AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

Working mechanism of two-direction reinforced composite foundation

Based on the discussion about working mechanism of horizontal reinforcement and that of vertical reinforcement,respectively,the working mechanism of two-direction reinforced composite foundation was studied.The enhancing effect of horizontal reinforcement on vertical reinforced composite foundation was analyzed.A simplified calculation method for such two-direction reinforced working system was presented.A model experiment was carried out to validate the proposed method.In the experiment,geocell reinforcement worked as the horizontal reinforcement,while gravel pile composite foundation worked as the vertical reinforcement.The results show that the calculated curve is close to the measured one.The installation of geosynthetic reinforcement can increase the bearing capacity of composite foundation by nearly 68% at normal foundation settlement,which suggests that the enhancing effect by geosynthetic reinforcement should be taken into account in current design/analysis methods.

A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.

ON TWO-DIRECTION SPATIAL SMOOTHING FOR ESTIMATION ANGLE-OF-DIRECTION OF COHERENT SIGNALS

Based on Evans’spatial smoothing preprocessing scheme,a new approach calledtwo-direction spatial smoothing preprocessing method is presented.It is proved that the decorre-lation,the effective aperture and the maximum number of distinguishable coherent signals(whenarray size is given)of the new method are better than those of the Evans’method.Simulationresults give a comparison between the eigenvector spectrums produced by the two methods.

F-interference law generation and its feature recognition

By using two-directional S-rough sets, the concepts of （f, f）-interference generation and （f, f）- interference law generation of knowledge, F-interference generation and F-interference law generation of two-directional S-rough sets are proposed. Based on the concepts above, the relation theoreras between F-interference loss and F-interference degree, the relation theorems between F-interference loss law and F-interference degree law, the dis- cernibility theorems between F-interference and F-interference law are presented. At last, the recognition criterion of F-interference law and its application are given.

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

S-Rough communication and its characteristics

In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication model. S-rough communication has two kinds of forms： one-direction S-rough communication and two-direction S-rough communication. The mathematical structure and characteristics of the one-direction S-rough communication and the two-direction S-rough communication, the relationship theorem between the one-direction S-rough communication and the two-direction S-rough communication are also presented. The S-rough communication is a dynamic communication method, and it is a novel research direction in rough sets field.

Optimal aeration management strategy for a small-scale food waste composting

Food waste is a significant contributor to greenhouse gas emissions when it ends up in landfills.Composting turns out to be a sustainable solution to this problem,but it requires controlled and continuous airflow for optimal performance.This study focused on the effect of aeration rates and airflow directions on food waste composting using a closed system with forced aeration.Air was entered into the composting vessel in three directions,which were upward,downward,and a combination of both directions.Each direction was run at aeration rates of 0.1,0.4,and 0.7 L/min.The findings showed that the compost pile aerated at 0.4 L/min by using two-directional airflow can reach the thermophilic temperature within half of the day.The compost pile achieved temperature of 40.94℃ after 10.5 h.Although the compost experienced slightly high in moisture loss(4.3%),the compost still attained the standard values for maturity.The compost produced from food waste could be applied in soil to improve its fertility.

Two-direction refinable functions and twodirection wavelets with high approximation order and regularity

The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.

Two-direction nonlocal model for image interpolation

How to sufficiently exploit the self-similarity of natural images for image restoration has attracted extensive interest in the field of image processing in recent years.In fact,the self-similarity implies two-direction similarity structures inherent in images,when a group of similar patches are rearranged to form a matrix,there exists similarity between both columns and rows of this matrix.In this paper,we propose a two-direction nonlocal model (TDNL) to symmetrically exploit the two-direction similarity structures in images,the model directly takes the similar patches as local adaptive dictionary to represent each patch in the image and constrain the representation coefficients by Tikhonov regularization.TDNL can achieve the best results so far and obtain significant gains over the existing methods,in terms of both peak signal to noise ratio (PSNR) measure and the visual quality when it is applied to the problem of image interpolation.

Construction tight wavelet of two-direction frames

We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple constructive method of two-direction tight wavelet frames is given. Third, based on the obtained two-direction tight wavelet frames, one can construct a symmetric multiwavelet frame easily. Finally, some examples are given to illustrate the results.

Interface Finite Volume Method with Low Calculating Amount for Step Size Varying Electro-Quasistatic Field Problem

In this paper,a novel numerical method called interface finite volume method(I-FVM)for calculation of step-varying Electro-quasistatic(EQS)field is proposed.First,the principle of I-FVM is derived.Then,with numerical example of double layers parallel plate structure under step voltage which has an analytical solution,effectiveness and correctness of the I-FVM are verified.It can be found the calculating time of I-FVM is only 30%of normal FVM without decreasing accuracy during the whole calculating process.Furthermore,an engineering example about the electric field of DBC(Direct Bonding Copper)structure in a high voltage IGBT device is given.It can be found that accuracy of the I-FVM is the same as normal FVM,while time cost of I-FVM is only 20.8%of normal FVM.At last,the I-FVM is extended to one dimension based on the two-direction tri-diagonal matrix algorithm(TDMA)method given in this paper which can save processing of LU decomposition compared to one-dimensional traditional TDMA.In conclusion,the novel method called I-FVM proposed in this paper can decrease calculating amount for a step size varying electro-quasistatic field calculation problem.It may be a good method for large-scale EQS field calculation.

Defects in the medical system and distortion in drug pricing

Through an analysis of China＇s healthcare system and the regulatory model of pharmaceutical pricing, the paper concludes that the prime cause of pharmaceutical pricing inflation is the twodirectional monopoly of public healthcare institutions on pharmaceutical retailing. The low cost of medical services means that public hospitals can legitimately use the sale of pharmaceuticals to subsidize the provision of services. Moreover, the policy of controlling the rate of return gives public hospitals a further incentive to buy and sell high-cost pharmaceuticals. In addition, the policy of independent pricing together with the laxity of the system for approving new drugs allows the makers of pharmaceutical products to charge higher prices and facilitates public hospitals＇ sale of high-priced drugs. All of these problems result from inappropriate government controls. Therefore, the basic strategy for solving the problem of inflated pharmaceutical prices should be to lessen government controls on healthcare, open up retail sales of prescription medicines, and reform the public healthcare system and medical insurance reimbursement, breaking the monopoly of public hospitals.