Search results for: Banach fixed point theorem

Authors: Yanling Zhu

Abstract:

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: F. Fissou Amigue, S. Ndjakomo Essiane, S. Pérabi Ngoffé, G. Abessolo Ondoa, G. Mengata Mengounou, T. P. Nna Nna

Abstract:

This document proposes a method for determining the optimal point of integration of distributed generation (DG) in distribution grid. Slime mould optimization is applied to determine best node in case of one and two injection point. Problem has been modeled as an optimization problem where the objective is to minimize joule loses and main constraint is to regulate voltage in each point. The proposed method has been implemented in MATLAB and applied in IEEE network 33 and 69 nodes. Comparing results obtained with other algorithms showed that slime mould optimization algorithms (SMOA) have the best reduction of power losses and good amelioration of voltage profile.

Keywords: Optimization, distributed generation, integration, slime mould algorithm.

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Authors: Changjin Xu

Abstract:

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Henrik L. Funke, Lars Ulke-Winter, Sandra Gelbrich, Lothar Kroll

Abstract:

This work reports about an approach for an automatic adaptation of concrete formulations based on genetic algorithms (GA) to optimize a wide range of different fit-functions. In order to achieve the goal, a method was developed which provides a numerical description of a fibre reinforced concrete (FRC) mixture regarding the production technology and the property spectrum of the concrete. In a first step, the FRC mixture with seven fixed components was characterized by varying amounts of the components. For that purpose, ten concrete mixtures were prepared and tested. The testing procedure comprised flow spread, compressive and bending tensile strength. The analysis and approximation of the determined data was carried out by GAs. The aim was to obtain a closed mathematical expression which best describes the given seven-point cloud of FRC by applying a Gene Expression Programming with Free Coefficients (GEP-FC) strategy. The seven-parametric FRC-mixtures model which is generated according to this method correlated well with the measured data. The developed procedure can be used for concrete mixtures finding closed mathematical expressions, which are based on the measured data.

Keywords: Concrete design, fibre reinforced concrete, genetic algorithms, GEP-FC.

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Authors: Asma Meziti, Hicham Meziti, Kaouthar Boudiaf, Benboubetra Mustapha, Hemama Bouriche.

Abstract:

Nigella sativa L. is an aromatic plant belonging to the family Ranunculaceae. It has been used traditionally, especially in the middle East and India, for the treatment of asthma, cough, bronchitis, headache, rheumatism, fever, influenza and eczema. Several biological activities have been reported in Nigella sativa seeds, including antioxidant. In this context we tried to estimate the antioxidant activity of various extracts prepared from Nigella sativa seeds, methanolic extract (ME), chloroformic extract (CE), hexanic extract (HE : fixed oil), ethyl acetate extract (EAE) water extract (WE). The Folin-Ciocalteu assay showed that CE and EAE contained high level of phenolic compounds 81.31 and 72.43μg GAE/mg of extract respectively. Similarly, the CE and EAE exhibited the highest DPPH radical scavenging activity, with IC50 values of 106.56μg/ml and 121.62μg/ml respectively. In addition, CE and HE showed the most scavenging activity against superoxide radical generated in the PMS-NADH-NBT system with respective IC50 values of 361.86 μg/ml and 371.80 μg/ml, which is comparable to the activity of the standard antioxidant BHT (344.59 μg/ml). Ferrous ion chelating capacity assay showed that WE, EAE and ME are the most active with 40.57, 39.70 and 22.02 mg EDTA-E/g of extract. The inhibition of linoleic acid/ß-carotene coupled oxidation was estimated by ßcarotene bleaching assay, this showed a highest relative antioxidant activity with CE and EAE (69.82% of inhibition). The antioxidant activities of the methanolic extract and the fixed oil are confirmed by an in vivo assay in mice, the daily oral administration of methanolic extract (500 and 800 mg/kg/day) and fixed oil (2 and 4 ml/kg/day) during 21 days, resulted in a significant enhancement of the blood total antioxidant capacity (measured by KRL test) and the plasmatic antioxidant capacity towards DPPH radical.

