Fuzzy linear programming approach for solving transportation problems with interval-valued trapezoidal fuzzy numbers

Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving interval-valued trapezoidal fuzzy numbers for the transportation costs and values of supplies and demands. We propose a fuzzy linear programming approach for solving interval-valued trapezoidal fuzzy numbers transportation problem based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To illustrate the proposed approach an application example is solved. It is demonstrated that study of interval-valued trapezoidal fuzzy numbers transportation problem gives rise to the same expected results as those obtained for TP with trapezoidal fuzzy numbers.     

Cu<Superscript>2+</Superscript> and Al<Superscript>3+</Superscript> co-substituted cobalt ferrite: structural analysis,morphology and magnetic properties

Cu–Al substituted Co ferrite nanopowders, Co_1?x Cu _x Fe_2?x Al _x O₄ (0.0 ≤ x ≤ 0.8) were synthesized by the co-precipitation method. The effect of Cu–Al substitution on the structural and magnetic properties have been investigated. X-ray diffraction (XRD) spectroscopy, Fourier transform infrared (FTIR) spectroscopy, field emission scanning electron microscopy (FESEM) and vibrating sample magnetometer (VSM) are used for studying the effect of variation in the Cu–Al substitution and its impact on particle size, magnetic properties such as M _s and H _c . Cu–Al substitution occurs and produce a secondary phase, α-Fe ₂ O ₃. The crystallite size of the powder calcined at 800 ^°C was in the range of 19–26 nm. The lattice parameter decreases with increasing Cu–Al content. The nanostructural features were examined by FESEM images. Infrared absorption (IR) spectra shows two vibrational bands; at around 600 (v ₁) and 400 cm ^?1 (v ₂). They are attributed to the tetrahedral and octahedral group complexes of the spinel lattice, respectively. It was found that the physical and magnetic properties have changed with Cu–Al contents. The saturation magnetization decreases with the increase in Cu–Al substitution. The reduction of coercive force, saturation magnetization and magnetic moments are may be due to dilution of the magnetic interaction.     

3，4-二氢吡咯[2，1-c][1，4]噘嗪-1-酮及其7-芳酰基衍生物的设计与合成

以2-吡咯基三氯乙酮为主要原料,经过乙二醇单酯化、羟基氯取代、环合三步反应制得了3,4-二氢吡咯[2,1-c][1,4]噁嗪-1-酮;又经过Friedel—Crafts酰基化和环合反应制得了未见文献报道的7-芳酰基-3,4-二氢吡咯[2,1-c][1,4]噁嗪-1-酮它们及其某些重要中间体的结构分别采用红外光谱、质谱、核磁共振氢谱、核磁共振碳谱以及高分辨率质谱进行了表征．     

Proposed Model to Match the Experimental Results for Oil Displaced by Externally Generated Foam

A mathematical model was developed to predict the performance of the oil displaced by water foam in porous media. In this model, the diffusivity equations of both water foam (the displacing phase) and oil (the displaced phase) were combined in a single equation, which was solved numerically by a finite difference method, using the implicit-explicit method. The proposed model was compared with Poiseueille's model which represents the porous media by straight capillary tubes. It was found that the proposed model is superior to that of Poiseueille, because the Poiseueille model does not take into account the variations in foam properties along the sand pack. The production data used for the proposed model were obtained experimentally from the displacement of oil by water foam of different qualities (externally generated foam). The plastic viscosity of the water foam was measured experimentally for four foam quality ranges using capillary tubes of different sizes. The effective viscosity of the water foam determined from the plastic viscosity was used in the proposed model. Foam viscosity was found to increase as the quality increases, and the water foam obeys a Bingham plastic fluid model. The porous medium was represented by a sand pack whose length was 36 cm and diameter was 6.3 cm. Its absolute permeability was 341 md and porosity was 22.8%. The foam consisted of tap water, surfactant, and nitrogen gas.     

不同电增压方式对米勒循环柴油机性能影响的模拟研究

利用GT-Power进行建模,探究独立式与一体式两种电增压方式对米勒循环柴油机性能的影响。仿真结果表明:两种电增压都可以拓宽米勒循环的应用范围,一体式电增压适用于过量空气系数高的工况,独立式电增压适用于过量空气系数低的工况。与高转速大进气量工况相比,低转速小进气量工况使用电增压能获得更好的增压效果。     

Tests on a simply supported rhombic plate

This paper deals with tests done on a simply supported isotropic rhombic plate subjected to certain conditions of lateral loading. The loading conditions used were (i) uniformly distributed load covering the whole plate, (ii) patch load at the centre of the plate, (Hi) uniformly distributed load over a quarter of the plate. Bending moments were obtained at certain important locations on the plate, using electrical resistance strain gauges. The central deflections were also recorded. The results obtained were compared with the available theoretical results. The correlation for the case of uniformly distributed load covering the whole plate was found to be good.