Local picture of twisted curves: with an Introduction to the Theory of Deligne-Mumford Stacks

A nodal curve C over a field is, roughly speaking, a curve whose singular points are ordinary double points. The classical way to describe families of such curves over a base scheme S is through a flat morphism f : C → S, whose fibers are nodal curves over the residue field. It is possible to endow nodal curves, over a base scheme S, with the action of a group of roots of unity. A twisted curve over a base scheme is a nodal curve which acquires an orbifold structure at its nodes, through the action of the roots of unity. The goal of this thesis is to prove a characterization of twisted curves over a base scheme in terms of its geometric fibers.ope

Double nested Hilbert schemes and the local stable pairs theory of curves

We propose a variation of the classical Hilbert scheme of points - the double nested Hilbert scheme of points - which parametrizes flags of zero-dimensional subschemes whose nesting is dictated by a Young diagram. Over a smooth quasi-projective curve, we compute the generating series of topological Euler characteristic of these spaces, by exploiting the combinatorics of reversed plane partitions. Moreover, we realize this moduli space as the zero locus of a section of a vector bundle over a smooth ambient space, which therefore admits a virtual fundamental class. We apply this construction to the stable pair theory of a local curve, that is the total space of the direct sum of two line bundles over a curve. We show that the invariants localize to virtual intersection numbers on double nested Hilbert scheme of points on the curve, and that the localized contributions to the invariants are controlled by three universal series for every Young diagram, which can be explicitly determined after the anti-diagonal restriction of the equivariant parameters. Under the anti-diagonal restriction, the invariants are matched with the Gromov-Witten invariants of local curves of Bryan-Pandharipande, as predicted by the MNOP correspondence. Finally, we discuss $K$-theoretic refinements \`a la Nekrasov-Okounkov.Comment: 46 pages, comments welcome

Effects of morphine on replication of herpes simplex virus type 1 and 2

Several drugs are being used in treatment of HSV (Herpesviridae) infection in human but still introducing an effective safe drug is desirable. We investigated the inhibitory effect of morphine on replication of HSV in vitro. The results indicated that a concentration of up to 200 ìg/ml morphine had a limited effect on Vero cell viability. At this concentration, the growth of HSV was inhibited considerably and after the third passage in presence of morphine it was completely eliminated. The presence of viral antigens in infected cells in presence of morphine by immunoflourescent staining showed that after the first passage a small number of infected cells contained viral proteins and at the third passage no cells with viral antigen was observed. This was confirmed by page and immunobloting techniques. Electronmicroscopy observation in cellular section indicated that there was no virus present in treated cells as compared with control untreated infected cells

KK-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds

Recently, Nekrasov discovered a new "genus" for Hilbert schemes of points on $\mathbb{C}^4$. We conjecture a DT/PT correspondence for Nekrasov genera for toric Calabi-Yau 4-folds. We verify our conjecture in several cases using a vertex formalism. Taking a certain limit of the equivariant parameters, we recover the cohomological DT/PT correspondence for toric Calabi-Yau 4-folds recently conjectured by the first two authors. Another limit gives a dimensional reduction to the $K$-theoretic DT/PT correspondence for toric 3-folds conjectured by Nekrasov-Okounkov. As an application of our techniques, we find a conjectural formula for the generating series of $K$-theoretic stable pair invariants of the local resolved conifold. Upon dimensional reduction to the resolved conifold, we recover a formula which was recently proved by Kononov-Okounkov-Osinenko.Comment: 45 pages, exposition improved, formula for local resolved conifold and orientations adde

A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$, and conjecture closed formulae for their generating series, expressed in terms of the root system of $G$. In the second part, we define degree zero Donaldson-Thomas invariants of Calabi-Yau 4-orbifolds, develop a vertex formalism that computes the invariants in the toric case and conjecture closed formulae for the quotient stacks $[\mathbb{C}^4/\mathbb{Z}_r]$, $[\mathbb{C}^4/\mathbb{Z}_2\times \mathbb{Z}_2]$. Combining these two parts, we formulate a crepant resolution correspondence which relates the above two theories.Comment: 41 pages. Published versio

