Exact solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation via the first integral method

In this article we find the exact traveling wave solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation by using the first integral method. This method is based on the theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones

Application of the generalized Kudryashov method to the Eckhaus equation

In this paper, the generalized Kudryashov method is presented to seek exact solutions of the Eckhaus equation. From these solutions, we can derive solitary wave solutions as a special case. The proposed method is direct, effective and convenient and can be applied to many nonlinear evolution equations in mathematical physics

Exact Soliton Solutions for Second-Order Benjamin-Ono Equation

The homogeneous balance method is proposed for seeking the travelling wave solutions of the second-order Benjamin-Ono equation. Many exact traveling wave solutions of second-order Benjamin-Ono equation, which contain soliton like and periodic-like solutions are successfully obtained. This method is straightforward and concise, and it may also be applied to other nonlinear evolution equations

New Exact Solutions of some Nonlinear Partial Differential Equations by the First Integral Method

The first integral method is an efficient method for obtaining exact solutions of nonlinear partial differential equations. The efficiency of the method is demonstrated by applying it for two selected equations. This method can be applied to nonintegrable equations as well as to integrable ones

Exact Travelling Wave Solutions of the Coupled Klein-Gordon Equation by the Infinite Series Method

In this paper, we employ the infinite series method for travelling wave solutions of the coupled Klein-Gordon equations. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons and periodic solutions

Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index

We analytically study the exact solitary wave solutions of the perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index, which describes the propagation of pulses of various types in optical fiber. We apply three efficient and reliable schemes, specifically, the simple equation method, the (G'/G)-expansion method, and the new Kudryashov method. These approaches lead to a range of solitons and other solutions comprising of the bright solitons, dark solitons, singular solitons, periodic, rational, and exponential solutions. These solutions are also presented graphically. Furthermore, all obtained solutions are verified by symbolic computations

The Effect of Shot-peening on the Fatigue Limits of Four Connecting Rod Steels

This work was carried out to study the effect of shot-peening on the fatigue behaviour of carbon steels. Differently heat treated medium and high carbon steel specimens were selected. Medium carbon steels, AISI 1141 and AISI 1151, were respectively air cooled and quenched-tempered. A high carbon steel, C70S6 (AISI 1070), was air cooled. The other material was a powder metal (0.5% C) steel. Each group of steels was divided into two. One was shot-peened. The other half remained in their original conditions. All were fatigue tested under fully reversed (R=-1) tension-compression loading conditions. Microhardness tests were carried out on both the grip and gage sections of selected non shot-peened and shot-peened specimens to determine the hardness profile and effect of cycling. Shot-peening was found to be deeper on one side of each specimen. Compressive residual stress profiles and surface roughness measurements were provided. Shot-peening increased the surface roughness from 0.26±0.03µm to 3.60±0.44µm. Compressive residual stresses induced by shot-peening reached a maximum of -463.9MPa at a depth of 0.1mm.The fatigue limit (N≈106 cycles) and microhardness profiles of the non shot-peened and shot-peened specimens were compared to determine the material behaviour changes after shot-peening and cycling. Also their fatigue properties were related to the manufacturing process including heat and surface treatments. Comparing the grip and gage microhardness profiles of each steel showed that neither cyclic softening nor hardening occurred in the non shot-peened condition. Cyclic softening was apparent in the shot-peened regions of all steels except powder metal (PM) steel. The amount of softening in the shot-peened region was 55.0% on the left side and 73.0% on the right in the AISI 1141 steel , 46.0% on the left side and 55.0% on the right in the C70S6AC steel and 31.0% on the right side in AISI 1151QT steel. Softening was accompanied by a decrease in the depth of surface hardness. It is suggested that although the beneficial effects of shot peening, compressive residual stresses and work hardening, were offset by surface roughness, crack initiation was more likely to occur below the surface. Surface roughness was not a significant factor in controlling the fatigue lives of AISI 1141AC and C70S6 steels, since they were essentially the same for the non shot-peened and shot-peened conditions. Shot-peening had very little effect on the push-pull fatigue limit of C70S6 steel (-2.1%), and its effect on AISI 1141AC steel was relatively small (6.0%). However, the influence of shot-peening on the AISI 1151QT and PM steels was more apparent. The fatigue limit of the PM steel increased 14.0% whereas the fatigue limit of the AISI 1151QT steel decreased 11.0% on shot peening

A mathematical model in cellular manufacturing system considering subcontracting approach under constraints

In this paper, a new mathematical model in cellular manufacturing systems (CMSs) has been presented. In order to increase the performance of manufacturing system, the production quantity of parts has been considered as a decision variable, i.e. each part can be produced and outsourced, simultaneously. This extension would be minimized the unused capacity of machines. The exceptional elements (EEs) are taken into account and would be totally outsourced to the external supplier in order to remove intercellular material handling cost. The problem has been formulated as a mixed-integer programming to minimize the sum of manufacturing variable costs under budget, machines capacity and demand constraints. Also, to evaluate advantages of the model, several illustrative numerical examples have been provided to compare the performance of the proposed model with the available classical approaches in the literature

Influence of menstrual cycle and salivary ß-estradiol on volatile sulfur compound

BACKGROUND: ß -estradiol is a steroid sex hormone that plays important role in oral physiology. The aim of this study was to determin the association of the menstrual cycle and salivary ß-estradiol with the production of volatile sulfur compounds (VSC). METHODS: In this cross-sectional study, twenty female dental students in good oral and general health were recruited for evaluation of VSC, salivary flow, ß-estradiol concentration, oral dryness feeling and dysmenorrhea. Data were analyzed by marginal homogeneity test and xtgee model. RESULTS: The only covariates that significantly related to VSC were being at the follicular phase (B = -0.21, P = 0.02), being at the pre-menstrual phase (B = -0.25, P = 0.01), stressfulness (B = 0.02, P = 0.01) and oral dryness feeling (B = 0.34, P = 0.02). Salivary ß-estradiol was at the level of 59.7 31.2 in those having halitosis (VSC ≥ 75) while in the others (VSC < 75) it was about 40.8 18.0 (P < 0.009). This difference was not statistically significant in multivariate analysis. CONCLUSIONS: The menstrual cycle, stress and oral dryness were the most important determinants of halitosis. The salivary ß-estradiol level could not explain such relationship as its effect was eliminated considering the other factors. KEY WORDS: Halitosis, menstrual cycle, ß-estradiol, volatile sulfur compound