Search results for: solid solutions

Authors: Zhouhong Li, Jiming Yang

Abstract:

In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.

Keywords: Positive periodic solutions, Predator-prey-chain model, coincidence degree, harvesting term.

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Authors: Sh. Gofurov, O. Ismailova, U. Makhmanov, A. Kokhkharov

Abstract:

The refractometric method has been used to determine optical properties of concentration features of aqueous solutions of ethanol, tetrahydrofuran and dimethylformamide at the room temperature. Changes in dielectric permittivity of aqueous solutions of ethanol, tetrahydrofuran and dimethylformamide in a wide range of concentrations (0÷1.0 molar fraction) have been studied using molecular dynamics method. The curves depending on the concentration of experimental data on excess refractive indices and excess dielectric permittivity were compared. It has been shown that stable heteromolecular complexes in binary solutions are formed in the concentration range of 0.3÷0.4 mole fractions. The real and complex part of dielectric permittivity was obtained from dipole-dipole autocorrelation functions of molecules. At the concentrations of C = 0.3 / 0.4 m.f. the heteromolecular structures with hydrogen bonds are formed. This is confirmed by the extremum values of excessive dielectric permittivity and excessive refractive index of aqueous solutions.

Keywords: Refractometric method, dielectric constant, molecular dynamics, aqueous solution.

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Authors: Fengshuo Zhang, Zhouhong Li

Abstract:

In this paper, we obtain sufficient conditions for the existence of at least four positive almost periodic solutions to an impulsive delayed periodic plankton allelopathy system with multiple exploited (or harvesting) terms. This result is obtained through the use of Mawhins continuation theorem of coincidence degree theory along with some properties relating to inequalities.

Keywords: Almost periodic solutions, plankton allelopathy system, coincidence degree, impulse.

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Authors: Nadia Belu, Laurentiu M. Ionescu, Agnieszka Misztal

Abstract:

In this paper we propose a computer-aided solution with Genetic Algorithms in order to reduce the drafting of reports: FMEA analysis and Control Plan required in the manufacture of the product launch and improved knowledge development teams for future projects. The solution allows to the design team to introduce data entry required to FMEA. The actual analysis is performed using Genetic Algorithms to find optimum between RPN risk factor and cost of production. A feature of Genetic Algorithms is that they are used as a means of finding solutions for multi criteria optimization problems. In our case, along with three specific FMEA risk factors is considered and reduce production cost. Analysis tool will generate final reports for all FMEA processes. The data obtained in FMEA reports are automatically integrated with other entered parameters in Control Plan. Implementation of the solution is in the form of an application running in an intranet on two servers: one containing analysis and plan generation engine and the other containing the database where the initial parameters and results are stored. The results can then be used as starting solutions in the synthesis of other projects. The solution was applied to welding processes, laser cutting and bending to manufacture chassis for buses. Advantages of the solution are efficient elaboration of documents in the current project by automatically generating reports FMEA and Control Plan using multiple criteria optimization of production and build a solid knowledge base for future projects. The solution which we propose is a cheap alternative to other solutions on the market using Open Source tools in implementation.

Keywords: Automotive industry, control plan, FMEA.

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Authors: A. S. Kipcak, N. Baran Acarali, E. Moroydor Derun, N. Tugrul, S. Piskin

Abstract:

Zinc borates can be used as multi-functional synergistic additives with flame retardant additives in polymers. Zinc borate is white, non-hygroscopic and powder type product. The most important properties are low solubility in water and high dehydration temperature. Zinc borates dehydrate above 290°C and anhydrous zinc borate has thermal resistance about 400°C. Zinc borates can be synthesized using several methods such as hydrothermal and solidstate processes. In this study, the solid-state method was applied at low temperatures of 600oC and 700oC using the starting materials of ZnO and H3BO3 with several mole ratios. The reaction time was determined as 4 hours after some preliminary experiments. After the synthesis, the crystal structure and the morphology of the products were examined by X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). As a result the forms of ZnB4O7, Zn3(BO3)2, ZnB2O4 were synthesized and obtained along with the unreacted ZnO.

Keywords: FT-IR, solid-state method, zinc borate, XRD.

