Search results for: dual integral equations

Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: W. Handoko, F. Pahlevani, V. Sahajwalla

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Dual-phase high carbon steels (DHCS) are commonly known for their improved strength, hardness, and abrasive resistance properties due to co-presence of retained austenite and martensite at the same time. Retained austenite is a meta-stable phase at room temperature, and stability of this phase governs the response of DHCS at different conditions. This research paper studies the effect of RA stability on corrosion behaviour of high carbon steels after they have been immersed into 1.0 M NaCl solution for various times. For this purpose, two different steels with different RA stabilities have been investigated. The surface morphology of the samples before and after corrosion attack was observed by secondary electron microscopy (SEM) and atomic force microscopy (AFM), along with the weight loss and Vickers hardness analysis. Microstructural investigations proved the preferential attack to retained austenite phase during corrosion. Hence, increase in the stability of retained austenite in dual-phase steels led to decreasing the weight loss rate.

Keywords: high carbon steel, austenite stability, atomic force microscopy, corrosion

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Xijun Yu, Zhenzhen Li, Zupeng Jia

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This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.

Keywords: cell-centered Lagrangian scheme, compressible Euler equations, RKDG method

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Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran

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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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Authors: Jana Abu Ahmada, Zaineb Mohamed, Ilyasse Aksikas

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The linear quadratic control system of hyperbolic first order partial differential equations (PDEs) are presented. The aim of this research is to control chemical reactions. This is achieved by converting the PDEs system to ordinary differential equations (ODEs) using the method of characteristics to reduce the system to control it by using the integral reinforcement learning. The designed controller is applied to a catalytic cracking reactor. Background—Transport-Reaction systems cover a large chemical and bio-chemical processes. They are best described by nonlinear PDEs derived from mass and energy balances. As a main application to be considered in this work is the catalytic cracking reactor. Indeed, the cracking reactor is widely used to convert high-boiling, high-molecular weight hydrocarbon fractions of petroleum crude oils into more valuable gasoline, olefinic gases, and others. On the other hand, control of PDEs systems is an important and rich area of research. One of the main control techniques is feedback control. This type of control utilizes information coming from the system to correct its trajectories and drive it to a desired state. Moreover, feedback control rejects disturbances and reduces the variation effects on the plant parameters. Linear-quadratic control is a feedback control since the developed optimal input is expressed as feedback on the system state to exponentially stabilize and drive a linear plant to the steady-state while minimizing a cost criterion. The integral reinforcement learning policy iteration technique is a strong method that solves the linear quadratic regulator problem for continuous-time systems online in real time, using only partial information about the system dynamics (i.e. the drift dynamics A of the system need not be known), and without requiring measurements of the state derivative. This is, in effect, a direct (i.e. no system identification procedure is employed) adaptive control scheme for partially unknown linear systems that converges to the optimal control solution. Contribution—The goal of this research is to Develop a characteristics-based optimal controller for a class of hyperbolic PDEs and apply the developed controller to a catalytic cracking reactor model. In the first part, developing an algorithm to control a class of hyperbolic PDEs system will be investigated. The method of characteristics will be employed to convert the PDEs system into a system of ODEs. Then, the control problem will be solved along the characteristic curves. The reinforcement technique is implemented to find the state-feedback matrix. In the other half, applying the developed algorithm to the important application of a catalytic cracking reactor. The main objective is to use the inlet fraction of gas oil as a manipulated variable to drive the process state towards desired trajectories. The outcome of this challenging research would yield the potential to provide a significant technological innovation for the gas industries since the catalytic cracking reactor is one of the most important conversion processes in petroleum refineries.

Keywords: PDEs, reinforcement iteration, method of characteristics, riccati equation, cracking reactor

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Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Mohamed K. Khalil, Mohamed S. Ragab

