Search results for: Derivatives

Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: J. Cecrdle

Abstract:

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 modeling 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: Nelly К. Akhmatova, Оlga V. Lebedinskaya, Ancha V. Baranova, Еlena А. Lebedinskaya, Ekaterina V. Sorokina, Elvin А. Akhmatov, Аnatoliy P. Godovalov, Stanislav G. Markushin

Abstract:

An influence of intranasal combined injection of live cold-adapted influenza vaccine with chitosan derivatives as adjuvants on the subpopulation structure of mononuclear leukocytes of mouse spleen which reflects the orientation of the immune response was studied. It is found that the inclusion of chitosan preparations promotes activation of cellular-level of immune response.

Keywords: Immunophenotype, chitosan, cold-adapted vaccine, intranasal injection.

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

Abstract:

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 directon, 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.

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Authors: Giovanni Incerti

Abstract:

The motion planning procedure described in this paper has been developed in order to eliminate or reduce the residual vibrations of electromechanical positioning systems, without augmenting the motion time (usually imposed by production requirements), nor introducing overtime for vibration damping. The proposed technique is based on a suitable choice of the motion law assigned to the servomotor that drives the mechanism. The reference profile is defined by a Bezier curve, whose shape can be easily changed by modifying some numerical parameters. By means of an optimization technique these parameters can be modified without altering the continuity conditions imposed on the displacement and on its time derivatives at the initial and final time instants.

Keywords: Servomechanism, residual vibrations, motion optimization.

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Authors: Jae-Hong Kwon, Myung-Ho Chung, Tae-Yeon Oh, Hyeon-Seok Bae, Byeong-Kwon Ju

Abstract:

End-substitution of quarterthiophene and sexithiophene with hexyl groups leads to highly soluble conjugated oligomers,DZ-dihexylquarterthiophene (DH-4T) and DZ-dihexylsexithiophene (DH-6T). We have characterized these oligomers for optical and electrical properties. We fabricated an organic thin film transistor (OTFT) using the above two air-stable p-type organic semiconductor materials. We obtained a stable characteristic curve. The field effect mobility, Pwas calculated to be 3.2910-4 cm2/Vs for DH-6T based OTFT; while the DH-4T based OTFT had 1.8810-5 cm2/Vs.KeywordsOrganic thin film transistor, DZ-dihexylquarterthiophene, DZ-dihexylsexithiophene.

Keywords: Organic thin film transistor, DZ-dihexylquarterthiophene, DZ-dihexylsexithiophene.

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Authors: Dmitriy Yu. Korulkin, Raissa A. Muzychkina

Abstract:

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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Authors: Yi-Fang Hung, Jinn-Tsyy Lai

Abstract:

Lycopene, which can be extracted from plants and is very popular for fruit intake, is restricted for healthy food development due to its high price. On the other hand, it will get great safety concerns, especially in the food or cosmetic application, if the raw material of lycopene is produced by chemical synthesis. In this project, we provide a key technology to bridge the limitation as mentioned above. Based on the abundant bioresources of BCRC (Bioresource Collection and Research Center, Taiwan), a promising lycopene output will be anticipated by the introduction of fermentation technology along with industry-related core energy. Our results showed that addition of tween 80(0.2%) and span 20 produced higher amount of lycopene. And piperidine, when was added at 48hr to the cultivation medium, could promote lycopene excretion effectively also.

Keywords: photosynthetic bacteria, lycopene, tween80, Piperidine

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Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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Authors: Chahid K. Ghaddar

Abstract:

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 functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.

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Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: Ali Safdari-Vaighani

Abstract:

Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: Radial basis function, basket option, jump diffusion, RBF-PUM.

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Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

Abstract:

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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Authors: Rabindra Prasad Dhakal, Tatsuya Oshima, Yoshinari Baba

Abstract:

The polyfunctional and highly reactive bio-polymer, the chitosan was first regioselectively converted into dialkylated chitosan using dimsyl anionic solution(NaH in DMSO) and bromodecane after protecting amino groups by phthalic anhydride. The dibenzo-18-crown-6-ether, on the other hand, was converted into its carbonyl derivatives via Duff reaction prior to incorporate into chitosan by Schiff base formation. Thus formed diformylated dibenzo-18-crown-6-ether was condensed with lipophilic chitosan to prepare the novel solvent extraction reagent. The products were characterized mainly by IR and 1H-NMR. Hence, the multidentate crown ether-embedded polyfunctional bio-material was tested for extraction of Pd(II) and Pt(IV) in aqueous solution.

