This work applied the lattice Boltzmann Method (LBM) to investigate the effect of CuO nanoparticles on natural convection with magnetohydrodynamic (MHD) flow in a square cavity. The left and right vertical walls of the cavity were kept at constant temperatures, Th and Tc, respectively, with two insulated walls at the top and bottom. A uniform magnetic field was used in a horizontal direction. Results were carried out for different Hartmann numbers ranging from 0-100, Rayleigh numbers from 103-105 and the solid volume fraction from 0 to 0.05. Effects of the solid volume fraction and magnetic field on hydrodynamic and thermal characteristics were investigated and discussed. The averaged Nusselt numbers, on hot wall, streamlines, temperature contours, and the vertical component of velocity for different values of a solid volume fraction, Hartmann and Rayleigh numbers were illustrated. The results indicate that the averaged Nusselt number increases for nanofluids when increasing the solid volume fraction, while, in the presence of a high magnetic field, this effect decreases.

The nature of dynamic loading is different due to the high force in a few milliseconds with static loading. The amount of energy absorption and energy loss in composite materials is a suitable measurement to evaluate the performance against impact loads. On the other hand, the use of selfcompacting composites due to its unique properties has attracted the attention of researchers. High compressive and tensile strength, high flexural strength, has attracted more attention from researchers to this kind of cement composites. In this research, in the form of a comprehensive laboratory work, using four basement mixing designs, 64 Rectangular composite panels were constructed in two groups of 100*100 mm with four thicknesses of 30, 45, 60 and 75 mm and tested under dynamic loading. Tensile and flexural strength tests were made on all four mixing designs. Steel fibers with percentages of 0, 0. 25, 0. 5 and 0. 75 with length of 25 mm were used for the construction of cement composites. The drop hammer test machine with weighs 180 kg and the power of 7500 J is used. According to laboratory results, the combined use of steel and fiber reinforced steel sheets increased the energy absorption considerably. Also, the initial peak force increased and the deformation length decreased.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating Rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

The systematic study of planar semimodular lattices started in 2007 with a series of papers by G. Gr¨, atzer and E. Knapp. These lattices have connections with group theory and geometry. A planar semimodular lattice L is slim if M3 it is not a sublattice of L. In his 2016 monograph, “, The Congruences of a Finite lattice, A Proof-by-Picture Approach”, , the second author asked for a characterization of congruence lattices of slim, planar, semimodular lattices. In addition to distributivity, both authors have previously found specific properties of these congruence lattices. In this paper, we present a new property, the Three-pendant Three-crown Property. The proof is based on the first author’, s papers: 2014 (multifork extensions), 2017 (C1-diagrams), and a recent paper (lamps), introducing the tools we need.

We study L-categories of lattice-valued convergence spaces. Such categories are obtained by "fuzzifying" the axioms of a lattice-valued convergence space. We give a natural example, study initial constructions and function spaces. Further we look into some L-subcategories. Finally we use this approach to quantify how close certain lattice-valued convergence spaces are to being lattice-valued topological spaces.

The main purpose of this study is finding a numerical solution of the modified Burger's equation with appropriate initial and boundary conditions, by using finite difference method for dimensionless state, and comparing the results with the other research. Finite difference method results were compared with those of LBM, and relevant figures and tables describe the comparison. This paper also addressed the effect of time, viscosity and the exponent of sedimentation velocity (in Burger equation) on sedimentation velocity. The results showed that an increase in time and viscosity parameters resulted in a decrease in the maximum sedimentation velocity, and the maximum sedimentation velocity occurrence was transported to the end of the range under investigation. In addition, the results indicated that if viscosity parameter was multiplied 100 times, the particles falling velocity at the peak point would decrease by 60%. The analysis of the results is included in the paper.

Let M be a lattice module over the multiplicative lattice L. An L-module M is called a multiplication lattice module if for every element NÎM there exists an element aÎL such that N=a1M. Our objective is to investigate properties of prime elements of multiplication lattice modules.

Let G be a simple, oriented connected graph with n vertices and m edges. Let I (B) be the binomial ideal associated to the incidence matrix B of the graph G. Assume that IL is the lattice ideal associated to the rows of the matrix B. Also let Bi be a sub matrix of B after removing the i -th row. We introduce a graph theoretical criterion for G which is a sufficient and necessary condition for I (B) =I (Bi) and I (Bi) =IL. After that we introduce another graph theoretical criterion for G which is a sufficient and necessary condition for I (B) =IL. It is shown that the heights of I (B) and I (Bi) are equal to n - 1 and the dimensions of I (B) and I (Bi) are equal to m - n+1; then I (Bi) is a complete intersection ideal.

Packing Rectangular shapes into a Rectangular space is one of the most important discussions on Cutting & Packing problems (C&P); such as: cutting problem, bin-packing problem and distributors pallet loading problem, etc. Assume a set of Rectangular pieces with specific lengths, widths and utility values. Also assume a Rectangular packing space with specific width and length. The objective function is, to pack the pieces into the space in Order to get the maximum sum of utility value of the packed pieces. To generate the related packing pattern this paper proposes a new formulation metl10dbased on the column generation, approach. In this method one each cycle of the algorithm; a one-dimensional pattern is generated based on the shadow prices 'Of the Simplex method. The set of generated one-dimensional patterns are used: to construct the two-dimensional packing pattern. Also, the proposed model and the present models in the.state-of-1beart have been compared.