The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, computation of c-fold tensor products is generally a difficult problem. Several authors have given upper bounds for the order of G, when G is a finite p-group. In this paper we determine a bound for the exponent triple tensor product which sharpens a bound of G. Ellis.Let G be a nilpotent group of nilpotency class k≥3 and prime power exponent P^e (where p is a prime and is not equal 3). In this paper, we show that the exponent of triple tensor product of G, that is, (G⨂G)⨂G, divides P^([k/2]-1)e where [k/2] denotes the smallest integer n such that n≥k/2. In this way, the exponent provided by Ellis is improved.

The bullet shape is critical in efficient bullet design because it affects the lift and drag forces. This paper proposes a new bullet shape with a logarithmic curve and analyzes the lift and drag coefficients of bullets with different curves under different angles of attack. The results are compared with a bullet whose shape is described by the power law curve. Fluent simulations demonstrate that the optimal power exponent values are 0.65, 0.6, and 0.65 for the bullet with the power law curve and 1.3, 1, and 1 for the bullet with the logarithmic curve at 0°, 30°, and 40° angles of attack, respectively. At a 0° angle of attack, the lift coefficient of the logarithmic curve is the largest. The lift force of the bullet with the logarithmic curve is 129.4% higher than that with the von Karman curve. The drag coefficient is the largest for the bullet with the rectilinear curve; it is 1.30% larger than that of the bullet with the logarithmic curve. At 30° and 40° angles of attack, the lift coefficient of the bullet with the power law curve is larger. The difference in the lift coefficients between the two angles of attack is 18.47%. The bullet’s drag coefficient is the largest for the logarithmic curve, and the difference in the drag coefficients between the two angles of attack is 18.59%.

Foam injection is widely applied in amounts of fields to drilling, production, and formation protection. Sometimes, the application result is disappointing, which is caused by the failure of bubble generation in foam flooding. Therefore, it is necessary to seek ways for improving the performance of foam injection. An increased disturbance to the stratum, like the vibration caused by a seismic oil recovery technique, would be helpful. In the current work, the seepage of air foam in porous media under low frequency (LF) vibration is analyzed with experiments and an investigation of bubble creation/destruction rate change is carried out using mathematical modeling. The resistance factor of foam flooding under indoor vibration increases by 1.5 times and the valid time is obviously extended compared with when no vibration is used. The optimal vibrating acceleration and frequency of 0.7 m/s2 and the natural frequency of the cores-nearby of 18 Hz are achieved in the indoor experiments. Under vibration, the bubble generation rate increases, while bubble break rate by internal expansion or by gas diffusion and transfer decreases. An interesting phenomenon is also observed, which might develop a power level formula between the initially defined dimensionless MRF (maximum foam flooding resistance factor) and dimensionless DMRF (duration of maximum foam flooding resistance factor). The power product and sum of the power exponents of the above formula both equal approximately to 1. With the assistance of LF vibration, the increase of security, adaptability, and efficiency in foam injection may improve the reservoir recovery and extend its application.

Permanent deformation of asphaltic materials has a major contribution to rutting. Under static loading, the steady-state deformation of asphaltic materials is the key component of the permanent deformation. The steady-state deformation behaviour of a standard 70/100 penetration grade pure bitumen and two types of asphaltic mixtures used in the UK pavements, namely a 10mm Dense Bitumen Macadam (DBM), which is a dense graded mixture, and a 30/10 Hot Rolled Asphalt (HRA), which is a gap graded mixture have been studied. Using Dynamic Shear Rheometer (DSR) Constant stress creep tests were conducted on the bitumen at 10°C and 20°C over a range of stress levels. Uniaxial creep and constant strain rate tests have been conducted over a range of stress levels, strain rates and temperatures, and triaxial creep tests have been conducted over a range of stress levels and confining pressures on the mixtures. The steady-state deformation behaviour of the bitumen is found to be linear at stress levels less than 100 kPa and non-linear power law creep with a power exponent of 2.6 at stress levels higher than 500 kPa. The steady-state deformation behaviour of both mixtures is found to be well captured by the Modified Cross Model which predicts linear viscous behaviour at low stress levels and non-linear viscous behaviour at high stress levels. The steady-state deformation behaviour of the DBM mixture is found to be more sensitive to the stress level. The temperature dependency of the steady-state deformation behaviour is found to be well captured by the Williams-Landel-Ferry (WLF) equation. It is found that confinement has a stiffening effect on the steady-state deformation behaviour of the mixtures. The stiffening effect of the confining stress is found to be higher for the DBM mixture.

