Search results for: Alkaline solutions
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1573

Search results for: Alkaline solutions

1573 Effects of Polymers and Alkaline on Recovery Improvement from Fractured Models

Authors: Payam Parvasi, Mohammad Hossein Sedaghat, Reza Janamiri, Amir Hatampour

Abstract:

In this work, several ASP solutions were flooded into fractured models initially saturated with heavy oil at a constant flow rate and different geometrical characteristics of fracture. The ASP solutions are constituted from 2 polymers i.e. a synthetic polymer, hydrolyzed polyacrylamide as well as a biopolymer, a surfactant and 2types of alkaline. The results showed that using synthetic hydrolyzed polyacrylamide polymer increases ultimate oil recovery; however, type of alkaline does not play a significant rule on oil recovery. In addition, position of the injection well respect to the fracture system has remarkable effects on ASP flooding. For instance increasing angle of fractures with mean flow direction causes more oil recovery and delays breakthrough time. This work can be accounted as a comprehensive survey on ASP flooding which considers most of effective factors in this chemical EOR method.

Keywords: ASP Flooding, Fractured System, Displacement, Heavy Oil.

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1572 Neutralization of Alkaline Waste-Waters using a Blend of Microorganisms

Authors: Rita Kumar, Alka Sharma, Purnima Dhall, Niha M. Kulshreshtha, Anil Kumar

Abstract:

The efficient operation of any biological treatment process requires pre-treatment of incompatible pollutants such as acids, bases, oil, toxic substances, etc. which hamper the treatment of other major components which are otherwise degradable. The pre-treatment of alkaline waste-waters, generated from various industries like textile, paper & pulp, potato-processing industries, etc., having a pH of 10 or higher, is essential. The pre-treatment, i.e., neutralization of such alkaline waste-waters can be achieved by chemical as well as biological means. However, the biological pretreatment offers better package over the chemical means by being safe and economical. The biological pre-treatment can be accomplished by using a blend of microorganisms able to withstand such harsh alkaline conditions. In the present study, for the proper pre-treatment of alkaline waste-waters, a package of alkalophilic bacteria is formulated to neutralise the alkaline pH of the industrial waste-waters. The developed microbial package is cost-effective as well as environmental friendly.

Keywords: alkaline, alkalophilic bacteria, biological, pollutants, textile.

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1571 Determination of Alkaline Protease Production In Serratia Marcescens Sp7 Using Agro Wastes As Substrate Medium, Optimization Of Production Parameters And Purification Of The Enzyme

Authors: Baby Joseph, Sankarganesh Palaniyandi

Abstract:

The enzyme alkaline protease production was determined under solid state fermentation using the soil bacteria Serratia marcescens sp7. The maximum production was obtained from wheat bran medium than ground nut shell and chemically defined medium. The physiological fermentation factors such as pH of the medium (pH 8), Temperature (40oC) and incubation time (48 hrs) played a vital role in alkaline protease production in all the above. 100Mm NaCl has given better resolution during elution of the enzymes. The enzyme production was found to be associated with growth of the bacterial culture.

Keywords: Alkaline protease, Wheat bran, Ground nut shell, Serratia marcescens

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1570 Compressive Strength and Microstructure of Hybrid Alkaline Cements

Authors: Z. Abdollahnejad, P. Torgal, J. Barroso Aguiar

Abstract:

Publications on the field of alkali-activated binders, state that this new material is likely to have high potential to become an alternative to Portland cement. Classical alkali-activated cements could be made more eco-efficient if the use of sodium silicate is avoided. Besides, most alkali-activated cements suffer from severe efflorescence originated by the fact that alkaline and/or soluble silicates that are added during processing cannot be totally consumed. This paper presents experimental results on hybrid alkaline cements. Compressive strength results and efflorescence’s observations show that the new mixes already analyzed are promising. SEM results show that no traditional porous ITZ was detected in these binders.

Keywords: Hybrid alkaline cements, Compressive strength, Efflorescence, SEM, ITZ.

