Some new properties of asynchronous algorithms of theta scheme combined with finite elements methods for an evolutionary implicit 2‐sided obstacle problem

In this paper, we give some new properties of the presented asynchronous algorithms of theta scheme combined with finite elements methods (App. Math. Comp., 217 (2011), 6443‐6450) for an evolutionary implicit 2‐sided obstacle problem to prove the existence and uniqueness of the discrete solution. Furthermore, an error estimate on the uniform norm is given.     

Modeling of tsunami generation and propagation by a spreading curvilinear seismic faulting in linearized shallow-water wave theory

The processes of tsunami evolution during its generation in search for possible amplification mechanisms resulting from unilateral spreading of the sea floor uplift is investigated. We study the nature of the tsunami build up and propagation during and after realistic curvilinear source models represented by a slowly uplift faulting and a spreading slip-fault model. The models are used to study the tsunami amplitude amplification as a function of the spreading velocity and rise time. Tsunami waveforms within the frame of the linearized shallow-water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the movable source models. We analyzed the normalized peak amplitude as a function of the propagated uplift length, width and the average depth of the ocean along the propagation path.     

Range of lower bounds

Each of n jobs is to be processed without interruption on a single machine. Each job becomes available for processing at time zero. The objective is to find a processing order of the jobs which minimizes the sum of weighted completion times added with maximum weighted tardiness. In this paper we give a general case of the theorem that given in [6]. This theorem shows a relation between the number of efficient solutions, lower bound LB and optimal solution. It restricts the range of the lower bound, which is the main factor to find the optimal solution. Also, the theorem opens algebraic operations and concepts to find new lower bounds.     

Radioactivity of sand,groundwater and wild plants in northeast Sinai,Egypt

The radioactivity levels are poorly studied in non-coastal arid regions. For this reason, 38 locations covering an area of about 350 km² in northeast Sinai, Egypt, were investigated by γ-ray spectroscopy. Moderately significant correlations among ²³⁸U, ²³⁴Th, and ²²⁶Ra isotopes and low significant correlations between the concentrations of ²³⁸U-series and ²³²Th in sand were obtained. No evidence of correlation was found between the concentrations of radioisotopes and pH, grain size, total organic matter content, bicarbonate or calcium carbonate concentrations of the sand samples. The mean values of soil-to-plant transfer factor were 0.15, 0.18, 1.52 and 0.74 for ²²⁶Ra, ²³²Th, ⁴⁰K, and ¹³⁷Cs, respectively. The range of concentrations of ²²⁶Ra, ²³²Th, and ⁴⁰K in water samples collected from five wells were<0.4–0.16,<0.4–0.13, and<0.15–1.62 Bq l^?1, respectively. The mean absorbed dose rate in outdoor air at a height of 1 m above the ground surface for the sand samples was 19.4 nGy h^?1. The Ra_eq activities of the sands are lower than the recommended maximum value of 370 Bq kg^?1 criterion limit for building materials.     

Orthotropic bone remodeling: case of plane stresses

Cancellous bone is constituted by a porous solid matrix filled with fluid. Matrix microstructure gives bone most of its mechanical strength properties. In our macroscopic approach, bone is seen as a continuous medium with a local (at our scale) time-dependent linearly elastic orthotropic behavior. Remodeling consists, by matrix material apposition or resorption, in microstructure modifications in order to optimize its mechanical characteristics. The proposed model is built on a time iterative procedure where the compliance tensor evolves such that, depending on the applied stresses, principal strains tend to fall within an admissible domain. The suggested remodeling laws in this work modify the elasticity “constants” as well as the orthotropy directions. The first results presented here correspond to the plane stresses case.     

Experimental investigation of flame/solid interactions in turbulent premixed combustion

An experimental study has been carried out to investigate the interaction between propagating turbulent premixed flames and solid obstacles. The experimental rig was configured specifically to allow detailed measurements with laser-based optical diagnostics. A wall-type solid obstacle was mounted inside a laboratory-scale combustion chamber with rectangular cross-section. The flame was initiated, by igniting a combustible mixture of methane in air at the center of the closed end of the combustion chamber. The flame front development was visualized by a high-speed (9000 frame/s) digital video camera and flame images were synchronized with ignition timing and chamber pressure data. The tests were carried out with lean, stoichiometric and rich mixtures of methane in air. The images were used to calculate highly resolved temporal and spatial data for the changes in flame shape, speed, and the length of the flame front. The results are discussed in terms of the influence of mixture equivalence ratio on the flame structure and resulting overpressure. The reported data revealed significant changes in flame structure as a result of the interaction between the propagating flame front and the transient recirculating flow formed behind the solid obstacle. Combustion images show that the flame accelerates and decelerates as it impinges on the obstacle wall boundaries. It is also found that the mixture concentrations have a significant influence on the nature of the flame/solid interactions and the resulting overpressure. The highest flame speed of 40 m/s was obtained with the unity fuel–air equivalence ratio. Burning of trapped mixture behind the solid obstruction was found to be highly correlated with the flame front length and the rate of pressure rise.     

Optimization of cutting conditions for end milling of Ti6Al4V Alloy by using a Gravitational Search Algorithm (GSA)

Surface roughness is commonly used to indicate the quality of machine parts. Optimizing cutting parameters throughout the machining process is an important aspect for manufacturers, as it allows them to achieve a minimum surface value. During this study, a new optimization technique known as the gravitational search algorithm (GSA) was employed in order to achieve minimum surface roughness when end milling a Ti6Al4V alloy under dry cutting conditions, with both PVD coated and uncoated cutting tools. Regression models have been created based on the results of real experimental data. Through use of SPSS software, it was possible to formulate the objective (fitness) functions which were used in the GSA optimization for each cutting tool. A MATLAB code was then created to instigate the optimization process. The results indicated that high cutting speed and low feed rate and depth of cut could result in a minimum surface roughness value of (0.6255 μm), based on the objective function for the PVD cutting tool. Alternatively, surface roughness of around (0.4165 μm) could be achieved by using an uncoated tool on a lower feed rate, depth of cut and cutting speed. The same GSA technique was used in another case study optimized by Genetic algorithm (GA). The GSA achieved the same results, and proved that it is faster than GA: GSA could reach the optimum solution in the third iteration; GA could only reach it in the 67th.     

Normal <Emphasis Type="Italic">π</Emphasis>-complements for finite groups

Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω₁(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω₁(P) ≦ Z(P) and N _G (Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result. This paper was partly supported by Hungarian National Foundation for Scientific Research Grant # T049841 and T038059.     

Optimal average sample number of the SPRT chart for monitoring fraction nonconforming

The Sequential Probability Ratio Test (SPRT) control chart is a powerful tool for monitoring manufacturing processes. It is highly suitable for the applications where testing is destructive or very expensive, such as the automobile airbags test. This article studies the effect of the Average Sample Number (ASN) (i.e., the average sample size) on the chart’s performance. A design algorithm is proposed to develop the optimal SPRT chart for monitoring the fraction nonconforming p of Bernoulli processes. By optimizing the ASN and other charting parameters, the average detection speed of the SPRT chart is almost doubled. It is also found that the optimal SPRT chart significantly outperforms the optimal np and binomial CUSUM charts, in terms of Average Number of Defectives (AND), under different combinations of the design specifications. It is observed that the SPRT chart using a relatively smaller ASN and a shorter sampling interval (h) has a higher overall detection effectiveness.