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Atomizers are used in many engineering applications including diesel engines, petrol engines and spray combustion in furnaces as well as gas turbine engines. These atomizers are used to increase the specific surface area of the fuel, which achieve a high rate of fuel mixing and evaporation. In all combustion systems reduction in mean drop size is a challenge which has many advantages since it leads to rapid and easier ignition, higher volumetric heat release rate, wider burning range and lower exhaust concentrations of the pollutant emissions. Pressure atomizers have a different configuration for design such as swirl atomizer (simplex), dual orifice, spill return, plain orifice, duplex and fan spray. Simplex pressure atomizers are the most common type of all. Among all types of atomizers, pressure swirl types resemble a special category since they differ in quality of atomization, the reliability of operation, simplicity of construction and low expenditure of energy. But, the disadvantages of these atomizers are that they require very high injection pressure and have low discharge coefficient owing to the fact that the air core covers the majority of the atomizer orifice. To overcome these problems, dual orifice atomizer was designed. This paper proposes a detailed mathematical model design procedure for both pressure swirl atomizer (Simplex) and dual orifice atomizer, examines the effects of varying fuel type and makes a clear comparison between the two types. Using five types of fuel (JP-5, JA1, JP-4, Diesel and Bio-Diesel) as a case study, reveal the effect of changing fuel type and its properties on atomizers design and spray characteristics. Which effect on combustion process parameters; Sauter Mean Diameter (SMD), spray cone angle and sheet thickness with varying the discharge coefficient from 0.27 to 0.35 during takeoff for high bypass turbofan engines. The spray atomizer performance of the pressure swirl fuel injector was compared to the dual orifice fuel injector at the same differential pressure and discharge coefficient using Excel. The results are analyzed and handled to form the final reliability results for fuel injectors in high bypass turbofan engines. The results show that the Sauter Mean Diameter (SMD) in dual orifice atomizer is larger than Sauter Mean Diameter (SMD) in pressure swirl atomizer, the film thickness (h) in dual orifice atomizer is less than the film thickness (h) in pressure swirl atomizer. The Spray Cone Angle (α) in pressure swirl atomizer is larger than Spray Cone Angle (α) in dual orifice atomizer.

Keywords: gas turbine engines, atomization process, Sauter mean diameter, JP-5

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Authors: Hilal Naimi, Amelbahahouda Adamou-Mitiche, Lahcene Mitiche

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The main problem in the area of medical imaging has been image denoising. The most defying for image denoising is to secure data carrying structures like surfaces and edges in order to achieve good visual quality. Different algorithms with different denoising performances have been proposed in previous decades. More recently, models focused on deep learning have shown a great promise to outperform all traditional approaches. However, these techniques are limited to the necessity of large sample size training and high computational costs. This research proposes a denoising approach basing on LDTCWT (Lifting Dual Tree Complex Wavelet Transform) using Hybrid Thresholding with Wiener filter to enhance the quality image. This research describes the LDTCWT as a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). To develop this approach, a hybrid thresholding function is modeled by integrating the Wiener filter into the thresholding function.

Keywords: lifting wavelet transform, image denoising, dual tree complex wavelet transform, wavelet shrinkage, wiener filter

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Authors: Bojan Radisic, Katarina Stavlic

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The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples.

Keywords: consumer surplus, producer surplus, definite integral, integration

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: Sajjad Negahban, Ruihe Wang, Baojiang Sun

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Gas-lift dual gradient drilling is a solution for deepwater drilling challenges. As well, Continuous development of drilling technology leads to increase employment of mineral oil based drilling fluids and synthetic-based drilling fluids, which have adequate characteristics such as: high rate of penetration, lubricity, shale inhibition and low toxicity. The paper discusses utilization of nitrified mineral oil base drilling for deepwater drilling and for more accurate prediction of pressure in DGD at marine riser, solubility and bubble pressure were considered in steady state hydraulic model. The Standing bubble pressure and solubility correlations, and two models which were acquired from experimental determination were applied in hydraulic model. The effect of the black oil correlations, and new solubility and bubble pressure models was evaluated on the PVT parameters such as oil formation volume factor, density, viscosity, volumetric flow rate. Eventually, the consequent simulated pressure profile due to these models was presented.

Keywords: solubility, bubble pressure, gas-lift dual gradient drilling, steady state hydraulic model

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Authors: Charlene N. T. Mfangnia, Henri E. Z. Tonnang, Berge Tsanou, Jeremy Herren

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Microsporidia MB is a recently discovered symbiont capable of blocking the transmission of Plasmodium from mosquitoes to humans. The symbiont can spread both horizontally and vertically among the mosquito population. This dual transmission gives the symbiont the ability to invade the mosquito population. The replacement of the mosquito population by the population of symbiont-infected mosquitoes then appears as a promising strategy for malaria control. In this context, the present study uses differential equations to model the transmission dynamics of Microsporidia MB in the population of female Anopheles mosquitoes. Long-term propagation scenarios of the symbiont, such as extinction, persistence or total infection, are obtained through the determination of the target and basic reproduction numbers, the equilibria, and the study of their stability. The stability is illustrated numerically, and the contribution of vertical and horizontal transmission in the spread of the symbiont is assessed. Data obtained from laboratory experiments are then used to explain the low prevalence observed in nature. The study also shows that the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes are the factors that most influence the transmission of the symbiont. In addition, the introduction of temperature and the study of bifurcations show the significant influence of the environmental condition in the propagation of Microsporidia MB. This finding proves the necessity of taking into account environmental variables for the potential establishment of the symbiont in a new area.

