Search results for: second and third order derivatives

Authors: E. C. Mattos, V. S. M. G. Daros, R. Dal Col, A. L. Nascimento

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The aim of this study is to present the results of a retrospective survey on the foreign matter found in foods analyzed at the Adolfo Lutz Institute, from July 2001 to July 2015. All the analyses were conducted according to the official methods described on Association of Official Agricultural Chemists (AOAC) for the micro analytical procedures and Food and Drug Administration (FDA) for the macro analytical procedures. The results showed flours, cereals and derivatives such as baking and pasta products were the types of food where foreign matters were found more frequently followed by condiments and teas. Fragments of stored grains insects, its larvae, nets, excrement, dead mites and rodent excrement were the most foreign matter found in food. Besides, foreign matters that can cause a physical risk to the consumer’s health such as metal, stones, glass, wood were found but rarely. Miscellaneous (shell, sand, dirt and seeds) were also reported. There are a lot of extraneous materials that are considered unavoidable since are something inherent to the product itself, such as insect fragments in grains. In contrast, there are avoidable extraneous materials that are less tolerated because it is preventable with the Good Manufacturing Practice. The conclusion of this work is that although most extraneous materials found in food are considered unavoidable it is necessary to keep the Good Manufacturing Practice throughout the food processing as well as maintaining a constant surveillance of the production process in order to avoid accidents that may lead to occurrence of these extraneous materials in food.

Keywords: extraneous materials, food contamination, foreign matter, surveillance

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Mahmoud H. Abu Elella, Riham R. Mohamed, Magdy W. Sabaa

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Firstly, synthesis of N-Quaternized Chitosan (NQC), then it was proven by FTIR and 1H-NMR analysis. The degree of quaternization(DQ 35% ) was determined by equation. Secondly, synthesis of cross-linked hydrogels composed of NQC and poly (vinyl alcohol) (PVA) in different weight ratios in presence of glutaraldehyde (GA) as cross-linking agent. Characterization of the prepared hydrogels was done using FTIR, SEM, XRD,and TGA. Swellability in simulated body fluid (SBF) solutions applied on NQC / PVA hydrogels and swelling rate(Wt%) and metal ions uptake was done on it.

Keywords: hydrogel, metal ions uptake, N-quaternized chitosan, poly (vinyl alcohol), swellability

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Authors: J. Cecrdle

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This paper deals with the whirl flutter of the turboprop aircraft structures. It is focused on the influence of the blade lift span-wise distribution on the whirl flutter stability. Firstly it gives the overall theoretical background of the whirl flutter phenomenon. After that the propeller blade forces solution and the options of the blade lift modelling are described. The problem is demonstrated on the example of a twin turboprop aircraft structure. There are evaluated the influences with respect to the propeller aerodynamic derivatives and finally the influences to the whirl flutter speed and the whirl flutter margin respectively.

Keywords: aeroelasticity, flutter, propeller blade force, whirl flutter

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

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The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: control, limits cycle, robot, stability

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Authors: Zeineb Baatout, Safa Teka, Nejmeddine Jaballah, Nawfel Sakly, Xiaonan Sun, Mustapha Majdoub

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Currently, the economic interests linked to the development of bio-based materials make biomass one of the most interesting areas for science development. We are interested in the β-cyclodextrin (β-CD), one of the popular bio-sourced macromolecule, produced from the starch via enzymatic conversion. It is a cyclic oligosaccharide formed by the association of seven glucose units. It presents a rigid conical and amphiphilic structure with hydrophilic exterior, allowing it to be water-soluble. It has also a hydrophobic interior enabling the formation of inclusion complexes, which support its application for the elaboration of electrochemical and optical sensors. Nevertheless, the solubility of β-CD in water makes its use as sensitive layer limit and difficult due to their instability in aqueous media. To overcome this limitation, we chose to precede by modification of the hydroxyl groups to obtain hydrophobic derivatives which lead to water-stable sensing layers. Hence, a series of benzylated β-CDs were synthesized in basic aqueous media in one pot. This work reports the synthesis of a new family of substituted amphiphilic β-CDs using a green methodology. The obtained β-CDs showed different degree of substitution (DS) between 0.85 and 2.03. These organic macromolecular materials were soluble in common organic volatile solvents, and their structures were investigated by NMR, FT-IR and MALDI-TOF spectroscopies. Thermal analysis showed a correlation between the thermal properties of these derivatives and the benzylation degree. The surface properties of the thin films based on the benzylated β-CDs were characterized by contact angle measurements and atomic force microscopy (AFM). These organic materials were investigated as sensitive layers, deposited on quartz crystal microbalance (QCM) gravimetric transducer, for humidity sensor at room temperature. The results showed that the performances of the prepared sensors are greatly influenced by the benzylation degree of β-CD. The partially modified β-CD (DS=1) shows linear response with best sensitivity, good reproducibility, low hysteresis, fast response time (15s) and recovery time (17s) at higher relative humidity levels (RH) between 11% and 98% in room temperature.