Keywords: Antioxidant Capacity, Chelating, Phenolic Compounds, Nigella Sativa, Scavenger

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Authors: Zhouhong Li

Abstract:

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

Keywords: Almost periodic solution, Multi-delay, Logarithmic population model, Coincidence degree.

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Authors: A. Sabzali, M. Nikaeen, B. Bina

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The purpose of the experiments described in this article was the comparison of integrated fixed film activated sludge (IFAS) and activated sludge (AS) system. The IFAS applied system consists of the cigarette filter rods (wasted filter in tobacco factories) as a biofilm carrier. The comparison with activated sludge was performed by two parallel treatment lines. Organic substance, ammonia and TP removal was investigated over four month period. Synthetic wastewater was prepared with ordinary tap water and glucose as the main sources of carbon and energy, plus balanced macro and micro nutrients. COD removal percentages of 94.55%, and 81.62% were achieved for IFAS and activated sludge system, respectively. Also, ammonia concentration significantly decreased by increasing the HRT in both systems. The average ammonia removal of 97.40 % and 96.34% were achieved for IFAS and activated sludge system, respectively. The removal efficiency of total phosphorus (TP-P) was 60.64%, higher than AS process by 56.63% respectively.

Keywords: Wastewater, biofilm carrier, cigarette filters rods, Activated Sludge, IFAS, nitrification.

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Authors: Bhupendra C. S. Chauhan, P. S. Bisht, O. P. S. Negi

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According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient, divergence and curl in seven dimension. It is shown that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We have tried to write all the vector inequalities and formulas in terms of seven dimensions and it is shown that same formulas loose their meaning in seven dimensions due to non-associativity of octonions. The vector formulas are retained only if we put certain restrictions on octonions and split octonions.

Keywords: Octonions, Vector Space and seven dimensions

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Authors: Massoud Masoumi, Hosseyn Mahdizadeh

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A new and highly efficient architecture for elliptic curve scalar point multiplication which is optimized for a binary field recommended by NIST and is well-suited for elliptic curve cryptographic (ECC) applications is presented. To achieve the maximum architectural and timing improvements we have reorganized and reordered the critical path of the Lopez-Dahab scalar point multiplication architecture such that logic structures are implemented in parallel and operations in the critical path are diverted to noncritical paths. With G=41, the proposed design is capable of performing a field multiplication over the extension field with degree 163 in 11.92 s with the maximum achievable frequency of 251 MHz on Xilinx Virtex-4 (XC4VLX200) while 22% of the chip area is occupied, where G is the digit size of the underlying digit-serial finite field multiplier.

Keywords: Elliptic curve cryptography, FPGA implementation, scalar point multiplication.

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Authors: Li Jiang, Baoguang Tian

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In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: Kai Wang, Yanling Zu

Abstract:

By utilizing the comparison theorem and Lyapunov second method, some sufficient conditions for the permanence and global attractivity of positive periodic solution for a predator-prey model with mutual interference m ∈ (0, 1) and delays τi are obtained. It is the first time that such a model is considered with delays. The significant is that the results presented are related to the delays and the mutual interference constant m. Several examples are illustrated to verify the feasibility of the results by simulation in the last part.

Keywords: Predator-prey model, Mutual interference, Delays, Permanence, Global attractivity

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Authors: Hadi Zarafshani, Shidvash Vakilipour, Shahin Teimori, Sara Barati

Abstract:

In the present study, the aerodynamic performance of a rigid two-dimensional pitching bio-inspired corrugate airfoil was numerically investigated at Reynolds number of 14000. The Open Field Operations And Manipulations (OpenFOAM) computational fluid dynamic tool is used to solve flow governing equations numerically. The k-ω SST turbulence model with low Reynolds correction (k-ω SST LRC) and the pimpleDyMFOAM solver are utilized to simulate the flow field around pitching bio-airfoil. The lift and drag coefficients of the airfoil are calculated at reduced frequencies k=1.24-4.96 and the angular amplitude of A=5^°-20^°. Results show that in a fixed reduced frequency, the absolute value of the sectional lift and drag coefficients increase with increasing pitching amplitude. In a fixed angular amplitude, the absolute value of the lift and drag coefficients increase as the pitching reduced frequency increases.

