GSI anomaly and spin–rotation coupling

We propose a model in which a recently reported modulation in the decay of the hydrogenlike ions ¹⁴⁰Pr⁵⁸⁺, ¹⁴²Pm⁶⁰⁺ and ¹²²I⁵²⁺ arises from the coupling of rotation to the spin of electron and nucleus. The model shows that the spin–spin coupling of electron and nucleus does not contribute to the modulation and predicts that the anomaly cannot be observed if the motion of the ions is rectilinear, or if the ions are stopped in a target. It also supports the notion that the modulation frequency is proportional to the inverse of the atomic mass and that no modulation is expected for the β⁺${\beta }^{+}$-decay. The model predicts that for He-like ions the modulation is still present.     

Excitonic condensation in a symmetric electron-hole bilayer

Using diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at T = 0. We find clear evidence of an excitonic condensate, whose stability however is affected by an in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or interlayer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low-order density matrices to give a microscopic characterization of correlations as well as to try and estimate the condensate fraction.     

Numerical solution of minimax problems of optimal control,part 2

In a previous paper (Part 1), we presented general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We considered two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).In this paper, the transformation techniques presented in Part 1 are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Both the single-subarc approach and the multiple-subarc approach are employed. Three test problems characterized by known analytical solutions are solved numerically.It is found that the combination of transformation techniques and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the analytical solutions from the point of view of the minimax performance index. The relative differences between the numerical values and the analytical values of the minimax performance index are of order 10^–3 if the single-subarc approach is employed. These relative differences are of order 10^–4 or better if the multiple-subarc approach is employed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Realization ofU q (so(N)) within the differential algebra onR q N

We realize the Hopf algebraU _q–1 (so(N)) as an algebra of differential operators on the quantum Euclidean spaceR _q ^N . The generators are suitableq-deformed analogs of the angular momentum components on ordinaryR ^N . The algebra Fun(R _q ^N ) of functions onR _q ^N splits into a direct sum of irreducible vector representations ofU _q–1 (so(N)); the latter are explicitly constructed as highest weight representations.     

Reaction of Sulfene wild Heterocyclic N,N-Disubstituted α-Aminomethylene Ketones IV. Synthesis of 3,4-Dihydro-5H-[1]benzothiopyratio [3,4-e]-1,2-oxathiin and 2,3,6,7-Tetrahydro-5H-thiopyrano[3,4-e]-1,2-oxathiin Derivatives

The reaction of sulfene with N,N-disubstituted 3-aminomethylene-2,3-dihydro-4-thiochromanones and-2,3,5,6-tetrahydro-4-thiopyranones gave 1,4-cycloadducts which are derivatives of new heterocyclic systems, namely 3,4-dihydro-5H-[1]benzothiopyrano[3,4-e]-1,2-oxathiin and 3,4,7,8-tetrahydro-5H-thiopyrano[3,4-e]-1,2-oxathiin, respectively. Furthermore, some pyrazole derivatives VII and VIII were prepared from 3-hydroxymethylene-2,3-dihydro-4-thiochromanone or 2,3,5,6-tetrahydro-4-thiopyranone and hydrazines.     

Reaction of ketenes with N,N-disubstituted 2-aminomethylenecycloalkanones. V. Synthesis of N,N-disubstituted 4′-aminospiro [1,3-dithiane-2,3′-(5′,6′-polymethylene-3′,4′-dihydro-α-pyrones)]

The reaction of 2-carbonyl-1,3-dithiane, a sulfene prepared in situ from 2-chloroearbonyl-1,3-dithiane and triethylamine, with N,N-disubstituted 2-aminomethylvnecycloalkanones gave the 1,4-cycloadducts, namely N,N-disubstituted 4′-aminospiro[1,3-dithiane-2,3′-(5′,6′-poly-methylene-3′,4′-dihydro-α-pyrones)].     

Proteomics of gluten: mapping of the 1Bx7 glutenin subunit in Chinese Spring cultivar by matrix-assisted laser desorption/ionization

The verification of the cDNA-deduced sequence of the high molecular weight glutenin subunit 1Bx7 in Chinese Spring cultivar was achieved by direct matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) analysis of the tryptic fragments. The published sequence of the 1Bx7 subunit contains 5 Lys and 15 Arg residues but, due to the presence of three Arg-Pro bonds, which are generally resistant to cleavage by trypsin, or cleaved to a very limited extent by trypsin, 19 peptides can be predicted. The identification of the tryptic fragments was achieved by direct MALDI-MS analysis by using three different matrices (DHB, SA and HCCA) in combination with the most compatible sample preparation procedures in order to obtain the maximum sequence coverage. MALDI analysis of the 1Bx7 tryptic digest resulted in the identification of the expected peptides and additional fragments arising from non-specific cleavages; the fragments that were not detected are peptides with low mass (from 147.2 to 317.4), so we obtained a sequence coverage of 98.8%. The results reported here also indicated that the sequence of the 1Bx7 subunit from cv. Chinese Spring is different from the cDNA-deduced sequence reported in the literature; in particular, a possible insertion of the hexapeptide QPGQGQ within the sequence Gln630-Tyr725 was suggested. Finally, it is possible to rule out glycosylation of the 1Bx7 subunit, or any other post-translational modification, to within the detection limits of the method.     

Numerical simulations of viscoelastic particle migration in a microchannel with triangular cross-section

The migration of a spherical particle immersed in a viscoelastic liquid flowing in a microchannel with a triangular cross-section is investigated by direct numerical simulations under inertialess conditions. The viscoelastic fluid is modeled through two constitutive equations to investigate the effect of the second normal stress difference and the resulting secondary flows on the migration phenomenon. The results are presented in terms of trajectories followed by the particles released at different initial positions over the channel cross-section in a wide range of Weissenberg numbers and confinement ratios. Particles suspended in a fluid with a negligible second normal stress difference migrate toward the channel centerline or the closest wall, depending on their initial position. A much more complex dynamics is found for particles suspended in a fluid with a relevant second normal stress difference due to the appearance of secondary flows that compete with the migration phenomenon. Depending on the Weissenberg number and confinement ratio, additional equilibrium positions (points or closed orbits) may appear. In this case, the channel centerline becomes unstable and the particles are driven to the corners or “entrapped” in recirculation regions within the channel cross-section. The inversion of the centerline stability can be exploited to design efficient size-based separation devices.