Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method

Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

Optimization of Shanghai marine environment monitoring sites by integrating spatial correlation and stratified heterogeneity

The water quality grades of phosphate（PO4-P） and dissolved inorganic nitrogen（DIN） are integrated by spatial partitioning to fit the global and local semi-variograms of these nutrients. Leave-one-out cross validation is used to determine the statistical inference method. To minimize absolute average errors and error mean squares,stratified Kriging（SK） interpolation is applied to DIN and ordinary Kriging（OK） interpolation is applied to PO4-P.Ten percent of the sites is adjusted by considering their impact on the change in deviations in DIN and PO4-P interpolation and the resultant effect on areas with different water quality grades. Thus, seven redundant historical sites are removed. Seven historical sites are distributed in areas with water quality poorer than Grade IV at the north and south branches of the Changjiang（Yangtze River） Estuary and at the coastal region north of the Hangzhou Bay. Numerous sites are installed in these regions. The contents of various elements in the waters are not remarkably changed, and the waters are mixed well. Seven sites that have been optimized and removed are set to water with quality Grades III and IV. Optimization and adjustment of unrestricted areas show that the optimized and adjusted sites are mainly distributed in regions where the water quality grade undergoes transition.Therefore, key sites for adjustment and optimization are located at the boundaries of areas with different water quality grades and seawater.

Kinetic Optimal Midcourse Guidance Law for Air-to-Air Missiles

A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air missile is referred to for comparing results using the kinetic optimal midcourse guidance law with those under both the kinematic optimal guidance law and singular perturbation sub-optimal guidance law, wherein the latter two laws are modified in this paper by adding a vertical g-bias command to each law for the sake of trajectory shaping. Simulation results show that using the new kinetic optimal mideourse guidance law can help save energy and maximize terminal velocity effectively.

Higher-order crack tip fields for functionally graded material plate with transverse shear deformation

The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.

Single-pulse chaotic dynamics of functionally graded materials plate

Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.

Grading method for tomato multi-view shape using machine vision

Owing to the requirements of a high yield and high-quality tomatoes, tomato grading is important-particularly for fruit morphology, and accuracy has become the focus of attention. Machine vision provides a fast and nondestructive manner to address this demand. In this study, the gamma correction method was used for preprocessing to enhance the edge information of tomatoes, and Otsu’s method was used to eliminate the tomato-image background in the A-component image under the LAB color model. On this basis, two levels of exploration were conducted. First, new evaluation indices were proposed for tomato shapes from different views. For the top view, two shape-evaluation indices were established: the area ratio of the maximum inscribed circle to the maximum circumscribed circle and the dispersion of the contour centroid distance (range and coefficient of variation), the highest accuracy was 94%. For the side view, the difference between the maximum and minimum centroid distances in the contour was established as a shape index, the highest accuracy was 91.91%. Second, an evaluation method based on multi-view fusion was developed by combining the advantage indices for different views. The classification accuracy reached 96%, with the highest identification accuracy of unqualified tomatoes. The results show that the proposed evaluation method combining top views (dispersion of centroid distance) with side views (difference between maximum and minimum centroid distances) is effective for classifying tomatoes.

Grading method of soybean mosaic disease based on hyperspectral imaging technology

Soybean is a crop with a long cultivation history that occupies an important position in agricultural production.Soybean mosaic virus disease(SMV)has caused a rapid decline in soybean yields,causing huge losses to the soybean industry,wherefrom its early detec-tion is particularly important.This study proposes a new classification method for the early SMV,dividing its severity into grades 0,1 and 2.In the case of a small number of experi-mental samples of soybeans,this study proposes a combined convolutional neural network and support vector machine(CNN-SVM)method for the early detection of SMV.Experimen-tal results showed that the accuracy of the training set of the CNN-SVM model reached 96.67%,and the accuracy rate of the test set reached 94.17%.The experiment proved the feasibility of using the proposed CNN-SVM model to classify early SMV under the new clas-sification method,and provided a new direction for early SMV detection based on hyper-spectral images.

Clinical guideline on topical growth factors for skin wounds

An increased number of patients with skin wounds have been witnessed in the past decades.Among the various kinds of treatments for skin wounds,topical exogenous growth factors are indispensable and have been used in many countries.However,whether they have reliable effects remains controversial,and their application for skin wound treatment needs to be further standardized and optimized in terms of socio-economic considerations.Thus,the Chinese Burn Association developed this guideline indicating efficacy,application details,adverse reactions and precautions of five clinically common topical growth factors using the Grading of Recommendations Assessment Development and Evaluation method to promote the rational application of topical exogenous growth factors in skin wounds and to benefit more patients.

Evaluation of regional water security using water poverty index

Water security is a widely concerned issue in the world nowadays.A new method,water poverty index(WPI),was applied to evaluate the regional water security.Twelve state farms in Heilongjiang Province,Northeastern China were selected to evaluate water security status based on the data of 2006 using WPI and mean deviation grading method.The method of WPI includes five key indices:resources(R),access(A),capacity(C),utilization(U)and environment(E).Each key index further consists of several sub-indices.According to the results of WPI,the grade of each farm was calculated by using the method of mean deviation grading.Thus,the radar images can be protracted of each farm.From the radar images,the conclusions can be drawn that the WPI values of Farm 853 and Hongqiling are under very safe status,while that of Farm Raohe is under safe status,those of Farms Youyi,597,852,291 and Jiangchuan are under moderate safe status,that of Farm Beixing is under low safe status and those of Farm Shuangyashan,Shuguang and Baoshan are under unsafe status.The results from this study can provide basic information for decision making on rational utilization of water resources and regulations for regional water safety guarantee system.

COUPLED THERMO-MECHANICAL ANALYSIS OF FUNCTIONALLY GRADIENT WEAK/MICRO-DISCONTINUOUS INTERFACE WITH GRADED FINITE ELEMENT METHOD

Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.

Analytical Solution for Time-dependent Flow of a Third Grade Fluid Induced Due to Impulsive Motion of a Flat Porous Plate

The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y 〉 0 over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity V（t）. Translational symmetries in variables t and y are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method（HAM）. Graphs representing the solution are plotted and discussed and proper conclusions are drawn.

Thermodynamic analysis for a third grade fluid through a vertical channel with internal heat generation

This paper makes the thermodynamic analysis in forced convective flow of a third grade fluid through a vertical channel. Due to the reactive nature of the fluid, the effect of internal heat generation is considered and assumed to be a linear function of temperature. The coupled nonlinear dimensionless ordinary differential equations governing the fluid flow are solved by using the Adomian decomposition method（ADM）. The effects of various physical parameters such as third grade material parameter, buoyancy parameter and heat generation parameter on the thermal structure of flow are presented and discussed.