Keywords: Bio-inspired pitching airfoils, OpenFOAM, low Reynolds k-ω SST model, lift and drag coefficients.

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Authors: Yongkun Li, Kaihong Zhao

Abstract:

By using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results.

Keywords: Positive periodic solutions, Lotka-Volterra competition system, coincidence degree, harvesting term.

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Authors: Vishal Awasthi, Atul Kumar Agnihotri

Abstract:

Face is a non-intrusive strong biometrics for identification of original and dummy facial by different artificial means. Face recognition is extremely important in the contexts of computer vision, psychology, surveillance, pattern recognition, neural network, content based video processing. The availability of a widespread face database is crucial to test the performance of these face recognition algorithms. The openly available face databases include face images with a wide range of poses, illumination, gestures and face occlusions but there is no dummy face database accessible in public domain. This paper presents a face detection algorithm based on the image segmentation in terms of distance from a fixed point and template matching methods. This proposed work is having the most appropriate number of nodal points resulting in most appropriate outcomes in terms of face recognition and detection. The time taken to identify and extract distinctive facial features is improved in the range of 90 to 110 sec. with the increment of efficiency by 3%.

Keywords: Face recognition, Principal Component Analysis, PCA, Linear Discriminant Analysis, LDA, Improved Support Vector Machine, iSVM, elastic bunch mapping technique.

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Authors: M. Tajdari, A. R. Nezamabadi, M. Naeemi, P. Pirali

Abstract:

Mechanical buckling analysis of rectangular plates with central circular cutout is performed in this paper. The finiteelement method is used to study the effects of plate-support conditions, aspect ratio, and hole size on the mechanical buckling strength of the perforated plates subjected to linearly varying loading. Results show that increasing the hole size does not necessarily reduce the mechanical buckling strength of the perforated plates. It is also concluded that the clamped boundary condition increases the mechanical buckling strength of the perforated plates more than the simply-supported boundary condition and the free boundary conditions enhance the mechanical buckling strength of the perforated plates more effectively than the fixed boundary conditions. Furthermore, for the bending cases, the critical buckling load of perforated plates with free edges is less than perforated plates with fixed edges.

Keywords: Buckling, Perforated plates, Boundary condition, Rectangular plates

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Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we deal with the optimal I/O point location in an automated parking system. In this system, the S/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I/O point is located at the middle of the left-hand above corner.

Keywords: Parking system, optimal location, response time, S/R machine.

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Authors: Aichun Feng, Zhi-Min Chen, Jing Tang Xing

Abstract:

A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.

Keywords: Source point distribution, panel method, Rankine source, desingularized algorithm.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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Authors: U. C. Amadi, N. A. Udoh

Abstract:

One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.

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Authors: Mohsen Nikaein

Abstract:

Because of importance of energy, optimization of power generation systems is necessary. Gas turbine cycles are suitable manner for fast power generation, but their efficiency is partly low. In order to achieving higher efficiencies, some propositions are preferred such as recovery of heat from exhaust gases in a regenerator, utilization of intercooler in a multistage compressor, steam injection to combustion chamber and etc. However thermodynamic optimization of gas turbine cycle, even with above components, is necessary. In this article multi-objective genetic algorithms are employed for Pareto approach optimization of Regenerative-Intercooling-Gas Turbine (RIGT) cycle. In the multiobjective optimization a number of conflicting objective functions are to be optimized simultaneously. The important objective functions that have been considered for optimization are entropy generation of RIGT cycle (Ns) derives using Exergy Analysis and Gouy-Stodola theorem, thermal efficiency and the net output power of RIGT Cycle. These objectives are usually conflicting with each other. The design variables consist of thermodynamic parameters such as compressor pressure ratio (Rp), excess air in combustion (EA), turbine inlet temperature (TIT) and inlet air temperature (T0). At the first stage single objective optimization has been investigated and the method of Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used for multi-objective optimization. Optimization procedures are performed for two and three objective functions and the results are compared for RIGT Cycle. In order to investigate the optimal thermodynamic behavior of two objectives, different set, each including two objectives of output parameters, are considered individually. For each set Pareto front are depicted. The sets of selected decision variables based on this Pareto front, will cause the best possible combination of corresponding objective functions. There is no superiority for the points on the Pareto front figure, but they are superior to any other point. In the case of three objective optimization the results are given in tables.

