Search results for: cyclic stretching

Authors: A. Baqqal, O. Abduhamid, H. Abdul-Hameed, T. Messager, G. Ayoub

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In this contribution, the effect of crystal content on the cyclic response of semi-crystalline polyethylene is studied over a large strain range. Experimental observations on a high-density polyethylene with 72% crystal content and an ultralow density polyethylene with 15% crystal content are reported. The cyclic stretching does appear a thermoplastic-like response for high crystallinity and an elastomeric-like response for low crystallinity, both characterized by a stress-softening, a hysteresis and a residual strain, whose amount depends on the crystallinity and the applied strain. Based on the experimental observations, a unified viscoelastic-viscoplastic constitutive model capturing the polyethylene cyclic response features is proposed. A two-phase representation of the polyethylene microstructure allows taking into consideration the effective contribution of the crystalline and amorphous phases to the intermolecular resistance to deformation which is coupled, to capture the strain hardening, to a resistance to molecular orientation. The polyethylene cyclic response features are captured by introducing evolution laws for the model parameters affected by the microstructure alteration due to the cyclic stretching.

Keywords: cyclic loading unloading, polyethylene, semi-crystalline polymer, viscoelastic-viscoplastic constitutive model

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Authors: Wei-Wen Hu, Yong-Zhi Zhong

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Depositing conductive polypyrrole (PPy) onto elastic polydimethylsiloxane (PDMS) substrate can obtain a highly stretchable conductive film, which can be used to construct a bioreactor to cyclically stretch and electrically stimulate surface cells. However, how to completely harvest these stimulated muscle tissue to repair damaged muscle is a challenge. To address this concern, N-isopropylacrylamide (NIPAAm), a monomer of temperature-sensitive polymer, was added during the polymerization of pyrrole on PDMS so that the resulting P(Py-co-NIPAAm)/PDMS should own both conductivity and thermo-sensitivity. Therefore, cells after stimulation can be completely harvested as cell sheets by reducing temperature. Mouse skeletal myoblast, C2C12 cells, were applied to examine our hypothesis. In electrical stimulation, C2C12 cells on P(Py-co-NIPAAm)/PDMS demonstrated the best myo-differentiation under the electric field of 1 V/cm. Regarding cyclic stretching, the strain equal to or higher than 9% can highly align C2C12 perpendicular to the stretching direction. The Western blotting experiments demonstrated that the cell sheets harvested by cooling reserved more extracellular matrix (ECM) than cells collected by the traditional trypsin digestion method. Immunostaining of myosin heavy chain protein (MHC) indicated that both mechanical and electrical stimuli effectively increased the number of myotubes and the differentiation ratio, and the myotubes can be aligned by cyclic stretching. Stimulated cell sheets can be harvested by cooling, and the alignment of myotubes was still maintained. These results suggested that the deposition of P(Py-co-NIPAAm) on PDMS can be applied to harvest intact cell sheets after cyclic stretching and electrical stimulation, which increased the feasibility of bioreactor for the application of tissue engineering and regenerative medicine.

Keywords: bioreactor, cell sheet, conductive polymer, cyclic stretching, electrical stimulation, muscle tissue engineering, myogenesis, thermosensitive hydrophobicity

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Authors: Yi Tse Wang, Che Hsiu Chen, Zih Jian Huang, Hon Wen Cheng

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Stretching treatments enhanced flexibility. On the other hand, decreases in hamstrings strength have been reported after stretching, especially with static stretching or passive stretching. Stretching has been shown to be more effective than static stretching to improve muscle performance, but a clear consensus for the effect of dynamic stretching on muscle performance has not been achieved. The purpose of this study was to compare the acute effect of a dynamic stretching, static stretching and eccentric exercise protocol on hamstrings stiffness, flexibility and muscle strength. Forty-five healthy active men (height 179.9 cm; weight 71.5 kg; age 22.5 years) were participated in 3 randomly ordered testing sessions: dynamic stretching (DS), active static stretching (ASS), and passive static stretching (PSS). All the stretch were performed 30 seconds and repeated 6 times. There was a 30-second interval between repetitions. The outcome measures were isokinetic concentric contraction (60°/s), eccentric contraction (30°/s) peak torque, muscle flexibility after stretching. The results showed that the muscle flexibility (3.6%, 3.9% and 1.59%, respectively) increased significantly after DS, PSS and ASS. Hamstring isokinetic concentric peak torque (-6.4%, -8.0% and -5.8%, respectively) and eccentric peak torque (-5.8%, -4.5% and -5.4%, respectively) decreased significantly after DS, PSS and ASS. Hence, although the stretching protocols improve hamstrings flexibility immediately, reduced hamstring muscle eccentric and concentric peak torque.

