Search results for: Alkaline solutions

Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: H. Junoh, K. Palanisamy, C. H. Yip, F. L. Pua

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This study investigates the influence of low temperature thermo-chemical pretreatment of organic food waste on performance of COD solubilisation. Both temperature and alkaline agent were reported to have effect on solubilizing any possible biomass including organic food waste. The three independent variables considered in this pretreatment were temperature (50-90oC), pretreatment time (30-120 minutes) and alkaline concentration, sodium hydroxide, NaOH (0.7-15 g/L). The maximal condition obtained were 90oC, 15 g/L NaOH for 2 hours. Solubilisation has potential in enhancing methane production by providing high amount of soluble components at early stage during anaerobic digestion.

Keywords: Food waste, pretreatments, respond surface methodology, ANOVA, anaerobic digestion.

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Authors: Anupma Bansal, R. K. Gupta

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In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

Keywords: New Modified Novikov Equation, Lie Classical Method, Nonclassical Method, Modified (G'/G)-Expansion Method, Traveling Wave Solutions.

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Authors: Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib

Abstract:

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating  that the flow equations possess an infinite set of solutions. 

Keywords: Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows

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Authors: Mardiana Ahamad Zabidi, Nurain Abdul Karim, Nur Shazrinna Sazali

Abstract:

Mangosteen (Garcinia mangostana) pericarp is considered as agricultural waste and not fully utilized in food products. It is widely reported that mangosteen pericarp contains high antioxidant properties. The objective of this study is to develop novel yellow alkaline noodle (YAN) substituted with different levels of mangosteen pericarp powder (MPP). YAN formulation was substituted with different levels of MPP (0%, 5%, 10% and 15%). The effect on nutritional and antioxidant properties was evaluated. Higher substitution levels of MPP resulted in significant increase (p<0.05) of ash, fibre, specific mineral elements and antioxidant properties (total phenolic, total flavonoid, anthocyanin and DPPH) than control sample.

Keywords: Yellow alkaline noodle, mangosteen pericarp powder, proximate composition, antioxidant properties.

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Authors: A. Khalina, K. Shaharuddin, M. S. Wahab, M. P. Saiman, H. A. Aisyah

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This paper investigates the effect of alkali treatment and mechanical properties of kenaf (Hibiscus cannabinus) fibre for the development of yarn. Two different fibre sources are used for the yarn production. Kenaf fibres were treated with sodium hydroxide (NaOH) in the concentration of 3, 6, 9, and 12% prior to fibre opening process and tested for their tensile strength and Young’s modulus. Then, the selected fibres were introduced to fibre opener at three different opening processing parameters; namely, speed of roller feeder, small drum, and big drum. The diameter size, surface morphology, and fibre durability towards machine of the fibres were characterized. The results show that concentrations of NaOH used have greater effects on fibre mechanical properties. From this study, the tensile and modulus properties of the treated fibres for both types have improved significantly as compared to untreated fibres, especially at the optimum level of 6% NaOH. It is also interesting to highlight that 6% NaOH is the optimum concentration for the alkaline treatment. The untreated and treated fibres at 6% NaOH were then introduced to fibre opener, and it was found that the treated fibre produced higher fibre diameter with better surface morphology compared to the untreated fibre. Higher speed parameter during opening was found to produce higher yield of opened-kenaf fibres.

Keywords: Alkaline treatment, Kenaf fibre, Tensile strength, Yarn production.

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Authors: Eiichi Sasaki, Shin-ichi Takehiro, Michio Yamada

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We study bifurcation structure of the zonal jet flow the streamfunction of which is expressed by a single spherical harmonics on a rotating sphere. In the non-rotating case, we find that a steady traveling wave solution arises from the zonal jet flow through Hopf bifurcation. As the Reynolds number increases, several traveling solutions arise only through the pitchfork bifurcations and at high Reynolds number the bifurcating solutions become Hopf unstable. In the rotating case, on the other hand, under the stabilizing effect of rotation, as the absolute value of rotation rate increases, the number of the bifurcating solutions arising from the zonal jet flow decreases monotonically. We also carry out time integration to study unsteady solutions at high Reynolds number and find that in the non-rotating case the unsteady solutions are chaotic, while not in the rotating cases calculated. This result reflects the general tendency that the rotation stabilizes nonlinear solutions of Navier-Stokes equations.

