Search results for: definite integral

Authors: Y.J. Wang, C. Q. Ru

Abstract:

A key issue of cohesive zone models is how to determine the cohesive zone model parameters based on real material test data. In this paper, uniaxial nominal stress-strain curve (SS curve) is used to determine two key parameters of a cohesive zone model (CZM): The maximum traction and the area under the curve of traction-separation law (TSL). To this end, the true SS curve is obtained based on the nominal SS curve, and the relationship between the nominal SS curve and TSL is derived based on an assumption that the stress for cracking should be the same in both CZM and the real material. In particular, the true SS curve after necking is derived from the nominal SS curve by taking the average of the power law extrapolation and the linear extrapolation, and a damage factor is introduced to offset the true stress reduction caused by the voids generated at the necking zone. The maximum traction of the TSL is equal to the maximum true stress calculated based on the damage factor at the end of hardening. In addition, a simple specimen is modeled by Abaqus/Standard to calculate the critical J-integral, and the fracture energy calculated by the critical J-integral represents the stored strain energy in the necking zone calculated by the true SS curve. Finally, the CZM parameters obtained by the present method are compared to those used in a previous related work for a simulation of the drop-weight tear test.

Keywords: dynamic fracture, cohesive zone model, traction-separation law, stress-strain curve, J-integral

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Authors: Y. J. Wang, C. Q. Ru

Abstract:

A key issue of cohesive zone models is how to determine the cohesive zone model (CZM) parameters based on real material test data. In this paper, uniaxial nominal stress-strain curve (SS curve) is used to determine two key parameters of a cohesive zone model: the maximum traction and the area under the curve of traction-separation law (TSL). To this end, the true SS curve is obtained based on the nominal SS curve, and the relationship between the nominal SS curve and TSL is derived based on an assumption that the stress for cracking should be the same in both CZM and the real material. In particular, the true SS curve after necking is derived from the nominal SS curve by taking the average of the power law extrapolation and the linear extrapolation, and a damage factor is introduced to offset the true stress reduction caused by the voids generated at the necking zone. The maximum traction of the TSL is equal to the maximum true stress calculated based on the damage factor at the end of hardening. In addition, a simple specimen is simulated by Abaqus/Standard to calculate the critical J-integral, and the fracture energy calculated by the critical J-integral represents the stored strain energy in the necking zone calculated by the true SS curve. Finally, the CZM parameters obtained by the present method are compared to those used in a previous related work for a simulation of the drop-weight tear test.

Keywords: dynamic fracture, cohesive zone model, traction-separation law, stress-strain curve, J-integral

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: ground surface relief, method of integral equations, numerical method, electromagnetic

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Authors: Sheren H. Salah

Abstract:

The inverted pendulum is a highly nonlinear and open-loop unstable system. An inverted pendulum (IP) is a pendulum which has its mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole. The characteristics of the inverted pendulum make identification and control more challenging. This paper presents the simulation study of several control strategies for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. For controlling the inverted pendulum. The simulation study that sliding mode control (SMC) control produced better response compared to Genetic Algorithm Control (GAs) and proportional-integral-derivative(PID) control.

Keywords: Inverted Pendulum (IP) Proportional-Integral-Derivative (PID), Genetic Algorithm Control (GAs), Sliding Mode Control (SMC)

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Authors: Matthew T. McCarthy, Sarah Janse, Natalie M. Pizzimenti, Anthony K. Savino, Brian Crosser, Sean C. Rose

Abstract:

Concussion is diagnosed clinically using a comprehensive history and exam, supported by ancillary testing. Frequently, symptom checklists are used as part of the evaluation of concussion. Existing symptom scales are based on a subjective Likert scale, without relation of symptoms to clinical or functional impairment. This is a retrospective review of 133 patients under age 30 seen in an outpatient neurology practice within 30 days of a probable or definite concussion. Each patient completed 2 symptom checklists at the initial visit – the SCAT-3 symptom evaluation (22 symptoms, 0-6 scale) and a scale based on the degree of clinical impairment for each symptom (22 symptoms, 0-3 scale related to functional impact of the symptom). Final clearance date was determined by the treating physician. 60.9% of patients were male with mean age 15.7 years (SD 2.3). Mean time from concussion to first visit was 6.9 days (SD 6.2), and 101 patients had definite concussions (75.9%), while 32 were diagnosed as probable (24.1%). 94 patients had a known clearance date (70.7%) with mean clearance time of 20.6 days (SD 18.6) and median clearance time of 19 days (95% CI 16-21). Mean total symptom score was 27.2 (SD 22.9) on the SCAT-3 and 14.7 (SD 11.9) for the functional impairment scale. Pearson’s correlation between the two scales was 0.98 (p < 0.001). After adjusting for patient and injury characteristics, an equivalent increase in score on each scale was associated with longer time to clearance (SCAT-3 hazard ratio 0.885, 95%CI 0.835-0.938, p < 0.001; functional impairment scale hazard ratio 0.851, 95%CI 0.802-0.902, p < 0.001). A concussion symptom scale based on degree of functional impairment correlates strongly with the SCAT-3 scale and demonstrates a similar association with time to clearance. By assessing the degree of impact on clinical functioning, this symptom scale reflects a more intuitive approach to rating symptoms and can be used in the management of concussion.

