Solvability and asymptotics of the heat equation with mixed variable lateral conditions and applications in the opening of the exocytotic fusion pore in cells

We investigate a mixed problem with variable lateral conditions for the heat equation that arises in modelling exocytosis, i.e. the opening of a cell boundary in specific biological species for the release of certain molecules to the exterior of the cell. The Dirichlet condition is imposed on a surface patch of the boundary and this patch is occupying a larger part of the boundary as time increases modelling where the cell is opening (the fusion pore), and on the remaining part, a zero Neumann condition is imposed (no molecules can cross this boundary). Uniform concentration is assumed at the initial time. We introduce a weak formulation of this problem and show that there is a unique weak solution. Moreover, we give an asymptotic expansion for the behaviour of the solution near the opening point and for small values in time. We also give an integral equation for the numerical construction of the leading term in this expansion.

An interdisciplinary approach to designing and evaluating a hybrid solar-biomass power plant

Purpose: Energy security is a major concern for India and many rural areas remain un-electrified. Thus, innovations in sustainable technologies to provide energy services are required. Biomass and solar energy in particular are resources that are widely available and underutilised in India. This paper aims to provide an overview of a methodology that was developed for designing and assessing the feasibility of a hybrid solar-biomass power plant in Gujarat. Design/methodology/approach: The methodology described is a combination of engineering and business management studies used to evaluate and design solar thermal collectors for specific applications and locations. For the scenario of a hybrid plant, the methodology involved: the analytical hierarchy process, for solar thermal technology selection; a cost-exergy approach, for design optimisation; quality function deployment, for designing and evaluating a novel collector - termed the elevation linear Fresnel reflector (ELFR); and case study simulations, for analysing alternative hybrid plant configurations. Findings: The paper recommended that for a hybrid plant in Gujarat, a linear Fresnel reflector of 14,000 m2 aperture is integrated with a 3 tonne per hour biomass boiler, generating 815 MWh per annum of electricity for nearby villages and 12,450 tonnes of ice per annum for local fisheries and food industries. However, at the expense of a 0.3 ¢/kWh increase in levelised energy costs, the ELFR can increase savings of biomass (100 t/a) and land (9 ha/a). Research limitations/implications: The research reviewed in this paper is primarily theoretical and further work will need to be undertaken to specify plant details such as piping layout, pump sizing and structure, and assess plant performance during real operational conditions. Originality/value: The paper considers the methodology adopted proved to be a powerful tool for integrating technology selection, optimisation, design and evaluation and promotes interdisciplinary methods for improving sustainable engineering design and energy management. © Emerald Group Publishing Limited.

Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Directions De Majoration D'une Fonction Quasiconvexe Et Applications

We introduce the convex cone constituted by the directions of majoration of a quasiconvex function. This cone is used to formulate a qualification condition ensuring the epiconvergence of a sequence of general quasiconvex marginal functions in finite dimensional spaces.

DML and RusDML – Virtual Library Initiatives for Covering All Mathematics Electronically

With the rapidly growing activities in electronic publishing ideas came up to install global repositories which deal with three mainstreams in this enterprise: storing the electronic material currently available, pursuing projects to solve the archiving problem for this material with the ambition to preserve the content in readable form for future generations, and to capture the printed literature in digital versions providing good access and search facilities for the readers. Long-term availability of published research articles in mathematics and easy access to them is a strong need for researchers working with mathematics. Hence in this domain some pioneering projects have been established addressing the above mentioned problems.

Faculty of Mathematics and Informatics, Sofia University

The Faculty of Mathematics and Informatics (FMI) of Sofia University “St. Kliment Ohridski” is briefly presented as an educational and research institution. The possible contribution of FMI to KT-DigiCULT-BG project is analyzed.

Frontal Solutions: an Information Technology Transfer to Abstract Mathematics

The paper introduces a method for dependencies discovery during human-machine interaction. It is based on an analysis of numerical data sets in knowledge-poor environments. The driven procedures are independent and they interact on a competitive principle. The research focuses on seven of them. The application is in Number Theory.

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Hankel Transform in Quantum Calculus and Applications

Mathematics Subject Classification: 44A15, 33D15, 81Q99

Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05