Pitman closeness results for Type-I censored data from exponential distribution

Recent work on Pitman closeness has compared estimators under Type-II censored samples from exponential distribution based on observed number of failures. In this paper, we carry out similar Pitman closeness comparisons for Type-I censored samples from exponential distribution based on time under test.     

Constrained Controllability of Fractional Dynamical Systems

The article deals with the controllability results for fractional dynamical systems with prescribed controls represented by the fractional integrodifferential equation in finite dimensional spaces. Sufficient conditions for the controllability results of nonlinear fractional dynamical systems are obtained using the contraction mapping principle. Examples are included to illustrate the theory.     

Multivariate risk models under heavy‐tailed risks

In this paper, we consider four common types of ruin probabilities for a discrete‐time multivariate risk model, where the insurer is assumed to be exposed to a vector of net losses resulting from a number of business lines over each period. By assuming a large initial capital for the risk model and regularly varying distributions for the net losses, we establish some interesting asymptotic estimates for ruin probabilities in terms of the upper tail dependence function of the net loss vector. Our results insightfully characterize how the dependence structure among the individual net losses affect the ruin probabilities in an asymptotic sense, and more importantly, from our main results, explicit asymptotic estimates for those ruin probabilities can be obtained via specifying a copula for the net loss vectors. Copyright © 2013 John Wiley & Sons, Ltd.     

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.     

Rectifying properties of a boron/nitrogen-doped C131-based molecular junction: A first-principles study

Using first-principles density functional theory and non-equilibrium Green′s function formalism for quantum transport calculation, we have investigated the electronic transport properties of the boron/nitrogen-doped C₁₃₁-based molecular junction. Our results show that an obvious rectifying behavior is observed. Moreover, the rectifying performance can be tuned by adjusting the doping sites. The mechanism for the rectifying phenomenon is suggested. The present findings could be helpful for the application of the C₁₃₁ molecule in the field of single molecular devices or nanometer electronics.     

Single-channel color image encryption using phase retrieve algorithm in fractional Fourier domain

A single-channel color image encryption is proposed based on a phase retrieve algorithm and a two-coupled logistic map. Firstly, a gray scale image is constituted with three channels of the color image, and then permuted by a sequence of chaotic pairs generated by the two-coupled logistic map. Secondly, the permutation image is decomposed into three new components, where each component is encoded into a phase-only function in the fractional Fourier domain with a phase retrieve algorithm that is proposed based on the iterative fractional Fourier transform. Finally, an interim image is formed by the combination of these phase-only functions and encrypted into the final gray scale ciphertext with stationary white noise distribution by using chaotic diffusion, which has camouflage property to some extent. In the process of encryption and decryption, chaotic permutation and diffusion makes the resultant image nonlinear and disorder both in spatial domain and frequency domain, and the proposed phase iterative algorithm has faster convergent speed. Additionally, the encryption scheme enlarges the key space of the cryptosystem. Simulation results and security analysis verify the feasibility and effectiveness of this method.     

ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

Application of Central Composite Design for the Determination of Exfoliating Agents in Cosmetics by Capillary Electrophoresis with Electroosmotic Flow Modulation

Multivariate analysis within central composite design is applied to simplify an optimization procedure and explore the interactions among experimental parameters in analytical chemistry. In this study, central composite design was used to identify the optimal capillary electrophoresis conditions with electroosmotic flow modulation to determine seven exfoliating agents in cosmetics. The influence of phosphate concentration, cetyltrimethylammonium bromide concentration, and methanol percentage on the response was evaluated by the use of the chromatographic exponential function to simultaneously investigate the resolution and separation under sixteen sets of capillary electrophoresis conditions. The optimized conditions were 150 mM phosphate solution (pH = 7) containing 0.5 mM cetyltrimethylammonium bromide, 3 mM γ-cyclodextrin, and 25% methanol as the running buffer. To shorten the analysis time, an electroosmotic flow modulating agent (cetyltrimethylammonium bromide) was added to the separation buffer. Calibration plots were linear (r ≧ 0.998) with high precision and accuracy in the homemade cosmetic matrix. The exfoliating agents in two commercial cosmetic products were determined using the optimized conditions, and the results correlated well with results obtained by high-performance liquid chromatography–mass spectrometry.     

Positive solutions for some second-order four-point boundary value problems

In this paper, the second-order four-point boundary value problem