Keywords: rotating sphere, two-dimensional flow, bifurcationstructure

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Authors: P. Shunmugapriya, S. Kanmani, P. Jude Fredieric, U. Vignesh, J. Reman Justin, K. Vivek

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Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem and it is quite difficult to find an optimal solution consisting of a set of routes for vehicles whose total cost is minimum. Evolutionary and swarm intelligent (SI) algorithms play a vital role in solving optimization problems. While the SI algorithms perform search, the diversity between the solutions they exploit is very important. This is because of the need to avoid early convergence and to get an appropriate balance between the exploration and exploitation. Therefore, it is important to check how far the solutions are diverse. In this paper, we measure the similarity between solutions, which ABC exploits while optimizing VRP. The similar solutions found are discarded at the end of the iteration and only unique solutions are passed on to the next iteration. The bees of discarded solutions become scouts and they start searching for new solutions. This process is continued and results show that the solution is optimized at lesser number of iterations but with the overhead of computing similarity in all the iterations. The problem instance from Solomon benchmarked dataset has been used for evaluating the presented methodology.

Keywords: ABC algorithm, vehicle routing problem, optimization, Jaccard’s similarity measure.

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Authors: S. S. Bendib, L. W. Mouss, S. Kalla

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This paper proposes a self-organization-based approach for real-time systems design. The addressed issue is the mapping of an application onto an architecture of heterogeneous processors while optimizing both makespan and reliability. Since this problem is NP-hard, a heuristic algorithm is used to obtain efficiently approximate solutions. The proposed approach takes into consideration the quality as well as the diversity of solutions. Indeed, an alternate treatment of the two objectives allows to produce solutions of good quality while a self-organization approach based on the neighborhood structure is used to reorganize solutions and consequently to enhance their diversity. Produced solutions make different compromises between the makespan and the reliability giving the user the possibility to select the solution suited to his (her) needs.

Keywords: Embedded real-time systems design, makespan, reliability, self-organization, compromises.

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Authors: Changjin Xu, Qianhong Zhang

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In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

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

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Authors: Hamid Reza Alipour, Ali Mohammadi Torkashvand

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In composting process, N high-organic wastes loss the great part of its nitrogen as ammonia; therefore, using compost amendments can promote the quality of compost due to the decrease in ammonia volatilization. With regard to the effect of pH on composting, microorganisms- activity and ammonia volatilization, sulfuric acid and alkaline wastewater of paper mill (as liming agent with Ca and Mg ions) were used as compost amendments. Study results indicated that these amendments are suitable for reclamation of compost quality properties. These held nitrogen in compost caused to reduce C/N ratio. Both amendments had a significant effect on total nitrogen, but it should be used sulfuric acid in fewer amounts (20 ml/kg fresh organic wastes); and the more amounts of acid is not proposed.

Keywords: Compost, Paper mill wastewater, sulfuric acid, Ammonia Volatilization.

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Authors: Djarot B. Darmadi, John Norrish, Anh Kiet Tieu

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Solutions for the temperature profile around a moving heat source are obtained using both analytic and finite element (FEM) methods. Analytic and FEM solutions are applied to study the temperature profile in welding. A moving heat source is represented using both point heat source and uniform distributed disc heat source models. Analytic solutions are obtained by solving the partial differential equation for energy conservation in a solid, and FEM results are provided by simulating welding using the ANSYS software. Comparison is made for quasi steady state conditions. The results provided by the analytic solutions are in good agreement with results obtained by FEM.

Keywords: Analytic solution, FEM, Temperature profile, HeatSource Model

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Authors: T. Boonraksa, B. Marungsri

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This paper presents the experimental results on role of ionic solutions affect water treeing propagation in cross-linked polyethylene insulation for high voltage cable. To study the water treeing expansion due to the ionic solutions, discs of 4mm thickness and 4cm diameter were taken from 115 kV XLPE insulation cable and were used as test specimen in this study. Ionic solutions composed of CuSO4, FeSO4, Na2SO4 and K2SO4 were used. Each specimen was immersed in 0.1 mole ionic solutions and was tested for 120 hrs. under a voltage stress at 7 kV AC rms, 1000 Hz. The results show that Na2SO4 and CuSO4solutions play an important role in the expansion of water treeing and cause degradation of the crosslinked polyethylene (XLPE) in the presence of the applied electric field.

