Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

The role of Ski/Sno oncoproteins as negative regulators of the TGF-beta/SMAD signaling pathway in B -cell non -Hodgkin's lymphoma (NHL-B)

Non-Hodgkin's lymphomas are common tumors of the human immune system, primarily of B cell lineage (NHL-B). Negative growth regulation in the B cell lineage is mediated primarily through the TGF-β/SMAD signaling pathway that regulates a variety of tumor suppressor genes. Ski was originally identified as a transforming oncoprotein, whereas SnoN is an isoform of the Sno protein that shares a large region of homology with Ski. In this study, we show that Ski/SnoN are endogenously over-expressed both in patients' lymphoma cells and NHL-B cell lines. Exogenous TGF-β1 treatment induces down-regulation of Ski and SnoN oncoprotein expression in an NHL-B cell line, implying that Ski and SnoN modulate the TGF-β signaling pathway and are involved in cell growth regulation. Furthermore, we have developed an NHL-B cell line (DB) that has a null mutation in TGF-β receptor type II. In this mutant cell line, Ski/SnoN proteins are not down-regulated in response to TGF-β1 treatment, suggesting that downregulation of Ski and SnoN proteins in NHL-B require an intact functional TGF-β signaling pathway Resting normal B cells do not express Ski until activated by antigens and exogenous cytokines, whereas a low level of SnoN is also present in peripheral blood Go B cells. In contrast, autonomously growing NHL-B cells over-express Ski and SnoN, implying that Ski and SnoN are important cell cycle regulators. To further investigate a possible link between reduction of the Ski protein level and growth inhibition, Ski antisense oligodeoxynucleotides were transfected into NHL-B cells. The Ski protein level was found to decrease to less than 40%, resulting in restoring the effect of TGF-β and leading to cell growth inhibition and G1 cell cycle arrest. Co-immunoprecipitation experiments demonstrated that Ski associates with Smad4 in the nucleus, strongly suggesting that over-expression of the nuclear protein Ski and/or SnoN negatively regulates the TGF-β pathway, possibly by modulating Smad-mediated tumor suppressor gene expression. Together, in NHL-B, the TGF-β/SMAD growth inhibitory pathway is usually intact, but over-expression of the Ski and/or SnoN, which binds to Smad4, abrogates the negative regulatory effects of TGF-β/SMAD in lymphoma cell growth and potentiates the growth potential of neoplastic B cells. ^

Acquisition of negative valence and modified attentional processing by non fear relevant stimuli

The current research examined valence and attentional processing of a priori fear relevant stimuli and investigated the extent to which these characteristics can be acquired by non fear relevant stimuli across an aversive learning episode. The first experiment compared pictures of snakes and spiders with pictures of birds and fish using affective priming, visual search and detection of a dot probe. Snakes and spiders were more negative than birds and fish as indexed by affective priming, and were preferentially attended to in the visual search task. The second experiment exposed the non fear relevant animal pictures, birds and fish, in an aversive learning episode involving an aversive shock US. Skin conductance responding was measured during acquisition. After acquisition, conditioned non fear relevant animal stimuli, CS1, and non conditioned, non fear relevant animal stimuli, CS, were compared across affective priming, visual search and dot probe tasks. During acquisition, skin conductance responses were larger during CS1 than during CS across all three response intervals. After acquisition, CS1 non fear relevant animal pictures were more negative than CS non fear relevant animal pictures as indexed by affective priming, and were preferentially attended to in a dot probe task. These studies provide evidence that negative valence and modified attentional processing can be acquired in a brief aversive learning episode.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

Non-Gaussian distribution of collective operators in quantum spin chains

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on thesame curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Primary Relapse Site Pattern In Women With Triple-negative Breast Cancer.

Despite the remarkable improvements in breast cancer (BC) characterization, accurate prediction of BC clinical behavior is often still difficult to achieve. Some studies have investigated the association between the molecular subtype, namely the basal-like BC and the pattern of relapse, however only few investigated the association between relapse pattern and immunohistochemical defined triple-negative breast cancers (TNBCs). The aim of this study was to evaluate the pattern of relapse in patients with TNBC, namely the primary distant relapse site. One-hundred twenty nine (129) invasive breast carcinomas with follow-up information were classified according to the molecular subtype using immunohistochemistry for ER, PgR and Her2. The association between TNBC and distant relapse primary site was analyzed by logistic regression. Using multivariate logistic regression analysis patients with TNBC displayed only 0.09 (95% CI: 0.00-0.74; p=0.02) the odds of the non-TNBC patients of developing bone primary relapse. Regarding visceral and lymph-node relapse, no differences between in this cohort were found. Though classically regarded as aggressive tumors, TNBCs rarely development primary relapse in bone when compared to non-TNBC, a clinical relevant fact when investigating a metastasis of an occult or non-sampled primary BC.

Analysis Of The Contribution Of Immunologically-detectable Her2, Steroid Receptors And Of The Triple-negative" Tumor Status To Disease-free And Overall Survival Of Women With Epithelial Ovarian Cancer."

