Search results for: invariant solutions

Authors: M. O. Olayiwola

Abstract:

Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Kanita Beširević

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Open-source software development activities highly rely on Internet gathering communities volunteering in software development projects. Additionally, the libraries and cultural institutions share their metadata in the form of linked metadata to enable dissemination and enrichment. The open-source software provides free alternatives to traditional software solutions. The article aims to investigate the ever-increasing options for the digital library open source software adoption. The software available is presented and compared to other software solutions as well as to their previous versions. The top three open-source digital library software solutions are presented and compared. The comparison criteria are adopted from the UNESCO study by Bankier, J., & Gleason, K. Institutional Repository Software Comparison comprising of twelve criteria to appraise software, namely: infrastructure, front-end design, content discovery, publication tools, interoperability, and preservation. This article adopts a descriptive methodology based on data and information collected through selected software websites and the literature review.

Keywords: open source software, digital library, DSpace, Fedora, Greenstone

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Authors: Godwin Makaudze

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The majority of women in contemporary Zimbabwe continue to hold marginalised and insignificant positions in society and to be accorded negative and stereotyped images in literature. In light of this, government and civic organisations and even writers channel many resources, time, and efforts towards the emancipation of the female gender. Using the Africana womanist and socio-historical literary theories and focussing on two post-colonial novels, this paper re-engages the dis-empowerment of women in contemporary Zimbabwe, examining the believed causes and suggested solutions. The paper observes that the writers whip the already whipped by blaming patriarchy, African men and cultural practices as the underlying causes of such a sorry state of affairs while at the same time celebrating war against all these, as well as education, unity among women, Christianity and single motherhood as panaceas to the problem. The paper concludes that the writers’ anger is misdirected as they have fallen trap to the very popular yet mythical victim-blame motif espoused by many writers who focus on Shona people’s problems.

Keywords: cultural practices, female dis-empowerment, patriarchy, Shona novel, solutions, Zimbabwe

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Authors: A. Belay, B. Kebede

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The concentration- and temperature-dependent refractive indices of solutions extracted from defective and non-defective coffee beans have been investigated using a He–Ne laser. The refractive index has a linear relationship with the presumed concentration of the coffee solutions in the range of 0.5–3%. Higher and lower values of refractive index were obtained for immature and non-defective coffee beans, respectively. The Refractive index of bean extracts can be successfully used to separate defective from non-defective beans.

Keywords: coffee extract, refractive index, temperature dependence

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Tomáš Bublík, Miroslav Virius

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This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and sub graph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

Keywords: AST, Java, tree matching, scripthon source code recognition

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Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

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It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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Authors: Shao-Yuan Huang

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We study the shape of the bifurcation curve of positive solutions for the semipositone problem with the Minkowski-curvature operator. The Minkowski-curvature problem plays an important role in certain fundamental issues in differential geometry and in the special theory of relativity. In addition, it is well known that studying the multiplicity of positive solutions is equivalent to studying the shape of the bifurcation curve. By the shape of the bifurcation curve, we can understand the change in the multiplicity of positive solutions with varying parameters. In this paper, our main technique is a time-map method used in Corsato's PhD Thesis. By this method, studying the shape of the bifurcation curve is equivalent to studying the shape of a certain function T with improper integral. Generally speaking, it is difficult to study the shape of T. So, in this paper, we consider two cases that the nonlinearity is convex or concave. Thus we obtain the following results: (i) If f''(u) < 0 for u > 0, then the bifurcation curve is C-shaped. (ii) If f''(u) > 0 for u > 0, then there exists η>β such that the bifurcation curve does not exist for 0 η. Furthermore, we prove that the bifurcation is C-shaped for L > η under a certain condition.

Keywords: bifurcation curve, Minkowski-curvature problem, positive solution, time-map method

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Authors: Abdulai Abubakari

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The rollercoaster relationship between farmers and herders in Sub-Saharan Africa has compelled most governments to undertake different mitigating strategies. Over the past two decades, the expulsion of migrant herdsmen, the killing of cattle and human beings, and fines have been used by the state and aggrieved individuals to resolve the conflicts. Unlike this paper, most of the research conducted on this subject matter has been largely theoretical and lacks practical solutions to the conflicts. This paper is unique because it focuses on concrete strategies and practical solutions to ending the century-old phenomenon of farmer-herder conflicts in Ghana. The paper employed power or compete (fight) theory as well as compromise and negotiation theories in the analyses. The paper employed, basically, socio-anthropological methods: interviews, focus group discussions, and observations to gather data. The paper found that compromises through negotiation with the stakeholders are the best ways of resolving these conflicts. Through this, we support the compromise and negotiation approach rather than expulsion to resolve farmer-herder conflicts.