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Authors: M. J. Shivaram, Shashi Bhushan Arya, Jagannath Nayak, Bharat Bhooshan Panigrahi

Abstract:

Titanium and its alloys have become more significant implant materials due to their mechanical properties, excellent biocompatibility and high corrosion resistance. Biomaterials can be produce by using the powder metallurgy (PM) methods and required properties can tailored by varying the processing parameters, such as ball milling time, space holder particles, and sintering temperature. The desired properties such as, structural and mechanical properties can be obtained by powder metallurgy method.  In the present study, deals with fabrication of solid and porous Ti-20Nb-5Ag alloy using high energy ball milling for different times (5 and 20 h). The resultant powder particles were used to fabricate solid and porous Ti-20Nb-5Ag alloy by adding space holder particles (NH₄HCO₃). The resultant powder particles, fabricated solid and porous samples were characterized by scanning electron microscopy (SEM). The compressive strength, elastic modulus and microhardness properties were investigated. Solid and porous Ti-20Nb-5Ag alloy samples showed good mechanical properties for 20 h ball milling time as compare to 5 h ball milling.

Keywords: Ball Milling, compressive strengths, microstructure, porous Titanium alloy.

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Authors: André Trudel, Haiyi Zhang

Abstract:

Over the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitrary IA networks. We then show how the implementation can be extended to find all the solutions to an IA network. One application of finding all the solutions, is solving probabilistic IA networks.

Keywords: Constraint logic programming, CSP, logic, temporalreasoning.

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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: Oriyomi M. Okeyinka, David A. Oloke, Jamal M. Khatib

Abstract:

Large quantities of solid wastes being generated worldwide from sources such as household, domestic, industrial, commercial and construction demolition activities, leads to environmental concerns. Utilization of these wastes in making building construction materials can reduce the magnitude of the associated problems. When these waste products are used in place of other conventional materials, natural resources and energy are preserved and expensive and/or potentially harmful waste disposal is avoided. Recycling which is regarded as the third most preferred waste disposal option, with its numerous environmental benefits, stand as a viable option to offset the environmental impact associated with the construction industry. This paper reviews the results of laboratory tests and important research findings, and the potential of using these wastes in building construction materials with focus on sustainable development. Research gaps, which includes; the need to develop standard mix design for solid waste based building materials; the need to develop energy efficient method of processing solid waste use in concrete; the need to study the actual behavior or performance of such building materials in practical application and the limited real life application of such building materials have also been identified. A research is being proposed to develop an environmentally friendly, lightweight building block from recycled waste paper, without the use of cement, and with properties suitable for use as walling unit. This proposed research intends to incorporate, laboratory experimentation and modeling to address the identified research gaps.

Keywords: Recycling, solid waste, construction, building materials.

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Authors: José Maria A. Pangilinan, Gerrit K. Janssens

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This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution. The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions. Results show that the evolutionary algorithm can find diverse solutions to the MSPP in polynomial time (based on several network instances) and can be an alternative when other methods are trapped by the tractability problem.

Keywords: Multiobjective evolutionary optimization, geneticalgorithms, shortest paths.

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Authors: Arash Esmaeili, Zhibang Liu, Yang Xiang, Jimmy Yun, Lei Shao

Abstract:

A high pressure carbon dioxide (CO₂) absorption from a specific gas in a conventional column has been evaluated by the Aspen HYSYS simulator using a wide range of single absorbents and blended solutions to estimate the outlet CO₂ concentration, absorption efficiency and CO₂ loading to choose the most proper solution in terms of CO₂ capture for environmental concerns. The property package (Acid Gas-Chemical Solvent) which is compatible with all applied solutions for the simulation in this study, estimates the properties based on an electrolyte non-random two-liquid (E-NRTL) model for electrolyte thermodynamics and Peng-Robinson equation of state for the vapor and liquid hydrocarbon phases. Among all the investigated single amines as well as blended solutions, piperazine (PZ) and the mixture of piperazine and monoethanolamine (MEA) have been found as the most effective absorbents respectively for CO₂ absorption with high reactivity based on the simulated operational conditions.

Keywords: Absorption, amine solutions, Aspen HYSYS, carbon dioxide, simulation.

