On the Distribution of Characteristic Roots of Delay Differential Equations

In this article we analyze the distribution in the complex plane of the roots of the characteristic functions for first and second order linear delay differential equations. We prove necessary and sufficient conditions which are satisfied with respect to the variation of the coefficients in order the characteristic roots have negative real parts.Key words: Delay differential equations advanced type; Characteristic roo

The significance of Survivin and Nectin-4 expression in the prognosis of breast carcinoma

To investigate the prognostic significance of Survivin and Nectin-4 expression in breast carcinomas. Imprint smears were obtained from 140 breast carcinoma specimens and studied immunocytochemically for the expression of Survivin and Nectin-4. The results were correlated with several clinicopathological parameters, including five-year survival. Increased Survivin staining pattern correlated with increased grade (p < 0.0001), increased lymph node invasion (p < 0.0001), increased tumor size and reduced survival (p < 0.0001). Elevated Nectin-4 expression also correlated significantly with increased grade (p < 0.0001), increased tumor size (p < 0.0001) and reduced survival (p < 0.0001). In addition, Survivin and Nectin-4 staining patterns correlated strongly with one another (p < 0.0001). However, on multivariate analysis, neither Survivin nor Nectin-4 expression seemed to have an independent impact on survival in our study cases. The findings of our study suggest that increased expression of Survivin and Nectin-4 may indicate a worse prognosis in breast cancer patients. The exact implications of the expression of these markers in breast cancer prognosis and treatment remain to be clarified. (Folia Histochemica et Cytobiologica 2011; Vol. 49, No. 1, pp. 26&#8211;33

Chondrule Formation in Bow Shocks around Eccentric Planetary Embryos

Recent isotopic studies of Martian meteorites by Dauphas & Pourmond (2011) have established that large (~ 3000 km radius) planetary embryos existed in the solar nebula at the same time that chondrules - millimeter-sized igneous inclusions found in meteorites - were forming. We model the formation of chondrules by passage through bow shocks around such a planetary embryo on an eccentric orbit. We numerically model the hydrodynamics of the flow, and find that such large bodies retain an atmosphere, with Kelvin-Helmholtz instabilities allowing mixing of this atmosphere with the gas and particles flowing past the embryo. We calculate the trajectories of chondrules flowing past the body, and find that they are not accreted by the protoplanet, but may instead flow through volatiles outgassed from the planet's magma ocean. In contrast, chondrules are accreted onto smaller planetesimals. We calculate the thermal histories of chondrules passing through the bow shock. We find that peak temperatures and cooling rates are consistent with the formation of the dominant, porphyritic texture of most chondrules, assuming a modest enhancement above the likely solar nebula average value of chondrule densities (by a factor of 10), attributable to settling of chondrule precursors to the midplane of the disk or turbulent concentration. We calculate the rate at which a planetary embryo's eccentricity is damped and conclude that a single planetary embryo scattered into an eccentric orbit can, over ~ 10e5 years, produce ~ 10e24 g of chondrules. In principle, a small number (1-10) of eccentric planetary embryos can melt the observed mass of chondrules in a manner consistent with all known constraints.Comment: Accepted for publication in The Astrophysical Journa

On Silicon Group Elements Ejected by Supernovae Type Ia

There is compelling evidence that the peak brightness of a Type Ia supernova is affected by the electron fraction Ye at the time of the explosion. The electron fraction is set by the aboriginal composition of the white dwarf and the reactions that occur during the pre explosive convective burning. To date, determining the makeup of the white dwarf progenitor has relied on indirect proxies, such as the average metallicity of the host stellar population. In this paper, we present analytical calculations supporting the idea that the electron fraction of the progenitor systematically influences the nucleosynthesis of silicon group ejecta in Type Ia supernovae. In particular, we suggest the abundances generated in quasi nuclear statistical equilibrium are preserved during the subsequent freezeout. This allows one to potential recovery of Ye at explosion from the abundances recovered from an observed spectra. We show that measurement of 28Si, 32S, 40Ca, and 54Fe abundances can be used to construct Ye in the silicon rich regions of the supernovae. If these four abundances are determined exactly, they are sufficient to recover Ye to 6 percent. This is because these isotopes dominate the composition of silicon-rich material and iron rich material in quasi nuclear statistical equilibrium. Analytical analysis shows that the 28Si abundance is insensitive to Ye, the 32S abundance has a nearly linear trend with Ye, and the 40Ca abundance has a nearly quadratic trend with Ye. We verify these trends with post-processing of 1D models and show that these trends are reflected in model synthetic spectra.Comment: Submitted to the Ap

Associations of Apolipoprotein A, High-Sensitivity C-Reactive Protein and Fasting Plasma Insulin in Obese Children With and Without Family History of Cardiovascular Disease

