Collineations of the curvature tensor in general relativity

Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.     

Ultra-fast nonlinear response around 1.5 μm in 2D AlGaAs/AlOx photonic crystal

We report the fast switching capabilities of a two-dimensional Al_0.3Ga_0.7As photonic crystal slab around 1.5 μm. The slab is supported by an AlOx low-index thick layer that plays the role of an efficient heat sink. By pumping at 0.8 μm in the absorption of the Al_0.3Ga_0.7As quantum wells, the optical response is modified in the transparency region: a 200% change in the reflectivity is obtained with a total response time of 8ps.     

On the Hardness of Computing Intersection,Union and Minkowski Sum of Polytopes

For polytopes P ₁,P ₂⊂ℝ ^d , we consider the intersection P ₁∩P ₂, the convex hull of the union CH(P ₁∪P ₂), and the Minkowski sum P ₁+P ₂. For the Minkowski sum, we prove that enumerating the facets of P ₁+P ₂ is NP-hard if P ₁ and P ₂ are specified by facets, or if P ₁ is specified by vertices and P ₂ is a polyhedral cone specified by facets. For the intersection, we prove that computing the facets or the vertices of the intersection of two polytopes is NP-hard if one of them is given by vertices and the other by facets. Also, computing the vertices of the intersection of two polytopes given by vertices is shown to be NP-hard. Analogous results for computing the convex hull of the union of two polytopes follow from polar duality. All of the hardness results are established by showing that the appropriate decision version, for each of these problems, is NP-complete.     

Steroids and related studies. Part 60. Crystal and molecular structures of 17β-(2-hydroxyethyl)-3β-and 3α-pyrrolidino-17a-aza-D-homo-5-androstenes: HS-625 form 1, (3β-pyrrolidino) and HS-625 form 2 (mixed-3α and -3β-pyrrolidino epimers)

The crystal structures of two forms of 17-(2-hydroxyethyl)-3-pyrrolidino-17a-aza-D-homo-5-androstene (HS-625) are reported. In HS-625 (aqueous solvate) form 1, moleculeA, and HS-625 (anhydride) form 2, moleculeB, the pyrrolidine group is 3- substituted, while in HS-625 (anhydride) form 2, moleculeC has its pyrrolidine ring -substituted. HS-625 form 1 is orthorhombic, space groupP2₁2₁2₁, witha=7.089(4),b=11.502(6),c=28.975(16) Å,Z=4; form 2 is triclinic, space groupP1, witha=14.013(8),b=12.572(6),c=6.688(4) Å, =95.187(20), =103.491(21); =86.210(20)°,Z=2. MoleculesA andB have similar geometry, differences in moleculeC being related to strain caused by the unusual 3- ring substituent which also produces a pronounced kink in the backbone of the molecule. An unusual feature of the analysis of form 1 is the location of the water hydrogens in the difference electron density well above background. None of the OH hydrogens was located. Both structures are hydrogen bonded, but the pyrrolidine nitrogen N(31) in moleculeC is heavily congested and is unable to act as an acceptor. The hydroxyethyl side chain, important for activity, has a different conformation in the three molecules (t,g, t,-g, andt,t respectively).     

Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

Editorial note: The complete text of this paper, dedicated to Professor Asim O. Barut, will appear in the August 1993 issue ofFoundations of Physics.     

Complexes of ruthenium(II) and -(III) with dimethylsulphoxide—III. Bis-iodo-tetrakis- dimethylsulphoxide ruthenium(II) and some other iodo complexes of ruthenium(II)

The ruthenium(II) complex [RuI₂(Me₂SO)₄] was synthesized and characterized. The Me₂SO ligands are all S-bonded. Reactions of RuI₂(Me₂SO)₄ with ligands containing P, N and S donor atoms have been carried out and the complexes obtained were characterized using different physical methods. [RuI₂L₄] (L= CH₃CN, Me₂SO and py), [RuI₂(CH₃CN)₂(PPh₃)₂] and [RuI₂(CS)(PPh₃)₃] have been synthesized using RuI₃ as the source material and characterized as above.     

Pseudo Green's function theory for dilute alloys ofd-band metals

Summary The pseudo Green's function formalism for dilute alloys ofd-band metals is expanded in an overcomplete set of basis functions. Thed-band effects are included through the nonlocal effective impurity potential. The present formalism leads to an exact expression for the change in density of states caused by the introduction of an impurity. Thed-band contribution to the density of states is calculated for dilute copper alloys by using a simple model for the electronic structure of thed-band metals. It is found that thed-band contribution is responsible for the resonances and antiresonances in the density of states. A systematic study of the effects of the variation of impurity potential,d-resonance width andd-band energy on the density of states is carried out. The repulsive potential scatters thed states towards the higher energy which may lead to bound and virtual bound states in the vicinity of the Fermi level, while the attractive potential scatters thed states towards the lower energy which may lead to bound and virtual bound states towards the bottom of the conduction band. The results also predict that the probability of a bound and a virtual bound state is higher for dilute alloys of copper with a narrowd-band.

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Riassunto Si espande il formalismo di una pseudofunzione di Green per leghe diluite di metalli nella bandad in una sovracompleta serie di funzioni di base. Gli effetti della bandad sono inclusi attraverso il potenziale di impurità efficace non locale. Questo formalismo porta ad un'espressione esatta per il cambiamento di densità degli stati causato dall'introduzione di un'impurità. Il contributo della bandad alla densità degli stati è calcolato per leghe diluite di rame usando un modello semplice di struttura elettronica dei metalli della bandad. Si è trovato che il contributo della bandad è responsabile delle risonanze e delle autorisonanze nella densità degli stati. Si ottiene uno studio sistematico degli effetti della variazione del potenziale d'impurità, dell'ampiezza di risonanzad e dell'energia della bandad sulla densità degli stati. Il potenziale repulsivo diffonde gli statid verso energie più alte che possono portare a stati legati e virtualmente legati in vicinanza del livello di Fermi, mentre il potenziale di attrazione diffonde gli statid verso energie più basse che possono portare a stati legati e virtualmente legati verso il fondo della banda di conduzione. I risultati prevedono anche che la probabilità di stati legati e virtualmente legati sia più grande per leghe diluite con rame con una bandad stretta.

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Резюме Развивается формализм псевдо-гриновских функций для малолеги-рованных сплавовd-зонных металлов.d-зонные эффекты включаются через нело-кальный эффективный потенциал примеси. Предложенный формализм приводит к точному выражению для изменения в плотности состояний, которое обусловлено введением примеси. Вычисляет вкладd-зоны в плотность состояний для малолеги-рованных сплавов меди, используя простую модель для электронной структурыd-зонных металлов. Обнаружено, что вклад,d-зоны ответственен за резонансы и антирезонансы в плотности состояний. Проводится систематическое исследование влияния изменения потенциала примеси, шириныd-резонанса и энергииd-зоны на плотность состояний. Потенциал отталкивания при рассеянии переводитd-состояния в область боляших энергий, что может привести к связанным состояниям и виртуаль-ным связанным состояниям в окрестности уровня Ферми. Потенциал притяжения при рассеянии переводитd-состояния в область меньших энергий, что может привести к связанным состояниям и виртуальным связанным состояниям вблизи дна зоны проводимости. Полученные результаты предсказывают, что вероятность связанного и виртуального связанного состояния окзывается больше для малолег ированного сплава меди с узкойd-зоной.

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To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.