The number of 4-cycles in 2-factorizations of K2n minus a 1-factor

In this paper we give a complete solution to problem of determining the number of 4-cycles in a 2-factorization of K-2n\ 1-factor. (C) 2000 Elsevier Science B.V. All rights reserved.

On a generalization of the Oberwolfach problem

Let e(1),e(2),... e(n) be a sequence of nonnegative integers Such that the first non-zero term is not one. Let Sigma(i=1)(n) e(i) = (q - 1)/2, where q = p(n) and p is an odd prime. We prove that the complete graph on q vertices can be decomposed into e(1) C-pn-factors, e(2) C-pn (1)-factors,..., and e(n) C-p-factors. (C) 2004 Elsevier Inc. All rights reserved.

Real rank zero algebras have the corona factorization property

The purpose of this short note is to prove that a stable separable C*-algebra with real rank zero has the so-called corona factorization property, that is, all the full multiplier projections are properly in finite. Enroute to our result, we consider conditions under which a real rank zero C*-algebra admits an injection of the compact operators (a question already considered in [21]).

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at=2.76 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Factorization and criticality in the anisotropic XY chain via correlations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Factorization and non-local 1/m b corrections in the decay B X s gamma

In this thesis, a systematic analysis of the bar B to X_sgamma photon spectrum in the endpoint region is presented. The endpoint region refers to a kinematic configuration of the final state, in which the photon has a large energy m_b-2E_gamma = O(Lambda_QCD), while the jet has a large energy but small invariant mass. Using methods of soft-collinear effective theory and heavy-quark effective theory, it is shown that the spectrum can be factorized into hard, jet, and soft functions, each encoding the dynamics at a certain scale. The relevant scales in the endpoint region are the heavy-quark mass m_b, the hadronic energy scale Lambda_QCD and an intermediate scale sqrt{Lambda_QCD m_b} associated with the invariant mass of the jet. It is found that the factorization formula contains two different types of contributions, distinguishable by the space-time structure of the underlying diagrams. On the one hand, there are the direct photon contributions which correspond to diagrams with the photon emitted directly from the weak vertex. The resolved photon contributions on the other hand arise at O(1/m_b) whenever the photon couples to light partons. In this work, these contributions will be explicitly defined in terms of convolutions of jet functions with subleading shape functions. While the direct photon contributions can be expressed in terms of a local operator product expansion, when the photon spectrum is integrated over a range larger than the endpoint region, the resolved photon contributions always remain non-local. Thus, they are responsible for a non-perturbative uncertainty on the partonic predictions. In this thesis, the effect of these uncertainties is estimated in two different phenomenological contexts. First, the hadronic uncertainties in the bar B to X_sgamma branching fraction, defined with a cut E_gamma > 1.6 GeV are discussed. It is found, that the resolved photon contributions give rise to an irreducible theory uncertainty of approximately 5 %. As a second application of the formalism, the influence of the long-distance effects on the direct CP asymmetry will be considered. It will be shown that these effects are dominant in the Standard Model and that a range of -0.6 < A_CP^SM < 2.8 % is possible for the asymmetry, if resolved photon contributions are taken into account.

Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

An Asp49 Phospholipase A2 From Snake Venom Induces Cyclooxygenase-2 Expression And Prostaglandin E2 Production Via Activation Of Nf-κb, P38mapk, And Pkc In Macrophages.

Phospholipases A2 (PLA2) are key enzymes for production of lipid mediators. We previously demonstrated that a snake venom sPLA2 named MT-III leads to prostaglandin (PG)E2 biosynthesis in macrophages by inducing the expression of cyclooxygenase-2 (COX-2). Herein, we explored the molecular mechanisms and signaling pathways leading to these MT-III-induced effects. Results demonstrated that MT-III induced activation of the transcription factor NF-κB in isolated macrophages. By using NF-κB selective inhibitors, the involvement of this factor in MT-III-induced COX-2 expression and PGE2 production was demonstrated. Moreover, MT-III-induced COX-2 protein expression and PGE2 release were attenuated by pretreatment of macrophages with SB202190, and Ly294002, and H-7-dihydro compounds, indicating the involvement of p38MAPK, PI3K, and PKC pathways, respectively. Consistent with this, MT-III triggered early phosphorylation of p38MAPK, PI3K, and PKC. Furthermore, SB202190, H-7-dihydro, but not Ly294002 treatment, abrogated activation of NF-κB induced by MT-III. Altogether, these results show for the first time that the induction of COX-2 protein expression and PGE2 release, which occur via NF-κB activation induced by the sPLA2-MT-III in macrophages, are modulated by p38MAPK and PKC, but not by PI3K signaling proteins.

