Banach spacesX withX** separable

LetX be a Banach space and letZ be a closed subspace ofX** which containsX. It is proved in this paper that, in the caseX** separable, there exists a closed subspaceY ofX such thatX+ =Z, the closure ofY inX** for the weak-star topology.     

Serum protein immunogenicity: implications for liver xenografting

The objectives of this study were threefold: (i) assess immunogenicity of donor plasma proteins following hepatic xenotransplantation, (ii) identify potential immunogens, and (iii) consider the implications of antibody formation against these plasma proteins in xenograft survival. We studied liver and heart xenografts in a concordant combination, hamster to rat. All grafts were examined at necropsy for evidence of rat immunoglobulin G (IgG) deposition. Cardiac xenografts were placed in recipients who had, or had not, been sensitized with hamster serum. Hepatic xenografts were placed in naive recipients to see if antibodies to hamster serum proteins could be eluted from the rejecting organ. Sera of immunized rats were examined for the presence of anti-hamster antibodies by immunoelectrophoresis and by Western blotting following sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) separation of hamster serum. Antibodies in sera of immunized rats were compared with those eluted from rejecting livers. Candidate antigens were identified by tandem mass spectrometry, sequence analysis, and reference to protein databases. Results showed that sera of immunized rats recognized a minimum of four different antigens in hamster serum by immunoelectrophoresis, and a minimum of seven by the more sensitive SDS-PAGE Western blot. IgG eluted from rejecting livers bound three of seven candidate antigens recognized by sera of the immunized animals. Sequence analysis searches revealed proteinase inhibitors in each of the three SDS-PAGE bands common to the above samples. All of these candidate proteinase inhibitor immunogens share a common catabolic fate, uptake via the lipoprotein-related protein (LRP/alpha 2-macroglobulin receptor (CD91). Sensitization to hamster serum proteins hastened cardiac xenograft rejection in 30-50% of recipients (depending on sensitization protocol). Vascular deposition of rat IgG occurred in all rejecting xenografts. Antibody binding to proteinase inhibitors could disturb their functional activity and contribute to the pathogenesis of delayed xenograft rejection.     

Titanocene-catalyzed cascade cyclization of epoxypolyprenes: straightforward synthesis of terpenoids by free-radical chemistry

The titanocene-catalyzed cascade cyclization of epoxypolyenes, which are easily prepared from commercially available polyprenoids, has proven to be a useful procedure for the synthesis of C(10), C(15), C(20), and C(30) terpenoids, including monocyclic, bicyclic, and tricyclic natural products. Both theoretical and experimental evidence suggests that this cyclization takes place in a nonconcerted fashion via discrete carbon-centered radicals. Nevertheless, the termination step of the process seems to be subjected to a kind of water-dependent control, which is unusual in free-radical chemistry. The catalytic cycle is based on the use of the novel combination Me(3)SiCl/2,4,6-collidine to regenerate the titanocene catalyst. In practice this procedure has several advantages: it takes place at room temperature under mild conditions compatible with different functional groups, uses inexpensive reagents, and its end step can easily be controlled to give exocyclic double bonds by simply excluding water from the medium.     

Some notes on convex sets

In [1] Tukey proves that if A and B are closed convex subsets in a Banach space, so that A is bounded and A-B is dense in the open unit ball U then A-BU. We shall give here a more general result than the former one which contains the Banach's isomorphism theorem as particular case. Other results over convex sets are also given.The author is indebted to the referee for the several very valuable comments.     

Experimental and Computational Study of the Thermal Decomposition of 3‐Methyl‐3‐buten‐1‐ol in m‐Xylene Solution

An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s^?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol^?1)·T^?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH₃ group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition.     

Structural and Kinetic Aspects of Blood Plasma Protein Adsorption on the Surface of Hydrophobic Polymers

Abstract

Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood.     

Fréchet Spaces of Holomorphic Functions without Copies of l1

Let X be a Banach space. Let H_w*(X*) the Fréchet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of H_w*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l₁ when this space contains no copy of l¹. We also show that if X is an Asplund space, then H_w*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.