Demicompactness Results for Strongly Continuous Semigroups,Generators and Resolvents

Let \((U(t))_ {t\ge 0}\) be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) \(t>0\). In addition, we study the demicompactness of similar, subspace and product semigroups. We also investigate the demicompactness of the resolvent. We close this paper by giving some conditions guaranteeing the demicompactness of a generator of a strongly continuous semigroup in a Hilbert space.     

Stable exact solutions in cosmological models with two scalar fields

We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory.     

Essential Spectra, Matrix Operator and Applications

This paper gives a survey on some recent results on the spectral theory of block operator matrices. We study the closeness in the product space and we give some conditions to characterize the essential spectra in the Browder resolvent set case. Furthermore, we apply the obtained results to several models such as delay equations, Sturm–Liouville problem and transport equations.     

On the proximinality of compact operators over spaces of measurable functions

The main results in this paper are, the characterization of all the σfinite positive measures μ and v, for which K(L₁(μ, L₁(v)) proximinal in K(L₁(μ, L₁(v)) all the a-finite positive measures fi and v, for which K(L_∞(μ), L_∞(v)) is proximinal in L(L_∞μ)), L_v(v)) and all the compact Hausdorff spaces Q, for which K(C(Q), L_∞(μ)) is proximinal in L(C(Q), :_∞(μ))     

Temperature dependent electrophysical characteristics of GaAs-polymer composite varistors

A composition of GaAs-polymer tiny particles was pressed at a temperature of 130 °C and a pressure of 60 MPa and its current–voltage characteristic was studied. The result shows that the prepared disk has varistor behavior and can therefore be used to protect circuits from low overvoltage transients higher than 62 V. Temperature dependence of current-voltage characteristic and the electrical conductivity of the sample were investigated in the temperature range of 25–100 °C. It has been found that increase in temperature results in lower breakdown voltage and nonlinearity coefficient. At high temperatures, nonlinearity in the I–V characteristic of sample disappears and the conductivity becomes Ohmic in nature. The sample has hysteresis which decreases through increase in temperature. Annealing effect on leakage current and breakdown voltage was both investigated and analyzed using SEM micrographs. Finally, the electrical bandgap of the sample was measured.     

Comparison of tumor histology to dynamic contrast enhanced magnetic resonance imaging-based physiological estimates

Purpose

The purpose of this study was to compare histologically determined cellularity and extracellular space to dynamic contrast-enhanced magnetic resonance imaging (DCE MRI)-based maps of a two-compartment model's parameters describing tumor contrast agent extravasation, specifically tumor extravascular extracellular space (EES) volume fraction (v_e), tumor plasma volume fraction (v_p) and volume-normalized contrast agent transfer rate between tumor plasma and interstitium (K_TRANS/V_T).

Materials and Methods

Obtained v_e, v_p and K_TRANS/V_T maps were estimated from gadolinium diethylenetriamine penta-acetic acid DCE T₁-weighted gradient-echo images at resolutions of 469, 938 and 2500 μm. These parameter maps were compared at each resolution to histologically determined tumor type, and the high-resolution 469-μm maps were compared with automated cell counting using Otsu's method and a color-thresholding method for estimated intracellular (V_{intracellular}) and extracellular (V_{extracellular}) space fractions.

Results

The top five K_TRANS/V_T values obtained from each tumor at 469 and 938 μm resolutions are significantly different from those obtained at 2500 μm (P<.0001) and from one another (P=.0014). Using these top five K_TRANS/V_T values and the corresponding tumor EES volume fractions v_e, we can statistically differentiate invasive ductal carcinomas from noninvasive papillary carcinomas for the 469- and 938-μm resolutions (P=.0017 and P=.0047, respectively), but not for the 2500-μm resolution (P=.9008). The color-thresholding method demonstrated that v_e measured by DCE MRI is statistically similar to histologically determined EES. The V_{extracellular} obtained from the color-thresholding method was statistically similar to the v_e measured with DCE MRI for the top 10 K_TRANS/V_T values (P>.05). DCE MRI-based K_TRANS/V_T estimates are not statistically correlated with histologically determined cellularity.

Conclusion

DCE MRI estimates of tumor physiology are a limited representation of tumor histological features. Extracellular spaces measured by both DCE MRI and microscopic analysis are statistically similar. Tumor typing by DCE MRI is spatial resolution dependent, as lower resolutions average out contributions to voxel-based estimates of K_TRANS/V_T. Thus, an appropriate resolution window is essential for DCE MRI tumor diagnosis. Within this resolution window, the top K_TRANS/V_T values with corresponding v_e are diagnostic for the tumor types analyzed in this study.     

Holographic Renormalization Group Flow in Anisotropic Matter

Theoretical and Mathematical Physics - We consider holographic renormalization group flow equations in an anisotropic quark—gluon plasma and present anisotropic solutions for some special cases.     

Anticancer activity of lanthanum (III) and europium (III) 5-fluorouracil complexes on Caco-2 cell line

Lanthanide complexes are of increasing importance in cancer diagnosis and therapy. In the present study 1:1 and 1:3 solid complexes of La (III)–5-FU (5-fluorouracil) were prepared and characterized. In solution, the formation of 1:1 La (III) and Eu (III) complexes enabled the enhancement of 5-FU's effectiveness. Binding constants of the 1:1 complexes of both metals were estimated using spectrophotometry and HPLC with fluorescence detection methods. The thermodynamic parameters ΔG ^° , ΔH ^° and ΔS ^° were calculated using differential scanning calorimetry. Evaluation of the cytotoxic activity of the 1:1 La (III)- and Eu (III)–5-FU complexes was performed through two methodologies, trypan blue for cell viability where La (III)- and Eu (III)–5-FU complexes were found to have 52,000 and 80,000 dead cells, respectively, and via flow cytometric analysis to measure the apoptotic values, which were found to be 59.87 and 86.86% respectively.