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1569 Activities of Alkaline Phosphatase and Ca2+ATPase over the Molting Cycle of mud Crab (Scylla serrata)

Authors: J. Salaenoi, A. Thongpan, M. Mingmuang

Abstract:

The activities of alkaline phosphatase and Ca2+ATPase in mud crab (Scylla serrata) collected from a soft-shell crab farm in Chantaburi Province, Thailand, in several stages of molting cycle were observed. The results showed that the activity of alkaline phosphatase in gill after molting was highly significant (p<0.05) comparing to those at intermolt and premolt stages. The activity profiles of alkaline phosphatase in integument and haemolymph were similar showing a decrease from intermolt to 2- week premolt stage and increased during 2-day premolt to 6-h postmolt stage before dropping at 7-day postmolt stage, while this enzyme in the gill was quite low at intermolt and premolt stages. For Ca2+ATPase, the activity profiles in gill and integument corresponded to the molting variation, especially the activities increased during 5-7 day postmolt stage were at highly significant levels (p<0.05) comparing to those at premolt and early postmolt stages. The highest activity of Ca2+ATPase in haemolymph was found at 2-week premolt stage (p<0.05). Changes in alkaline phosphatase and Ca2+ATPase activities over the molting cycle clearly indicated their active functions on calcification.

Keywords: Scylla serrata, molting cycle, alkaline phosphatase, Ca2+ATPase

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1568 Thermal and Morphological Evaluation of Chemically Pretreated Sugarcane Bagasse

Authors: Glauber Cruz, Patrícia A. S. Monteiro, Carlos E. M. Braz, Paulo Seleghin Jr., Igor Polikarpov, Paula M.Crnkovic

Abstract:

Enzymatic hydrolysis is one of the major steps involved in the conversion from sugarcane bagasse to yield ethanol. This process offers potential for yields and selectivity higher, lower energy costs and milder operating conditions than chemical processes. However, the presence of some factors such as lignin content, crystallinity degree of the cellulose, and particle sizes, limits the digestibility of the cellulose present in the lignocellulosic biomasses. Pretreatment aims to improve the access of the enzyme to the substrate. In this study sugarcane bagasse was submitted chemical pretreatment that consisted of two consecutive steps, the first with dilute sulfuric acid (1 % (v/v) H2SO4), and the second with alkaline solutions with different concentrations of NaOH (1, 2, 3 and 4 % (w/v)). Thermal Analysis (TG/ DTG and DTA) was used to evaluate hemicellulose, cellulose and lignin contents in the samples. Scanning Electron Microscopy (SEM) was used to evaluate the morphological structures of the in natura and chemically treated samples. Results showed that pretreatments were effective in chemical degradation of lignocellulosic materials of the samples, and also was possible to observe the morphological changes occurring in the biomasses after pretreatments.

Keywords: Alkaline solutions, bioethanol production, dilute acid, enzymatic hydrolysis, lignocellulosic biomass.

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1567 One-Pot Facile Synthesis of N-Doped Graphene Synthesized from Paraphenylenediamine as Metal-Free Catalysts for the Oxygen Reduction Used for Alkaline Fuel Cells

Authors: Leila Samiee, Amir Yadegari, Saeedeh Tasharrofi

Abstract:

In the work presented here, nitrogen-doped graphene materials were synthesized and used as metal-free electrocatalysts for oxygen reduction reaction (ORR) under alkaline conditions. Paraphenylenediamine was used as N precursor. The N-doped graphene was synthesized under hydrothermal treatment at 200°C. All the materials have been characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), Transmission electron microscopy (TEM) and X-ray photo-electron spectroscopy (XPS). Moreover, for electrochemical evaluation of samples, Rotating Disk electrode (RDE) and Cyclic Voltammetry techniques (CV) were employed. The resulting material exhibits an outstanding catalytic activity for the oxygen reduction reaction (ORR) as well as excellent resistance towards methanol crossover effects, indicating their promising potential as ORR electrocatalysts for alkaline fuel cells.

Keywords: Alkaline fuel cell, graphene, metal-free catalyst, paraphenylenediamine.

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1566 Measurement of Rainwater Chemical Composition in Malaysia based on Ion Chromatography Method

Authors: S.H. Khoon, G.I. Issabayeva, L.W. Lee

Abstract:

Air quality in Setapak district of Kuala Lumpur was studied by analysing the rainwater chemical composition using ion chromatography method. Twelve sampling sites were selected and 120 rainwater samples were collected in the period of 10 weeks. The results of this study were compared to the earlier published data and the evaluation showed that the NO3 - ion concentration increased from 0.41 to 3.32 ppm, while SO4 2- ion concentration increased from 0.39 to 3.26 ppm over the past two decades that is mostly due to rapid urban development of the city. However, it was found that the chemical composition for both residential and industrial areas does not have significant difference. Most of the rainwater samples showed alkaline pH (pH > 5.6). The possible factors for such alkaline pH in rainwater samples are assumed to be the marine sources, biomass burning and alkaline character of soil particles.

