Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of L 2 approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) L 2 estimates for the extension in the case of non reduced subvarieties -- the case when Y has singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292, arXiv:1510.0523

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Integrable Euler top and nonholonomic Chaplygin ball

We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio

Estimating the inelasticity with the information theory approach

Using the information theory approach, in both its extensive and nonextensive versions, we estimate the inelasticity parameter $K$ of hadronic reactions together with its distribution and energy dependence from $p\bar{p}$ and $pp$ data. We find that the inelasticity remains essentially constant in energy except for a variation around $K\sim 0.5$, as was originally expected.Comment: 14 pages, 8 figures. Misprints correcte

Analysis of the genomic homologous recombination in Theilovirus based on complete genomes

At present, Theilovirus is considered to comprise four distinct serotypes, including Theiler's murine encephalomyelitis virus, Vilyuisk human encephalomyelitis virus, Thera virus, and Saffold virus. So far, there is no systematical study that investigated the genomic recombination of Theilovirus. The present study performed the phylogenetic and recombination analysis of Theilovirus over the complete genomes. Seven potentially significant recombination events were identified. However, according to the strains information and references related to the recombinants and their parental strains, four of the recombination events might happen non-naturally. These results will provide valuable hints for future research on evolution and antigenic variability of Theilovirus

Expression and prognostic significance of cox-2 and p-53 in hodgkin lymphomas: a retrospective study

<p>Abstract</p> <p>Background</p> <p>Cyclooxygenase (cox) is the rate-limiting enzyme, which catalyzes the conversion of arachidonic acid into prostaglandins and contributes to the inflammatory process. Cyclooxygenase-2 (cox-2), which is one of the two isoforms, plays a role in tumor progression and carcinogenesis. p53 contributes to apoptosis, DNA renewal and cell cycle. Studies concerning the relationship of cox-2 and p53 expressions and carcinogenesis are available, but the association between cox-2 and p53 in Hodgkin lymphoma (HL) is not exactly known.</p> <p>In our study, we examined the association of cox-2 and p53 expression, with age, stage, histopathological subtype, and survival in HL. We also examined correlation between cox-2 and p53 expression.</p> <p>Methods</p> <p>Cox-2 and p53 expressions in Hodgkin-Reed Sternberg cells (HRS) were examined in 54 patients with HL depending on cox-2 expression, stained cases were classified as positive, and unstained cases as negative. Nuclear staining of HRS cells with p53 was evaluated as positive. The classifications of positivity were as follows: negative if<10%; (1+) if 10-25%; (2+) if 25-50%; (3+) if 50-75%, (4+) if >75%.</p> <p>Results</p> <p>Cox-2 and p53 expressions were found in 49 (80%) and 29 (46%) patients, respectively. There were differences between histological subtypes according to cox-2 expression (p = 0.012). Mixed cellular (MC) and nodular sclerosing (NS) subtypes were seen most of the patients and cox-2 expression was evaluated mostly in the mixed cellular subtype.</p> <p>There were no statistically significant relationships between p53 and the histopathological subtypes; or between p53, cox-2 and the factors including stage, age and survival; or between p53 and cox-2 expression (p > 0.05).</p> <p>Conclusion</p> <p>Considering the significant relationship between the cox-2 expression and the subtypes of HL, cox-2 expression is higher in MC and NS subtypes. However the difference between these two subtypes was not significant. This submission must be advocated by studies with large series</p

Combined analysis of cell growth and apoptosis-regulating proteins in HPVs associated anogenital tumors