The influence of solid/liquid separation techniques on the sugar yield in two-step dilute acid hydrolysis of softwood followed by enzymatic hydrolysis

<p>Abstract</p> <p>Background</p> <p>Two-step dilute acid hydrolysis of softwood, either as a stand-alone process or as pretreatment before enzymatic hydrolysis, is considered to result in higher sugar yields than one-step acid hydrolysis. However, this requires removal of the liquid between the two steps. In an industrial process, filtration and washing of the material between the two steps is difficult, as it should be performed at high pressure to reduce energy demand. Moreover, the application of pressure leads to more compact solids, which may affect subsequent processing steps. This study was carried out to investigate the influence of pressing the biomass, in combination with the effects of not washing the material, on the sugar yield obtained from two-step dilute acid hydrolysis, with and without subsequent enzymatic digestion of the solids.</p> <p>Results</p> <p>Washing the material between the two acid hydrolysis steps, followed by enzymatic digestion, resulted in recovery of 96% of the mannose and 81% of the glucose (% of the theoretical) in the liquid fraction, regardless of the choice of dewatering method (pressing or vacuum filtration). Not washing the solids between the two acid hydrolysis steps led to elevated acidity of the remaining solids during the second hydrolysis step, which resulted in lower yields of mannose, 85% and 74% of the theoretical, for the pressed and vacuum-filtered slurry, respectively, due to sugar degradation. However, this increase in acidity resulted in a higher glucose yield (94.2%) from pressed slurry than from filtered slurry (77.6%).</p> <p>Conclusion</p> <p>Pressing the washed material between the two acid hydrolysis steps had no significant negative effect on the sugar yields of the second acid hydrolysis step or on enzymatic hydrolysis. Not washing the material resulted in a harsher second acid hydrolysis step, which caused greater degradation of the sugars during subsequent acid hydrolysis of the solids, particularly in case of the vacuum-filtered solids. However, pressing in combination with not washing the material between the two steps enhanced the sugar yield of the enzymatic digestion step. Hence, it is suggested that the unwashed slurry be pressed to as high a dry matter content as possible between the two acid hydrolysis stages in order to achieve high final sugar yields.</p

Teorema di Følner e Integrale di Haar su Gruppi Topologici Abeliani Localmente Compatti

La misura di Haar è una misura invariante in un gruppo topologico. L'approccio classico alla sua costruzione nasce nella teoria della misura, con strumenti di carattere analitico. In questo lavoro, tuttavia, si presenta una linea dimostrativa complementare: si dimostra direttamente l'esistenza del suo integrale come funzionale lineare, caratterizzandolo in modo algebrico attraverso i caratteri continui del gruppo, con i quali si può inoltre descrivere completamente le topologie deboli dei caratteri.ope

Expression, purification and immunogenic description of a hepatitis c virus recombinant coreE1E2 protein expressed by yeast pichia pastoris

Background: Gradual development of a useful vaccine can be the main point in the control and eradication of Hepatitis C virus (HCV) infection. Hepatitis C Virus envelope glycoproteins are considered as the main HCV vaccine candidate. Objectives: In this study, the Pichia pastoris expression system was used to express a recombinant HCV CoreE1E2 protein, which consists of Core (269 nt-841nt) E1 (842 nt-1417nt) and E2 (1418 nt-2506nt). Materials and Methods: By a codon optimization technique based on the P. pastoris expression system, we could increase the rate of recombinant proteins. Moreover, the purified protein can efficiently induce anti-CoreE1E2 antibodies in rabbits, and also by developing a homemade Enzyme-Linked ELISA kit we can detect antibody of HCV Iranian patients with genotype 1a. Results: In our study, the virus-like particle of rCoreE1E2 with 70 nm size, was shown by Electron microscopy and proved the self-assembly in vitro in a yeast expression system. Conclusions: These findings of the present study indicate that the recombinant CoreE1E2 glycoprotein is effective in inducing neutralizing antibodies, and is an influential HCV vaccine candidate. © 2015, Kowsar Medical Publishing Company. All rights reserved