Some Coincidence and Fixed Point Results for Hybrid Contraction

Fixed point theory for multi-valued mappings has many useful applications in applied sciences, in particular in Game theory and Mathematical Economics. Thus it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multi-valued mappings. Some theorems of existence of fixed points of single-valued mappings have been extended to the multi-valued case. For example, in 1969 Nadler extended the Banach contraction principle to multi-valued contractive mappings in complete metric space. However, many other questions remain open. Moreover, the study of existence of coincidence and fixed points for hybrid contraction that is a pair of single-valued and multi-valued maps became more interesting due to the recent investigation of Corley in 1986. He gave a good relationship between hybrid fixed points and optimization problems. Here we present the main known results and current research direction in this subject .This talk can be considered as a survey, but some new results are also included. Mathematics Subject Classifications: 47H10, 54H25

Coincidence Points for Mappings under Generalized Contraction

In this paper we establish some results on the existence of coincidence and fixed points for multi-valued and single valued mappings extending the result of Feng and Liu [2] and Liu et.al [5]. It is also proved with counter example that our results generalize and extend some well known results. Key Words: common fixed point, Coincidence point, multi-valued mappings

Exposure of Human Lung Cells to Tobacco Smoke Condensate Inhibits the Nucleotide Excision Repair Pathway

Exposure to tobacco smoke is the number one risk factor for lung cancer. Although the DNA damaging properties of tobacco smoke have been well documented, relatively few studies have examined its effect on DNA repair pathways. This is especially true for the nucleotide excision repair (NER) pathway which recognizes and removes many structurally diverse DNA lesions, including those introduced by chemical carcinogens present in tobacco smoke. The aim of the present study was to investigate the effect of tobacco smoke on NER in human lung cells. We studied the effect of cigarette smoke condensate (CSC), a surrogate for tobacco smoke, on the NER pathway in two different human lung cell lines; IMR-90 lung fibroblasts and BEAS-2B bronchial epithelial cells. To measure NER, we employed a slot-blot assay to quantify the introduction and removal of UV light-induced 6–4 photoproducts and cyclobutane pyrimidine dimers. We find a dose-dependent inhibition of 6–4 photoproduct repair in both cell lines treated with CSC. Additionally, the impact of CSC on the abundance of various NER proteins and their respective RNAs was investigated. The abundance of XPC protein, which is required for functional NER, is significantly reduced by treatment with CSC while the abundance of XPA protein, also required for NER, is unaffected. Both XPC and XPA RNA levels are modestly reduced by CSC treatment. Finally, treatment of cells with MG-132 abrogates the reduction in the abundance of XPC protein produced by treatment with CSC, suggesting that CSC enhances proteasome-dependent turnover of the protein that is mediated by ubiquitination. Together, these findings indicate that tobacco smoke can inhibit the same DNA repair pathway that is also essential for the removal of some of the carcinogenic DNA damage introduced by smoke itself, increasing the DNA damage burden of cells exposed to tobacco smoke

Effect of Cigarette Smoke Exposure and Mutant Kras Overexpression on Pancreatic Cell Proliferation

Pancreatic cancer is the fourth leading cause of cancer‑associated mortality. The major risk factor for pancreatic cancer is cigarette smoking. Kras mutations are commonly observed in human pancreatic cancers. The present study examined the hypothesis that exposure to cigarette smoke and overexpression of a mutant Kras gene in the pancreas affects pancreatic cell proliferation in mice. Mice overexpressing the mutant Kras gene (KRasG12D) in the pancreas as well as wild‑type mice were exposed to environmental tobacco smoke for 2 weeks. Overexpression of mutant Kras increased cell proliferation in pancreatic ductal, acinar and islet cells. Notably, cigarette smoke exposure decreased cell proliferation in pancreatic ductal and acinar cells, and had no effect in islet cells. Cigarette smoke did not affect pancreatic protein levels of tumor necrosis factor (TNF)α, p53, or cyclin D1, but mutant Kras overexpression slightly decreased TNFα and p53 protein levels. Therefore, pancreatic cell proliferation in mice overexpressing mutant Kras is associated with the later development of pancreatic tumors, but effects of cigarette smoke on pancreatic cell proliferation do not provide a good model for human pancreatic carcinogenesis