Keywords: Lipophilic chitosan, Duff reaction, crown ether and precious metal ions extraction.

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Authors: Vicente F. P. Aleixo, Augusto C. F. Saraiva, Jordan Del Nero

Abstract:

The production of devices in nanoscale with specific molecular rectifying function is one of the most significant goals in state-of-art technology. In this work we show by ab initio quantum mechanics calculations coupled with non-equilibrium Green function, the design of an organic two-terminal device. These molecular structures have molecular source and drain with several bridge length (from five up to 11 double bonds). Our results are consistent with significant features as a molecular rectifier and can be raised up as: (a) it can be used as bi-directional symmetrical rectifier; (b) two devices integrated in one (FET with one operational region, and Thyristor thiristor); (c) Inherent stability due small intrinsic capacitance under forward/reverse bias. We utilize a scheme for the transport mechanism based on previous properties of ¤Ç bonds type that can be successfully utilized to construct organic nanodevices.

Keywords: ab initio, Carotenoid, Charge Transfer, Nanodevice

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Authors: A. Komarovska, V. Kreicbergs, F. Diminš

Abstract:

Hydroxymethylfurfural (HMF) is formed by thermally treating products rich in carbohydrates. HMF and other furan derivatives are toxic. The aim of the research was to establish the content of HMF in gingerbread biscuits with honey and sugar syrup additives by using three leavening agents— ammonium carbonate (NH4HCO3 and (NH4)2CO3), baking powder, and baking soda (NaHCO3). The content of HMF is significantly affected by the leavening agent used. The content of HMF with honey where ammonium carbonate was used as additive range from 5.7 to 27.3mg 100g-1, but when sugar syrup is used the content varies from 2.3 to 7.4mg 100g-1. When baking powder and baking soda are used as leavening agents, the content of HMF exceeds 4mg 100g-1 in the event honey had been added and the baking time had been longer (10 minutes at 180°C or 9 minutes at 200°C).

Keywords: gingerbread biscuits, honey, hydroxymethylfurfural, rippers.

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Authors: Kazem Ghanbari, Yousef Gholami

Abstract:

This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators.

Keywords: Fractional derivatives and integrals, Hamiltonian system, Lyapunov type inequalities, stability, disconjugacy.

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Authors: Daomao Yang, Qizhi Wang

Abstract:

Monoterpenoids are mainly found in plant essential oils and they are ideal substrates for biotransformation into oxygen-containing derivatives with important commercial value due to their low price and simple structure. In this paper, eleven strains of endophytic fungi from Praxelis clematidea were used as test strains to conduct the whole cell biotransformation of the monoterpenoids: (+)-limonene, (-)-limonene and myrcene. The fungi were inoculated in 50 ml Sabouraud medium and incubated at 30 ℃ with the agitation of 150 r/min for 6 d, and then 0.5% (v/v) substrates were added into the medium and biotransformed for further 3 d. Afterwards the cultures were filtered, and extracted using equal volume of ethyl acetate. The metabolites were analyzed by GC-MS technique with NIST database. The Total Ion Chromatogram of the extractions from the eleven strains showed that the main product of (+)- and (-)-limonene biotransformation was limonene-1,2-diol, while it is limonene and linalool oxide for biotransformation of myrcene. This work will help screen the microorganisms to biotransform the monoterpenes.

Keywords: Endophytic fungi, (+)–limonene, (-)–limonene, myrcene.