Keywords: checklist, concussion, neurology, scale, sports, symptoms

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Authors: Felix Ehimare Enegho

Abstract:

The issue of the Christian mission among various people in our world has become a subject of discussion for quite a while now considering the many challenges faced by people of different religions. The understanding of who we are and how we choose to live our life as a people is quite imperative in many societies. The Christian Church down through the ages attempted to define itself so as to become relevant in human society. In Africa, the question of identity and self-realization is quite imperative if Africans are to define themselves and place themselves in the proper perspective as Christians. With the high level of insecurity bedevilling the world and especially Nigerian society, there is the need for Christians in Nigeria to see themselves as one body belonging to the same family. It is however disheartening that for several years now, there is a high level of disunity, lack of trust, disharmony, and vices of all kinds even among Christians who are often too quick to segment themselves into denominations thereby making themselves weak, segmented ad powerless in the midst of great oppositions, as if the Christian church in Nigeria is a divided house. The significance of this paper is to explore the areas of conflict among Christians in Nigeria with a view to finding possible solutions that would lead to the integral formation and in the long run a common identity and invariably self-realization. This paper utilized the socio-historical method of research. Among the major findings in the work is the fact that it is only people that can truly be responsible and held accountable for how they define their identity and self-realization. This entails that Christianity’s identity and self-realization in Nigeria will not only lead to a better and more defined form of Christianity but would ultimately assist in the integral development of Christian mission in Nigeria, a kind of development that would lead to a better Nigerian society.

Keywords: contemporary, Christian, mission, Nigeria, identity, self-realization

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Authors: Abdolvahab Ehsani Rad, Mohd Shafry Mohd Rahim, Alireza Norouzi

Abstract:

Medical image analysis is one of the great effects of computer image processing. There are several processes to analysis the medical images which the segmentation process is one of the challenging and most important step. In this paper the segmentation method proposed in order to segment the dental radiograph images. Thresholding method has been applied to simplify the images and to morphologically open binary image technique performed to eliminate the unnecessary regions on images. Furthermore, horizontal and vertical integral projection techniques used to extract the each individual tooth from radiograph images. Segmentation process has been done by applying the level set method on each extracted images. Nevertheless, the experiments results by 90% accuracy demonstrate that proposed method achieves high accuracy and promising result.

Keywords: integral production, level set method, morphological operation, segmentation

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Authors: Martha C. Orazulume, Jibril D. Jiya

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Flexible satellites are equipped with various appendages which vibrate under the influence of any excitation and make the attitude of the satellite to be unstable. Therefore, the system must be able to adjust to balance the effect of these appendages in order to point accurately and satisfactorily which is one of the most important problems in satellite design. Proportional Integral Derivative (PID) Controller is simple to design and computationally efficient to implement which is used to stabilize the effect of these flexible appendages. However, manual turning of the PID is time consuming, waste energy and money. Particle Swarm Optimization (PSO) is used to tune the parameters of PID Controller. Simulation results obtained show that PSO tuned PID Controller is able to re-orient the spacecraft attitude as well as dampen the effect of mechanical resonance and yields better performance when compared with manually tuned PID Controller.

