• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.575-588
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• 2023

In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an n-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.

• Steel and Composite Structures
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• v.21 no.1
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• pp.1-36
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• 2016

In the present study, the nonlinear magneto-electro-mechanical free vibration behavior of rectangular double-bonded sandwich microbeams based on the modified strain gradient theory (MSGT) is investigated. It is noted that the top and bottom sandwich microbeams are considered with boron nitride nanotube reinforced composite face sheets (BNNTRC-SB) with electrical properties and carbon nanotube reinforced composite face sheets (CNTRC-SB) with magnetic fields, respectively, and also the homogenous core is used for both sandwich beams. The connections of every sandwich beam with its surrounding medium and also between them have been carried out by considering Pasternak foundations. To take size effect into account, the MSGT is introduced into the classical Timoshenko beam theory (CT) to develop a size-dependent beam model containing three additional material length scale parameters. For the CNTRC and BNNTRC face sheets of sandwich microbeams, uniform distribution (UD) and functionally graded (FG) distribution patterns of CNTs or BNNTs in four cases FG-X, FG-O, FG-A, and FG-V are employed. It is assumed that the material properties of face sheets for both sandwich beams are varied in the thickness direction and estimated through the extended rule of mixture. On the basis of the Hamilton's principle, the size-dependent nonlinear governing differential equations of motion and associated boundary conditions are derived and then discretized by using generalized differential quadrature method (GDQM). A detailed parametric study is presented to indicate the influences of electric and magnetic fields, slenderness ratio, thickness ratio of both sandwich microbeams, thickness ratio of every sandwich microbeam, dimensionless three material length scale parameters, Winkler spring modulus and various distribution types of face sheets on the first two natural frequencies of double-bonded sandwich microbeams. Furthermore, a comparison between the various beam models on the basis of the CT, modified couple stress theory (MCST), and MSGT is performed. It is illustrated that the thickness ratio of sandwich microbeams plays an important role in the vibrational behavior of the double-bonded sandwich microstructures. Meanwhile, it is concluded that by increasing H/lm, the values of first two natural frequencies tend to decrease for all amounts of the Winkler spring modulus.

• Smart Structures and Systems
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• v.19 no.3
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• pp.309-322
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• 2017

In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.

• Asian Pacific Journal of Cancer Prevention
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• v.17 no.9
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• pp.4251-4257
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• 2016

Background: Testicular cancer is one of the most common cancers among young men between ages 20-34 in countries with high or very high levels of the Human Development Index (HDI). This study investigated the incidence and mortality of prostate cancer and the relationship with the HDI and its dimensions in Asia in 2012. Materials and Methods: The study was conducted based on data from the world data of cancer and the World Bank (including the HDI and its components). Standardized incidence and mortality rates of testicular cancer were calculated for Asian countries. Correlations between incidence and/ormortality rates, and the HDI and its components were assessed with the use of the correlation test, using SPSS software. Results: There was a total of 14902 incidences and 5832 death were recorded in Asian countries in 2012. Among the Asian countries, the five countries with the highest standardized incidence rates of testicular cancer were Israel, Georgia, Turkey, Lebanon and Kazakhstan and the five countries with the highest standardized mortality rates were Turkey, Georgia, Jordan, Cambodia and the Syrian Arab Republic. A positive correlation of 0.382 was observed between the standardized incidence rates of testicular cancer and the HDI (p=0.009). Also a negative correlation of 0.298 between the standardized mortality rate of testicular cancer and the Human Development Index was noted although this relation was statistically non-significant (p=0.052). Conclusions: There is a positive correlation between HDI and the standardized incidence rate of testicular cancer and negative correlation with standardized mortality rate.

• Wind and Structures
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• v.29 no.6
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• pp.457-469
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• 2019

In this paper, a numerical solution is presented for supersonic flutter analysis of cantilever non-symmetric functionally graded (FG) sandwich plates. The plate is considered to be composed of two different functionally graded face sheets and an isotropic homogeneous core made of ceramic. Based on the first order shear deformation theory (FSDT) and linear piston theory, the set of governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and solved numerically using generalized differential quadrature method (GDQM) and critical velocity and flutter frequencies are calculated. For various values of the yaw angle, effect of different parameters like aspect ratio, thickness of the plate, power law indices and thickness of the core on the flutter boundaries are investigated. Numerical examples show that wings and tail fins with larger length and shorter width are more stable in supersonic flights. It is concluded for FG sandwich plates made of Al-Al₂O₃ that increase in volume fraction of ceramic (Al₂O₃) increases aeroelastic stability of the plate. Presented study confirms that improvement of aeroelastic behavior and weight of wings and tail fins of aircrafts are not consistent items. It is shown that value of the critical yaw angle depends on aspect ratio of the plate and other parameters including thickness and variation of properties have no considerable effect on it. Results of this paper can be used in design and analysis of wing and tail fin of supersonic airplanes.