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: U.K. Saha, L.K. Arora

Abstract:

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

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Authors: A. V. Goncharova, T. A. Karpenyuk, Y. S. Tsurkan, R. U. Beisembaeva, A. M. Kalbaeva, T. D. Mukasheva, L. V. Ignatova

Abstract:

Microorganisms isolated from water and soil of Kazakhstan to identify potential high-effective producers of the arachidonic acid, exhibiting a wide range of physiological activity and having practical applications were screened. Based on the results of two independent tests (the test on the sensitivity of the growth processes of microorganisms to acetylsalicylic acid - an irreversible inhibitor of PGH-synthase involved in the metabolism of arachidonic acid and its derivatives, the test for inhibition of peroxidase activity of membrane-bounding fraction of PGH - synthase by acetylsalicylic acid) were selected microbial cultures which are potential highproducer of arachidonic acid. They are characterized by a stable strong growth in the laboratory conditions. Identification of microorganism cultures based on morphological, physiological, biochemical and molecular genetic characteristics was performed.

Keywords: Arachidonic acid, aspirin-sensitive culture, bacteria, producers, screening.

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Authors: A. N. K. Nasir, R. M. T. Raja Ismail, M. A. Ahmad

Abstract:

The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum-s angle and cart-s position. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. Two controllers are presented such as Sliding Mode Control (SMC) and Proportional- Integral-Derivatives (PID) controllers for controlling the highly nonlinear system of inverted pendulum model. Simulation study has been done in Matlab Mfile and simulink environment shows that both controllers are capable to control multi output inverted pendulum system successfully. The result shows that Sliding Mode Control (SMC) produced better response compared to PID control strategies and the responses are presented in time domain with the details analysis.

Keywords: SMC, PID, Inverted Pendulum System.

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Authors: A. Bahrampour, A. Iadicicco, G. De Luca, M. Giordano, A. Cutolo, L. Monsù Scolaro, A. Cusano

Abstract:

In this work we report on preliminary analysis of a novel optoelectronic gas sensor based on an optical fiber integrated with a tetrakis(4-sulfonatophenyl)porphyrin (TPPS) thin film. The sensitive materials are selectively deposited on the core region of a fiber tip by UV light induced deposition technique. A simple and cheap process which can be easily extended to different porphyrin derivatives. When the TPPS film on the fiber tip is exposed to acid and/or base vapors, dramatic changes occur in the aggregation structure of the dye molecules in the film, from J- to H-type, resulting in a profound modification of their corresponding reflectance spectra. From the achieved experimental results it is evident that the presence of intense and narrow band peaks in the reflected spectra could be monitored to detect hazardous vapors.

Keywords: Optical fiber sensor, Porphyrins, Thin films UV induced deposition, TPPS.

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Authors: Giovanni Incerti

Abstract:

The motion planning technique described in this paper has been developed to eliminate or reduce the residual vibrations of belt-driven rotary platforms, while maintaining unchanged the motion time and the total angular displacement of the platform. The proposed approach is based on a suitable choice of the motion command given to the servomotor that drives the mechanical device; this command is defined by some numerical coefficients which determine the shape of the displacement, velocity and acceleration profiles. Using a numerical optimization technique, these coefficients can be changed without altering the continuity conditions imposed on the displacement and its time derivatives at the initial and final time instants. The proposed technique can be easily and quickly implemented on an actual device, since it requires only a simple modification of the motion command profile mapped in the memory of the electronic motion controller.

Keywords: Command shaping, residual vibrations, belt transmission, servomechanism.

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Authors: Denis Trcek

Abstract:

Trust is essential for further and wider acceptance of contemporary e-services. It was first addressed almost thirty years ago in Trusted Computer System Evaluation Criteria standard by the US DoD. But this and other proposed approaches of that period were actually solving security. Roughly some ten years ago, methodologies followed that addressed trust phenomenon at its core, and they were based on Bayesian statistics and its derivatives, while some approaches were based on game theory. However, trust is a manifestation of judgment and reasoning processes. It has to be dealt with in accordance with this fact and adequately supported in cyber environment. On the basis of the results in the field of psychology and our own findings, a methodology called qualitative algebra has been developed, which deals with so far overlooked elements of trust phenomenon. It complements existing methodologies and provides a basis for a practical technical solution that supports management of trust in contemporary computing environments. Such solution is also presented at the end of this paper.