Keywords: differential equations, stability analysis, malaria, microsporidia MB, horizontal transmission, vertical transmission, numerical illustration

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Authors: M. R. Akbari, S. Akbari, L. Abdollahpour

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The present paper is concerned with calculating the 2-dimensional velocity profile of a viscous flow for an incompressible fluid along the leading edge of a flat plate by using the continuity and motion equations with a simple and innovative approach. A Comparison between Numerical method and AGM has been made and the results have been revealed that AGM is very accurate and easy and can be applied for a wide variety of nonlinear problems. It is notable that most of the differential equations can be solved in this approach which in the other approaches they do not have this capability. Moreover, there are some valuable benefits in this method of solving differential equations, for instance: Without any dimensionless procedure, we can solve many differential equation(s), that is, differential equations are directly solvable by this method. In addition, it is not necessary to convert variables into new ones. According to the afore-mentioned expressions which will be proved in this literature, the process of solving nonlinear differential equation(s) will be very simple and convenient in contrast to the other approaches.

Keywords: leading edge, new idea, flat plate, incompressible fluid

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Authors: Zunnurain Ahmad

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This work presents design of a dual band antenna for the 5G communications in the millimeter wave band. As opposed to conventional patch antennas which are limited to single narrow band operation a shared aperture concept is utilized for this antenna. The patch aperture is coupled through two rectangular slots etched on a thin printed circuit board (100μm). The patch is elevated in air thus avoiding excitation of surface waves and minimizing dielectric losses at millimeter wave frequencies. With this approach the radiator can cover lower band of 28 GHz and upper band of 37/ 39 GHz dedicated for the fifth generation communications. The simulated radiation efficiency of the antenna stays above 90%.

Keywords: antenna, millimeter wave, 5G, 3D

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Authors: Deena Moustafa

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The purpose of this paper is to describe the sources of parenting stress in mothers of Dual Diagnosis children (n =60) and examine the relationship between parenting stress and maternal psychological status (depression and well-being), also examine if there is any difference between the previous variables in different disabilities associated with Autism. A descriptive correlational design was used. Data were collected via online questionnaires. The study finds that there was no significant relationship between Autism Parenting Stress Index (APSI) scores and types of disability which associated with Autism, although Mothers with deaf autistic reported more parenting stress, Similar findings were found regarding Depressive Symptoms, as there was no significant relationship between (CESD-R) scores and types of disability which associated with Autism, also study finds that there was a significant correlation of the (APSI) with the (CESD-R) Mothers with higher overall parenting stress reported more depressive symptoms. Likewise, there was also a significant correlation between the (APSI) and the (RPWB) Mothers reporting more parenting stress also reported lower levels of well-being.

Keywords: parenting stress, maternal psychological statues, mothers of dual diagnosis, autism

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Authors: N. Chayaopas, W. Assawinchaichote

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In order to maximize energy capturing from wind energy, controlling the doubly fed induction generator to have optimal power from the wind, generator speed and output electrical power control in wind energy system have a great importance due to the nonlinear behavior of wind velocities. In this paper purposes the design of a control scheme is developed for power control of wind energy system via H∞ fuzzy integral controller. Firstly, the nonlinear system is represented in term of a TS fuzzy control design via linear matrix inequality approach to find the optimal controller to have an H∞ performance are derived. The proposed control method extract the maximum energy from the wind and overcome the nonlinearity and disturbances problems of wind energy system which give good tracking performance and high efficiency power output of the DFIG.

Keywords: doubly fed induction generator, H-infinity fuzzy integral control, linear matrix inequality, wind energy system

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Authors: Mukul R. Gupta, Rajkumar Gandhi, Rajitha Sachan, Naveen K. Khare

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The field of glycoscience has burgeoned in the last several decades, leading to the identification of many glycosides which could serve critical roles in a wide range of biological processes. This has prompted a resurgence in synthetic interest, with a particular focus on new approaches to construct the selective glycosidic bond. Despite the numerous elegant strategies and methods developed for the formation of glycosidic bonds, stereoselective construction of glycosides remains challenging. Here, we have recently developed the novel Hexafluoroisopropanol (HFIP) catalyzed stereoselective glycosylation methods by using KDN imidate glycosyl donor and a variety of alcohols in excellent yield. This method is broadly applicable to a wide range of substrates and with excellent selectivity of glycoside. Also, herein we are reporting the functionalization of the unbiased side of newly formed glycosides by dual-catalytic transition metal systems (Ru- or Fe-). We are using the innovative Reverse & Catalyst strategy, i.e., a reversible activation reaction by one catalyst with a functionalization reaction by another catalyst, together with enabling functionalization of substrates at their inherently unreactive sites. As well, we are targeting the diSia derivative synthesis by Wittig reaction. This synthetic method is applicable in mild conditions, functional group tolerance of the dual-catalytic systems and also highlights the potential of the multicatalytic approach to address challenging transformations to avoid multistep procedures in carbohydrate synthesis.