Keywords: Exergy, Entropy Generation, Brayton Cycle, DesignParameters, Optimization, Genetic Algorithm, Multi-Objective.

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Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

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This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: Power system, Transient stability, Critical trajectory method, Energy function method.

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Authors: Zhaohui Wen

Abstract:

In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin-s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Periodic solutions, food chain model, coincidence degree, time scales.

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Authors: Mojahid F. Saeed Osman

Abstract:

Repairable items inventory system is a management tool used to incorporate all information concerning inventory levels and movements for repaired and new items. This paper presents development of an effective simulation model for managing the inventory of repairable items for a production system where production lines send their faulty items to a repair shop considering the stochastic failure behavior and repair times. The developed model imitates the process of handling the on-hand inventory of repaired items and the replenishment of the inventory of new items using Economic Order Quantity and Reorder Point ordering policy in a flexible and risk-free environment. We demonstrate the appropriateness and effectiveness of the proposed simulation model using an illustrative case problem. The developed simulation model can be used as a reliable tool for estimating a healthy on-hand inventory of new and repaired items, backordered items, and downtime due to unavailability of repaired items, and validating and examining Economic Order Quantity and Reorder Point ordering policy, which would further be compared with other ordering strategies as future work.

Keywords: Inventory system, repairable items, simulation, maintenance, economic order quantity, reorder point.

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Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems

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Authors: Khairul Nizam Tahar, Anuar Ahmad

Abstract:

This paper has introduced a slope photogrammetric mapping using unmanned aerial vehicle. There are two units of UAV has been used in this study; namely; fixed wing and multi-rotor. Both UAVs were used to capture images at the study area. A consumer digital camera was mounted vertically at the bottom of UAV and captured the images at an altitude. The objectives of this study are to obtain three dimensional coordinates of slope area and to determine the accuracy of photogrammetric product produced from both UAVs. Several control points and checkpoints were established Real Time Kinematic Global Positioning System (RTK-GPS) in the study area. All acquired images from both UAVs went through all photogrammetric processes such as interior orientation, exterior orientation, aerial triangulation and bundle adjustment using photogrammetric software. Two primary results were produced in this study; namely; digital elevation model and digital orthophoto. Based on results, UAV system can be used to mapping slope area especially for limited budget and time constraints project.

Keywords: Slope mapping, 3D, DEM, UAV, Photogrammetry, image processing.

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Authors: K. D. Ro, J. T. Park, J. H. Kim

Abstract:

This experiment was conducted in attempt of improving hydrodynamic efficiency of the propulsion mechanism by installing a spring to the wing so that the opening angle of the wing in one stroke can be changed automatically, compared to the existing method of fixed maximum opening angle in Weis-Fogh type ship propulsion mechanism. Average thrust coefficient was almost fixed with all velocity ratio with the prototype, but with the spring type, thrust coefficient increased sharply as velocity ratio increased. Average propulsive efficiency was larger with bigger opening angle in the prototype, but in the spring type, the one with smaller spring coefficient had larger value. In the range over 1.0 in velocity ratio where big thrust can be generated, spring type had more than twice of propulsive efficiency increase compared to the prototype.

Keywords: Hydraulic Machine, Propulsion Mechanism, FluidForce, Elastic Wing.

