Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

Experimental selective choriocapillaris photothrombosis using a modified indocyanine green formulation

Background: This in vivo study assessed and compared the effectiveness of an aqueous indocyanine green (ICG) formulation (R-ICG) and a lipid ICG formulation (L-ICG) in occluding the rabbit choriocapillaris, and determined the singlet oxygen quantum yields and aggregation properties of both formulations in vitro. Methods: Singlet oxygen production and aggregation were compared. The eye fundus of 30 albino rabbits was irradiated 0-15 min after dye injection using an 810 nm diode laser. Fluorescein angiography and light microscopy were used to evaluate the safety and efficacy of R-ICG and L-ICG. Results: L-ICG decreased the dimerisation constant and the tendency of ICG to form aggregates, and increased the efficiency of ICG in generating singlet oxygen (R-ICG, Phi Delta= 0.120 and L-ICG, Phi Delta= 0.210). Using a 10 mg/kg dose, choriocapillaris occlusion was achieved at a light dose of 35.8 J/cm(2) with L-ICG and 71.6 J/cm(2) with R-ICG with minimal damage to the neurosensory retina. Conclusion: Restrictions to the use of ICG in aqueous solution, low singlet oxygen quantum yields and high aggregation tendency, were overcome with L-ICG. The lower laser irradiance required to obtain choriocapillaris occlusion may suggest that L-ICG is a more potent and selective photosensitiser than R-ICG.

Cytotoxic effects and pulpal response caused by a mineral trioxide aggregate formulation and calcium hydroxide

Purpose: To evaluate: the in vivo pulpal response after pulpotomy with different capping agents. In addition, the in vitro cytotoxic effects of both materials were assessed by applying them on culture of pulp cells. Methods: For the in vivo test, the coronal pulp of 28 teeth of dogs was mechanically removed and the root pulps were capped with the following dental materials: Group 1: Pro-Root NITA (PRMTA); and Group 2 (control): calcium hydroxide saline paste (CH). After 60 days, the animals were sacrificed and the teeth processed for histological analysis. In the in vitro test, experimental extracts obtained from both capping agents were applied on the cultured MDPC-23 odontoblast-like cells. Results: In the root pulps capped with PRMTA or CH, coagulation necrosis partially replaced by dystrophic calcification as well as tubular dentin matrix laid down by elongated pulp cells was observed. None or mild inflammatory response occurred beneath the capped pulpal wound. Regarding the pulpal response, PRMTA and CH presented no statistical difference. However, the teeth capped CH presented greater healthy pulp loss which resulted in convex shape of the hard barrier than PRMTA. When applied on the cultured cells, it was demonstrated that PRMTA and CH solutions decreased the cell metabolic activity by 9.9% and 29.4%, respectively. CH caused higher cytotoxic effects to the MDPC-23 cells as well as deeper healthy pulp tissue loss than PRMTA. However, similar sequence of healing occurred after pulpotomy with both dental materials.

QoS-based surrogates selection and service proposal formulation in offloading environments

Resource constraints are becoming a problem as many of the wireless mobile devices have increased generality. Our work tries to address this growing demand on resources and performance, by proposing the dynamic selection of neighbor nodes for cooperative service execution. This selection is in uenced by user's quality of service requirements expressed in his request, tailoring provided service to user's speci c needs. In this paper we improve our proposal's formulation algorithm with the ability to trade o time for the quality of the solution. At any given time, a complete solution for service execution exists, and the quality of that solution is expected to improve overtime.

The effects of a diet formulation with oats, soybeans, and flax on lipid profiles and uricemia in patients with AIDS and dyslipidemia

Introduction Although the initiation of highly active antiretroviral therapy (HAART) is accompanied by an attenuation of viral load, metabolic disorders characterized by hyperglycemia, dyslipidemia, and lipodystrophy are often observed in patients under this treatment. Certain foods, such as oat bran, soy protein, and flaxseed, have been shown to improve a patient's lipid profile despite possible increases in uricemia. Thus, a bioactive compound was formulated using these foods to help patients with HIV/AIDS control metabolic disorders resulting from HAART. Methods An uncontrolled before and after study was performed. The total cholesterol, HDL-cholesterol, LDL-cholesterol, triglycerides, and uric acid before and after 3 months of consuming the formulation were compared in patients. The compound was formulated such that 40g (the recommended daily intake) contained approximately 10g of flaxseed, 20g of oat bran, and 10g of textured soy protein. Results The study population consisted of 139 patients, 31 of whom were included in the final analysis. There were no significant variations between the laboratory results obtained before and after consumption of the compound. Conclusions The regular consumption of the formulation together with individualized dietary guidance did not reduce lipid levels and did not contribute to an increase in uricemia in the study group. However, new studies with higher doses of the foods that compose the formulation should be encouraged to investigate whether these foods can positively influence the lipid profiles of these patients.