Keywords: KDN, stereoselective glycosylation, dual-catalytic functionalization, Wittig reaction

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Authors: Kouzi Katia

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This paper proposes a Direct Torque Control (DTC) algorithm of dual Stator Induction Motor (DSIM) drive using two approach intelligent techniques: Artificial Neural Network (ANN) approach replaces the switching table selector block of conventional DTC and Mamdani Fuzzy Logic controller (FLC) is used for stator resistance estimation. The fuzzy estimation method is based on an online stator resistance correction through the variations of stator current estimation error and its variation. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of suggested algorithm control is to reduce the hardware complexity of conventional selectors, to avoid the drive instability that may occur in certain situation and ensure the tracking of the actual of the stator resistance. The effectiveness of the technique and the improvement of the whole system performance are proved by results.

Keywords: artificial neural network, direct torque control, dual stator induction motor, fuzzy logic estimator, switching table

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Authors: S. Sonkham, U. Pinsopon, W. Chatlatanagulchai

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This paper presents a method of sliding mode control (SMC) designing and developing for the servo system in a dual-stage actuator (DSA) hard disk drive. Mathematical modelling of hard disk drive actuators is obtained, extracted from measuring frequency response of the voice-coil motor (VCM) and PZT micro-actuator separately. Matlab software tools are used for mathematical model estimation and also for controller design and simulation. A model-reference approach for tracking requirement is selected as a proposed technique. The simulation results show that performance of a model-reference SMC controller design in DSA servo control can be satisfied in the tracking error, as well as keeping the positioning of the head within the boundary of +/-5% of track width under the presence of internal and external disturbance. The overall results of model-reference SMC design in DSA are met per requirement specifications and significant reduction in %off track is found when compared to the single-state actuator (SSA).

Keywords: hard disk drive, dual-stage actuator, track following, hdd servo control, sliding mode control, model-reference, tracking control

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Authors: Ya-Chuan Tseng, Hsin-Yi Liu, Meei-Fang Lou, Guey-Shiun Huang

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Purpose: Sensory impairments are common in older adults. Hearing and visual impairments affect their physical and mental health and quality of life (QOL) adversely. However, systematic reviews of the relationship between hearing impairment, visual impairment, dual sensory impairment and quality of life are scarce. The purpose of this systematic review was to determine the relationship between hearing impairment, visual impairment, dual sensory impairment and quality of life. Methods: Searches of EMBASE, PubMed, CINAHL, MEDLINE, Cochrane Library and Airiti Library were conducted between January 2006 and December 2017 using the keywords ‘quality of life,’ ‘life satisfaction,’ ‘well-being,’ ‘hearing impairment’ and ‘visual impairment’ Two authors independently assessed methodologic quality using a modified Downs and Black tool. Data were extracted by the first author and then cross-checked by the second author. Results: Twenty-three studies consisting mostly of community-dwelling older adults were included in our review. Sensory impairment was found to be in significant association with quality of life, with an increase in hearing impairment or visual impairment severity resulting in a lower quality of life. Quality of life for dual sensory impairment was worse than for hearing impairment or visual impairment individually. Conclusions: A significant association was confirmed between hearing impairment, visual impairment, dual sensory impairment and quality of life. Our review can be used to enhance health care personnel’s understanding of sensory impairment in older adults and enable healthcare personnel to actively assess older adults’ sensory functions so that they can help alleviate the negative impact of sensory impairments on QOL in older adults.

Keywords: nursing, older adults, quality of life, systematic review, hearing impairment, visual impairment

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Authors: H. Al-Qassem, L. Cheng, Y. Pan

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In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness

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Authors: J. Jayaletchmi

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In seeking to manage a multiracial and multi-religious society, Singapore provides a unique solution – a dual court system whereby a common law system co-exists with a Syariah law system that administers Syariah law for the Muslim population. In this respect, Singapore seems to provide a feasible example of legal pluralism to countries grappling with a burgeoning Muslim population. However, problems have arisen regarding this peaceful coexistence of secular and religious laws that seek to balance the rights of women and religious freedom. Singapore’s interpretation of Syariah law in the context of marriage and divorce has resulted in certain inequalities for Muslim women, which are exemplified in light of the Women’s Charter, a landmark piece of legislation which provides the legal basis for equity between husband and wife, but excludes Muslims from its ambit. The success of Singapore’s dual court system has largely been at the expense of Muslim women’s rights, and, as a result, the Muslim community as a whole has begun trailing behind the progressive society it forms a part of. This paper explores the prevailing unfairness of rules governing Muslim marriage and divorce in Singapore, and puts forth bold reforms.