• Journal of Electrochemical Science and Technology
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• v.8 no.1
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• pp.43-52
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• 2017

In this paper, for the first time, the electroanalytical study of Triethylenediamine, TEDA was done on a typically graphene modified carbon paste electrode (Gr/CPE) in pH=10.5 of phosphate buffer solutions (PBS). The surface morphology of the bare and modified electrodes was characterized by scanning electron microscopy (SEM), electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV). The electro-oxidation of TEDA was investigated at the surface of modified electrode. The results revealed that the oxidation peak current of TEDA at the surface of Gr/CPE is 2.70 times than that shown at bare-CPE. A linear calibration plot was observed in the range of 1.0 to 202.0 ppm. In this way, the detection limit was found to be 0.18 ppm. The method was then successfully applied to determination of TEDA in aqueous samples obtained from two kinds of activated carbon from the masks of war. On the other hand, density functional theory (DFT) method at B3LYP/6-311++G** level of theory and a conductor-like Polarizable Continuum Model (CPCM) was used to calculate the $pK_a$ values of TEDA. The energies of lowest unoccupied molecular orbital ($E_{LUMO}$) and highest occupied molecular orbital ($E_{HOMO}$), gap energy (${\Delta}E$) and some thermodynamic parameters such as Gibbs free energy of TEDA and its conjugate acid ($HT^+$) were calculated. The results of calculated $pK_a$ were found to be in good agreement with the experimental values.

• Advances in nano research
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• v.8 no.1
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• pp.59-68
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• 2020

In the present study, buckling analysis of sandwich composite (carbon nanotube reinforced composite and fiber reinforced composite) Euler-Bernoulli beam in two configurations (core and layers material), three laminates (combination of different angles) and two models (relative thickness of core according to peripheral layers) using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and different types of porosity distribution on critical buckling load are discussed. Using sandwich beam, it shows a considerable enhancement in the critical buckling load when compared to ordinary composite. Actually, resistance against buckling in sandwich beam is between two to four times more. It is also showed the critical buckling loads of laminate 1 and 3 are significantly larger than the results of laminate 2. When Configuration 2 is used, the critical buckling load rises about 3 percent in laminate 1 and 3 compared to the results of configuration 1. The amount of enhancement for laminate 3 is about 17 percent. It is also demonstrated that the influence of the core height (thickness) in the case of lower carbon volume fractions is ignorable. Even though, when volume fraction of fiber increases, differences grow smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Among three porosity patterns investigated, beam with the distribution of porosity Type 2 (downward parabolic) has the maximum critical buckling load. At the end, the first three modes of buckling will be demonstrated to investigate the effect of spring constants.

• Steel and Composite Structures
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• v.33 no.4
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• pp.509-523
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• 2019

In the present work, the buckling analysis of micro sandwich plate with an isotropic/orthotropic cores and piezoelectric/polymeric nanocomposite face sheets is studied. In this research, two cases for core of micro sandwich plate is considered that involve five isotropic Devineycell materials (H30, H45, H60, H100 and H200) and an orthotropic material also two cases for facesheets of micro sandwich plate is illustrated that include piezoelectric layers reinforced by carbon and boron-nitride nanotubes and polymeric matrix reinforced by carbon nanotubes under temperature-dependent and hydro material properties on the elastic foundations. The first order shear deformation theory (FSDT) is adopted to model micro sandwich plate and to apply size dependent effects from modified strain gradient theory. The governing equations are derived using the minimum total potential energy principle and then solved by analytical method. Also, the effects of different parameters such as size dependent, side ratio, volume fraction, various material properties for cores and facesheets and temperature and humidity changes on the dimensionless critical buckling load are investigated. It is shown from the results that the dimensionless critical buckling load for boron nitride nanotube is lower than that of for carbon nanotube. It is illustrated that the dimensionless critical buckling load for Devineycell H200 is highest and lowest for H30. Also, the obtained results for micro sandwich plate with piezoelectric facesheets reinforced by carbon nanotubes (case b) is higher than other states (cases a and c).The results of this research can be used in aircraft, automotive, shipbuilding industries and biomedicine.

• Computers and Concrete
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• v.27 no.2
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• pp.111-130
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• 2021

In the present work, an extensive study for predicting efficiency parameters (��i) of various simulated nanocomposites including Polymethyl methacrylate (PMMA) as matrix and different structures including various sizes of graphene platelets (GPLs), single, double, and multi-walled carbon nanotubes (SWCNTs-DWCNTs-MWCNTs), and single and double-walled boron nitride nanotubes (SWBNNTs-DWBNNTs) are investigated. It should be stated that GPLs, carbon and boron nitride nanotubes (CNTs, BNNT) with different chiralities (5, 0), (5, 5), (10, 0), and (10, 10) as reinforcements are considered. In this research, molecular dynamics (MDs) method with Materials studio software is applied to examine the mechanical properties (Young's modulus) of simulated nanocomposite boxes and calculate η1 of each nanocomposite boxes. Then, it is noteworthy that by changing length (6.252, 10.584, and 21.173 nm) and width (7.137, 10.515, and 19.936) of GPLs, ��1, ��2, and ��3 approximately becomes (0.101, 0.114, and 0.124), (1.15, 1.22, and 1.26), (1.04, 1.05, and 1.07) respectively. After that efficiency parameters of SWCNTs, DWCNTs, and MWCNTs are calculated and discussed separately. Finally efficiency parameters of SWBNNTs and DWBNNTs with different chiralities by PMMA as matrix are determined by MD and discussed separately. It is known that the accurate efficiency parameters helps a lot to calculate the properties of nanocomposite analytically. In particular, the obtained results from this research can be used for analytical work based on the extended rule of mixture (ERM) in bending, buckling and vibration analysis of structure in future study.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.217-227
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• 2005

Let G be a finite group and $\#$Cent(G) denote the number of centralizers of its elements. G is called n-centralizer if $\#$Cent(G) = n, and primitive n-centralizer if $\#$Cent(G) = $\#$Cent($\frac{G}{Z(G)}$) = n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and if G is a finite group such that G/Z(G)$\simeq$$A_5$, then $\#$Cent(G) = 22 or 32. Moreover, we prove that As is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of As in terms of the number of centralizers