Keywords: internet security, trust management, multi-agent systems, reasoning and judgment, modeling and simulation, qualitativealgebra

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Authors: Fatma Keskin Arabul, Ibrahim Senol, Ahmet Yigit Arabul, Ali Rifat Boynuegri

Abstract:

On account of the concern of the fossil fuel is depleting and its negative effects on the environment, interest in alternative energy sources is increasing day by day. However, considering the importance of transportation in human life, instead of oil and its derivatives fueled vehicles with internal combustion engines, electric vehicles which are sensitive to the environment and working with electrical energy has begun to develop. In this study, simulation was carried out for providing energy management and recovering regenerative braking in fuel cell-battery hybrid electric vehicle. The main power supply of the vehicle is fuel cell on the other hand not only instantaneous power is supplied by the battery but also the energy generated due to regenerative breaking is stored in the battery. Obtained results of the simulation is analyzed and discussed.

Keywords: Electric vehicles, fuel cell, battery, regenerative braking, energy management.

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Authors: Marita Pigłowska, Beata Kurc, Maciej Galiński

Abstract:

The application of carbon materials in the branches of the electrochemical industry shows an increasing tendency each year due to the many interesting properties they possess. These are, among others, a well-developed specific surface, porosity, high sorption capacity, good adsorption properties, low bulk density, electrical conductivity and chemical resistance. All these properties allow for their effective use, among others in supercapacitors, which can store electric charges of the order of 100 F due to carbon electrodes constituting the capacitor plates. Coals (including expanded graphite, carbon black, graphite carbon fibers, activated carbon) are commonly used in electrochemical methods of removing oil derivatives from water after tanker disasters, e.g., phenols and their derivatives by their electrochemical anodic oxidation. Phenol can occupy practically the entire surface of carbon material and leave the water clean of hydrophobic impurities. Regeneration of such electrodes is also not complicated, it is carried out by electrochemical methods consisting in unblocking the pores and reducing resistances, and thus their reactivation for subsequent adsorption processes. Graphite is commonly used as an anode material in lithium-ion cells, while due to the limited capacity it offers (372 mAh g-1), new solutions are sought that meet both capacitive, efficiency and economic criteria. Increasingly, biodegradable materials, green materials, biomass, waste (including agricultural waste) are used in order to reuse them and reduce greenhouse effects and, above all, to meet the biodegradability criterion necessary for the production of lithium-ion cells as chemical power sources. The most common of these materials are cellulose, starch, wheat, rice, and corn waste, e.g., from agricultural, paper and pharmaceutical production. Such products are subjected to appropriate treatments depending on the desired application (including chemical, thermal, electrochemical). Starch is a biodegradable polysaccharide that consists of polymeric units such as amylose and amylopectin that build an ordered (linear) and amorphous (branched) structure of the polymer. Carbon is also used as a catalyst. Elemental carbon has become available in many nano-structured forms representing the hybridization combinations found in the primary carbon allotropes, and the materials can be enriched with a large number of surface functional groups. There are many examples of catalytic applications of coal in the literature, but the development of this field has been hampered by the lack of a conceptual approach combining structure and function and a lack of understanding of material synthesis. In the context of catalytic applications, the integrity of carbon environmental management properties and parameters such as metal conductivity range and bond sequence management should be characterized. Such data, along with surface and textured information, can form the basis for the provision of network support services.

Keywords: carbon materials, catalysis, BET, capacitors, lithium ion cell

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Ponco Iswanto, Mochammad Chasani, Muhammad Hanafi, Iqmal Tahir, Eva Vaulina YD, Harjono, Lestari Solikhati, Winkanda S. Putra, Yayuk Yuliantini

Abstract:

Quantitative Structure-Activity Relationship (QSAR) approach for discovering novel more active Calanone derivative as anti-leukemia compound has been conducted. There are 6 experimental activities of Calanone compounds against leukemia cell L1210 that are used as material of the research. Calculation of theoretical predictors (independent variables) was performed by AM1 semiempirical method. The QSAR equation is determined by Principle Component Regression (PCR) analysis, with Log IC50 as dependent variable and the independent variables are atomic net charges, dipole moment (μ), and coefficient partition of noctanol/ water (Log P). Three novel Calanone derivatives that obtained by this research have higher activity against leukemia cell L1210 than pure Calanone.

Keywords: AM1 semiempirical calculation, Calanone, Principle Component Regression, QSAR approach.

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

Abstract:

Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: Monomial form, rectangular surfaces, CAGD curves, monomial matrix applications.

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