Solutions for the prescribing mean curvature equation

By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^＋ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

Simultaneous Spectrophotometric Determination of Zinc and Nickel in Water Samples by Mean Centering of Ratio Kinetic Profiles

The mean centering of ratio kinetic profiles method was used for the simultaneous determination of binary mixtures of Ni(II) and Zn(II) in water samples, without prior separation steps. The method is based on the difference in the rate of the reaction of Ni(II) and Zn(II) with xylenol orange at pH 5.3. The method allows rapid and accurate determination of Ni(II) and Zn(II). The analytical characteristics of the methods for the simultaneous determination of binary mixtures of Ni(II) and Zn(II) were calculated. The linear range was 0.025‐2.400 μg mL^?1 and 0.025‐2.20 μg mL^?1 for Zn(II) and Ni(II), respectively. Interference effects of common anions and cations were studied, and the method was successfully applied to the simultaneous determination of Zn(II) and Ni(II) in water samples.     

Distance graphs with maximum chromatic number

The distance graph G(D) has the set of integers as vertices and two vertices are adjacent in G(D) if their difference is contained in the set D⊂Z. A conjecture of Zhu states that if the chromatic number of G(D) achieves its maximum value |D|+1 then the graph has a triangle. The conjecture is proven to be true if |D|?3. We prove that the chromatic number of a distance graph with D={a,b,c,d} is five only if either D={1,2,3,4k} or D={a,b,a+b,b-a}. This confirms a stronger version of Zhu's conjecture for |D|=4, namely, if the chromatic number achieves its maximum value then the graph contains K₄.     

Uniqueness of maximum planar five-distance sets

A subset X in the Euclidean plane is called a k-distance set if there are exactly k distances between two distinct points in X. We denote the largest possible cardinality of k-distance sets by g(k). Erdős and Fishburn proved that g(5)=12 and also conjectured that 12-point five-distance sets are unique up to similar transformations. We classify 8-point four-distance sets and prove the uniqueness of the 12-point five-distance sets given in their paper. We also introduce diameter graphs of planar sets and characterize these graphs.     

Effect of pearlitic morphology with varying fineness on the cavitation erosion behavior of eutectoid rail steel

The present work discusses the effect of the pearlitic morphology with varying fineness on the cavitation erosion behavior of eutectoid rail steel. Cavitation erosion of three different types of the pearlitic steels (furnace-cooled, air-cooled, and forced-air-cooled) consisting of coarse, fine, and very fine microstructures were tested in 3.5% NaCl solution and compared with that of the as-received pearlitic rail steel. The variation in the mean depth of erosion (MDE) and mean depth erosion rate (MDER) with erosion time was analyzed. Furthermore, the cavitation erosion resistance of the as-received, the air-cooled, and the forced-air-cooled was found to be 1.03, 1.51, and 2.14 times better than the furnace-cooled pearlitic steel, respectively. It was concluded that the cavitation erosion resistance of the pearlitic steel increased with the increase in the fineness of the microstructure.     

Development and Validation of Hierarchical Models for the Design of Engine Control Strategies

The development of mathematical models for the design of controlstrategies for spark ignition automotive engines is described. The objectiveof the models, used for both simulation and optimization analysis, is theprediction of the effects of control strategies on fuel consumption andemissions of a vehicle over arbitrary driving cycles. In order to achievethe best compromise between precision, experimental costs, computationaltime and flexibility, a mixed modelling approach is used, withphenomenological and input-output models integrated within a hierarchicalsystem.Mean value models have been used to describe the most significant dynamiceffects: (i) air flow. (ii) two phases fuel flow in the intake manifold, and(iii) thermal flow in the cylinder walls. Stochastic effects due to sensorsand actuators can be also predicted.Two-zone and multizone thermodynamic models for the prediction ofpressure cycle sub-models for engine emissions (HC, CO, andNO _x and mechanical losses have been developed. Experimentaldesign techniques are also under development to optimize the interactionsbetween experimental analysis and models. Most of the models have beenintegrated in a computer code, used by a major automotive supplier.     

The mean activity coefficients of LaCl3 in dilute aqueous solution at 298.15 K

The electromotive forces of a symmetrical concentration cell with transference, Ag; AgCl|LaCl₃ (m*):LaCl₃ (m)|AgCl; Ag, were measured over the concentration range from 8.762 × 10⁻⁴ mol kg⁻¹ to 6.788 × 10⁻² mol kg⁻¹ at 298.15 K to obtain the mean activity coefficients of LaCl₃. The mean activity coefficient for reference solution at 298.15 K and the ion size parameter for LaCl₃ in the extended Debye–Hückel equation are evaluated by using an approach extrapolating concentration to unlimited dilution. A modified Debye–Hückel equation with new parameters has been established for the studied concentration range. A comparison is done of the thermodynamic data of LaCl₃ that are determined by this experiment with those reported by previous literatures, and evaluated by some models.     

A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At first, we show the existence and the uniqueness of a viscosity solution to this problem. Then we propose a numerical scheme for solving the nonlinear level set equation on unstructured triangulations adapted to the data sample. We show the consistency of this scheme. In addition, we show how to compute nodewise first and second order derivatives. Some application examples of curve or surface construction are provided to illustrate the potential and to demonstrate the accuracy of this method.