Keywords: hamstrings injury, warm-up, muscle performance, muscle stretching

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Authors: Poonam Yadav, Dong Bok Lee

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Isothermal oxidation at 800°C for 50h and Cyclic oxidation at 600°C and 800°C for 40h of Pure Ti and Ti64 were performed in a muffle furnace. In Cyclic oxidation, massive scale spallation occurred, and the oxide scale cracks and peels off were observed at high temperature, it represents oxide scale that formed during cyclic oxidation was spalled out owing to stresses due to thermal shock generated during repetitive oxidation and subsequent cooling. The thickness of scale is larger in cyclic oxidation than the isothermal case. This is due to inward diffusion of oxygen through oxide scales and/or pores and cracks in cyclic oxidation.

Keywords: cyclic, diffusion, isothermal, cyclic

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Authors: Gulsun Guven

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The aim of this study was to examine the acute effects of static stretching exercises on the flexibility and sprint performance in 10-12 years old inactive healthy girls. A total of 27 girls were randomly divided into control group (n=15) and stretching group (n=12) who performed static stretching. Sit and reach flexibility and 30-meter sprint pre-tests were performed for both groups. Static stretching exercises were performed three times, 30 sec. practice and 15 sec. rest for each leg only on five muscle by stretching group. The post-tests were performed in five minutes after static stretching exercise. Paired t-test was used to analyze differentiations among the group parameters. According to research results, there is a significant difference between pre-test and post-test flexibility (p < 0.05) and sprint test results (p < 0.01). As a conclusion of the study, static stretching exercises improve flexibility but decrease sprint performance in 10-12 years old inactive healthy girls.

Keywords: flexibility, inactive girl, sprint, static stretching

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Authors: Jing Li, Xiuli Li

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This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= F_q+uF_q+…+u^k-1F_q, where q is a prime power. A Gray map ɸ from R to F_q and a Gray map ɸ' from Rⁿ to Fⁿ_q are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over F_q, and they still keep the dual relation.

Keywords: skew cyclic code, gray map, automorphism, cyclic code

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Authors: Levan Nadareishvili, Roland Bakuradze, Barbara Kilosanidze, Nona Topuridze, Liana Sharashidze, Ineza Pavlenishvili

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Some regularities of formation of a new structural state of the thermoplastic polymers-gradually oriented (stretched) state (GOS) are discussed. Transition into GOS is realized by the graded oriented stretching-by action of inhomogeneous mechanical field on the isotropic linear polymers or by zonal stretching that is implemented on a standard tensile-testing machine with using a specially designed zone stretching device (ZSD). Both technical approaches (especially zonal stretching method) allows to manage the such quantitative parameters of gradually oriented polymers as a range of change in relative elongation/orientation degree, length of this change and profile (linear, hyperbolic, parabolic, logarithmic, etc.). Uniaxial graded stretching method should be considered as an effective technological solution to create polymer materials with a predetermined gradient of physical properties.

Keywords: controlled graded stretching, gradually oriented state, linear polymers, zone stretching device

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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Authors: Shuyi Wu, Chuang Li, Quanshui Zheng, Luping Xu

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Stretching and snipping DNA molecule by microfluidic has important application value in gene analysis by lab on a chip. Movement, deformation and fragmenting of DNA in microfluidic are typical fluid-solid coupling problems. An efficient and common simulation system for researching the movement, deformation and fragmenting of DNA by microfluidic has not been well developed. In our study, Brownian dynamics-finite element method (BD-FEM) is used to simulate the dynamic process of stretching and fragmenting DNA by contraction flow. The shape and parameters of micro-channels are changed to optimize the stretching and fragmenting properties of DNA. Our results indicate that strain rate, resulting from contraction microchannel, is the main control parameter for stretching and fragmenting DNA. There is good consistency between the simulation data and previous experimental result about the single DNA molecule behavior and averaged fragmenting properties in this study. BD-FEM method is an efficient calculating tool to research stretching and fragmenting behavior of single DNA molecule and optimize microfluidic devices for manipulating, stretching and fragmenting DNA.