The residual efficacy of a cypermethrin pour-on formulation applied on goats on the mortality and blood intake of Triatoma infestans

Triatoma infestans is the main vector of Trypanosoma cruzi, the aetiological agent of Chagas disease in the Gran Chaco region of South America. As a frequent blood meal source for triatomine bugs, domestic goats play a key role in the eco-epidemiology of Chagas disease. The aim of this study was to evaluate the mortality and blood intake of T. infestans fed on goats that had been treated with different doses of pour-on insecticide. Third-instar nymphs were fed on goats that had been treated with 0 cc, 5 cc, 10 cc or 15 cc of a pour-on formulation of cypermethrin. The exposure of T. infestans to animals treated at different post-application intervals revealed a residual activity of the insecticide. The mortality rate in the treated groups was higher than in the control groups until 30 days post-insecticide application (p = 0.03), except in the group treated with 5 cc, in which no mortality was detected after seven days of insecticide application. Rainfall affected the triatomicide effect, reducing the time of residual activity. The cypermethrin pour-on treatment decreased the blood intake of T. infestans. Thirty days after the cypermethrin application, nymph mortality was 16% (± 13) with both doses (10 cc and 15 cc). The 15 cc dose did not result in higher insect mortality or increased persistence compared to the 10 cc dose.

Dimensional reduction and gauge group reduction in Bianchi-type cosmology

In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-type cosmologies. We address problems raised in the literature concerning the Lagrangian and the Hamiltonian formulations: We prove their equivalence, make clear the role of the homogeneity preserving diffeomorphisms in the phase space approach, and show that the number of physical degrees of freedom is the same in the Hamiltonian and Lagrangian formulations. Residual gauge transformations play an important role in our approach, and we suggest that Poincaré transformations for special relativistic systems can be understood as residual gauge transformations. In the Appendixes, we give the general computation of the equations of motion and the Lagrangian for any Bianchi-type vacuum metric and for spatially homogeneous Maxwell fields in a nondynamical background (with zero currents). We also illustrate our counting of degrees of freedom in an appendix.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Evaluation of the performance of a castor-oil based formulation in limiting pesticide residues in strawberry crops

A study was made to evaluate the effect of a castor oil-based detergent on strawberry crops treated with different classes of pesticides, namely deltamethrin, folpet, tebuconazole, abamectin and mancozeb, in a controlled environment. Experimental crops of greenhouse strawberries were cultivated in five different ways with control groups using pesticides and castor oil-based detergent. The results showed that the group 2, which was treated with castor oil-based detergent, presented the lowest amount of pesticide residues and the highest quality of fruit produced.

Complement activation-related pseudoallergy in dogs following intravenous administration of a liposomal formulation of meglumine antimoniate

The increasing use of nanotechnologies in advanced therapies has allowed the observation of specific adverse reactions related to nanostructures. The toxicity of a novel liposome formulation of meglumine antimoniate in dogs with visceral leishmaniasis after single dose has been investigated. Groups of 12 animals received by the intravenous route a single dose of liposomal meglumine antimoniate (group I [GI], 6.5 mg Sb/kg), empty liposomes (GII) or isotonic saline (GIII). Evaluation of hematological and biochemical parameters showed no significant changes 4 days after administration. No undesired effects were registered in the GIII. However, adverse reactions were observed in 67.7% of dogs from both groups that received liposomal formulations. The side effects began moments after bolus administration and disappeared during the first 15 minutes after treatment. Prostation, sialorrhea and defecation were the most frequent clinical signs, registered in 33.3% and 41.6 % of animals from the groups GI and GII, respectively. Tachypnea, mydriasis, miosis, vomiting and cyanosis were also registered in both groups. The adverse reactions observed in this study were attributed to the activation of the complement system by lipid vesicles in a phenomenon known as Complement Activation-Related Pseudoallergy (CARPA). The influence of the physical-chemical characteristics of liposomal formulation in the triggering of CARPA is discussed.