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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: Wajeeha A. Qazi, Mohammed-Hasham Azam, Umais A. Mehmood, Ghithaa A. Al-Mufragi, Noor-Alhuda Alrawahi, Mohammed F. M. Abushammala

Abstract:

Municipal Solid Waste (MSW) disposed in landfill sites decompose under anaerobic conditions and produce gases which mainly contain carbon dioxide (CO₂) and methane (CH₄). Methane has the potential of causing global warming 25 times more than CO₂, and can potentially affect human life and environment. Thus, this research aims to determine MSW generation and the annual CH₄ emissions from the generated waste in Oman over the years 1971-2030. The estimation of total waste generation was performed using existing models, while the CH₄ emissions estimation was performed using the intergovernmental panel on climate change (IPCC) default method. It is found that total MSW generation in Oman might be reached 3,089 Gg in the year 2030, which approximately produced 85 Gg of CH₄ emissions in the year 2030.

Keywords: Methane, emissions, landfills, solid waste.

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Authors: Marcus C. Garcia, Giselle C. Guimarães, Luciana H. Yamane, Renato R. Siman

Abstract:

The environmental indicators and the classification of beach waste are essential tools to diagnose the current situation and to indicate ways to improve the quality of this environment. The purpose of this paper was to perform a quali-quantitative analysis of the beach waste on the Curva da Jurema Beach (Espírito Santo - Brazil). Three transects were used with equidistant positioning over the total length of the beach for the solid waste collection. Solid wastes were later classified according to their use and primary raw material from the low and high summer season. During the low season, average values of 7.10 items.m^-1, 18.22 g.m^-1 and 0.91 g.m^-2 were found for the whole beach, and transect 3 contributed the most waste, with the total sum of items equal to 999 (49%), a total mass of 5.62 kg and a total volume of 21.31 L. During the high summer season, average values of 8.22 items.m^-1, 54.40 g.m^-1 and 2.72 g.m^-2 were found, with transect 2 contributing the most to the total sum with 1,212 items (53%), a total mass of 10.76 kg and a total volume of 51.99 L. Of the total collected, plastic materials represented 51.4% of the total number of items, 35.9% of the total mass and 68% of the total volume. The implementation of reactive and proactive measures is necessary so that the management of the solid wastes on Curva da Jurema Beach is in accordance with principles of sustainability.

Keywords: Beach solid waste, environmental indicators, quali-quantitative analysis, waste management.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

Abstract:

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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Authors: Rong Liu, Kuiying Chen, Ju Chen, Jingrong Zhao, Ming Liang

Abstract:

This article presents modeling studies of NiAl alloy under solid-particle erosion and liquid-drop erosion. In the solid-particle erosion simulation, attention is paid to the oxide scale thickness variation on the alloy in high-temperature erosion environments. The erosion damage is assumed to be deformation wear and cutting wear mechanisms, incorporating the influence of the oxide scale on the eroded surface; thus the instantaneous oxide thickness is the result of synergetic effect of erosion and oxidation. For liquid-drop erosion, special interest is in investigating the effects of drop velocity and drop size on the damage of the target surface. The models of impact stress wave, mean depth of penetration, and maximum depth of erosion rate (Max DER) are employed to develop various maps for NiAl alloy, including target thickness vs. drop size (diameter), rate of mean depth of penetration (MDRP) vs. drop impact velocity, and damage threshold velocity (DTV) vs. drop size.

Keywords: Liquid-drop erosion, NiAl alloy, oxide scale thickness, solid-particle erosion.

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Authors: Abbas Ali Mahmood Karwi

Abstract:

For gamma radiation detection, assemblies having scintillation crystals and a photomultiplier tube, also there is a preamplifier connected to the detector because the signals from photomultiplier tube are of small amplitude. After pre-amplification the signals are sent to the amplifier and then to the multichannel analyser. The multichannel analyser sorts all incoming electrical signals according to their amplitudes and sorts the detected photons in channels covering small energy intervals. The energy range of each channel depends on the gain settings of the multichannel analyser and the high voltage across the photomultiplier tube. The exit spectrum data of the two main isotopes studied ,putting data in biomass program ,process it by Matlab program to get the solid holdup image (solid spherical nuclear fuel)

Keywords: Multichannel analyzer, Spectrum, Energies, Fluids holdup, Image

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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: J. Tospornsampan, I. Kita, M. Ishii, Y. Kitamura

Abstract:

In this paper a combination approach of two heuristic-based algorithms: genetic algorithm and tabu search is proposed. It has been developed to obtain the least cost based on the split-pipe design of looped water distribution network. The proposed combination algorithm has been applied to solve the three well-known water distribution networks taken from the literature. The development of the combination of these two heuristic-based algorithms for optimization is aimed at enhancing their strengths and compensating their weaknesses. Tabu search is rather systematic and deterministic that uses adaptive memory in search process, while genetic algorithm is probabilistic and stochastic optimization technique in which the solution space is explored by generating candidate solutions. Split-pipe design may not be realistic in practice but in optimization purpose, optimal solutions are always achieved with split-pipe design. The solutions obtained in this study have proved that the least cost solutions obtained from the split-pipe design are always better than those obtained from the single pipe design. The results obtained from the combination approach show its ability and effectiveness to solve combinatorial optimization problems. The solutions obtained are very satisfactory and high quality in which the solutions of two networks are found to be the lowest-cost solutions yet presented in the literature. The concept of combination approach proposed in this study is expected to contribute some useful benefits in diverse problems.

Keywords: GAs, Heuristics, Looped network, Least-cost design, Pipe network, Optimization, TS

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Authors: Muhammad Naveed, Richard Stechow, Sebastian Bolz, Katharina Hobusch, Sabine Weiß

Abstract:

Solid particle erosion has been identified as a critical wear phenomenon which takes place during operation of aeroengines in dusty environment. The present work discusses the erosion behavior of Ti-44.5Al-6.25Nb-0.8Mo-0.1B alloy (TNB-V4) which finds its application in low pressure gas turbines and can be used for high pressure compressors too. Prior to the erosion tests, the alloy was heat treated to improve the mechanical properties. Afterwards, specimens were eroded at impact angles of 30° and 90° at room and high temperatures (100 °C-400 °C). Volume loss and erosion behavior are studied through gravimetric analysis, whereas erosion mechanisms are characterized through scanning electron microscopy. The results indicate a clear difference in the erosion mechanism for different impact angles. The influence of the test temperature on the erosion behavior of the alloy is also discussed in the present contribution.

Keywords: Solid particle erosion, gamma TiAl, TNB-V4, high temperature erosion.

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Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai

Abstract:

In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.

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Authors: Kouassi Dongo, Christian Zurbrügg, Gueladio Cissé1, Brigit Obrist, Marcel Tanner, Jean Biémi

Abstract:

This study analyzed environmental health risks and people-s perceptions of risks related to waste management in poor settlements of Abidjan, to develop integrated solutions for health and well-being improvement. The trans-disciplinary approach used relied on remote sensing, a geographic information system (GIS), qualitative and quantitative methods such as interviews and a household survey (n=1800). Mitigating strategies were then developed using an integrated participatory stakeholder workshop. Waste management deficiencies resulting in lack of drainage and uncontrolled solid and liquid waste disposal in the poor settlements lead to severe environmental health risks. Health problems were caused by direct handling of waste, as well as through broader exposure of the population. People in poor settlements had little awareness of health risks related to waste management in their community and a general lack of knowledge pertaining to sanitation systems. This unfortunate combination was the key determinant affecting the health and vulnerability. For example, an increased prevalence of malaria (47.1%) and diarrhoea (19.2%) was observed in the rainy season when compared to the dry season (32.3% and 14.3%). Concerted and adapted solutions that suited all the stakeholders concerned were developed in a participatory workshop to allow for improvement of health and well-being.

Keywords: Abidjan, environmental health risks, informalsettlements, vulnerability, waste management.

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Authors: Vignesh Rangaraj, Jerin John, N. Naveen, M. Karuppasamy Pandian, P. Sathyan, V. R. Sanal Kumar

Abstract:

In this paper parametric analytical studies have been carried out to examine the intrinsic flow physics pertaining to the liftoff time of solid propellant rockets. Idealized inert simulators of solid rockets are selected for numerical studies to examining the preignition chamber dynamics. Detailed diagnostic investigations have been carried out using an unsteady two-dimensional k-omega turbulence model. We conjectured from the numerical results that the altered variations of the igniter jet impingement angle, turbulence level, time and location of the first ignition, flame spread characteristics, the overall chamber dynamics including the boundary layer growth history are having bearing on the time for nozzle flow chocking for establishing the required thrust for the rocket liftoff. We concluded that the altered flow choking time of strap-on motors with the pre-determined identical ignition time at the lift off phase will lead to the malfunctioning of the rocket. We also concluded that, in the light of the space debris, an error in predicting the liftoff time can lead to an unfavorable launch window amounts the satellite injection errors and/or the mission failures.