Keywords: legal pluralism, Singapore, Syariah law, women’s rights

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Authors: Vaia N. Koukou, Niki D. Martini, George P. Fountos, Christos M. Michail, Athanasios Bakas, Ioannis S. Kandarakis, George C. Nikiforidis

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Various substitute materials of calcifications are used in phantom measurements and simulation studies in mammography. These include calcium carbonate, calcium oxalate, hydroxyapatite and aluminum. The aim of this study is to compare the contrast-to-noise ratio (CNR) values of the different calcification types using the dual energy method. The constructed calcification phantom consisted of three different calcification types and thicknesses: hydroxyapatite, calcite and calcium oxalate of 100, 200, 300 thicknesses. The breast tissue equivalent materials were polyethylene and polymethyl methacrylate slabs simulating adipose tissue and glandular tissue, respectively. The total thickness was 4.2 cm with 50% fixed glandularity. The low- (LE) and high-energy (HE) images were obtained from a tungsten anode using 40 kV filtered with 0.1 mm cadmium and 70 kV filtered with 1 mm copper, respectively. A high resolution complementary metal-oxide-semiconductor (CMOS) active pixel sensor (APS) X-ray detector was used. The total mean glandular dose (MGD) and entrance surface dose (ESD) from the LE and HE images were constrained to typical levels (MGD=1.62 mGy and ESD=1.92 mGy). On average, the CNR of hydroxyapatite calcifications was 1.4 times that of calcite calcifications and 2.5 times that of calcium oxalate calcifications. The higher CNR values of hydroxyapatite are attributed to its attenuation properties compared to the other calcification materials, leading to higher contrast in the dual energy image. This work was supported by Grant Ε.040 from the Research Committee of the University of Patras (Programme K. Karatheodori).

Keywords: calcification materials, CNR, dual energy, X-rays

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Authors: Mohammed Berka, Khaled Merit

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Recent works on microwave filters show that the constituent materials such filters are very important in the design and realization. Several solutions have been proposed to improve the qualities of filtering. In this paper, we propose a new dual band-pass filter based on the coupling of a composite (CRLH) coplanar waveguide with complementary split ring resonators (CSRRs). The (CRLH) CPW is composed of two resonators, each one has an interdigital capacitor (CID) and two short-circuited stubs parallel to top ground plane. On the lower ground plane, we use defected ground structure technology (DGS) to engrave two (CSRRs) offered with different shapes and dimensions. Between the top ground plane and the substrate, we place a ferrite layer to control the electromagnetic coupling between (CRLH) CPW and (CSRRs). The global filter that has coplanar access will have a dual band-pass behavior around the magnetic resonances of (CSRRs). Since there’s no scientific or experimental result in the literature for this kind of complicated structure, it was necessary to perform simulation using HFSS Ansoft designer.

Keywords: complementary split ring resonators, coplanar waveguide, ferrite, filter, stub.

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Authors: Hassan Manouzi

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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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Authors: Y. J. Zhou, G. Lu

Abstract:

In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

Procedia PDF Downloads 238

Authors: Man-Ching Yu

Abstract:

In Chinese music, pentatonic collection is central in constituting all the harmonic and melodic elements; most of the traditional Chinese musicians particularly emphasize the importance of the smoothness between pentatonic collections when one collection modulates to another collection, articulating the roles of the pentatonic common tones. On the contrary, in post-tonal Chinese music the central features of the pentatonic modulations tend to reflect a larger number of semitonal relationships with a lesser number of common tones. This paper offers an analytical account of the transformations between pentatonic collections that arise in post-tonal Chinese music by adopting the methodology of the Tonnetz, in particular, Dual Interval Space (DIS), to elaborate and reexamine pentatonicism by focusing on the transformations between pentatonic elements, especially semitonal motion and common tones. In the essay, various pentatonic passages will be analyzed by means of DIS for highlighting the transformation of the collections. It will be shown that the pentatonic collections that are in semitonal, third, and augmented fourth relationships exhibit the maximum number of semitonal shifts.

Keywords: tonnetz, pentatonicism, post-tonal Chinese music, dual interval space, transformation

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Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

Procedia PDF Downloads 464