On the socle of a noncommutative Jordan algebra

In this paper we study some questions related to the socle of a nondegenerate noncommutative Jordan algebra. First we show that elements of finite rank belong to the socle, and that every element in the socle is von Neumann regular and has finite spectrum. Next we show that for Jordan Banach algebras the socle coincides with the maximal von Neumann regular ideal. For a nondegenerate noncommutative Jordan algebra, the annihilator of its socle can be regarded as a radical which is, generally, larger than Jacobson radical. Moreover, a nondegenerate noncommutative Jordan algebra whose socle has zero annihilator is isomorphic to a subdirect sum of primitive algebras having nonzero socle (which were described in [4]). Finally, these results are specialized to the particular case of an alternative algebra.The authors wish to thank the referee for his suggestions for improving the presentation of the paper.     

A comparison of drug loading capacity of cellactose with two ad hoc processed lactose-cellulose direct compression excipients

This study compares the drug loading capacity of Cellactose and two excipients of similar composition and similar particle size, prepared by dry granulation and extrusion-spheronization respectively. The drugs evaluated were acetaminophen and furosemide. Acetaminophen did not significantly affect the flow properties of any of the excipients, whereas furosemide markedly worsened flow properties, eliminating the differences initially existing among the three excipients. For both drugs, tablet mechanical properties were clearly better with Cellactose than with the other excipients. Acetaminophen dissolution rate was very similar regardless of the excipient used, but furosemide dissolution rate was lower from Cellactose tablets than from tablets prepared with the other excipients. This important difference is discussed in terms of micropore structure, specific surface area, and wettability of tablets, and is attributable to the special structure of Cellactose particles.     

Exact Controllability and Perturbation Analysis for Elastic Beams

The Rayleigh beam is a perturbation of the Bernoulli–Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli–Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials.     

Banach Spaces Whose Algebras of Operators are Unitary: A Holomorphic Approach

An element u of a norm-unital Banach algebra A is said to beunitary if u is invertible in A and satisfies ||u|| = ||u^–1||= 1. The norm-unital Banach algebra A is called unitary if theconvex hull of the set of its unitary elements is norm-densein the closed unit ball of A. If X is a complex Hilbert space,then the algebra BL(X) of all bounded linear operators on Xis unitary by the Russo–Dye theorem. The question of whetherthis property characterizes complex Hilbert spaces among complexBanach spaces seems to be open. Some partial affirmative answersto this question are proved here. In particular, a complex Banachspace X is a Hilbert space if (and only if) BL(X) is unitaryand, for Y equal to X, X* or X** there exists a biholomorphicautomorphism of the open unit ball of Y that cannot be extendedto a surjective linear isometry on Y. 2000 Mathematics SubjectClassification 46B04, 46B10, 46B20.     

Intramolecular addition of benzylic radicals onto ketenimines. Synthesis of 2-alkylindoles

The inter- and intramolecular addition of free radicals onto ketenimines is studied. All the attempts to add intermolecularly several silicon, oxygen or carbon centered radicals to N-(4-methylphenyl)-C,C-diphenyl ketenimine were unsuccessful. In contrast, the intramolecular addition of benzylic radicals, generated from xanthates, onto the central carbon of a ketenimine function with its N atom linked to the ortho position of the aromatic ring occurred under a variety of reaction conditions. These intramolecular cyclizations provide a novel radical-mediated synthesis of 2-alkylindoles.     

A positional scanning combinatorial library of peptoids as a source of biological active molecules: identification of antimicrobials

A positional scanning library of N-alkylglycine trimers (peptoids) containing over 10 000 compounds has been synthesized on solid phase. The synthetic pathway involved the use of the submonomer strategy and a set of 22 commercially available primary amines as a chemical diversity source. The unbiased nature of the library allowed its screening against a variety of biological targets, leading to the identification of individual peptoids exhibiting remarkable biological activities (García-Martínez, C. et al. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 2374. Montoliu, et al. J. Pharm. Exp. Therap. 2002, 302, 29. Planells-Cases, R., et al. J. Pharm. Exp. Therap. 2002, 302, 163). In the present work, the screening of this library against a panel of Gram-positive and Gram-negative bacteria led to the identification of different compounds exhibiting antimicrobial activity.     

Synthesis of glycosyl derivatives as dopamine prodrugs: interaction with glucose carrier GLUT-1

Glucosyl dopamine (DA) derivatives may represent a new class of DA prodrugs that would interact with glucose transporter GLUT-1, present in the blood-brain barrier, and generate DA in the brain. Therefore, compounds bearing the sugar moiety linked to either the amino group or the catechol ring of DA through amide, ester, carbamate, peptide or glycosidic bonds were synthesized. The behavior of the compounds as prodrugs was monitored in different media and the affinity of the glycoconjugates for the glucose carrier GLUT-1 using human erythrocytes was also studied. Most of the compounds were markedly stable in buffer and plasma, and several compounds released DA when incubated with brain extracts and the rate was related to the bond linking DA with glucose. The new glucosyl conjugates substituted at the C-6 position of the sugar were more potent inhibitors of glucose transport when compared to C-1 and C-3 substituted derivatives. This work provides structure-activity information about the interaction of substituted glucose with the GLUT-1 transporter.     

Bound excitons in time-dependent density-functional theory: optical and energy-loss spectra

A robust and efficient frequency dependent and nonlocal exchange correlation f(xc)(r,r(');omega) is derived by imposing time-dependent density-functional theory (TDDFT) to reproduce the many-body diagrammatic expansion of the Bethe-Salpeter polarization function. As an illustration, we compute the optical spectra of LiF, SiO2, and diamond and the finite momentum transfer energy-loss spectrum of LiF. The TDDFT results reproduce extremely well the excitonic effects embodied in the Bethe-Salpeter approach, both for strongly bound and resonant excitons. We provide a working expression for f(xc) that is fast to evaluate and easy to implement.     

Crystal structure of a (25R)-2α,3α-epoxy-5α-spirostan-6, 23-dione hemi-ethyl acetate solvate

The compound (25R)-2,3-epoxy-5-spirostan-6,23-dione, crystallizes as a hemi-ethyl acetate solvate, having two host molecules of similar conformation per molecule of ethyl acetate, in the asymmetric unit. The O atom of the epoxy group is -oriented. The presence of the epoxy group disturbs the chair conformation in the ring A of the steroidal nucleus. Ring A has a C5,C10 half-chair conformation. The six-membered rings B, C, and F have chair conformation as expected. The D ring adopts a C14-envelope conformation and the E ring is midway between a C22,O3 half-chair and a C22-envelope conformations. The A/B, B/C, and C/D ring junctions are trans. Crystal data: C₂₇H₃₈O₅·1/2C₄H₈O₂, Monoclinic, space group P2₁, a = 7.7363(18) b = 28.769(12) c = 12.038(6) Å, = 90.88(5), V = 2679.0(10) ų, Z = 4. The packing of the molecules is assumed to be dictated by van der Waals interactions and by intermolecular C—H ··· O hydrogen bonds.