Keywords: Ionic Solutions, Water Treeing, Water treeing Expansion, Cross-linked Polyethylene (XLPE).

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Authors: G.Anjali, M.Bhavya, N.Arvind Kumar

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In order to avoid the potentially devastating consequences of global warming and climate change, the carbon dioxide “CO2" emissions caused due to anthropogenic activities must be reduced considerably. This paper presents the first study examining the feasibility of carbon sequestration in construction and demolition “C&D" waste. Experiments were carried out in a self fabricated Batch Reactor at 40ºC, relative humidity of 50-70%, and flow rate of CO2 at 10L/min for 1 hour for water-to-solids ratio of 0.2 to 1.2. The effect of surface area was found by comparing the theoretical extent of carbonation of two different sieve sizes (0.3mm and 2.36mm) of C&D waste. A 38.44% of the theoretical extent of carbonation equating to 4% CO2 sequestration extent was obtained for C&D waste sample for 0.3mm sieve size. Qualitative, quantitative and morphological analyses were done to validate carbonate formation using X-ray diffraction “X.R.D.," thermal gravimetric analysis “T.G.A., “X-Ray Fluorescence Spectroscopy “X.R.F.," and scanning electron microscopy “S.E.M".

Keywords: Alkaline waste, construction and demolition waste, CO2 sequestration, mineral carbonation.

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Authors: Said Laachir, Aziz Laaribi

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The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.

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Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.

Keywords: positive solutions, concave-convex, sub-super solution method, pseudo arclength method.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

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Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.

Keywords: Homotopy perturbation method, Padé approximants, cubic Boussinesq equation, modified Boussinesq equation.

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Authors: Shankar Kambhampaty, Harish Rohan Kambhampaty

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Data in IT systems in enterprises have been growing at phenomenal pace. This has provided opportunities to run analytics to gather intelligence on key business parameters that enable them to provide better products and services to customers. While there are several Artificial Intelligence/Machine Learning (AI/ML) and Business Intelligence (BI) tools and technologies available in marketplace to run analytics, there is a need for an integrated view when developing intelligent solutions in enterprises. This paper progressively elaborates a reference model for enterprise solutions, builds an integrated view of data, information and intelligence components and presents a reference architecture for intelligent enterprise solutions. Finally, it applies the reference architecture to an insurance organization. The reference architecture is the outcome of experience and insights gathered from developing intelligent solutions for several organizations.

Keywords: Architecture, model, intelligence, artificial intelligence, business intelligence, AI, BI, ML, analytics, enterprise.

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Authors: Nisha Goyal, R.K. Gupta

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This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,

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Authors: Fadi Awawdeh, O. Alsayyed

Abstract:

New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

Keywords: Soliton Solution, Hirota Bilinear Method, ANNV System.

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Authors: Alireza Arab, Morteza Elsa, Amirhossein Moghanian

Abstract:

In this study, experiments were carried out to achieve a promising multifunctional and modified silicate based bioactive glass (BG). The main aim of the study was investigating the effect of lithium (Li) and magnesium (Mg) substitution, on in vitro bioactivity of substituted-58S BG. Moreover, it is noteworthy to state that modified BGs were synthesized in 60SiO₂–(36-x)CaO–4P₂O₅–(x)Li₂O and 60SiO₂–(36-x)CaO–4P₂O₅–(x)MgO (where x = 0, 5, 10 mol.%) quaternary systems, by sol-gel method. Their performance was investigated through different aspects such as biocompatibility, antibacterial activity as well as their effect on alkaline phosphatase (ALP) activity, and proliferation of MC3T3 cells. The antibacterial efficiency was evaluated against methicillin-resistant Staphylococcus aureus bacteria. To do so, CaO was substituted with Li₂O and MgO up to 10 mol % in 58S-BGs and then samples were immersed in simulated body fluid up to 14 days and then, characterized by X-ray diffraction, Fourier transform infrared spectroscopy, inductively coupled plasma atomic emission spectrometry, and scanning electron microscopy. Results indicated that this modification led to a retarding effect on in vitro hydroxyapatite (HA) formation due to the lower supersaturation degree for nucleation of HA compared with 58s-BG. Meanwhile, magnesium revealed further pronounced effect. The 3-(4,5 dimethylthiazol-2-yl)-2,5 diphenyltetrazolium bromide (MTT) and ALP analysis illustrated that substitutions of both Li₂O and MgO, up to 5 mol %, had increasing effect on biocompatibility and stimulating proliferation of the pre-osteoblast MC3T3 cells in comparison to the control specimen. Regarding to bactericidal efficiency, the substitution of either Li or Mg for Ca in the 58s BG composition led to statistically significant difference in antibacterial behaviors of substituted-BGs. Meanwhile, the sample containing 5 mol % CaO/Li₂O substitution (BG-5L) was selected as a multifunctional biomaterial in bone repair/regeneration due to the improved biocompatibility, enhanced ALP activity and antibacterial efficiency among all of the synthesized L-BGs and M-BGs.

Keywords: Alkaline, alkaline earth, bioactivity, biomedical applications, sol-gel processes.

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Authors: Imran Siddique

Abstract:

This paper deals with the helical flow of a Newtonian fluid in an infinite circular cylinder, due to both longitudinal and rotational shear stress. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms and satisfy all imposed initial and boundary conditions. For large times, these solutions reduce to the well-known steady-state solutions.

Keywords: Newtonian fluids, Velocity field, Exact solutions, Shear stress, Cylindrical domains.

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Authors: Fahad Al Shidi, Reginald Victor

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This study was conducted in Northern Oman to assess the physical and chemical characteristics of 40 thermal springs distributed in Al Hajar Mountains in northern Oman. Physical measurements of water samples were carried out in two main seasons in Oman (winter and summer 2019). Studied springs were classified into three groups based on water temperature, four groups based on water pH values and two groups based on conductivity. Ten thermal alkaline springs that originated in Ophiolite (Samail Napp) were dominated by high pH (> 11), elevated concentration of Cl- and Na+ ions, relatively low temperature and discharge ratio. Other springs in the Hajar Super Group massif recorded high concentrations of Ca²+ and SO^2-₄ ions controlled by rock dominance, geochemistry processes, and mineralization. There was only one spring which has brackish water with very high conductivity (5500 µs/cm) and Total Dissolved Solids and it is not suitable for irrigation purposes because of the high abundance of Na+, Cl−, and Ca²+ ions.

Keywords: Alkaline springs, geothermal, Hajar Super Group, Northern Oman, ophiolite.

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Authors: Janjira Triped, Wipada Sanongraj, Bovornlak Oonkhanond, Sompop Sanongraj

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The main objective of this research is to synthesize silk fibroin fiber for indoor air particulate removal. Silk cocoons were de-gummed using 0.5 wt % Na2CO3 alkaline solutions at 90 Ó╣ìC for 60 mins, washed with distilled water, and dried at 80 Ó╣ìC for 3 hrs in a vacuum oven. Two sets of experiment were conducted to investigate the impacts of initial particulate matter (PM) concentration and that of air flow rate on the removal efficiency. Rice bran collected from a local rice mill in Ubonratchathani province was used as indoor air contaminant in this work. The morphology and physical properties of silk fibroin (SF) fiber were measured. The SEM revealed the deposition of PM on the used fiber. The PM removal efficiencies of 72.29 ± 3.03 % and 39.33 ± 1.99 % were obtained of PM10 and PM2.5, respectively, when using the initial PM concentration at 0.040 mg/m3 and 0.020 mg/m3 of PM10 and PM2.5, respectively, with the air flow rate of 5 L/min.

Keywords: Indoor air, Particulate matter, Scanning electron microscope (SEM), Silk fibroin fiber.