Keywords: Liftoff, Nozzle Choking, Solid Rocket, Takeoff.

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Authors: C. Santhana Krishnan, A. M. Mimi Sakinah, Lakhveer Singh, Zularisam A. Wahid

Abstract:

This study was initiated to evaluate and optimize the conversion of animal fat from tannery wastes into methyl ester. In the pre-treatment stage, animal fats feedstock was hydrolysed and esterified through solid state fermentation (SSF) using Microbacterium species immobilized onto sand silica matrix. After 72 hours of fermentation, predominant esters in the animal fats were found to be with 83.9% conversion rate. Later, esterified animal fats were transesterified at 3 hour reaction time with 1% NaOH (w/v %), 6% methanol to oil ratio (w/v %) to produce 89% conversion rate. C₁₃ NMR revealed long carbon chain in fatty acid methyl esters at 22.2817-31.9727 ppm. Methyl esters of palmitic, stearic, oleic represented the major components in biodiesel.

Keywords: Tannery wastes, fatty animal fleshing, trans-esterification, immobilization, solid state fermentation.

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Authors: H. Y. Jung, Ju H. Park, S. M. Lee

Abstract:

Sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: Sampled-data control, Sector bound, Solid oxide fuel cell, Time-delay.

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Authors: Benshi Zhu

Abstract:

In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.

Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem

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Authors: A. Abdulkadir, Y. M. Bello, A. A. Okhimamhe, H. Ibrahim, M. B. Matazu, L. S. Barau

Abstract:

The increasing volume of solid waste generated, collected and disposed daily complicate adequate management of solid waste by relevant agency like Niger State Environmental Protection Agency (NISEPA). In addition, the impacts of solid waste on the natural environment and human livelihood require identification of cost-effective ways for sustainable municipal waste management in Nigeria. These signal the need for identifying environment-friendly initiative and local solution to address the problem of municipal solid waste. A research field was secured at Pago, Minna, Niger State which is located in the guinea savanna belt of Nigeria, within longitude 60 361 4311 - 4511 and latitude 90 291 37.6111 - .6211 N. Poultry droppings, decomposed household waste manure and NPK treatments were used. The experimental field was divided into three replications and four (4) treatments on each replication making a total of twelve (12) plots. The treatments were allotted using Randomized Complete Block Design (RCBD) and Data collected was analyzed using SPSS software and RCBD. The result depicts variation in plant height and number of leaves at 50% flowering; Poultry dropping records the highest height while the number of leaves for waste manure competes fairly well with NPK treatment. Similarly, the varying treatments significantly increase vegetable yield, as the control (non-treatment) records the least yield for the three vegetable samples. Adoption of this organic manure for cultivation does not only enhance environment quality and attainment of food security but will contribute to local economic development, poverty alleviation as well as social inclusion.

Keywords: Environmental issues, food security, NISEPA, solid waste.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: Pandaba Patro, Brundaban Patro

Abstract:

The numerical simulation of fully developed gas–solid flow in a horizontal pipe is done using the eulerian-eulerian approach, also known as two fluids modeling as both phases are treated as continuum and inter-penetrating continua. The solid phase stresses are modeled using kinetic theory of granular flow (KTGF). The computed results for velocity profiles and pressure drop are compared with the experimental data. We observe that the convection and diffusion terms in the granular temperature cannot be neglected in gas solid flow simulation along a horizontal pipe. The particle-wall collision and lift also play important role in eulerian modeling. We also investigated the effect of flow parameters like gas velocity, particle properties and particle loading on pressure drop prediction in different pipe diameters. Pressure drop increases with gas velocity and particle loading. The gas velocity has the same effect ((proportional toU2 ) as single phase flow on pressure drop prediction. With respect to particle diameter, pressure drop first increases, reaches a peak and then decreases. The peak is a strong function of pipe bore.

Keywords: CFD, Eulerian modeling, gas solid flow, KTGF.

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Authors: Yongkun Li, Erliang Xu

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of multiple positive periodic solutions of a competitor-competitor-mutualist Lotka-Volterra system with harvesting terms. Finally, an example is given to illustrate our results.

Keywords: Positive periodic solutions, competitor-competitor mutualist Lotka-Volterra systems, coincidence degree, harvesting term.

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