BACKGROUND: The worldwide prevalence of childhood obesity has increased from 4.2% to 6.7% during the last two decades. Pediatric obesity is a major health problem, which is dramatically increasing in Greece. A variety of inflammatory variables have been also found to associate with cardiometabolic (CV) risk in obese children. The purpose of this study was to identify and examine the effects of possible CV risk factors in obese and non-obese children with and without family history (FH) of cardiovascular disease (CVD). METHODS: Sixty-eight (68) healthy children and adolescents aged 7 - 13 years participated in the study. Anthropometrical and biochemical indexes were obtained from all children as well as FH of CVD. RESULTS: Systolic blood pressure (SBP), total cholesterol (TC), triglyceride (TG), high-sensitivity C-reactive protein (hsCRP), fasting plasma insulin (FPI) and homeostasis model assessment of insulin resistance (HOMA-IR) levels were found statistically significantly higher in the obese group compared to the non-obese one. High-density lipoprotein (HDL) levels were observed to be statistically significantly lower in the obese children compared to their normal peers. CONCLUSIONS: Apolipoprotein A, hsCRP and FPI levels were significantly higher in the obese children with FH of CVD compared to the ones without FH of CVD. TC and SBP were found to be independently associated with obesity (odds ratio (OR): 1.965, 95% confidence interval (CI): 1.935 - 2.97, P \u3c 0.031 and OR: 1.045, 95% CI: 1.016 - 1.074, P \u3c 0.002, respectively)

Displacement spectra and displacement modification factors, based on records from Greece

Elastic and inelastic displacement spectra (for periods up to 4.0 s) are derived, using a representative sample of acceleration records from Greece, carefully selected based on magnitude, distance and peak ground acceleration criteria, and grouped into three ground type categories according to the Eurocode 8 (EC8) provisions. The modification factor for the elastic design spectrum adopted in EC8 for accounting for damping is verified herein and is found to be satisfactory in the short to medium period range and less so in the long period range. The equivalent viscous damping ratio concept is also evaluated and is found to lead to underestimation of inelastic displacement spectra. Finally, based on the previously derived elastic and inelastic spectra, equations suitable for design and/or assessment purposes, are proposed for the corresponding displacement modification factors

Tiam1 Protein Expression in Primary and Metastatic Colorectal Carcinoma: A Retrospective Study of 200 Cases

Objective: T-cell Lymphoma Invasion and Metastasis 1 (Tiam1)protein is a guanine nucleotide exchange factor that activates proteins of the Rho family of GTPases, specifically Rac1. Expression of Tiam1 protein has been reported in various human cancers and has been associated with lymphangiogenesis and promotion of tumor metastasis. The objective of this study was to further evaluate the expression of Tiam1 in primary and metastatic colorectal cancer (CRC) and its association withvariousclinicopathological parameters, includinggender, age, tumor size, Dukes stage, tumor grade, lymph node status and original location of the primary tumor (colon versus rectum).Methods: The expression of Tiam1 was detected by immunohistochemistry in 200 samples of primary CRC tissues and in 100 samples of lymph node tissue with CRC metastases.Results: Tiam1 was overexpressed in the majority of both primary (69,5% of the cases) and metastatic (63% of the cases) CRC tumor tissues. Overexpression of Tiam1 in primary CRC was statistically associated withlowertumor grade(P=0,04), whereas in metastatic CRC a statistically significant association between Tiam1 expression and  female gender (P=0,003), tumor size 5cm (P=0,001) and localization  of the primary tumor in the colon (P=0,009) was found.Conclusion: Overexpression of Tiam1 protein may represent a frequent event in CRC. Additional studies are warranted to further investigate its potential value as a marker of prognosis and treatment response in this form of cancer

Dimensional analysis of the earthquake-induced pounding between adjacent structures

In this paper the dynamic response of two and three pounding oscillators subjected to pulse-type excitations is revisited with dimensional analysis. Using Buckingham's Π-theorem the number of variables that govern the response of the system is reduced by three. When the response is presented in the dimensionless Π-terms remarkable order emerges. It is shown that regardless of the acceleration level and duration of the pulse all response spectra become self-similar and follow a single master curve. This is true despite the realization of finite duration contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachments) are captured via a linear complementarity approach. The study confirms the existence of three spectral regions. The response of the most flexible among the two oscillators amplifies in the low range of the frequency spectrum (flexible structures); whereas, the response of the most stiff among the two oscillators amplifies at the upper range of the frequency spectrum (stiff structures). Most importantly, the study shows that pounding structures such as colliding buildings or interacting bridge segments may be most vulnerable for excitations with frequencies very different from their natural eigenfrequencies. Finally, by applying the concept of intermediate asymptotics, the study unveils that the dimensionless response of two pounding oscillators follows a scaling law with respect to the mass ratio, or in mathematical terms, that the response exhibits an incomplete self-similarity or self-similarity of the second kind with respect to the mass ratio