Keywords: acid deposition; atmospheric pollution; deposition fluxes; trajectories

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1565 SELF-Cured Alkali Activated Slag Concrete Mixes- An Experimental Study

Authors: Mithun B. M., Mattur C. Narasimhan

Abstract:

Alkali Activated Slag Concrete (AASC) mixes are manufactured by activating ground granulated blast furnace slag (GGBFS) using sodium hydroxide and sodium silicate solutions. The aim of the present experimental research was to investigate the effect of increasing the dosages of sodium oxide (Na2O, in the range of 4 to 8%) and the activator modulus (Ms) (i.e. the SiO2/Na2O ratio, in the range of 0.5 to 1.5) of the alkaline solutions, on the workability and strength characteristics of self-cured (air-cured) alkali activated Indian slag concrete mixes. Further the split tensile and flexure strengths for optimal mixes were studied for each dosage of Na2O.It is observed that increase in Na2O concentration increases the compressive, split-tensile and flexural strengths, both at the early and later-ages, while increase in Ms, decreases the workability of the mixes. An optimal Ms of 1.25 is found at various Na2O dosages. No significant differences in the strength performances were observed between AASCs manufactured with alkali solutions prepared using either of potable and de-ionized water.

Keywords: Alkali activated slag, self-curing, strength characteristics.

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1564 Some Static Isotropic Perfect Fluid Spheres in General Relativity

Authors: Sachin Kumar, Y. K. Gupta, J. R. Sharma

Abstract:

In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subjected to the reality conditions. As far as the authors are aware the solutions are new.

Keywords: Einstein's equations, General Relativity, PerfectFluid, Spherical symmetric.

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1563 Optical Properties of Some A2BCl4 Type Chlorides

Authors: D. H. Gahane, B. M. Bahirwar, S. V. Moharil

Abstract:

Efficient luminescence is reported for the first time in Eu2+ activated double Chlorides A2BCl4 (A=Alkali metal, B=Alkaline earth element). A simple wet-chemical preparation is described. Emission intensities are comparable to that of the commercial phosphor. Excitation covers near UV region. These phosphors may be useful for applications like solid state lighting, scintillation detectors and X-ray storage using photo-stimulable phosphors.

Keywords: Alkaline Earth, Chloride, Luminescence.

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1562 Porous Ni and Ni-Co Electrodeposits for Alkaline Water Electrolysis – Energy Saving

Authors: I. Herraiz-Cardona, C. González-Buch, E. Ortega, V. Pérez-Herranz, J. García-Antón

Abstract:

Hydrogen is considered to be the most promising candidate as a future energy carrier. One of the most used technologies for the electrolytic hydrogen production is alkaline water electrolysis. However, due to the high energy requirements, the cost of hydrogen produced in such a way is high. In continuous search to improve this process using advanced electrocatalytic materials for the hydrogen evolution reaction (HER), Ni type Raney and macro-porous Ni-Co electrodes were prepared on AISI 304 stainless steel substrates by electrodeposition. The developed electrodes were characterized by SEM and confocal laser scanning microscopy. HER on these electrodes was evaluated in 30 wt.% KOH solution by means of hydrogen discharge curves and galvanostatic tests. Results show that the developed electrodes present a most efficient behaviour for HER when comparing with the smooth Ni cathode. It has been reported a reduction in the energy consumption of the electrolysis cell of about 25% by using the developed coatings as cathodes.

Keywords: Alkaline water electrolysis, energy efficiency, porous nickel electrodes

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1561 Commercializing Technology Solutions- Moving from Products to Solutions

Authors: Anand Dass, Hiroaki Murakami

Abstract:

The paper outlines the drivers behind the movement from products to solutions in the Hi-Tech Business-to-Business markets. The paper lists out the challenges in enabling the transformation from products to solutions and also attempts to explore strategic and operational recommendations based on the authors- factual experiences with Japanese Hi-tech manufacturing organizations. Organizations in the Hi-Tech Business-to-Business markets are increasingly being compelled to move to a solutions model from the conventional products model. Despite the added complexity of solutions, successful technology commercialization can be achieved by making prudent choices in defining a relevant solutions model, by backing the solution model through appropriate organizational design, and by overhauling the new product development process and supporting infrastructure.