We assessed associations between steroid receptors including: estrogen-alpha, estrogen-beta, androgen receptor, progesterone receptor, the HER2 status and triple-negative epithelial ovarian cancer (ERα-/PR-/HER2-; TNEOC) status and survival in women with epithelial ovarian cancer. The study included 152 women with primary epithelial ovarian cancer. The status of steroid receptor and HER2 was determined by immunohistochemistry. Disease-free and overall survival were calculated and compared with steroid receptor and HER2 status as well as clinicopathological features using the Cox Proportional Hazards model. A mean follow-up period of 43.6 months (interquartile range=41.4 months) was achieved where 44% of patients had serous tumor, followed by mucinous (23%), endometrioid (9%), mixed (9%), undifferentiated (8.5%) and clear cell tumors (5.3%). ER-alpha staining was associated with grade II-III tumors. Progesterone receptor staining was positively associated with a Body Mass Index≥25. Androgen receptor positivity was higher in serous tumors. In stand-alone analysis of receptor contribution to survival, estrogen-alpha positivity was associated with greater disease-free survival. However, there was no significant association between steroid receptor expression, HER2 status, or TNEOC status, and overall survival. Although estrogen-alpha, androgen receptor, progesterone receptor and the HER2 status were associated with key clinical features of the women and pathological characteristics of the tumors, these associations were not implicated in survival. Interestingly, women with TNEOC seem to fare the same way as their counterparts with non-TNEOC.

High Prevalence Of Insulin Resistance Assessed By The Glucose Clamp Technique In Hormonal And Non-hormonal Contraceptive Users.

Objective To assess the prevalence of insulin resistance (IR) and associated factors in contraceptive users. Methods A total of 47 women 18 to 40 years of age with a body mass index (kg/m(2)) < 30, fasting glucose levels < 100 mg/dl and 2-hour glucose level < 140 mg/dl after a 75-g oral glucose load were submitted to a hyperinsulinemic-euglycemic clamp. The women were distributed in tertiles regarding M-values. The analysed variables were use of combined hormonal/non-hormonal contraception, duration of use, body composition, lipid profile, glucose levels and blood pressure. Results IR was detected in 19% of the participants. The women with low M-values presented significantly higher body fat mass, waist-to-hip ratio, fasting insulin, HOMA-IR and were nulligravida, showed > 1 year of contraceptive use and higher triglyceride levels. IR was more frequent among combined oral contraceptive users, however no association was observed after regression analysis. Conclusions The prevalence of IR was high among healthy women attending a family planning clinic independent of the contraceptive method used with possible long-term negative consequences regarding their metabolic and cardiovascular health. Although an association between hormonal contraception and IR could not be found this needs further research. Family planning professionals should be proactive counselling healthy women about the importance of healthy habits.

Chronic Continuous Exenatide Infusion Does Not Cause Pancreatic Inflammation And Ductal Hyperplasia In Non-human Primates.

In this study, we aimed to evaluate the effects of exenatide (EXE) treatment on exocrine pancreas of nonhuman primates. To this end, 52 baboons (Papio hamadryas) underwent partial pancreatectomy, followed by continuous infusion of EXE or saline (SAL) for 14 weeks. Histological analysis, immunohistochemistry, Computer Assisted Stereology Toolbox morphometry, and immunofluorescence staining were performed at baseline and after treatment. The EXE treatment did not induce pancreatitis, parenchymal or periductal inflammatory cell accumulation, ductal hyperplasia, or dysplastic lesions/pancreatic intraepithelial neoplasia. At study end, Ki-67-positive (proliferating) acinar cell number did not change, compared with baseline, in either group. Ki-67-positive ductal cells increased after EXE treatment (P = 0.04). However, the change in Ki-67-positive ductal cell number did not differ significantly between the EXE and SAL groups (P = 0.13). M-30-positive (apoptotic) acinar and ductal cell number did not change after SAL or EXE treatment. No changes in ductal density and volume were observed after EXE or SAL. Interestingly, by triple-immunofluorescence staining, we detected c-kit (a marker of cell transdifferentiation) positive ductal cells co-expressing insulin in ducts only in the EXE group at study end, suggesting that EXE may promote the differentiation of ductal cells toward a β-cell phenotype. In conclusion, 14 weeks of EXE treatment did not exert any negative effect on exocrine pancreas, by inducing either pancreatic inflammation or hyperplasia/dysplasia in nonhuman primates.

Use of flowable composite as intermediary layer in non-carious cervical lesions restored with composite resin: 48-month follow-up

PURPOSE: In this case report, the clinical performance of a microhybrid resin composite placed with or without a flowable resin composite was compared, over a 48-month period. CASE DESCRIPTION: The patient of this case report presented 2 pairs of equivalent cervical abfraction lesions, under occlusion. Four restorations were placed in teeth 34, 35, 44 and 45. The restorations were divided into groups (Single Bond + Filtek-Flow + Filtek Z250 or Single Bond + Filtek Z250) and the materials were applied according to the manufactures instructions. Two previously calibrated operators placed the restorations and two other independent examiners evaluated the restorations at baseline and after 48 months, according to the USPHS criteria and modified criteria for color match. CONCLUSION: After 48 months of evaluation the lesions restored with Filtek-Flow as a liner under Filtek Z250 did not show better clinical performance than the restorations without Filtek-Flow. All restorations showed a trend toward dark yellowing after 48 months.