Keywords: fragmenting, DNA, microfluidic, optimize.

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation

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Authors: Chungyu Chen, Hui-Ju Chang, Pei-Shan Guo, Huei-Ling Jhan, Yi-Ping Lin

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The purpose of this study was to investigate the effect of the amount of acutely static stretching on muscular strength and power. There were 15 males, and 7 females recruited voluntarily as the participants in the study. The mean age, body height, and weight of participants were 23.4 ± 2.8 years old, 171.0 ± 7.2 cm, and 65.7 ± 8.7 kg, respectively. Participants were repeated to stretch hamstring muscles 2 or 6 30-s bouts randomly on a separate day spaced 5-7 days apart in a passive, static, sit-and-reach stretching exercise. Before and after acutely static stretching, the Biodex System 4 Pro was used to acquire the peak torque, power, total work, and range of motion for right knee under the loading of 180 deg/s. The 2 (test-retest) × 2 (number of stretches) repeated measures two-way analysis of variance were used to compare the parameters of muscular strength/power (α = .05). The results showed that the peak torque, power, and total work increased significantly after acutely passive static stretching (ps < .05) in flexor and extensor of knee. But there were no significant differences found between the 2 and 6 30-s bouts hamstring muscles stretching (ps > .05). It indicated that the performance of muscular strength and power in knee flexion and extension do not inhibit following the increase of amount of stretching.

Keywords: knee, power, flexibility, strength

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Authors: Deepshikha Verma, V. N. Rajasekharan Pillai

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The present study reports the synthesis of cyclic PNC-28 peptides with solid-phase peptide synthesis method. In the first step, we synthesize the linear PNC-28 Peptide and in the second step, we cyclize (N-to-C or head-to-tail cyclization) the linear PNC-28 peptide. The molecular formula of cyclic PNC-28 peptide is C64H88N12O16 and its m/z mass is ≈1233.64. Elemental analysis of cyclic PNC-28 is C, 59.99; H, 6.92; N, 13.12; O, 19.98. The characterization of LC-MS, CD, FT-IR, and 1HNMR has been done to confirm the successful synthesis and cyclization of linear PNC-28 peptides.

Keywords: CD, FTIR, 1HNMR, cyclic peptide

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Authors: Che Hsiu Chen, Kuo Wei Tseng, Zih Jian Huang, Hon Wen Cheng

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A typical warm-up contains both stretching exercises and jogging. The static stretching prior to training or competition may cause detrimental effects to athletic performance. However, it is unclear whether different types of dynamic stretching exercises had different acute effects on knee flexors stiffness, flexibility, and strength. The purpose of this study was to analyze the knee flexors stiffness, flexibility, and strength gains after dynamic straight leg raise (DSLR) and dynamic modified toe-touch (MTT) stretching. Sixteen healthy university active men (height 176.27 ± 4.03 cm; weight 72.27 ± 8.90 kg; age 22.09 ± 2.31 years). After 5 minutes (8km/h) of running subjects performed 2 randomly ordered stretching protocols: DSLR and MTT stretching protocols. There were a total of six, 30 seconds bouts of dynamic stretching (15 repetitions) with 30seconds rest between bouts. The outcome measures were maximal voluntary isokinetic concentric hamstring strength (60°/s), muscle flexibility test by passive straight leg raise (PSLR), active straight leg raise (ASLR), and muscle stiffness using ultrasound Acoustic Radiation Forced Impulse (ARFI) elastography before and immediately after stretching. The muscle stiffness and concentric strength decreased significantly (p < .05), the flexibility no significant change after DSLR protocol (p > .05). The concentric strength decreased significantly (p < .05), the flexibility and muscle stiffness no significant change after MTT protocol (p > .05), whereas no significant differences were found for the DSLR and MTT. Our findings suggest that dynamic stretching (30s x 6 bouts) resulted in change in muscle stiffness or may be induced slack in the musculotendinous unit thereby, reducing force production. Therefore, 30s x 6 bouts of dynamic stretching adversely affects efforts of hamstring muscle maximal concentric strength.