The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond

T(3)-gauge model of defects based on the gauge Lagrangian quadratic in the gauge field strength is considered. The equilibrium equation of the medium is fulfilled by the double curl Kroner's ansatz for stresses. The problem of replication of the static edge dislocation along third axis is analysed under a special, though conventional, choice of this ansatz. The translational gauge equation is shown to constraint the functions parametrizing the ansatz (the stress functions) so that the resulting stress component $\sigma_{3 3}$ is not that of the edge defect. Another translational gauge equation with the double curl differential operator is shown to reproduce both the stress functions, as well as the stress tensors, of the standard edge and screw dislocations. Non-linear extension of the newly proposed translational gauge equation is given to correct the linear defect solutions in next orders. New gauge Lagrangian is suggested in the Hilbert-Einstein form.Comment: 21 pages, LaTeX, no figure

Regge Calculus in Teleparallel Gravity

In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller an smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.Comment: Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Gra

Quantum thermodynamics at critical points during melting and solidification processes

We systematically explore and show the existence of finite-temperature continuous quantum phase transition (CTQPT) at a critical point, namely, during solidification or melting such that the first-order thermal phase transition is a special case within CTQPT. Infact, CTQPT is related to chemical reaction where quantum fluctuation (due to wavefunction transformation) is caused by thermal energy and it can occur maximally for temperatures much higher than zero Kelvin. To extract the quantity related to CTQPT, we use the ionization energy theory and the energy-level spacing renormalization group method to derive the energy-level spacing entropy, renormalized Bose-Einstein distribution and the time-dependent specific heat capacity. This work unambiguously shows that the quantum phase transition applies for any finite temperatures.Comment: To be published in Indian Journal of Physics (Kolkata

Dizajniranje, sinteza, kinetika hidrolize i farmakodinamski profili konjugata aceklofenaka s histidinom i alaninom

The gastrointestinal toxicity associated with aceclofenac can be reduced by condensing its carboxylic acid group with methyl esters of amino acids like histidine and alanine to give amide linkage by the Schotten-Baumann method. Physicochemical characterization of the conjugates was carried out by various analytical and spectral methods. The synthesized conjugates were also subjected to in vitro hydrolysis in simulated gastric fluid (SGF) at pH 1.2, simulated intestinal fluid (SIF) at pH 7.4 and SIF + 80 % human plasma at pH 7.4. The release of free aceclofenac from histidine and alanine conjugated aceclofenac showed negligible hydrolysis in SGF compared to SIF. This indicated that the conjugates do not break in stomach, but release aceclofenac in SIF. Both synthesized conjugates showed excellent pharmacological response and encouraging hydrolysis rate in SIF and SIF + 80 % human plasma. Marked reduction of the ulcer index and comparable increase in analgesic and anti-inflammatory activities were obtained in both cases compared to aceclofenac alone. These findings suggest that the conjugates are better in action compared to the parent drug and have fewer gastrointestinal side-effects.Gastrointestinalna toksičnost aceklofenaka može se umanjiti kondenzacijom karboksilne skupine aceklofenaka s metilnim esterima aminokiselina poput histidina i alanina, pri čemu se stvaraju nove amidne veze po Schotten-Baumannovoj metodi. Fizikokemijska karakterizacija konjugata provedena je različitim analitičkim i spektralnim metodama. Nadalje, praćena je hidroliza sintetiziranih konjugata in vitro u simuliranoj gastričnoj tekućini (SGF) pri pH 1,2, simuliranoj intestinalnoj tekućini (SIF) pri pH 7,4 i simuliranoj intestinalnoj tekućini s 80 % humane plazme pri pH 7,4. Oslobađanje aceklofenaka iz konjugata s histidinom, odnosno alaninom, bilo je zanemarivo u SGF-u, u odnosu na oslobađanje u SIF-u. To ukazuje da su konjugati stabilni u želucu, dok se u SIF-u iz njih oslobađa aceklofenak. Oba konjugata daju izvrstan farmakološki odgovor i zadovoljavajući stupanj hidrolize u SIF-u i smjesi SIF-a i humane plazme. Oba konjugata pokazala su značajno smanjenu ulcerogenost i pojačano analgetsko i protuupalno djelovanje u odnosu na aceklofenak. Rezultati ukazuju na prednost konjugata u odnosu na samu ljekovitu tvar