Keywords: farmer-herder, conflict, prevention, strategies, stakeholders

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: Mojtaba Hakimi-Moghaddam

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Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Anuar Ishak

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The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: Sara Ramezanzadeh, Nashid Nabian

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Historically, pandemics in different periods have caused compulsory changes in human life. In the case of Covid-19, according to the limitations and established care instructions, spatial alignment with the conditions is important. Following the outbreak of Covid-19, the question raised in this study is how to do spatial design in five scales, namely object, space, architecture, city, and infrastructure, in response to the consequences created in the realms under study. From the beginning of the pandemic until now, some changes in the spatial realm have been created spontaneously or by space users. These transformations have been mostly applied in modifiable parts such as furniture arrangement, especially in work-related spaces. To implement other comprehensive requirements, flexibility and adaptation of space design to the conditions resulting from the pandemics are needed during and after the outbreak. Studying the effects of pandemics from the past to the present, this research covers eight major realms, including three categories of ramifications, solutions, and paradigm shifts, and analytical conclusions about the solutions that have been created in response to them. Finally, by the consideration of epidemiology as a modern discipline influencing the design, spatial solutions in the five scales mentioned (in response to the effects of the eight realms for spatial adaptation in the face of pandemics and their following conditions) are presented as a series of guidelines. Due to the unpredictability of possible pandemics in the future, the possibility of changing and updating the provided guidelines is considered.

Keywords: pandemics, Covid 19, spatial design, ramifications, solutions, paradigm shifts, guidelines

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

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

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

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Authors: Enqing Chen, Jianbo Wang

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It is well known that the wavelet transform provides a very effective framework for multiscale edges analysis. However, wavelets are not very effective in representing images containing distributed discontinuities such as edges. In this paper, we propose a novel multiscale edge detection method in nonsubsampled contourlet transform (NSCT) domain, which is based on the dominant multiscale, multidirection edge expression and outstanding edge location of NSCT. Through real images experiments, simulation results demonstrate that the proposed method is better than other edge detection methods based on Canny operator, wavelet and contourlet. Additionally, the proposed method also works well for noisy images.

Keywords: edge detection, NSCT, shift invariant, modulus maxima

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Authors: Mallappa A. Devani, John U. Kennedy Oubagaranadin, Basudeb Munshi

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In this preliminary work, locally available husk of Cajanus cajan (commonly known in India as Tur or Arhar), a bio-waste, has been used in its physically treated and chemically activated form for the removal of binary Cu (II) and Zn(II) ions from the real waste water obtained from an electroplating industry in Bangalore, Karnataka, India and from laboratory prepared binary solutions having almost similar composition of the metal ions, for comparison. The real wastewater after filtration and dilution for five times was used for biosorption studies at the normal pH of the solutions at room temperature. Langmuir's binary model was used to calculate the metal uptake capacities of the biosorbents. It was observed that Cu(II) is more competitive than Zn(II) in biosorption. In individual metal biosorption, Cu(II) uptake was found to be more than that of the Zn(II) and a similar trend was observed in the binary metal biosorption from real wastewater and laboratory prepared solutions. FTIR analysis was carried out to identify the functional groups in the industrial wastewater and EDAX for the elemental analysis of the biosorbents after experiments.

Keywords: biosorption, Cajanus cajan, multi metal remediation, wastewater

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Authors: Sepideh Jabbari Behnam, Elnaz Mohsenin

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Today, with the rapid growth of urbanization, urban issues are so problematic more than ever. These problems have various origins and they should be studied in different aspects. One of these problems is destroying the structure and identity of urban-rural textures around cities. This destruction appears due to an uncontrolled and unplanned growth of large cities inside and/or connecting suburban areas to the cities. These textures which were called urban-rural areas are faced with the dual identity of rural and urban tissues. It should be noted that, urban-rural areas have the potential for creating urban habitats with the rural nature. However; these areas, due to lack of planning and proper management have encountered serious problems. The main objective of this article is offering some solutions for the structural-physical problems of urban-rural areas with the using of morphological principles and studies. In this case, after morphological studies of one of urban-rural texture example, and also with the use of offered research literature, general solutions have been suggested to solve some of these textures' issues.