<p>Abstract</p> <p>Background</p> <p>The clinical course of human papillomavirus (HPV) associated with Bowenoid papulosis and condyloma acuminatum of anogenital tumors are still unknown. Here we evaluated molecules that are relevant to cellular proliferation and regulation of apoptosis in HPV associated anogenital tumors.</p> <p>Methods</p> <p>We investigated the levels of telomerase activity, and inhibitor of apoptosis proteins (IAPs) family (c-IAP1, c-IAP2, XIAP) and c-Myc mRNA expression levels in 20 specimens of Bowenoid papulosis and 36 specimens of condyloma acuminatum in anogenital areas. Overall, phosphorylated (p-) AKT, p-ribosomal protein S6 (S6) and p-4E-binding protein 1 (4EBP1) expression levels were examined by immunohistochemistry in anogenital tumors both with and without positive telomerase activity.</p> <p>Results</p> <p>Positive telomerase activity was detected in 41.7% of Bowenoid papulosis and 27.3% of condyloma acuminatum compared to normal skin (<it>p </it>< 0.001). In contrast, the expression levels of Bowenoid papulosis indicated that c-IAP1, c-IAP2 and XIAP mRNA were significantly upregulated compared to those in both condyloma acuminatum samples (<it>p </it>< 0.001, <it>p </it>< 0.001, <it>p </it>= 0.022, respectively) and normal skin (<it>p </it>< 0.001, <it>p </it>= 0.002, <it>p </it>= 0.034, respectively). Overall, 30% of Bowenoid papulosis with high risk HPV strongly promoted IAPs family and c-Myc but condyloma acuminatum did not significantly activate those genes. Immunohistochemically, p-Akt and p-S6 expressions were associated with positive telomerase activity but not with p-4EBP1 expression.</p> <p>Conclusion</p> <p>Combined analysis of the IAPs family, c-Myc mRNA expression, telomerase activity levels and p-Akt/p-S6 expressions may provide clinically relevant molecular markers in HPV associated anogenital tumors.</p

Three-dimensional printing of porous load-bearing bioceramic scaffolds

This article reports on the use of the binder jetting three-dimensional printing process combined with sintering to process bioceramic materials to form micro- and macroporous three-dimensional structures. Three different glass-ceramic formulations, apatite–wollastonite and two silicate-based glasses, have been processed using this route to create porous structures which have Young’s modulus equivalent to cortical bone and average bending strengths in the range 24–36 MPa. It is demonstrated that a range of macroporous geometries can be created with accuracies of ±0.25 mm over length scales up to 40 mm. Hot-stage microscopy is a valuable tool in the definition of processing parameters for the sintering step of the process. Overall, it is concluded that binder jetting followed by sintering offers a versatile process for the manufacture of load-bearing bioceramic components for bone replacement applications

Review of Dental Impression Materials

Major advances in impression materials and their application have occurred during the last decade, with greater emphasis being placed on rubber impression materials than on dental compound, zinc oxide-eugenol, and agar and alginate. Of particular interest has been the effect of disinfection solutions on the qualities of impressions and the biocompatibility of impression materials. The principal advance in hydrocolloids has been the introduction of the agar/alginate impression technique, which has simplified the procedure and improved the quality of gypsum dies compared with those prepared in alginate impressions. The tear strength of some alginates has been improved, and some have been formulated so that the powder is dustless, thus reducing the health hazard as a result of patient inhalation of dust during the dispensing process. Polyether and silicone impression materials have been modified so that the working time, viscosity, and flexibility of the polyethers have been improved and, with the introduction of addition silicones, their accuracy has become exceptional. Although the early addition silicones liberated hydrogen after setting, thus delaying the pouring of models and dies, most addition silicones have been improved so that no hydrogen is released and dies can be poured immediately. The introduction of automatic mixing systems for addition silicones has simplified their manipulation, has reduced the number of voids in impressions, and has reduced the amount of material wasted. The incorporation of surfactants into addition silicones has made them hydrophilic, with wetting properties similar to those of polyethers, and has made pouring bubble-free gypsum dies easier. This review is confined to published and unpublished information of the past decade. It will also suggest trends that should be anticipated in the near future based on this information. The review will not present information developed before 1975, which is available in several textbooks on dental materials by Craig (1985a), Phillips (1982), and Williams and Cunningham (1979).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66604/2/10.1177_08959374880020012001.pd