In Iran like other developing countries, age of breast cancer is lower, in comparison to the developed countries. The purpose of this study was to investigate the relationship of mammography behavior with demographic factors and health belief model constructs to perform mammography behavior and also to assess the predictive power of this model. In this cross-sectional study we selected 593 non lactating and non-pregnant women of 40 years of age and older without breast cancer by random clustered sampling method. Demographic data, history of previous mammography and data about HBM (perceived susceptibility, severity, self-efficacy, health motivation, benefits, and barriers) were collected by using self-report questionnaires. SPSS and LISREL software were used for data analysis. Following perceived susceptibility (r=0.48) and perceived barriers, (r=0.17), self-efficacy showed the highest correlation (r=0.61) with mammogram performance (p<0.001). Breast problem, marital status, family history of breast cancer had significant effects on mammography performance. Self-efficacy (regression coefficient=0.86) and perceived susceptibility (regression coefficient=0.65) had the most direct effect on mammography (p<0.01-0.001). High power exponent of the variance in mammography behavior shows efficacy of HBM as a theoretical framework for studying the behavior of mammography. Low rate of mammogram performance indicates the need for intervention programs aimed at increasing mammography behavior.

The free vibration features of rotating functionally graded microbeams in thermal environmentare presented in this paper. The governing equations are extracted on the basis of the Euler-Bernoulli beam assumptions beside the modified couple stress theory. The finite elementmethod is applied on the weak form of the strain and the kinetic energies to extract the naturalfrequencies and the associated modeshapes. The nonlinear static equations of motion due to therotation and the thermal environment are treated employing the Newton-Raphson technique.Moreover, the natural frequencies are estimated from the linearized equations of motion aboutthe static configuration. After the validation of the present results, the rotation speed, thematerial length scale parameter, the temperature change, the power law exponent and theslenderness ratio impacts on the fundamental natural frequency and the first and the secondmodeshapes are examined. The outcomes indicate the increment of the natural frequency aftera threshold value of the power law exponent depends on a given rotation speed for the rotatingmicrobeams in comparison with the stationary microbeams. Furthermore, the modeshapes ofrotating functionally graded microbeams vary by the power law exponent while for stationaryfunctionally graded microbeams the modeshapes are invariant with respect to the power lawexponent even in the presence of the thermal environment.

In this research, the dielectric barrier discharge plasma driven channel flow has been proposed for use as a thruster in the propulsion’s applictions and has been experimentally studied. Measurments of the thrust and consumed power with different values of barrier thicknesses and electrodes’ lenghths have been performed. The data of the mentioned parameters have been taken in order to quantify the effects of operating voltage on the effectiveness parameter of thruster, showing a peak-shaped profile for the effectiveness with maximum value of 0.19 mN/W at the profile summit. Also, a power law analysis has been used to derive relationships for the effectiveness, thrust and consumed power in terms of the applied voltage. It has been found that the thruster’s power is proportional to the voltage with exponent of 4, and the thrust is function of voltage with exponent of 2.2 and 5.8 for the glow and filamentary regimes, respectively. Finally, it has been shown that the effectiveness can be correlated to applied voltage with exponent of 1/8 and -1.8 for the glow and filamentary regimes, respectively.

The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change in the neutron density. Lyapunov exponent method is a powerful tool for investigating the range of stability and the transient behavior of the reactor power. In contrast to the other linear stability methods, this method can be used for large perturbations and is not needed to construct Lyapunov function. In this work, the range of stability using Lyapunov exponent method is evaluated for neutron point kinetics equations with six-groups delayed neutrons. Here, effects of four set of applications, namely, step, ramp, sinusoidal, and temperature feedback reactivities on power reactor were investigated with Lyapunov exponent method. The results of qualitative analysis were compared with traditional methods and were in good agreement with other works.

Nanoflares are the small impulsive sudden energy releases, due to the explosion of solar background. Thus, determination of their energies and distributions is important. Recent observations and simulation models have shown that the frequency of their energies follows power-law. According to Parker hypothesis, if these exponents are greater than critical value 2, the contributions of nanoflares to the heating of solar corona is more significan. Here, the extreme ultra-violet (EUV) emission radiances of corona observed by STEREO/EUVI taken on 11 and 12 Jun 2007 are analyzed. To simulate the EUV irradiance, a simple nanoflare model with three key parameters (the flare rate, the flare duration time, and the exponent of the power- law) is applied. Based on genetic algorithm, the lengths of data points are reduced. The resultant light curves are fed to the Support Vector Machine (SVM) classifier. The produced light curves of quiet and active regions of the solar corona are classified and the set of power- law exponent, the flare duration time and the flare rate parameters are obtained. The flare duration time is estimated about 80 minutes. The power-low exponents range about 2.5-2.7.

‎For a given odd prime $p$‎, ‎we investigate the power graphs of three classes of finite groups‎: ‎the elementary abelian groups of exponent $p$‎, ‎and the extra special groups of exponents $p$ or $p^2$‎. ‎We show that these power graphs are Eulerian for every $p$‎. ‎As a corollary‎, ‎we describe two classes of non-isomorphic groups with isomorphic power graphs‎. ‎In addition‎, ‎we prove that the clique graphs of the power graphs of two considered classes are complete‎. 

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