Keywords: sport injury, ultrasound, eccentric exercise, performance

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Authors: L. Pavithra, R. Sharmila, Shivani Sridhar

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Columns severe structural damage needs proportioning a significant portion of earthquake energy can be dissipated yielding in the beams. Presence of axial load along with cyclic loading has a significant influence on column. The objective of this paper is to present the analytical results of columns subjected to biaxial cyclic loading.

Keywords: RC column, Seismic behaviour, cyclic behaviour, biaxial testing, ductile behaviour

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Authors: S. A. Naeini, Z. Eftekhari

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Liquefaction phenomenon in sand is nowadays a classical soil mechanics subject. Using a cyclic triaxial test apparatus, we use non-woven geotextile reinforcement to improve the liquefaction resistance of sand. The layer configurations used are zero, one, two and three horizontal reinforcing layers in a triaxial test sample. The influences of the number of geotextile layers, and cyclic stress ratio (CSR) were studied and described. The results illustrated that the geotextile inclusion increases liquefaction resistance.

Keywords: liquefaction resistance, geotextile, sand, cyclic triaxial test, cyclic stress ratio

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Authors: Maria Melania Muda, Retno Wibawanti, Retno Asti Werdhani

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Background: Flight attendant (FA) is a job that is often exposed to ergonomic stressors; thus, they are very susceptible to symptoms of musculoskeletal disorders (MSDs). One of the ways to overcome musculoskeletal complaints is by stretching. This study aimed to examine the prevalence of MSDs and the effect of a 2-week stretching exercise program using the Indonesian Ministry of Health's stretching video on changes in musculoskeletal pain intensity in FA on commercial aircraft in Indonesia. Methods: A pre-post study was conducted using Nordic Musculoskeletal Questionnaire (NMQ) for MSDs’ identification and Visual Analog Scale (VAS) as pain intensity measurement. Data was collected and then analyzed using SPSS with Wilcoxon test. The change in pain intensity was considered significant if the p value was less than 0.05. Results: The results showed that 92% of the FA (n=75) had MSDs in at least 1 area of the body in the last 12 months. Thirty-four respondents participated as subjects. The complaint level score in 28 body areas before intervention was a median of 34 (29-84), with pain intensity of a median of 6 (2-9) became a median of 32 (28-67) and a median of 3 (0-9) after the intervention, respectively, with p-value <0.001. Conclusion: The stretching exercise program showed significant changes in the complaint level scores in 28 body areas (p < 0.001) and pain intensity before and after the stretching exercise intervention (p < 0.001).

Keywords: flight attendant, MSDs, Nordic Musculoskeletal Questionnaire, stretching exercise program, visual analog scale

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Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: E. E. S. Uy, T. Noda, K. Nakai, J. R. Dungca

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Cyclic threshold shear strain is the cyclic shear strain amplitude that serves as the indicator of the development of pore water pressure. The parameter can be obtained by performing either cyclic triaxial test, shaking table test, cyclic simple shear or resonant column. In a cyclic triaxial test, other researchers install measuring devices in close proximity of the soil to measure the parameter. In this study, an attempt was made to estimate the cyclic threshold shear strain parameter using full-field measurement technique. The technique uses a camera to monitor and measure the movement of the soil. For this study, the technique was incorporated in a strain-controlled consolidated undrained cyclic triaxial test. Calibration of the camera was first performed to ensure that the camera can properly measure the deformation under cyclic loading. Its capacity to measure deformation was also investigated using a cylindrical rubber dummy. Two-dimensional image processing was implemented. Lucas and Kanade optical flow algorithm was applied to track the movement of the soil particles. Results from the full-field measurement technique were compared with the results from the linear variable displacement transducer. A range of values was determined from the estimation. This was due to the nonhomogeneous deformation of the soil observed during the cyclic loading. The minimum values were in the order of 10-2% in some areas of the specimen.