Prognostic Value Of Dna And Mrna E6/e7 Of Human Papillomavirus In The Evolution Of Cervical Intraepithelial Neoplasia Grade 2.

This study aimed at evaluating whether human papillomavirus (HPV) groups and E6/E7 mRNA of HPV 16, 18, 31, 33, and 45 are prognostic of cervical intraepithelial neoplasia (CIN) 2 outcome in women with a cervical smear showing a low-grade squamous intraepithelial lesion (LSIL). This cohort study included women with biopsy-confirmed CIN 2 who were followed up for 12 months, with cervical smear and colposcopy performed every three months. Women with a negative or low-risk HPV status showed 100% CIN 2 regression. The CIN 2 regression rates at the 12-month follow-up were 69.4% for women with alpha-9 HPV versus 91.7% for other HPV species or HPV-negative status (P < 0.05). For women with HPV 16, the CIN 2 regression rate at the 12-month follow-up was 61.4% versus 89.5% for other HPV types or HPV-negative status (P < 0.05). The CIN 2 regression rate was 68.3% for women who tested positive for HPV E6/E7 mRNA versus 82.0% for the negative results, but this difference was not statistically significant. The expectant management for women with biopsy-confirmed CIN 2 and previous cytological tests showing LSIL exhibited a very high rate of spontaneous regression. HPV 16 is associated with a higher CIN 2 progression rate than other HPV infections. HPV E6/E7 mRNA is not a prognostic marker of the CIN 2 clinical outcome, although this analysis cannot be considered conclusive. Given the small sample size, this study could be considered a pilot for future larger studies on the role of predictive markers of CIN 2 evolution.

Solid Lipid Nanoparticles For Hydrophilic Biotech Drugs: Optimization And Cell Viability Studies (caco-2 & Hepg-2 Cell Lines).

Insulin was used as model protein to developed innovative Solid Lipid Nanoparticles (SLNs) for the delivery of hydrophilic biotech drugs, with potential use in medicinal chemistry. SLNs were prepared by double emulsion with the purpose of promoting stability and enhancing the protein bioavailability. Softisan(®)100 was selected as solid lipid matrix. The surfactants (Tween(®)80, Span(®)80 and Lipoid(®)S75) and insulin were chosen applying a 2(2) factorial design with triplicate of central point, evaluating the influence of dependents variables as polydispersity index (PI), mean particle size (z-AVE), zeta potential (ZP) and encapsulation efficiency (EE) by factorial design using the ANOVA test. Therefore, thermodynamic stability, polymorphism and matrix crystallinity were checked by Differential Scanning Calorimetry (DSC) and Wide Angle X-ray Diffraction (WAXD), whereas the effect of toxicity of SLNs was check in HepG2 and Caco-2 cells. Results showed a mean particle size (z-AVE) width between 294.6 nm and 627.0 nm, a PI in the range of 0.425-0.750, ZP about -3 mV, and the EE between 38.39% and 81.20%. After tempering the bulk lipid (mimicking the end process of production), the lipid showed amorphous characteristics, with a melting point of ca. 30 °C. The toxicity of SLNs was evaluated in two distinct cell lines (HEPG-2 and Caco-2), showing to be dependent on the concentration of particles in HEPG-2 cells, while no toxicity in was reported in Caco-2 cells. SLNs were stable for 24 h in in vitro human serum albumin (HSA) solution. The resulting SLNs fabricated by double emulsion may provide a promising approach for administration of protein therapeutics and antigens.