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.     

THE EFFECTS OF ALTITUDE ON FRUIT QUALITY AND COMPRESSION LOAD FOR CRACKING OF WALNUTS (Juglans regia L.)

Nuts of walnut (Juglans regia L.), cultivated in the district of Denizli (altitude of 300 m) and Cameli (altitude, 1200 m) in the Aegean region of Turkey, were used to determine the effects of altitude on fruit quality and the force and energy required to crack the nuts. The varieties used were Bilecik, Sebin, Yalova‐1, Yalova‐3 and Yalova‐4. For all cultivars, walnut trees grown at the higher altitude produced small size nuts with thick shells. Based on the average for all cultivars, kernel removal quality decreased with high altitude. The nuts obtained from the high‐altitude location were lighter‐colored and required more force to fracture the nuts than those harvested at the low altitude. The amount of energy required to crack the nuts was higher for the nuts grown at the low‐altitude location except for the cultivar, Sebin.     

Electrical properties and scaling behaviour of Sm<Superscript>3 + </Superscript> doped CaF<Subscript>2</Subscript>-bismuth borate glasses

The electrical properties for 20Bi₂O₃–60B₂O₃ (20−x)–CaF₂–xSm₂O₃ glasses (0 ≤ x ≤ 2) were measured in the temperature range 297 K up to 629 K and in the frequency range 0·1–100 kHz. The d.c. and a.c. conductivity values and the dielectric loss (tan δ) values were found to increase with increasing Sm₂O₃ content, whereas the activation energy of conductivities and the dielectric constant decreased. These results were attributed to the introduction of the rare earth ions; promote the formation of a high number of non-bridging oxygen atoms, which facilitate the mobility of charge carriers. The frequency dependence of the a.c. conductivity follows the power law σ _ac(ω) = Aω ^s . The frequency exponent (s) values (0·64 < s < 0·8) decrease with increasing temperature. This suggested that the a.c. conduction mechanism follows the correlated barrier hopping model (CBH). The dielectric constant (ε ^′) and dielectric loss (tan δ values) were found to increase with increasing temperature and increasing Sm₂O₃ concentration in the glass. The a.c. conductivities as a function of frequency at different temperatures of a given glass superimposed onto a master curve (Roling scaling model). Furthermore, we have performed to scale the data as a function of composition. Two master curves were obtained, which suggested that there are differences in dominant charge carriers between glasses having Sm₂O₃ concentration ≥1 and glass of Sm₂O₃ concentration <1.     

New public-key cryptosystem

The development of a new public-key cryptosystem is discussed. This system is a hybrid combination of the RSA (Rivest-Shamir-Adleman) and knapsack crypto-systems. The message is encrypted in two stages using the knapsack algorithm followed by the RSA algorithm, and then decrypted in reverse order. The mathematics of the knapsack and RSA algorithms, a security analysis of the hybrid system, and a small computer simulation example are all included. The major advantages of this system, when compared with the knapsack and RSA crypto-systems, are higher speed and greater security.     

Effects of Mentha longifolia L. essential oil on viability and cellular ultrastructure of Lactobacillus casei during ripening of probiotic Feta cheese

The effects of Mentha longifolia L. essential oil during ripening and storage probiotic Feta cheese were studied, in relation to viability and cellular ultrastructure of Lactobacillus casei. The addition of the essential oil in the concentrations from 0.0 to 0.03% was trialled: the 0.03% treatment resulted in the highest viability of L. casei and the lowest pH value compared with other treatments (P < 0.05). Electron microscopy showed that essential oil caused no harm to L. casei. This study demonstrated the favourable effects of M. longifolia on optimal maintenance of L. casei at the end of cheese storage period.     

Effect of water removal on the textural properties of resorcinol/formaldehyde gels by azeotropic distillation

The resorcinol/formaldehyde gels containing 5% (w/v) of reactants have been prepared. After curing for seven days, the gel is treated with trifluoroacetic acid to initiate the condensation of hydroxymethyl groups. Drying of the prepared gels is done by removing water with the help of vacuum heterogeneous azeotropic distillation using amyl acetate and n-butanol. The textural properties of the gels thus obtained are compared with the properties of the gel obtained from exchange of water by acetone (control experiment). The pore volume and average pore diameter of the gel obtained from the azeotropic distillation of water with amyl acetate are 0.7663 × 10–3 m3/kg and 0.0145 m, respectively. These values are 1.5 times higher than the values obtained by vacuum heterogeneous azeotropic distillation with n-butanol and about twice than the values obtained in the control experiment. The surface areas in all the three gels are almost constant.     

A Microscopical Study of the Structure of Meat Emulsions and Its Relationship to Thermal Stability

Meat emulsions were examined by light microscopy to determine the relationships between structure and emulsion stability. Beef-meat based emulsions were prepared either by varying chopping temperature or by adding soy plastic fats of different hardness. Formation of fat channels was observed in uncooked emulsions prepared either at a chopping temperature of 26°C or with soft plastic fat of 0.25cm^?1 hardness index. Such fat channel formations caused discontinuity of protein matrix, leading to fat separation during cooking and weakening of textural strength of products. Changes in fat globule size and distribution as affected by melting properties or hardness of fats were clearly reflected by changes in emulsion stability. Results suggest that emulsion stability is determined largely by the physical properties of protein matrix and fat incorporated. Stable emulsions were obtained with fats of appropriate melting properties and hardness and relatively cohesive protein matrix under given comminution conditions which allowed uniform fat distribution.     

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.