chain lengths on the rate of crystallization is determined from a comparative study with the reported analogous compounds.     

On the supersingular reduction of elliptic curves

Let a∈Q and denote byE _a the curvey ² = (x ² + l)(x + a). We prove thatE _a(F_p) is cyclic for infinitely many primesp. This fact was known previously only under the assumption of the generalized Riemann hypothesis. Research partially supported by NSERC grant A9418.     

Electron Capture Probabilities in105Ag

TheK-electron capture probabilities for the 1/2^? → 3/2^? and 1/2^? → 1/2⁺ transitions in the decay of¹⁰⁵Ag were measured for the first time using the sum coincidence method. The experimental P_K values were estimated to be 0.824 ± 0.042 and 0.851 ±0.046 for the allowed and first-forbidden beta transitions, respectively in agreement with the theory. The P_L experimental values to these two levels were also computed using the experimental P_L/P_K values reported by earlier authors. These results are also found to be consistent with the theoretical P_L values.     

On Artin's conjecture

Let $\text{F}$ be a family of number fields which are normal and of finite degree over a given number field K. Consider the lattice L(scF) spanned by all the elements of $\text{F}$. The generalized Artin problem is to determine the set of prime ideals of K which do not split completely in any element H of L(scF), H≠K. Assuming the generalized Riemann hypothesis and some mild restrictions on $\text{F}$, we solve this problem by giving an asymptotic formula for the number of such prime ideals below a given norm. The classical Artin conjecture on primitive roots appears as a special case. In another case, if $\text{F}$ is the family of fields obtained by adjoining to $\text{Q}$ the q-division points of an elliptic curve E over $\text{Q}$, the Artin problem determines how often E($\text{F}$_p) is cyclic. If E has complex multiplication, the generalized Riemann hypothesis can be removed by using the analogue of the Bombieri-Vinogradov prime number theorem for number fields.     

Linear programming under uncertainty: A basic property of the optimal solution

Summary We show that if the two-stage linear programming problem under uncertainty has an optimal solution, then it has an optimal solution in which the column vectors corresponding to the positive first stage decision variables are linearly independent. This leads to the result that if an optimal solution exists, then there exists an optimal solution in which not more than m + ¯m of the first stage decision variables are positive. These results extend to the multi-stage case.This research was partially supported by the Office of Naval Research under Contract Nonr-222(83), the National Science Foundation under Contract GP-4593, the Army Research Office under Contract DA-31-124-ARO-D-331 and the University of California. Reproduction in whole or part is permitted for any purpose of the United States Government.     

Die analytische Chemie des Zirkoniums

Ohne Zusammenfassung