Linear combinations of prime powers in X-coordinates of Pell equations

The Ramanujan Journal - We give q-analogues of three Ramanujan-type series for $$1/\pi $$ from q-analogues of ordinary WZ pairs. The first one is a new q-analogue of the following Ramanujan’s...     

A simple comparison between Skorokhod & Russo-Vallois integration for insider trading

We consider a simplified version of the problem of insider trading in a financial market. We approach it by means of anticipating stochastic calculus and compare the use of the Skorokhod and the Russo-Vallois forward integrals within this context. We conclude that, while the forward integral yields results with a clear financial meaning, the Skorokhod integral does not provide a suitable formulation for this problem.     

Properties of interpolatory quadrature with equidistant nodes on the unit circle

In this paper, we study the computation of the moments associated to rational weight functions given as a power spectrum with known or unknown poles of any order in the interior of the unit disc. A recursive algebraic procedure is derived that computes the moments in a finite number of steps. We also study the associated interpolatory quadrature formulas with equidistant nodes on the unit circle. Explicit expressions are given for the positive quadrature weights in the case of a polynomial weight function. For rational weight functions with simple poles, mostly real or uniformly distributed on a circle in the open unit disc, we also obtain expressions for the quadrature weights and sufficient conditions that guarantee that they are positive. The Poisson kernel is a simple example of a rational weight function, and in the last section, we derive an asymptotic expansion of the quadrature error.     

Choreographies in the <Emphasis Type="Italic">n</Emphasis>-vortex Problem

We consider the equations of motion of n vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference. We use numerical continuation in a boundary value setting to determine the Lyapunov families of periodic orbits that arise from the polygonal relative equilibrium. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, the orbit is also periodic in the inertial frame. A dense set of Lyapunov orbits, with frequencies satisfying a Diophantine equation, corresponds to choreographies of n vortices. We include numerical results for all cases, for various values of n, and we provide key details on the computational approach.     

Frames of exponentials and sub-multitiles in LCA groups

In this note, we investigate the existence of frames of exponentials for $L^2(\mathrm{\Omega })$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $\mathrm{\Omega }?\stackrel{?}{G}$ with respect to a uniform lattice Γ of $\stackrel{?}{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames.     

A renorming in some Banach spaces with applications to fixed point theory

We consider a Banach space X endowed with a linear topology τ and a family of seminorms {Rk(⋅)} which satisfy some special conditions. We define an equivalent norm ?⋅? on X such that if C is a convex bounded closed subset of (X,?⋅?) which is τ-relatively sequentially compact, then every nonexpansive mapping T:C→C has a fixed point. As a consequence, we prove that, if G is a separable compact group, its Fourier-Stieltjes algebra B(G) can be renormed to satisfy the FPP. In case that G=T, we recover P.K. Lin's renorming in the sequence space ?₁. Moreover, we give new norms in ?₁ with the FPP, we find new classes of nonreflexive Banach spaces with the FPP and we give a sufficient condition so that a nonreflexive subspace of L₁(μ) can be renormed to have the FPP.     

Phospholipid Bilayers as Molecular Models for Drug-Cell Membrana Interactions. The Case of the Antiinflamatory Drug Diclofenac

Phospholipids are amphipatic molecules with long hydrophobic acyl chains and zwitterionic polar heads which assemble into different types of molecular aggregates. The most relevant is the bilayer because of its relation with cell membranes, which are very complex entities. For this reason, simpler molecular models based on phospholipids bilayers are widely used. We have determined the bilayer structure of phospholipids located in the outer and inner monolayers of most cell membranes, and use them as molecular models to study the way different chemicals of biological interest interact with cell membranes. We present the results of our studies on the nonsteroidal anti-inflammatory drug diclofenac, from which little is known about its effects on human erythrocytes. This report presents the following evidence that diclofenac interacts with the human red cell membrane: a) X-ray diffraction and fluorescence spectroscopy of phospholipids bilayers show that diclofenac interacts with a class of lipids found in the outer moiety of the erythrocyte membrane; b) in isolated unsealed human erythrocyte membranes the drug induced a disordering effect on the acyl chains of the membrane lipid bilayer; c) in scanning electron microscopy studies on human erythrocytes it was observed that the drug induced morphological changes different from their normal biconcave shape.     

Mesophases in a Gel from Hydroxypropyl Cellulose/Polyacrylamide

The objective of the present work is to analyze the different mesophases observed in a gel synthesized from hydroxypropyl cellulose (HPC) and polyacrylamide (PAAm) and its phase behavior in water. Hydroxypropyl cellulose is a material derived from cellulose it is non toxic and degradable. HPC is widely used in pharmaceutics, food additives, stabilizer, thickener, etc., HPC is approved by the FDA for use in the food industry. HPC has the characteristic that it forms liquid crystals, depending on the solvent and on the concentration of the polymer. In this work a lower critical solution temperature (LCST) and an upper critical solution temperature (UCST) were observed, the resulting gel showed anisotropic, nematic and cholesteric phases in water, the phase formed depended on the concentration of the polymer.     

A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.