Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Nd：YbVO4晶体的拉曼光谱和荧光光谱研究

用群论的方法计算了Nd：YbVO4晶体的拉曼活性振动模数目，在室温下测得了其极化拉曼谱线，并指认了在不同几何配置下，各振动模式所对应的频率。同时，测得了室温下晶体的吸收谱，得到了中心波长为808am吸收峰的半高宽为12nm，并在J-O理论的基础上计算了晶体的光学参数，其三个晶场参数分别为Ω2=6．88945×10^-20cm^2。Ω4=4．13394×10^-20cm^2、Ω6=4．54503×10^-20cm^2，并由此得到^4F3／2能级的荧光寿命为178．69炉，1062nm处的荧光分支比为48．85％，积分发射截面为2．786710^-18cm^2。分别在808nm、940nm激发下测得晶体室温发射谱，观察到了Nd→Yb以及Nd←Yb间的能量传递现象。

Differential Neuroprotective Effects of 5 '-Deoxy-5 '-Methylthioadenosine

Background: 5'-deoxy-5'-methylthioadenosine (MTA) is an endogenous compound produced through the metabolism of polyamines. The therapeutic potential of MTA has been assayed mainly in liver diseases and, more recently, in animal models of multiple sclerosis. The aim of this study was to determine the neuroprotective effect of this molecule in vitro and to assess whether MTA can cross the blood brain barrier (BBB) in order to also analyze its potential neuroprotective efficacy in vivo. Methods: Neuroprotection was assessed in vitro using models of excitotoxicity in primary neurons, mixed astrocyte-neuron and primary oligodendrocyte cultures. The capacity of MTA to cross the BBB was measured in an artificial membrane assay and using an in vitro cell model. Finally, in vivo tests were performed in models of hypoxic brain damage, Parkinson's disease and epilepsy. Results: MTA displays a wide array of neuroprotective activities against different insults in vitro. While the data from the two complementary approaches adopted indicate that MTA is likely to cross the BBB, the in vivo data showed that MTA may provide therapeutic benefits in specific circumstances. Whereas MTA reduced the neuronal cell death in pilocarpine-induced status epilepticus and the size of the lesion in global but not focal ischemic brain damage, it was ineffective in preserving dopaminergic neurons of the substantia nigra in the 1-methyl-4-phenyl-1,2,3,6-tetrahydro-pyridine (MPTP)-mice model. However, in this model of Parkinson's disease the combined administration of MTA and an A(2A) adenosine receptor antagonist did produce significant neuroprotection in this brain region. Conclusion: MTA may potentially offer therapeutic neuroprotection.

Differential activity of GSK-3 isoforms regulates NF-kappa B and TRAIL- or TNF alpha induced apoptosis in pancreatic cancer cells

While TRAIL is a promising anticancer agent due to its ability to selectively induce apoptosis in neoplastic cells, many tumors, including pancreatic ductal adenocarcinoma (PDA), display intrinsic resistance, highlighting the need for TRAIL-sensitizing agents. Here we report that TRAIL-induced apoptosis in PDA cell lines is enhanced by pharmacological inhibition of glycogen synthase kinase-3 (GSK-3) or by shRNA-mediated depletion of either GSK-3 alpha or GSK-3 beta. In contrast, depletion of GSK-3 beta, but not GSK-3 alpha, sensitized PDA cell lines to TNF alpha-induced cell death. Further experiments demonstrated that TNF alpha-stimulated I kappa B alpha phosphorylation and degradation as well as p65 nuclear translocation were normal in GSK-3 beta-deficient MEFs. Nonetheless, inhibition of GSK-3 beta function in MEFs or PDA cell lines impaired the expression of the NF-kappa B target genes Bcl-xL and cIAP2, but not I kappa B alpha. Significantly, the expression of Bcl-xL and cIAP2 could be reestablished by expression of GSK-3 beta targeted to the nucleus but not GSK-3 beta targeted to the cytoplasm, suggesting that GSK-3 beta regulates NF-kappa B function within the nucleus. Consistent with this notion, chromatin immunoprecipitation demonstrated that GSK-3 inhibition resulted in either decreased p65 binding to the promoter of BIR3, which encodes cIAP2, or increased p50 binding as well as recruitment of SIRT1 and HDAC3 to the promoter of BCL2L1, which encodes Bcl-xL. Importantly, depletion of Bcl-xL but not cIAP2, mimicked the sensitizing effect of GSK-3 inhibition on TRAIL-induced apoptosis, whereas Bcl-xL overexpression ameliorated the sensitization by GSK-3 inhibition. These results not only suggest that GSK-3 beta overexpression and nuclear localization contribute to TNF alpha and TRAIL resistance via anti-apoptotic NF-kappa B genes such as Bcl-xL, but also provide a rationale for further exploration of GSK-3 inhibitors combined with TRAIL for the treatment of PDA.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Variation in trawl geometry due to unequal warp length

Survey standardization procedures can reduce the variability in trawl catch efficiency thus producing more precise estimates of biomass. One such procedure, towing with equal amounts of trawl warp on both sides of the net, was experimentally investigated for its importance in determining optimal trawl geometry and for evaluating the effectiveness of the recent National Oceanic and Atmospheric Administration (NOAA) national protocol on accurate measurement of trawl warps. This recent standard for measuring warp length requires that the difference between warp lengths can be no more than 4% of the distance between the otter doors measured along the bridles and footrope. Trawl performance data from repetitive towing with warp differentials of 0, 3, 5, 7, 9, 11, and 20 m were analyzed for their effect on three determinants of flatfish catch efficiency: footrope distance off-bottom, bridle length in contact with the bottom, and area swept by the net. Our results indicated that the distortion of the trawl caused by asymmetry in trawl warp length could have a negative inf luence on flatfish catch efficiency. At a difference of 7 m in warp length, the NOAA 4% threshold value for the 83112 Eastern survey trawl used in our study, we found no effect on the acous-tic-based measures of door spread, wing spread, and headrope height off-bottom. However, the sensitivity of the trawl to 7 m of warp offset could be seen as footrope distances off-bottom increased slightly (particularly in the center region of the net where flatfish escapement is highest), and as the width of the bridle path responsible for flatfish herding, together with the effective net width, was reduced. For this survey trawl, a NOAA threshold value of 4% should be considered a maximum. A more conservative value (less than 4%) would likely reduce potential bias in estimates of relative abundance caused by large differences in warp length approaching 7 m.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.