Arbitrage Bounds for Prices of Weighted Variance Swaps

We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating strategies which enforce them. We find that market quotes for variance swaps are surprisingly close to the model-free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi-infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model-independent and probability-free setup. In particular we use and extend F\"ollmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the 'log contract' and similar connections for weighted variance swaps. Our results take form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk-neutral expectations of discounted payoffs.Comment: 25 pages, 4 figure

Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups; Part 1: Two Killing fields spanned on u^{\alpha} and w^{\alpha }

For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Pleba\'nski based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and G\"{o}del are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution.Comment: 23 pages, LaTe

ISOLATION OF CYTOTOXIC CONSTITUENT FROM BIOACTIVITY GUIDED FRACTION OF ALYSICARPUS MONILIFER L. (DC.)

Objective: Alysicarpus monilifer (Family Papilionaceae) has been used in the Indigenous system of medicine in tumor removal. The present study was designed to isolate and identify the constituent responsible for cytotoxic (anti-tumor) effects of the plant Alysicarpus monilifer. Methods: The plant was powdered and extracted to give a methanolic extract. Initially, Hexane, chloroform, ethyl acetate and methanolic fractions of the methanolic extract of the plant were subjected to cytotoxic screening using cell line based assay (MTT assay and NRU assay). The chloroform fraction showed significant cytotoxicity, so it was further subjected to column chromatography, to separate the cytotoxic phytoconstituent. The cell lines selected were breast cancer cells (MCF-7 and MDA-MB-468) and Liver cancer cells (HepG2 and HLE cell). Results were calculated as percentage growth inhibition with respect to untreated (control) cells versus treated cells. Result: A triterpene, Betulinic acid, was isolated from the aerial parts of Alysicarpus monilifer. The cytotoxic activity of the identified compound against MCF-7, MDA-MB-231, HLE and HepG2 cells was also found to be highly significant with 90% growth inhibition. Conclusion: The triterpene was identified to be betulinic acid, to which the cytotoxic activity can be attributed. It is a first report of isolation of betulinic acid from the Alysicarpus species

A Non - Singular Cosmological Model with Shear and Rotation

We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.Comment: 10 pages, late

CYTOTOXIC EFFECT OF CORCHORUS DEPRESSUS AGAINST HEPG2 AND HLE HUMAN LIVER CANCER CELLS

Objective: The present study was designed to examine the cytotoxic effects of methanolic extract of aerial parts of Corchorus depressus and hexane, chloroform, ethyl acetate, and aqueous fractions of the same extract in the human hepatocellular carcinoma (HCC) (HepG2) and invasive hepatocellular carcinoma cell lines (HLE).Methods: Anti-proliferative effects were evaluated using 3-(4,5-dimethythiazol2-yl)-2,5-diphenyl tetrazolium bromide (MTT) and neutral red uptake (NRU) assay. Human HCC (HepG2) and invasive hepatocellular carcinoma cell lines (HLE) were treated with different concentrations of methanolic extract (10, 25, 50, 100, 200, 300, 400, and 500 μg/mL) of aerial parts of C. depressus as well as hexane, chloroform, ethyl acetate, and aqueous fractions (200 μg/mL) for 24 and 48 h. The cell viability and the half maximal inhibitory concentration (IC50) were determined.Results: The maximum cytotoxic effect was noticed with a maximum dose of methanolic extract (500 μg/mL) and alkaloidal fraction (200 μg) in this study with an IC50 value of about 200 μg.Conclusion: The set of studies showed that methanolic extract of aerial parts of C. depressus and alkaloidal, chloroform and ethyl acetate fractions fractions was capable of inhibiting cell growth and cell proliferation by inducing cytotoxicity of HepG2 and HLE cells

Molecular Clock on a Neutral Network

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating the topological structure of a neutral network from empirical measurements of the substitution process.Comment: 10 page

Crystal structure of a mixed solvated form of amoxapine acetate

The mixed solvated salt 4-(2-chloro­dibenzo[b,f][1,4]oxazepin-11-yl)piperazin-1-ium acetate-acetic acid-cyclo­hexane (2/2/1), C17H17ClN3O+·C2H3O2-·C2H4O2·0.5C6H12, crystallizes with one mol­ecule of protonated amoxapine (AXPN), an acetate anion and a mol­ecule of acetic acid together with half a mol­ecule of cyclo­hexane. In the centrosymmetric crystal, both enanti­omers of the protonated AXPN mol­ecule stack alternatively along [001]. Acetate anions connect the AXPN cations through N-H...O hydrogen bonding in the [010] direction, creating a sheet lying parallel to (100). The acetic acid mol­ecules are linked to the acetate anions via O-H...O hydrogen bonds within the sheets. Within the sheets there are also a number of C-H...O hydrogen bonds present. The cyclo­hexane solvent mol­ecules occupy the space between the sheets

Biochemical and Pathomorphological Study of Potassium Dichromate-induced Nephrotoxicity in Wistar Rat

An experiment was conducted to study biochemical and pathomorphological alterations induced by potassium dichromate toxicity. Forty colony bred Albino Wistar strain rats of both sexes, divided uniformly into four equal groups Group A, Group B, Group C, and Group D. Each Group contains five male and five female. Group A rats received only deionised water and served as control. Group B (low dose), Group C (mid dose) and Group D (high dose) rats were given potassium dichromate orally by gavage for 28 days at the rate of 0.625 mg/kg body weight (b.wt.), 1.25 mg/kg b.wt. and 2.5 mg/kg b.wt. respectively. A dose dependant significant rise in plasma alanine aminotransferase (ALT), plasma aspartate aminotransferase (AST), plasma alkaline phosphatase (ALP), creatinine and blood urea nitrogen was observed in treatment group, whereas, a significant decrease in total protein and albumin was observed in treatment group. Histopathological sections of kidney, liver, lung and testes revealed varying degrees of congestion, haemorrhage, degeneration and necrosis in rats of different treatment groups. The present study indicates nephric and hepatic toxicity in albino wistar rats due to potassium dichromate toxicity