A mathematical study of energy dissipation due to atrioventricular valve vibration

A mathematical model of the dynamic response of atrioventricular valve leaflets to the systolic pressure pulse is used to calculate the resultant energy dissipation under the action of viscous damping. The energy dissipated from mitral and tricuspid leaflets is compared, and the effects of leaflet size, closing velocity, the magnitude of the damping force, and the rate of change of the atrioventricular pressure gradient are investigated. The results are interpreted in relation to experimentally documented first heart sound determinants.     

A computational evaluation of some free mathematical software for scientific computing

The purpose of this paper is to present a computational comparison of some well-known free mathematical programs. Specifically, these programs are FreeMat, Mathnium, Octave, R and Scilab. All these programs are designed in order to be used either in the scientific community or the industry. Moreover, an additional aim of this paper is to propose open source alternative software which can replace commercial mathematical software. Several issues concerning available operating system platforms, data structures, languages’ structure, matrix operations, program modularization, libraries, packages, profiling tools and online help facilities are addressed in this paper. Discussions on their weaknesses and strengths characteristics are presented. Finally, a speed comparison of some frequently used algorithms, procedures and operations within software is also presented.     

A free boundary problem arising from DCIS mathematical model

Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd.     

The free streaming operator: A mathematical model for diffusive multiplying boundary conditions

We show that the free streaming operator with diffusive multiplying boundary conditions is the generator of a quasi-bounded semigroup. We also examine some spectral properties of such an operator.     

Stokes efficiency of molecular motors with inertia

A molecular motor utilizes chemical free energy to generate a unidirectional motion in a viscous media. The stochastic motion of a motor is governed by a Langevin equation coupled to the chemical occupancy state. The change of chemical occupancy state is governed by a discrete Markov process. The Stokes efficiency was introduced to measure how “efficiently” the motor uses chemical free energy to drive through the surrounding fluid. For the overdamping case where the effect of inertia is ignored, it was proved that the Stokes efficiency is bounded by 100% [H. Wang, G. Oster, The Stokes efficiency for molecular motors and its applications, Europhysics Letters 57 (2002) 134–140]. Here we present a proof for the general case.     

The mechanochemical stochastic processes of molecular motors

In this article, we develop a rigorous mathematical foundation of microscopic motors. The main characteristic is the combination of Brownian and Poisson noises.     

A mathematical flat integral realization and a large deviation result for the free Euclidean field

In this paper, we give a nonstandard construction of the free Euclidean field via S-white noise. This provides a flat integral realization of the free Euclidean field measure, which extends N. J. Cutland's flat integral representation of Wiener measure. Moreover, we show how a Cameron-Martin type formula for translations of the free field measure and a Schilder type large deviation principle for the scalar free field measure can be deduced from our nonstandard construction.SFB 237 Essen-Bochum-Düseldorf; BiBoS-Research Centre; CERFIM, Locarno, Switzerland.     

A mathematical modeling for incorporating energy price hikes into total natural gas consumption forecasting

In some countries that energy prices are low, price elasticity of demand may not be significant. In this case, large increase or hike in energy prices may impact energy consumption in a way which cannot be drawn from historical data. This paper proposes an integrated adaptive fuzzy inference system (FIS) to forecast long-term natural gas (NG) consumption when prices experience large increase. To incorporate the impact of price hike into modeling, a novel procedure for construction and adaptation of Takagi–Sugeno fuzzy inference system (TS-FIS) is suggested. Linear regressions are used to construct a first order TS-FIS. Furthermore, adaptive network-based FIS (ANFIS) is used to forecast NG consumption in power plants. To cope with random uncertainty in small historical data sets, Monte Carlo simulation is utilized to generate training data for ANFIS. To show the applicability and usefulness of the proposed model, it is applied for forecasting of annual NG consumption in Iran where removing energy subsidies has resulted in a hike in NG prices.     

A multiobjective based approach for mathematical programs with linear flexible constraints

In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced.     

The minimum free energy for incompressible viscoelastic fluids

A general closed expression is given in the frequency domain for the isothermal minimum free energy of an incompressible viscoelastic fluid, whose constitutive equation is expressed by a linear functional of the history of strain. Another equivalent form of the minimum free energy is also derived and used to study the particular case of a discrete model material response. Copyright © 2006 John Wiley & Sons, Ltd.     

Droplet minimizers for the Cahn-Hilliard free energy functional

We prove theorems characterizing the minimizers for the Cahn-Hilliard free energy functional, which is used to describe the liquid vapor phase transition (or the 2 state magnetization transition). In particular, we exactly determine the critical density for droplet formation, and the geometry of the droplets.     

The minimum free energy for an electromagnetic conductor

We consider the linear theory of the electromagnetism characterized by a constitutive equation for the current density with memory effects. We find in the frequency domain a first expression of the minimum free energy, which is the maximum recoverable work we can obtain from a given state of the material. By using another equivalent formulation of the minimum free energy, we give the explicit formulae for the particular case of a discrete spectrum model material response.     

Pre-service teachers' free and structured mathematical problem posing

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing conditions, because the structured posing condition would guide PSTs to more closely consider the mathematical relationships in a posing situation. Sixty-five PSTs – 61 participating in a written assessment and 4 participating in task-based interviews – responded to problem-posing tasks under free or structured posing conditions. Two-way independent samples t-tests and chi-square tests were used to test the hypothesis, along with a qualitative analysis of the task-based interviews. We found that while the task format had limited impact on the complexity of problems posed, PSTs in the structured-posing condition may have more closely attended to the mathematical concepts in each task, and may have also impacted their process of posing problems than those in the free posing condition.     

A mathematical study of the transport of auxin

Starting with the one-dimensional equation of diffusion (Fick's equation) and the law governing transport across a membrane, the concentrations of auxin in the walls of n cells forming a linear array are expressed as infinite series in the time t for several stipulations of the concentration of auxin at the two ends of the array. Surprisingly the structure of these series depends on whether n is prime or composite. Complex variable theory, the Laplace transform and Tschebycheff polynomials all find a place in the study.     

A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing

This work studies the build-up method for the global minimization problem for molecular conformation, especially protein folding. The problem is hard to solve for large molecules using general minimization approaches because of the enormous amount of required computation. We therefore propose a build-up process to systematically construct the optimal molecular structures. A prototype algorithm is designed using the anisotropic effective energy simulated annealing method at each build-up stage. The algorithm has been implemented on the Intel iPSC/860 parallel computer, and tested with the Lennard-Jones microcluster conformation problem. The experiments showed that the algorithm was effective for relatively large test problems, and also very suitable for massively parallel computation. In particular, for the 72-atom Lennard-Jones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.     

A mathematical model for unemployment

In this paper we have proposed and analyzed a non-linear mathematical model for unemployment by considering three variables, namely the numbers of unemployed, temporarily employed and regularly employed persons. The model is studied using the stability theory of differential equations. It is found that the model has only one equilibrium, which is non-linearly stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results.     

A mathematical study of the linear theory for orthotropic elastic simple shells

The theory of simple shells is a surface‐related Cosserat model for thin elastic shells. In this direct approach, each material point is connected with a triad of rigidly rotating directors. This paper presents a study of the governing equations for orthotropic elastic simple shells in the framework of the linearized theory. We establish the uniqueness of classical solutions, without any restrictive assumption on the strain energy function. The continuous dependence of solutions on the body loads and initial data is proved. Also, the existence of weak solutions to the equations of simple shells is proved by means of an inequality of Korn's type established for such directed surfaces. Copyright © 2009 John Wiley & Sons, Ltd.