Keywords: β-cyclodextrin, green synthesis, humidity sensor, quartz crystal microbalance

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Authors: Kiwon Yeom

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Change points are abrupt variations in a data sequence. Detection of change points is useful in modeling, analyzing, and predicting time series in application areas such as robotics and teleoperation. In this paper, a change point is defined to be a discontinuity in one of its derivatives. This paper presents a reliable method for detecting discontinuities within a three-dimensional trajectory data. The problem of determining one or more discontinuities is considered in regular and irregular trajectory data from teleoperation. We examine the geometric detection algorithm and illustrate the use of the method on real data examples.

Keywords: change point, discontinuity, teleoperation, abrupt variation

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Authors: Enoch Kudoahor, Nan Zheng

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We describe the use of readily available self-doped TiO2 and visible light, under a mild condition to synthesize a class of monocyclic, bicyclic, and benzocyclobutene amino compounds containing the endoperoxide bridges; their derivatives and further test their effective clinical activities against malaria, cancer, and their resistances. Considering their stable under photooxidation conditions and recyclability, we use a self-doped TiO2 under a visible condition to synthesize these classes of amino endoperoxides. These amino endoperoxides are stable over a period compared to classes of endoperoxides.

Keywords: catalysis, endoperoxides, titanium dioxide, visible light

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Vivek Singh Bhadauria, Abhishek Pandey

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Indole-2,3-diones are known for their various biological activities. By suitable control of a substituent, different novel indole-2,3-diones were synthesized. In this present study, various Schiff and Mannich bases were synthesized and characterized, and evaluated their for different pharmacological activities. The compounds were prepared by reacting indole-2,3-dione with benzyl chloride and 4-substituted thiosemicarbazides. All the synthesized compounds were characterized by the TLC, MP, Elemental analysis, FTIR, 1H-NMR and Mass spectroscopy. The compounds have been evaluated for their anticancer, antituberculosis, anticonvulsant, antiinflammatory as well as anti-SARS activity and the results are presented. Some of compounds possessed different pharmacological activity at a concentration of 200 mg/kg body weight and even at lower concentration.

Keywords: indoles, isatin, NMR, biological activities

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Authors: Fouzi Aboura

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The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s.

Keywords: FOPID controller, fractional order, AVR system, objective function, optimization, GA, PSO, HGAPSO

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Authors: Adnan Bekhit, Eskedar Lodebo, Ariaya Hymete, Hanan Ragab, Alaa El-Din Bekhit

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Malaria and leishmaniasis have emerged as serious universal health problems throughout history of mankind. According to the WHO 2008 malarial report, half of the world population is at risk of malarial infection with an estimate of 1 million deaths occurring annually mainly in the African region. Furthermore, 12-15 million people are infected with Leishmaniasis worldwide. Despite the continuous introduction of a large number of agents for the treatment of malaria, there is still unmet medical needs due to the emergence of resistance. Resistance has occurred for almost all therapeutic agents approved for the treatment of malaria. Accordingly, it was the aim of this work to design and synthesis a group of antimalarial-antileshmanial agents that would show inhibitory activity against chloroquine-resistant strain of Plasmodium falciparum. The synthesized compounds were designed to contain a pyrazolylpyrazoline moiety having an aromatic group (p-tolyl or p-chlorophenyl) at N1-position of one pyrazoline ring due to the reports of promising activities of such compounds. A formyl or acyl substituent was introduced at the N1-position of the other pyrazoline ring, to investigate the effect of bulkiness of acyl substituents at this position. The synthesized compounds were evaluated for their in-vivo antimalarial activity against Plasmodium berghei infected mice at dose levels of 20 and 30 mg/Kg. the two most active compounds were evaluated for their antimalarial activity against chloroquin-resistant strain (RKL9) of Plasmodium falciparum. In addition, the synthesized compounds were tested for their in-vitro antileshmanial activity against Leishmania aethiopica promastigotes and amastigotes. For both antimalarial and antileishmanial activities, compounds having an N1-p-tolyl group at the first pyrazoline ring did not require bulkiness at the second pyrazoline ring nitrogen where the compound bearing an acetyl group proved to be the most active of the whole series. On the other hand, bulkiness at the N1-position of the second pyazoline ring was necessary in case of compounds carrying the p-chlorophenyl group, where the two derivatives having an N1-butanoyl and an N1-benzoyl moieties at the second pyrazoline showed the best activity. Furthermore, the toxicity of the active compounds were tested and were proved to be non-toxic at 125, 250 and 500 mg/Kg. In addition, docking of the most active compound (having a p-tolyl group at the first pyrazoline-N and an acetyl moiety on the other pyrazoline-N) was performed against dihydrofolate reductase enzyme.