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Authors: Deepak Mohan, Sushma Sharma

Abstract:

Non-Steroidal Anti-Inflammatory Drugs (NSAIDs) are a group of widely used drugs for the treatment of rheumatoid diseases and to relieve pain and inflammation due to their analgesic anti-pyretic and anti-inflammatory properties. The therapeutic and many of the toxic effects of NSAIDs result from reversible inhibition of enzymes in the cyclooxygenase (COX) group. In the present investigation the effect of the drug on the concentration of lipids, and on the activity of the enzymes i.e. acid and alkaline phosphatase, GOT, GPT and lipid peroxidase were studied. There was a significant enhancement in the activities of both acid and alkaline phosphatase after 21 days of treatment. Proportionate increase in the MDA contents was observed after different days of diclofenac treatment. Cellular damage in the liver resulted in decrease in the activity of both GOT (Glutamate oxaloacetate transaminase) and GPT (Glutamate pyruvate transaminase) in both low and high dose groups. Significant decrease in the liver contents was also observed in both dose groups.

Keywords: Anti-inflammatory, cyclooxygenase, glutamate oxaloacetate transaminase, malondialdehyde.

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Authors: Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

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We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Keywords: Nonlinear Control, Optimal Control, Hamilton-Jacobi Equation, Virtual-Time

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Authors: A. C. Amaro de Faria Jr, A. M. Canone

Abstract:

Considering a scenario where our universe is taken as a 3d domain wall embedded in a 5d dimensional Minkowski space-time, we explore the existence of a richer class of solitonic solutions and their consequences for accelerating universes driven by collisions of bulk particle excitations with the walls. In particular it is shown that some of these solutions should play a fundamental role at the beginning of the expansion process. We present some of these solutions in cosmological scenarios that can be applied to models that describe the inflationary period of the Universe.

Keywords: Solitons, topological defects, Branes, kinks, accelerating universes in Brane scenarios.

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Authors: Mustafa Hasan Omar

Abstract:

The destruction effect of hydrocarbon solutions on concrete besides its high permeability have led researchers to try to improve the performance of concrete exposed to these solutions, hence improving the durability and usability of oil concrete structures. Recently, polymer concrete is considered one of the most important types of concrete, and its behavior after exposure to oil products is still unknown. In the present work, an experimental study has been carried out, in which the prepared epoxy polymer concrete immersed in different types of hydrocarbon exposure solutions (gasoline, kerosene, and gas oil) for 120 days and compared with the reference concrete left in the air. The results for outdoor specimens indicate that the mechanical properties are increased after 120 days, but the specimens that were immersed in gasoline, kerosene, and gas oil for the same period show a reduction in compressive strength by -21%, -27% and -23%, whereas in splitting tensile strength by -19%, -24% and -20%, respectively. The reductions in ultrasonic pulse velocity for cubic specimens are -17%, -22% and -19% and in cylindrical specimens are -20%, -25% and -22%, respectively.

Keywords: Epoxy resin, hydrocarbon solutions, mechanical properties, polymer concrete, ultrasonic pulse velocity.

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Authors: Aswin Kumar Krishnan, Yat Choy Wong, Reiza Mukhlis, Zipeng Zhang, Arul Arulrajah

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The continuous increase in vehicle uptake escalates the number of rubber tyres waste which need to be managed to avoid landfilling and stockpiling. The present research focused on the sustainable use of crumb rubber in clay roof tiles. The properties of roof tiles composed of clay, crumb rubber, NaOH, and Na2SiO3 with 10 wt.% alkaline activator were studied. Tile samples were fabricated by heating the compacted mixtures at 50 °C for 72 hours, followed by a higher heating temperature of 200 °C for 24 hours. The effect of crumb rubber aggregates as a substitution for the raw clay materials were investigated by varying their concentration from 0 wt.% to 2.5 wt.%. X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses have been conducted to study the phases and microstructures of the samples. It was found that the optimum rubber crumbs concentration was at 0.5 wt.% and 1 wt.%, while cracks and larger porosity were found at higher crumbs concentration. Water absorption, and compressive strength test results demonstrated that rubber crumbs and clay satisfied the standard requirement for the roof tiles.

Keywords: Crumb rubber, clay, roof tiles, alkaline activators.

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Authors: Anupma Bansal

Abstract:

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions

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