Keywords: Technology commercialization, Solutions, Hi-Tech companies, Japan, Management of technology

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1560 Selective Solvent Extraction of Calcium and Magnesium from Concentrate Nickel Solutions Using Mixtures of Cyanex 272 and D2EHPA

Authors: Alexandre S. Guimarães, Marcelo B. Mansur

Abstract:

The performance of organophosphorus extractants Cyanex 272 and D2EHPA on the purification of concentrate nickel sulfate solutions was evaluated. Batch scale tests were carried out at pH range of 2 to 7 using a laboratory solution simulating concentrate nickel liquors as those typically obtained when sulfate intermediates from nickel laterite are re-leached and treated for the selective removal of cobalt, zinc, manganese and copper with Cyanex 272 ([Ca] = 0.57 g/L, [Mg] = 3.2 g/L, and [Ni] = 88 g/L). The increase on the concentration of D2EHPA favored the calcium extraction. The extraction of magnesium is dependent on the pH and of ratio of extractants D2EHPA and Cyanex 272 in the organic phase. The composition of the investigated organic phase did not affect nickel extraction. The number of stages is dependent on the magnesium extraction. The most favorable operating condition to selectively remove calcium and magnesium was determined.

Keywords: Solvent extraction, organophosphorus extractants, alkaline earth metals, nickel.

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1559 Phenolic-Based Chemical Production from Catalytic Depolymerization of Alkaline Lignin over Fumed Silica Catalyst

Authors: S. Totong, P. Daorattanachai, N. Laosiripojana

Abstract:

Lignin depolymerization into phenolic-based chemicals is an interesting process for utilizing and upgrading a benefit and value of lignin. In this study, the depolymerization reaction was performed to convert alkaline lignin into smaller molecule compounds. Fumed SiO₂ was used as a catalyst to improve catalytic activity in lignin decomposition. The important parameters in depolymerization process (i.e., reaction temperature, reaction time, etc.) were also investigated. In addition, gas chromatography with mass spectrometry (GC-MS), flame-ironized detector (GC-FID), and Fourier transform infrared spectroscopy (FT-IR) were used to analyze and characterize the lignin products. It was found that fumed SiO₂ catalyst led the good catalytic activity in lignin depolymerization. The main products from catalytic depolymerization were guaiacol, syringol, vanillin, and phenols. Additionally, metal supported on fumed SiO₂ such as Cu/SiO₂ and Ni/SiO₂ increased the catalyst activity in terms of phenolic products yield.

Keywords: Alkaline lignin, catalytic, depolymerization, fumed SiO2, phenolic-based chemicals.

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1558 Exact Pfaffian and N-Soliton Solutions to a (3+1)-Dimensional Generalized Integrable Nonlinear Partial Differential Equations

Authors: Magdy G. Asaad

Abstract:

The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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1557 Investigation of Compressive Strength of Slag-Based Geopolymer Concrete Incorporated with Rice Husk Ash Using 12M Alkaline Activator

Authors: Festus A. Olutoge, Ahmed A. Akintunde, Anuoluwapo S. Kolade, Aaron A. Chadee, Jovanca Smith

Abstract:

Geopolymer concrete's (GPC) compressive strength was investigated. The GPC was incorporated with rice husk ash (RHA) and ground granulated blast furnace slag (GGBFS), which may have potential in the construction industry to replace Portland limestone cement (PLC) concrete. The sustainable construction binders used were GGBFS and RHA, and a solution of sodium hydroxide (NaOH) and sodium silicate gel (Na2SiO3) was used as the 12-molar alkaline activator. Five GPC mixes comprising fine aggregates, coarse aggregates, GGBS, and RHA, and the alkaline solution in the ratio 2: 2.5: 1: 0.5, respectively, were prepared to achieve grade 40 concrete, and PLC was substituted with GGBFS and RHA in the ratios of 0:100, 25:75, 50:50, 75:25, and 100:0. A control mix was also prepared which comprised of 100% water and 100% PLC as the cementitious material. The GPC mixes were thermally cured at 60-80 ºC in an oven for approximately 24 h. After curing for 7 and 28 days, the compressive strength test results of the hardened GPC samples showed that GPC-Mix #3, comprising 50% GGBFS and 50% RHA, was the most efficient geopolymer mix. The mix had compressive strengths of 35.71 MPa and 47.26 MPa, 19.87% and 8.69% higher than the PLC concrete samples, which had 29.79 MPa and 43.48 MPa after 7 and 28 days, respectively. Therefore, GPC containing GGBFS incorporated with RHA is an efficient method of decreasing the use of PLC in conventional concrete production and reducing the high amounts of CO2 emitted into the atmosphere in the construction industry.