Keywords: morphology, typo- morphology, urban-rural, urban texture

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Authors: Umm-E-Hani, Faiza Babar, Hanif Durad

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Malware-detecting approaches suffer many limitations, due to which all anti-malware solutions have failed to be reliable enough for detecting zero-day malware. Signature-based solutions depend upon the signatures that can be generated only when malware surfaces at least once in the cyber world. Another approach that works by detecting the anomalies caused in the environment can easily be defeated by diligently and intelligently written malware. Solutions that have been trained to observe the behavior for detecting malicious files have failed to cater to the malware capable of detecting the sandboxed or protected environment. Machine learning and deep learning-based approaches greatly suffer in training their models with either an imbalanced dataset or an inadequate number of samples. AI-based anti-malware solutions that have been trained with enough samples targeted a selected feature vector, thus ignoring the input of leftover features in the maliciousness of malware just to cope with the lack of underlying hardware processing power. Our research focuses on producing an anti-malware solution for detecting malicious PE files by circumventing the earlier-mentioned shortcomings. Our proposed framework, which is based on automated feature engineering through autoencoders, trains the model over a fairly large dataset. It focuses on the visual patterns of malware samples to automatically extract the meaningful part of the visual pattern. Our experiment has successfully produced a state-of-the-art accuracy of 99.54 % over test data.

Keywords: malware, auto encoders, automated feature engineering, classification

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Authors: Hidouri Sami, Aguili Taoufik

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We consider fast and accurate solutions of scattering problems by large perfectly conducting objects (PEC) formulated by an optimization of the Method of Auxiliary Sources (MAS). We present various techniques used to reduce the total computational cost of the scattering problem. The first technique is based on replacing the object by an array of finite number of small (PEC) object with the same shape. The second solution reduces the problem on considering only the half of the object.These two solutions are compared to results from the reference bibliography.

Keywords: method of auxiliary sources, scattering, large object, RCS, computational resources

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Authors: Elionai Moura, José A. Cunha, César Analide

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This work introduces a proposal scheme for an Intelligent System applied to Pedagogical Advising using Case-Based Reasoning, to find consolidated solutions before used for the new problems, making easier the task of advising students to the pedagogical staff. We do intend, through this work, introduce the motivation behind the choices for this system structure, justifying the development of an incremental and smart web system who learns bests solutions for new cases when it’s used, showing technics and technology.

Keywords: case-based reasoning, pedagogical advising, educational data-mining (EDM), machine learning

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Authors: Rabih Al-Kaysi

Abstract:

When quasi-stable solutions of 9-methylanthracene (pi-electron donor, 0.0005 M) and 1,2,4,5-Tetracyanobenzene (pi-electron acceptor, 0.0005 M) in aqueous sodium dodecyl sulfate (SDS, 0.025 M) were gently mixed, uniform-shaped rectangular charge-transfer nanocrystals precipitated out. These red colored charge-transfer (CT) crystals were composed of a 1:1-mole ratio of acceptor/ donor and are highly insoluble in water/SDS solution. The rectangular crystals morphology is semi hollow with symmetrical twin pockets reminiscent of nanocapsules. For a typical crop of nanocapsules, the dimensions are 21 x 6 x 0.5 microns with an approximate hollow volume of 1.5 x 105 nm3. By varying the concentration of aqueous SDS, mixing duration and incubation temperature, we can control the size and volume of the nanocapsules. The initial number of CT seed nanoparticles, formed by mixing the D and A solutions, determined the number and dimensions of the obtained nanocapsules formed after several hours of incubation under still conditions. Prolonged mixing of the donor and acceptor solutions resulted in plenty of initial seeds hence smaller nanocapsules. Short mixing times yields less seed formation and larger micron-sized capsules. The addition of Doxorubicin in situ with the quasi-stable solutions while mixing leads to the formation of CT nanocapsules with Doxorubicin sealed inside. The Doxorubicin can be liberated from the nanocapsules by cracking them using ultrasonication. This method can be extended to other binary CT complex crystals as well.

Keywords: charge-transfer, nanocapsules, nanocrystals, doxorubicin

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Authors: Michael Zimba

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A novel set of features for copy-move image forgery, CMIF, detection method is proposed. The proposed set presents a new approach which relies on electrostatic field theory, EFT. Solely for the purpose of reducing the dimension of a suspicious image, firstly performs discrete wavelet transform, DWT, of the suspicious image and extracts only the approximation subband. The extracted subband is then bijectively mapped onto a virtual electrostatic field where concepts of EFT are utilised to extract robust features. The extracted features are shown to be invariant to additive noise, JPEG compression, and affine transformation. The proposed features can also be used in general object matching.

