Diffusion mechanism of water vapour in a zeolitic tuff rich in clinoptilolite

The adsorption kinetics of H₂O in a clinoptilolite rich zeolitic tuff was experimentally investigated at 18°C. In the identification of the diffusion mechanism the isothermal adsorption model equation was used. It was found out that the intraparticle mass transfer becomes more dominant over the heat transfer with increase in particle size and the adsorptive dose pressure. Although initially intraparticle mass transfer was the controlling resistance later external heat transfer also contributes to the transfer mechanism.     

The effect of time fractality on the transition coefficients: Historical Stern–Gerlach experiment revisited

In this article, the influence of time discreteness on the transition coefficients is investigated within the framework of time fractional development of quantum systems which has been developed recently by the present authors [22]. In this formalism, fractional mathematics which is a powerful tool to study the non-Markovian and non-Gaussian properties of physical processes is used in order to obtain time fractional evolution operator and transition probability. They are given in terms of Mittag–Leffler function which plays an important role in the mathematical structure as well as the physical interpretation of the phenomena under investigation. In order to place the presented formalism on a concrete basis, historical Stern–Gerlach experiment has been revisited with the purpose of studying transition coefficients which have a non-Markovian feature. The effect of the time fractionalization has been clearly illustrated in the figures via fractional derivative order α.     

Parameter estimation of an agent‐based stock price model

The influence of the behavior and strategies of traders on stock price formation has attracted much interest. It is assumed that there is a positive correlation between the total net demand and the price change. A buy order is expected to increase the price, whereas a sell order is assumed to decrease it. We perform data analysis based on a recently proposed stochastic model for stock prices. The model involves long‐range dependence, self‐similarity, and no arbitrage principle, as observed in real data. The arrival times of orders, their quantity, and their duration are created by a Poisson random measure. The aggregation of the effect of all orders based on these parameters yields the log‐price process. By scaling the parameters, a fractional Brownian motion or a stable Levy process can be obtained in the limit. In this paper, our aim is twofold; first, to devise statistical methodology to estimate the model parameters with an application on high‐frequency price data, and second, to validate the model by simulations with the estimated parameters. We find that the statistical properties of agent level behavior are reflected on the stock price, and can affect the entire process. Moreover, the price model is suitable for prediction through simulations when the parameters are estimated from real data. The methods developed in the present paper can be applied to frequently traded stocks in general. Copyright © 2013 John Wiley & Sons, Ltd.     

A function of direction associated with n congruences of an orthogonal ennuple in a Riemannian hypersurface

In a hypersurface V_n belonging to a Riemannian space V_n+1 we choose n congruences of an orthogonal ennuple of unit vectors of contravariant components λ _h¦ ⁱ (h=1,2,...,n) and denote, by ω_kk the normal curvature of the hypersurface in the direction of the unit vector of components λ _k¦ ⁱ . In the present paper, we have shown that the expression $$\frac{\partial }{{\partial s_k }}\omega _{kk} - 2\mathop \Sigma \limits_{h = 1}^n \omega _{kh} \gamma _{hkk}$$ is a function of direction, where the symbol ?/?s_k indicates the differentiation in the direction of the vector of components λ _k¦ ⁱ and that ω_kh (h≠k) and γ_?hk (?,h,k=1,2,...,n) are, respectively, the invariants of the geodesic torsion of the curve of the congruence with unit tangent vector of components λ _k¦ ⁱ and Ricci's coefficients of rotation of the orthogonal ennuple.     

On the problem of isometry of a hypersurface preserving mean curvature

The problem of determining the Bonnet hypersurfaces in R ⁿ⁺¹, for n > 1, is studied here. These hypersurfaces are by definition those that can be isometrically mapped to another hypersurface or to itself (as locus) by at least one nontrivial isometry preserving the mean curvature. The other hypersurface and/or (the locus of) itself is called Bonnet associate of the initial hypersurface. The orthogonal net which is called A-net is special and very important for our study and it is described on a hypersurface. It is proved that, non-minimal hypersurface in R ⁿ⁺¹ with no umbilical points is a Bonnet hypersurface if and only if it has an A-net.     

Polynomial Basis Multiplication over GF(2 m )

In this paper, we describe, analyze and compare various multipliers. Particularly, we investigate the standard modular multiplication, the Montgomery multiplication, and the matrix–vector multiplication techniques.     

Inference of the stochastic MAPK pathway by modified diffusion bridge method

The MAPK pathway is one of the well-known systems in oncogene researches of eukaryotes due to its important role in cell life. In this study, we perform the parameter estimation of a realistic MAPK system by using western blotting data. In inference, we use the modified diffusion bridge algorithm with data augmentation technique by modelling the realistically complex system via the Euler–Maruyama approximation. This approximation, which is the discretized version of the diffusion model, can be seen as an alternative OR approach with respect to the (hidden) Markov chain method in stochastic modelling of the biochemical systems where the data can be fully or partially observed and the time-course measurements are though to be collected at small time steps. Hereby, the modified diffusion bridge technique, which is based on the Markov Chain Monte Carlo (MCMC) methods, enables us to accurately estimate the model parameters, presented as the stochastic reaction rate constants, of the diffusion model under high dimensional systems despite loss in computational demand. In the estimation of the parameters, due to the complexity in the decision-making problems of the MCMC updates at different stages, we face with the dependency challenges. We unravel them by checking the singularity of the system in every stage of updates. In modelling, we also assume with/without-measurement error approaches in all states. But in order to evaluate the performance of both models, we initially implement them in a toy system. From the results, we observe that the model with measurement error performs better than the model without measurement error in terms of the mixing features of the MCMC runs and the accuracy of estimates, thereby, it is used for the parameter estimation of the realistic MAPK pathway. From the outcomes, we consider that the suggested approach can be seen as a promising alternative method in inference of parameters via different OR techniques in system biology.     

Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.     

Dual Split Quaternions and Chasles’ Theorem in 3-Dimensional Minkowski Space {\mathbb{E}^{3}_{1}}

In 1831, Michel Chasles proved the existence of a fixed line under a general displacement in ${\mathbb{R}^3}$ . The fixed line called the screw axis of displacement was obtained by McCharthy in [10]. The purpose of this paper is to develop the method which is given for the pure rotation in [14], and thus to obtain the screw axis of spatial displacement in 3-dimensional Minkowski space. Firstly, we give a relation between dual vectors and lines in ${\mathbb{E}^{3}_{1}}$ , characterize the screw axis. Also, we discuss the dual split quaternion representation of a spatial displacement.