Keywords: cyclic loading, cyclic threshold shear strain, full-field measurement, optical flow

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Sahar Mohammadyari Ghareh Bolagh, Behnaz Seyedi Aghdam, Jalal Shamlou

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This study was done to compare the effects of sports massage and stretching along the cold on pain intensity in elite female volleyball players with trigger points in shoulder girdle region. This study was conducted on 32 female volleyball players with latent trigger points in shoulder girdle region. Patients were randomly assigned to three groups: sports massage (n=11) stretching along the cold (n=11) and control group (n=10). One session treatment program during 15 minutes was performed. Pain intensity with VAS + algometer was assessed before and after intervention and improved in both of massage and cold groups. After treatment there were no significant difference between two treatment groups (P < 0. 050). Results of present research showed sports massage and stretching along the cold were effective on pain intensity of myofascial trigger points.

Keywords: sports massage، stretching along the cold، pain intensity، trigger points, elite, volleyball players, shoulder girdle region

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Authors: Ahmed Hosny Abdel-Rahman, Mohamed Abdel-Moneim

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Reinforced earth structures are generally subjected to cyclic loading generated from earthquakes. This paper presents a summary of the results and analyses of a testing program carried out in a large-scale multi-function geosynthetic testing apparatus that accommodates soil samples up to 1.0 m3. This apparatus performs different shear and pullout tests under both static and cyclic loading. The testing program was carried out to investigate the controlling factors affecting soil/geogrid interaction under cyclic loading. The extensibility of the geogrids, the applied normal stresses, the characteristics of the cyclic loading (frequency, and amplitude), and initial static load within the geogrid sheet were considered in the testing program. Based on the findings of the testing program, the effect of these parameters on the pullout resistance of geogrids, as well as the displacement mobility under cyclic loading were evaluated. Conclusions and recommendations for the design of reinforced earth walls under cyclic loading are presented.

Keywords: geogrid, soil, interface, cyclic loading, pullout, large scale testing

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Authors: M. Y. Malik, Farzana Khan

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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.

Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Y. Sunita Rani, Y. Hari Krishna, M. V. Ramana Murthy, K. Sudhaker Reddy

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This article studied effects of radiation and chemical reaction on MHD casson fluoid flow past a Permeable Stretching Sheet in a Porous Medium. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like Runge- Kutta – Fehlberg shooting technique method. The effects of various governing parameters, on the velocity, temperature and concentration are displayed through graphs and discussed numerically.

Keywords: MHD, Casson fluid, porous medium, permeable stretching sheet

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Khyati Sharma, A. Satyanarayana Reddy

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The topic of how many subgroups exist within a certain finite group naturally arises in the study of finite groups. Over the years, different researchers have investigated this issue from a variety of angles. The significant contributions of the key mathematicians over the time have been summarized in this article. To this end, we classify finite groups into three categories viz. (a) Groups for which the number of subgroups is less than |G|, (b) equals to |G|, and finally, (c) greater than |G|. Because every element of a finite group generates a cyclic subgroup, counting cyclic subgroups is the most important task in this endeavor. A brief survey on the number of cyclic subgroups of finite groups is also conducted by us. Furthermore, we also covered certain arithmetic relations between the order of a finite group |G| and the number of its distinct cyclic subgroups |C(G)|. In order to provide pertinent context and possibly reveal new novel areas of potential research within the field of research on finite groups, we finally pose and solicit a few open questions.