Keywords: virtual electrostatic field, features, affine transformation, copy-move image forgery

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Authors: Timothy Akinwande, Eddie C. M. Hui

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Housing the urban poor has remained a challenge for many years across the world, especially in developing economies, despite the apparent research attention and policy interventions. It is apt to investigate the prevalent affordable housing (AH) provision challenges using unconventional approaches. It is pragmatic to thoroughly examine housing experts to provide supply-side solutions to AH challenges and investigate informal settlers to deduce solutions from AH demand viewpoints. This study being the supply-side investigation of an ongoing research, interrogated housing experts to determine significant expert solutions. Focus group discussions and in-depth interviews were conducted with housing experts in Nigeria. Through descriptive, content, and systematic thematic analyses of data, major findings are that deliberate finance models designed for the urban poor are the most significant housing finance solution in developing economies. Other findings are that adequately implemented rent control policies, deliberate PPP approaches like inclusionary housing and land-value capture, and urban renewal programmes to enlighten and tutor the urban poor on how to earn more, spend wisely, and invest in their own better housing will effectively solve AH finance challenges. Study findings are informative for the best approaches to achieve effective, affordable housing finance for the urban poor in Nigeria, which is indispensable for the achievement of sustainable development goals. This research’s originality lies in the exploration of experts’ opinions in relation to AH finance to produce an equation model of critical solutions to AH finance challenges. Study data are useful resources for future pro-poor housing studies. This study makes housing policy-oriented recommendations toward effective, affordable housing for the urban poor in developing countries.

Keywords: affordable housing, effective affordable housing, housing policy, housing research, sustainable development, urban poor

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Oral Lacin, Turan Calban, Fatih Sevim, Taner Celik

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In this study, Pb²⁺ uptake by the hydroxyapatite nanopowders (n-Hap) from aqueous solutions was investigated by using batch adsorption techniques. The adsorption equilibrium studies were carried out as a function of contact time, adsorbent dosage, pH, temperature, and initial Pb²⁺ concentration. The results showed that the equilibrium time of adsorption was achieved within 60 min, and the effective pH was selected to be 5 (natural pH). The maximum adsorption capacity of Pb²⁺ on n-Hap was found as 565 mg.g^-1. It is believed that the results obtained for adsorption may provide a background for the detailed mechanism investigations and the pilot and industrial scale applications.

Keywords: nanopowders, hydroxyapatite, heavy metals, adsorption

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Pramod Kumar, A. V. N. Swamy, C. V. Sowjanya, C. V. Ramachandra Murthy

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Biosorption is one of the effective methods for the removal of heavy metal ions from aqueous solutions. Results are presented showing the sorption of Pb(II) from solutions by biomass of commonly available marine algae Chlorella sp. The ability of marine algae Chlorella pyrenoidosa to remove heavy metal ion (Pb(II)) from aqueous solutions has been studied in this work. The biosorption properties of the biosorbent like equilibrium agitation time, optimum pH, temperature and initial solute concentration were investigated on metal uptake by showing respective profiles. The maximum metal uptake was found to be 10.27 mg/g. To achieve this metal uptake, the optimum conditions were found to be 30 min as equilibrium agitation time, 4.6 as optimum pH, 60 ppm of initial solute concentration. Lead concentration is determined by atomic absorption spectrometer. The process was found to be well fitted for pseudo-second order kinetics.

Keywords: biosorption, heavy metal ions, agitation time, metal uptake, aqueous solution

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Authors: Megh Patel, Arjun Chauhan, Jay Thakkar

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Hydrofracturing is the most prominent but at the same time expensive, highly skilled and time consuming well stimulation technique. Due to high cost and skilled labor involved, it is generally carried out as the consummate solution among other well stimulation techniques. Considering today’s global petroleum market, no gaffe or complications could be entertained during fracturing, as it would further hamper the current dwindling economy. The literature would be dealing with the challenges encountered during fracturing low temperature waxy reservoirs and the prominent solutions to overcome such teething troubles. During fracturing treatment for, shallow and high freezing point waxy oil reservoirs, the first line problems are to overcome uncompleted breakdown, uncompleted cleanup of fracturing fluids and cold damages to the formations by injecting cold fluid (fluid at ambient conditions). Injecting fracturing fluids at ambient conditions have the tendency to decrease the near wellbore reservoir temperature below the freezing point of oil reservoir and hence leading to wax deposition around the wellbore thereby hampering the fluid production as well as fracture propagation. To overcome such problems, solutions such as hot fracturing fluid injection, encapsulated heat generating hydraulic fracturing fluid system, and injection of wax inhibitor techniques would be discussed. The paper would also be throwing light on changes in rheological properties occurred during heating fracturing fluids and solutions to deal with it taking economic considerations into account.

Keywords: hydrofracturing, waxy reservoirs, low temperature, viscosity, crosslinkers

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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