Keywords: pyrazoline derivatives, in-vivo antimalarial activity, docking, dihydrofolate reductase

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Ariesny Vera, Rodrigo Montecinos

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The rare-earth elements (REEs) or rare-earth metals (REMs), correspond to seventeen chemical elements composed by the fifteen lanthanoids, as well as scandium and yttrium. Lanthanoids corresponds to lanthanum and the f-block elements, from cerium to lutetium. Scandium and yttrium are considered rare-earth elements because they have ionic radii similar to the lighter f-block elements. These elements were called rare earths because they are simply more difficult to extract and separate individually than the most metals and, generally, they do not accumulate in minerals, they are rarely found in easily mined ores and are often unfavorably distributed in common ores/minerals. REEs show unique chemical and physical properties, in comparison to the other metals in the periodic table. Nowadays, these physicochemical properties are utilized in a wide range of synthetic, catalytic, electronic, medicinal, and military applications. Because of their applications, the global demand for rare earth metals is becoming progressively more important in the transition to a self-sustaining society and greener economy. However, due to the difficult separation between lanthanoid ions, the high cost and pollution of these processes, the scientists search the development of a method that combines selectivity and quantitative separation of lanthanoids from the leaching liquor, while being more economical and environmentally friendly processes. This motivation has favored the design and development of more efficient and environmentally friendly cation extractors with the incorporation of compounds as ionic liquids, membrane inclusion polymers (PIM) and supramolecular systems. Supramolecular chemistry focuses on the development of host-guest systems, in which a host molecule can recognize and bind a certain guest molecule or ion. Normally, the formation of a host-guest complex involves non-covalent interactions Additionally, host-guest interactions can be influenced among others effects by the structural nature of host and guests. The different macrocyclic hosts for lanthanoid species that have been studied are crown ethers, cyclodextrins, cucurbituryls, calixarenes and pillararenes.Among all the factors that can influence and affect lanthanoid (III) coordination, perhaps the most basic of them is the systematic control using macrocyclic substituents that promote a selective coordination. In this sense, macrocycles pillar[n]arenes (P[n]As) present a relatively easy functionalization and they have more π-rich cavity than other host molecules. This gives to P[n]As a negative electrostatic potential in the cavity which would be responsible for the selectivity of these compounds towards cations. Furthermore, the cavity size, the linker, and the functional groups of the polar headgroups could be modified in order to control the association of lanthanoid cations. In this sense, different P[n]As systems, specifically derivatives of the pentamer P[5]A functionalized with amide, amine, phosphate and sulfate derivatives, have been designed in terms of experimental synthesis and molecular dynamics, and the interaction between these P[5]As and some lanthanoid ions such as La³+, Eu³+ and Lu³+ has been studied by physicochemical characterization by 1H-NMR, ITC and fluorescence in the case of Eu³+ systems. The molecular dynamics study of these systems was developed in hexane as solvent, also taking into account the lanthanoid ions mentioned above, and the respective comparison studies between the different ions.

Keywords: lanthanoids, macrocycles, pillar[n]arenes, rare-earth metal extraction, supramolecular chemistry, supramolecular complexes.

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Authors: Anelise Leal Vieira Cubas, Marina de Medeiros Machado, Marília de Medeiros Machado

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The volatile organic compounds - BTEX (Benzene, Toluene, Ethylbenzene, and Xylene) petroleum derivatives, have high rates of toxicity, which may carry consequences for human health, biota and environment. In this direction, this paper proposes a method of treatment of these compounds by using corona discharge plasma technology. The efficiency of the method was tested by analyzing samples of BTEX after going through a plasma reactor by gas chromatography method. The results show that the optimal residence time of the sample in the reactor was 8 minutes.

Keywords: BTEX, degradation, cold plasma, ecological sciences

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Authors: Mamdouh Abu-Zaied, K. Mohamed, Galal A. Nawwar

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Microwave-assisted synthesis of a new class of pyridine or purine thioglycoside analogs from readily available starting materials has been described. The key step of this protocol is the formation of sodium pyridine 4-thiolate 4 and pyrazolo[1,5-a]pyrimidine-7-thiolate 5 derivatives via condensation of 1 with cyanoacetanilide derivative 2 or 5-aminopyrazole derivative 3 respectively under microwave irradiation, followed by coupling with halo sugars to give the corresponding pyridine and purine thioglycoside analogs. The obtained compounds were evaluated in vitro against lung (A549), colon (HCT116), liver (HEPG2), and MCF-7(breast) cancer cell lines. Some of them recorded promising activities.