Keywords: Alkaline solution, cementitious material, geopolymer concrete, ground granulated blast furnace slag, rice husk ash.

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1556 Influence of Various Factors on Stability of CoSPc in LPG Sweetening Process

Authors: Ali Samadi Afshar, Hamed Harrafi, S.M.Javad Gharib Zahedi

Abstract:

IFP Group Technology “Sulfrex process" was used in Iran-s South Pars Gas Complex Refineries for removing sulfur compounds such as mercaptans, carbonyl sulfide and hydrogen sulfide, which uses sulfonated cobalt phthalocyanine dispersed in alkaline solution as catalyst. In this technology, catalyst and alkaline solution were used circularly. However the stability of catalyst due to effect of some parameters would reduce with the running of the unit and therefore sweetening efficiency would be decreased. Hence, the aim of this research is study the factors effecting on the stability of catalyst.

Keywords: sulfonated cobalt phthalocyanine, mercaptans, stability, catalyst, sulfur.

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1555 Exploring Solutions in Extended Horava-Lifshitz Gravity

Authors: Aziza Altaibayeva, Ertan Gudekli, Ratbay Myrzakulov

Abstract:

In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.

Keywords: Quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times.

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1554 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions

Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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1553 Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method

Authors: Anjali Verma, Ram Jiwari, Jitender Kumar

Abstract:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.

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1552 The Pell Equation x2 − (k2 − k)y2 = 2t

Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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1551 Characteristics of Nanosilica-Geopolymer Nanocomposites and Mixing Effect

Authors: H. Assaedi, F. U. A. Shaikh, I. M. Low

Abstract:

This paper presents the effects of mixing procedures on mechanical properties of flyash-based geopolymer matrices containing nanosilica (NS) at 0.5%, 1.0%, 2.0%, and 3.0% by weight. Comparison is made with conventional mechanical dry-mixing of NS with flyash and wet-mixing of NS in alkaline solutions. Physical and mechanical properties are investigated using X-Ray Diffraction (XRD) and Scanning Electron Microscope (SEM). Results show that generally the addition of NS particles enhanced the microstructure and improved flexural and compressive strengths of geopolymer nanocomposites. However, samples, prepared using dry-mixing approach, demonstrate better physical and mechanical properties comparing to wet-mixing samples.

Keywords: Geopolymer, mechanical properties, nanosilica.

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1550 Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation

Authors: Mohammad Najafi, Ali Jamshidi

Abstract:

We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.

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1549 Periodic Solutions for a Delayed Population Model on Time Scales

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales

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1548 Positive Solutions for a Class of Semipositone Discrete Boundary Value Problems with Two Parameters

Authors: Benshi Zhu

Abstract:

In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method.

Keywords: Discrete boundary value problems, nonsmoothcritical point theory, positive solutions, semipositone, sub-super solutions method

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1547 Comparison Results of Two-point Fuzzy Boundary Value Problems

Authors: Hsuan-Ku Liu

Abstract:

This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

Keywords: Fuzzy derivative, lateral type of H-derivative, fuzzy differential equations, fuzzy boundary value problems, boundary value problems.

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1546 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim

Abstract:

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

Keywords: Pell equation, Diophantine equation.

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1545 The Pell Equation x2 − Py2 = Q

Authors: Ahmet Tekcan, Arzu Özkoç, Canan Kocapınar, Hatice Alkan

Abstract:

Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.

Keywords: Pell equation, solutions of Pell equation.

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1544 Behavior of Solutions of the System of Recurrence Equations Based on the Verhulst-Pearl Model

Authors: Vladislav N. Dumachev, Vladimir A. Rodin

Abstract:

By utilizing the system of the recurrence equations, containing two parameters, the dynamics of two antagonistically interconnected populations is studied. The following areas of the system behavior are detected: the area of the stable solutions, the area of cyclic solutions occurrence, the area of the accidental change of trajectories of solutions, and the area of chaos and fractal phenomena. The new two-dimensional diagram of the dynamics of the solutions change (the fractal cabbage) has been obtained. In the cross-section of this diagram for one of the equations the well-known Feigenbaum tree of doubling has been noted.Keywordsbifurcation, chaos, dynamics of populations, fractals

Keywords: bifurcation, chaos, dynamics of populations, fractals

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