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Authors: Adilah Shariff, Radin Hakim, Nurhayati Abdullah

Abstract:

Utilisation of biomass feedstock for biochar has received increasing attention because of their potential for carbon sequestration and soil amendment. The aim of this study is to investigate the characteristics of rubber wood as a biomass feedstock for biochar via slow pyrolysis process. This was achieved by using proximate, ultimate, and thermogravimetric analysis (TGA) as well as heating value, pH and lignocellulosic determination. Rubber wood contains 4.13 mf wt.% moisture, 86.30 mf wt.% volatile matter, 0.60 mf wt.% ash content, and 13.10 mf wt.% fixed carbon. The ultimate analysis shows that rubber wood consists of 44.33 mf wt.% carbon, 6.26 mf wt.% hydrogen, 19.31 mf wt.% nitrogen, 0.31 mf wt.% sulphur, and 29.79 mf wt.% oxygen. The higher heating value of rubber wood is 22.5 MJ/kg, and its lower heating value is 21.2 MJ/kg. At 27 °C, the pH value of rubber wood is 6.83 which is acidic. The lignocellulosic analysis revealed that rubber wood composition consists of 2.63 mf wt.% lignin, 20.13 mf wt.% cellulose, and 65.04 mf wt.% hemicellulose. The volatile matter to fixed carbon ratio is 6.58. This led to a biochar yield of 25.14 wt.% at 500 °C. Rubber wood is an environmental friendly feedstock due to its low sulphur content. Rubber wood therefore is a suitable and a potential feedstock for biochar production via slow pyrolysis.

Keywords: Biochar, biomass, rubber wood, slow pyrolysis.

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Authors: G. Vici, L. Cesanelli, L. Belli, R. Ceci, V. Polzonetti

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Several factors contribute to success in sport and diet is one of them. Evidence-based sport nutrition guidelines underline the importance of macro- and micro-nutrients’ balance and timing in order to improve athlete’s physical status and performance. Nevertheless, a high content of proteins is commonly found in resistance training athletes’ diet with carbohydrate intake that is not enough or not well planned. The aim of the study was to evaluate the impact of different protein and carbohydrate diet contents on body composition and sport performance on a group of resistance training athletes. Subjects were divided as study group (n=16) and control group (n=14). For a period of 4 months, both groups were subjected to the same resistance training fitness program with study group following a specific diet and control group following an ab libitum diet. Body compositions were evaluated trough anthropometric measurement (weight, height, body circumferences and skinfolds) and Bioimpedence Analysis. Physical strength and training status of individuals were evaluated through the One Repetition Maximum test (RM1). Protein intake in studied group was found to be lower than in control group. There was a statistically significant increase of body weight, free fat mass and body mass cell of studied group respect to the control group. Fat mass remains almost constant. Statistically significant changes were observed in quadriceps and biceps circumferences, with an increase in studied group. The MR1 test showed improvement in study group’s strength but no changes in control group. Usually people consume hyper-proteic diet to achieve muscle mass development. Through this study, it was possible to show that protein intake fixed at 1,7 g/kg/d can meet the individual's needs. In parallel, the increased intake of carbohydrates, focusing on quality and timing of assumption, has enabled the obtainment of desired results with a training protocol supporting a hypertrophic strategy. Therefore, the key point seems related to the planning of a structured program both from a nutritional and training point of view.

Keywords: Body composition, diet, exercise, protein.

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Authors: Da-Xue Chen, Guang-Hui Liu

Abstract:

In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples.

Keywords: Oscillation theorem, second-order nonlinear neutral dynamic equation, variable delay, damping, Riccati transformation.

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Authors: M. R. Dolatian, A. Jalilian

Abstract:

The behavior of three phase five leg transformer under voltage sag is studied in this paper. This paper proposes a simple, practical model of a three phase-five leg, saturated transformer with accurate performance. Transformer saturation is produced when the voltage sag is recovered and it causes inrush current in transformer. Effects of voltage sag depth, duration and initial point on wave have been analyzed in this paper. Initial point on wave can produce maximum inrush current in five leg transformers while comparing with three leg transformers. The magnetic circuit symmetry of five leg transformer produces the more symmetrical shape of inrush current curves versus initial point on wave and sag duration than three leg transformer. The simulations show that current peak has a periodical dependence on sag duration and linear dependence on sag depth. Inrush current that is produced in three phase five leg transformer is higher than three phase three leg transformer.

Keywords: Inrush current, three phase five leg transformer, saturation, voltage sag.

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