Keywords: antitumor, cyclic sugars, pyrazoles, pyridines, pyrimidines, purines, thioglycosides

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Matthew C. Best

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Linear Multi-Input Multi-Output (MIMO) dynamic models can be identified, with no a priori knowledge of model structure or order, using a new Generalised Identifying Filter (GIF). Based on an Extended Kalman Filter, the new filter identifies the model iteratively, in a continuous modal canonical form, using only input and output time histories. The filter’s self-propagating state error covariance matrix allows easy determination of convergence and conditioning, and by progressively increasing model order, the best fitting reduced-order model can be identified. The method is shown to be resistant to noise and can easily be extended to identification of smoothly nonlinear systems.

Keywords: system identification, Kalman filter, linear model, MIMO, model order reduction

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Authors: F. Boudet, V. Galano, D. Gmira, L. Munoz, A. Reina

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Commodities pricing needs a specific approach as they are often linked to each other and so are expectedly doing their prices. They are called co-integrated when at least one stationary linear combination exists between them. Though widespread in economic literature, and even if many equilibrium relations and co-movements exist in the economy, this principle of co-movement is not developed in derivatives field. The present study focuses on the following problem: How can the price of a forward agreement on a commodity be simulated, when it is co-integrated with other ones? Theoretical analysis is developed from Gibson-Schwartz model and an analytical solution is given for short maturities contracts and under risk-neutral conditions. The application has been made to crude oil and heating oil energy commodities and result confirms the applicability of proposed method.

Keywords: co-integration, commodities, forward pricing, Gibson-Schwartz

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Claus Bier, Dennis Binder, Alexander Gruenberger, Dagmar Drobietz, Dietrich Kohlheyer, Anita Loeschcke, Karl Erich Jaeger, Thomas Drepper, Joerg Pietruszka

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Light absorbing chromophoric systems are important optogenetic tools for biotechnical and biophysical investigations. Processes such as fluorescence or photolysis can be triggered by light-absorption of chromophores. These play a central role in life science. Photocaged compounds belong to such chromophoric systems. The photo-labile protecting groups enable them to release biologically active substances with high temporal and spatial resolution. The properties of photocaged compounds are specified by the characteristics of the caging group as well as the characteristics of the linked effector molecule. In our research, we work with different types of photo-labile protecting groups and various effector molecules giving us possible access to a large library of caged compounds. As a function of the caged effector molecule, a nearly limitless number of biological systems can be directed. Our main interest focusses on photocaging carbohydrates (e.g. arabinose) and their derivatives as effector molecules. Based on these resulting photocaged compounds a precisely controlled photoinduced gene expression will give us access to studies of numerous biotechnological and synthetic biological applications. It could be shown, that the regulation of gene expression via light is possible with photocaged carbohydrates achieving a higher-order control over this processes. With the one-step cleavable photocaged carbohydrate, a homogeneous expression was achieved in comparison to free carbohydrates.

Keywords: bacterial gene expression, biotechnology, caged compounds, carbohydrates, optogenetics, photo-removable protecting group

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Van Tran Thi Thuy, Dukjoon Kim

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A series of pH- and thermosensitive poly(N-isopropyl acrylamide-co-acrylic acid) were synthesized by radical polymerization and grafted on poly succinimide backbones. The poly succinimide derivatives synthesized were coated on iron oxide magnetic nanoparticles for potential applications in drug delivery systems with theranostic and molecular imaging. The structure of polymer shell was confirmed by FT-IR, H-NMR spectroscopies. Its thermal behavior was tested by UV-Vis spectroscopy. The particle size and its distribution are measured by dynamic light scattering (DLS) and transmission electron microscope (TEM). The mean diameter of the core-shell structure is from 20 to 80 nm.

Keywords: magnetic, nano, PNIPAM, polysuccinimide

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Authors: Dmitriy Yu. Korulkin, Raissa A. Muzychkina

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The article represents the results of research of antitumor activity of different structural types of plant flavonoids extracted by authors from Polygonum L. plants in commercial reserves at the territory of the Republic of Kazakhstan. For the first time ever the results comparative research of antitumor activity of plant flavonoids of different structural groups and their synthetic derivatives have been represented. The results of determination of toxicity of flavonoids in single parenteral infusion conditions have been represented. Experimental substantiation of possible mechanisms of antiproliferative and cytotoxic action of flavonoids has been suggested. The perspectives of usage of plant flavonoids as medications and creation of effective dosage forms of antitumor medicines on their basis have been substantiated.

Keywords: antitumor activity, cytotoxicity, flavonoids, Polygonum L., secondary metabolites

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