Keywords: abstract algebra, cyclic subgroup, finite group, subgroup

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Authors: Paolo Ragazzi, Olivier Peillon, Paul Fauris, Mathias Simon, Raul Navarro, Juan Carlos Martin, Oriol Casasayas, Laura Pacheco, Albert Perez-Bellmunt

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Introduction: The use of stretching techniques in the sports world is frequent and widely used for its many effects. One of the main benefits is the gain in flexibility, range of motion and facilitation of the sporting performance. Recently the use of Roller-Foam (RF) has spread in sports practice both at elite and recreational level for its benefits being similar to those observed in stretching. The objective of the following study is to compare the results of the Roller-Foam with the proprioceptive neuromuscular facilitation stretching (PNF) (one of the stretchings with more evidence) on the hamstring muscles. Study design: The design of the study is a single-blind, randomized controlled trial and the participants are 40 healthy volunteers. Intervention: The subjects are distributed randomly in one of the following groups; stretching (PNF) intervention group: 4 repetitions of PNF stretching (5seconds of contraction, 5 second of relaxation, 20 second stretch), Roller-Foam intervention group: 2 minutes of Roller-Foam was realized on the hamstring muscles. Main outcome measures: hamstring muscles flexibility was assessed at the beginning, during (30’’ of intervention) and the end of the session by using the Modified Sit and Reach test (MSR). Results: The baseline results data given in both groups are comparable to each other. The PNF group obtained an increase in flexibility of 3,1 cm at 30 seconds (first series) and of 5,1 cm at 2 minutes (the last of all series). The RF group obtained a 0,6 cm difference at 30 seconds and 2,4 cm after 2 minutes of application of roller foam. The results were statistically significant when comparing intragroups but not intergroups. Conclusions: Despite the fact that the use of roller foam is spreading in the sports and rehabilitation field, the results of the present study suggest that the gain of flexibility on the hamstrings is greater if PNF type stretches are used instead of RF. These results may be due to the fact that the use of roller foam intervened more in the fascial tissue, while the stretches intervene more in the myotendinous unit. Future studies are needed, increasing the sample number and diversifying the types of stretching.

Keywords: hamstring muscle, stretching, neuromuscular facilitation stretching, roller foam

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Authors: Rashid S. Mohammad, Shicheng Zhang, Sun Lu, Syed Jamal-Ud-Din, Xinzhe Zhao

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A compositional reservoir simulation model (CMG-GEM) was used for cyclic CO₂ injection process in unconventional tight reservoir. Cyclic CO₂ injection is an enhanced oil recovery process consisting of injection, shut-in, and production. The study of cyclic CO₂ injection and hydrocarbon recovery in ultra-low permeability reservoirs is mainly a function of rock, fluid, and operational parameters. CMG-GEM was used to study several design parameters of cyclic CO₂ injection process to distinguish the parameters with maximum effect on the oil recovery and to comprehend the behavior of cyclic CO₂ injection in tight reservoir. On the other hand, permeability reduction induced by asphaltene precipitation is one of the major issues in the oil industry due to its plugging onto the porous media which reduces the oil productivity. In addition to asphaltene deposition, solubility of CO₂ in the aquifer is one of the safest and permanent trapping techniques when considering CO₂ storage mechanisms in geological formations. However, the effects of the above uncertain parameters on the process of CO₂ enhanced oil recovery have not been understood systematically. Hence, it is absolutely necessary to study the most significant parameters which dominate the process. The main objective of this study is to improve techniques for designing cyclic CO₂ injection process while considering the effects of asphaltene deposition and solubility of CO₂ in the brine in order to prevent asphaltene precipitation, minimize CO₂ emission, optimize cyclic CO₂ injection, and maximize oil production.

Keywords: tight reservoirs, cyclic O₂ injection, asphaltene, solubility, reservoir simulation

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

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The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: curved stretching sheet, finite difference method, MHD, variable thermal conductivity

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Authors: Raj Nandkeolyar, Precious Sibanda

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The flow of a viscous, incompressible, and electrically conducting fluid under the influence of aligned magnetic field acting along the direction of fluid flow over an exponentially stretching sheet is investigated numerically. The nonlinear partial differential equations governing the flow model is transformed to a set of nonlinear ordinary differential equations using suitable similarity transformation and the solution is obtained using a local linearization method followed by the Chebyshev spectral collocation method. The effects of various parameters affecting the flow and heat transfer as well as the induced magnetic field are discussed using suitable graphs and tables.

Keywords: aligned magnetic field, exponentially stretching sheet, induced magnetic field, magnetohydrodynamic flow

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