Uniqueness of the Topology on Spaces of Vector-Valued Functions

Let be a topological space without isolated points, let E bea topological linear space which is continuously embedded intoa product of countably boundedly generated topological linearspaces, and let X be a linear subspace of C(, E). If a C()is not constant on any open subset of and aX X, then it isshown that there is at most one F-space topology on X that makesthe multiplication by a continuous. Furthermore, if U is a subsetof C() which separates strongly the points of and UX X, thenit is proved that there is at most one F-space topology on Xthat makes the multiplication by a continuous for each a U. These results are applied to the study of the uniqueness ofthe F-space topology and the continuity of translation invariantoperators on the Banach space L₁(G, E) for a noncompact locallycompact group G and a Banach space E. Furthermore, the problemsof the uniqueness of the F-algebra topology and the continuityof epimorphisms and derivations on F-algebras and some algebrasof vector-valued functions are considered.     

Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Thymidine 3',5'-diphosphoric acid derived cations and radicals: ab initio study

The relative stabilities of thymidine-3',5'-diphosphoric acid (1) derived isomeric cations and radicals were calculated and key geometric parameters were thoroughly analyzed. The most probable sites of a hydride-ion (1', 2', 5-Me) and H-atom (4', 5', 5-Me) abstraction were identified, thus allowing prediction of the regioselectivity of potential damage to the deoxyribose ring and thymine moiety caused by carcinogenic agents of electrophilic and radical nature. [structure: see text]     

A note on the path holomorphy of random functions holomorphic in mean

Every random function holomorphic in mean on an open subset of the complex field is equivalent to a random function with almost all its paths holomorphic on .

     

A pericyclic cascade to the stereocontrolled synthesis of 9-cis-retinoids

A domino reaction that is pericyclic in nature is thought to be triggered upon treatment of alkenynol 10 with arylsulfenyl chlorides. The process comprises an ordered sequence of sigmatropic rearrangements: a reversible [2,3]-allyl sulfenate to allyl sulfoxide shift, followed by a [2,3]-propargyl sulfenate to allenyl sulfoxide rearrangement, and last a stereodifferentiating [1,5]-sigmatropic hydrogen migration leading to polyene 13. The occurrence of the C7 to C11 hydrogen migration has been demonstrated by labeling experiments. The double diastereoselection of the [1,5]-sigmatropic hydrogen shift to afford a single isomer of the final polyene 13 is thought to arise from a combination of the electronic effect of the sulfoxide at one terminus, and the steric effect imparted by the bulky trimethylcyclohexenyl substituent at the other terminus. The overall process thus constitutes a stereoselective synthesis of an E,Z,Z-triene fragment from an alkenynol and, in particular, a retinoid with the 7E,9Z,11Z,13E configuration on the conjugated polyenic side chain. Application of this method to the synthesis of retinoids, including labeled analogues, is straightforward.     

The Molecular Basis of Different Approaches for the Study of Cancer Stem Cells and the Advantages and Disadvantages of a Three-Dimensional Culture

Cancer stem cells (CSCs) are a rare tumor subpopulation with high differentiation, proliferative and tumorigenic potential compared to the remaining tumor population. CSCs were first discovered by Bonnet and Dick in 1997 in acute myeloid leukemia. The identification and isolation of these cells in this pioneering study were carried out through the flow cytometry, exploiting the presence of specific cell surface molecular markers (CD34⁺/CD38⁻). In the following years, different strategies and projects have been developed for the study of CSCs, which are basically divided into surface markers assays and functional assays; some of these techniques also allow working with a cellular model that better mimics the tumor architecture. The purpose of this mini review is to summarize and briefly describe all the current methods used for the identification, isolation and enrichment of CSCs, describing, where possible, the molecular basis, the advantages and disadvantages of each technique with a particular focus on those that offer a three-dimensional culture.     

Chemical Composition,Antioxidant and Anticancer Activities of Leptocarpha rivularis DC Flower Extracts

An evaluation of antioxidant and anticancer activity was screened in Leptocarpha rivularis DC flower extracts using four solvents (n-hexane (Hex), dichloromethane (DCM), ethyl acetate (AcOEt), and ethanol (EtOH)). Extracts were compared for total extract flavonoids and phenol contents, antioxidant activity (2,2-diphenyl-1-picryl-hydrazyl-hydrate (DPPH), ferric reducing antioxidant potential (FRAP), total reactive antioxidant properties (TRAP) and oxygen radical absorbance capacity (ORAC)) across a determined value of reduced/oxidized glutathione (GSH/GSSG), and cell viability (the sulforhodamine B (SRB) assay). The most active extracts were analyzed by chromatographic analysis (GC/MS) and tested for apoptotic pathways. Extracts from Hex, DCM and AcOEt reduced cell viability, caused changes in cell morphology, affected mitochondrial membrane permeability, and induced caspase activation in tumor cell lines HT-29, PC-3, and MCF-7. These effects were generally less pronounced in the HEK-293 cell line (nontumor cells), indicating clear selectivity towards tumor cell lines. We attribute likely extract activity to the presence of sesquiterpene lactones, in combination with other components like steroids and flavonoids.     

Semileptonic (Λ b → Λcev) decay in a field theoretic quark model

The semileptonic decay width of heavy baryons such as (Λ _b → Λcev) has been estimated in the framework of a nonrelativistic field theoretic quark model where four component quark field operators along with a harmonic oscillator wave function are used to describe translationally invariant hadronic states. The present estimation does not make an explicit use of heavy quark symmetry and has a reasonable agreement with the experimentally measured decay width, polarisation ratio and form factors with the harmonic oscillator radii and quark momentum distribution inside the hadron as free parameters.