Keywords: Attitude Control, Flexible Satellite, Particle Swarm Optimization, PID Controller and Optimization

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Authors: Irina Peterburgsky

Abstract:

Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Ali Essam El Shazly

Abstract:

The slum survey of 'Sequina' area in Alexandria details the building rooms of twenty-building samples according to the integral measure of space syntax. The essence of room organization sets the most integrative 'visitor' domain between the 'inhabitant' wings of less integrated 'parent' than the 'children' structure with visual ring of 'balcony' space. Despite the collective real relative asymmetry of 'pheno-type' aggregation, the relative asymmetry of individual layouts reveals 'geno-type' structure of spatial diversity. The multifunction of rooms optimizes the integral structure of graph and visibility merge, which contrasts with the deep tailing structure of distinctive social domains. The most integrative layout inverts the geno-type into freed rooms of shallow 'inhabitant' domain against the off-centered 'visitor' space, while the most segregated layout further restricts the pheno-type through isolated 'visitor' from 'inhabitant' domains across the 'staircase' public domain. The catalyst 'kitchen & living' spaces demonstrate multi-structural dimensions among the various social domains. The former ranges from most exposed central integrity to the most hidden 'motherhood' territories. The latter, however, mostly integrates at centrality or at the further ringy 'childern' domain. The study concludes social structure of spatial integrity for redevelopment, which is determined through the micro-level survey of rooms with integral dimensions.

Keywords: Alexandria, Sequina slum, spatial integration, space syntax

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Authors: Artion Kashuri, Rozana Liko

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In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

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Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

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This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: load frequency control, fuzzy-pid controller, type 2 fuzzy system, harmony search algorithm

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Authors: Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The discontinuities is characterized using a hybrid spectral/numerical technique. This structure presents an arbitrary number of ports, each one with different orientation and dimensions. This article presents a hybrid method based on multimode contour integral and mode matching techniques. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape discontinuities. Finally, the multimode scattering matrix of the whole structure can be found by cascading the blocks. Therefore, the new method is suitable for analysis of a wide range of waveguide problems. Therefore, the present approach can be applied easily to the analysis of any multiport junctions and cascade blocks. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method proposed.

Keywords: segmentation, s parameters, simulation, optimization

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Authors: Felix Damilola Ajibade, Opeyemi O. Enoch, Taiwo Paul Fajusigbe

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This paper is centered on conducting an inquiry into the stability of the F* iterative algorithm to the fixed point of a strongly pseudo-contractive mapping in the framework of uniformly convex Banach spaces. To achieve the desired result, certain existing inequalities in convex Banach spaces were utilized, as well as the stability criteria of Harder and Hicks. Other necessary conditions for the stability of the F* algorithm on strong pseudo-contractive mapping were also obtained. Through a numerical approach, we prove that the F* iterative algorithm is H-stable for strongly pseudo-contractive mapping. Finally, the solution of the mixed-type Volterra-Fredholm functional non-linear integral equation is estimated using our results.

Keywords: stability, F* -iterative algorithm, pseudo-contractive mappings, uniformly convex Banach space, mixed-type Volterra-Fredholm integral equation

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

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The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Bode’s ideal transfer function, fractional calculus, fractional–order proportional integral (FOPI) controller, cascade control system

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Authors: Natalia D. Vaysfel’d, Zinaida Y. Zhuravlova

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The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed.

Keywords: semi strip, Green's Matrix, fourier transformation, orthogonal polynomials method

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Authors: Anna Sikharulidze, Gia Sirbiladze

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For the evaluation of unreliability levels of movement on the closed routes in the vehicle routing problem, the fuzzy operators family is constructed. The interactions between routing factors in extreme conditions on the roads are considered. A multi-criteria decision-making model (MCDM) is constructed. Constructed aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are proved. Connections between the operators and the compositions of dual triangular norms are described. The conjugate connections between the constructed operators are shown. Operators reflect interactions among all the combinations of the factors in the fuzzy MCDM process. Several variants of constructed operators are used in the decision-making problem regarding the assessment of unreliability and possibility levels of movement on closed routes.

Keywords: vehicle routing problem, associated probabilities of a fuzzy measure, choquet integral, fuzzy aggregation operator

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Authors: Jorge Gonzalez-Camus

Abstract:

In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Wenlong Feng, Zhenchun Du, Jianguo Yang

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To decrease the grating scale thermal expansion error, a novel method which based on multiple temperature detections is proposed. Several temperature sensors are installed on the grating scale and the temperatures of these sensors are recorded. The temperatures of every point on the grating scale are calculated by interpolating between adjacent sensors. According to the thermal expansion principle, the grating scale thermal expansion error model can be established by doing the integral for the variations of position and temperature. A novel compensation method is proposed in this paper. By applying the established error model, the grating scale thermal expansion error is decreased by 90% compared with no compensation. The residual positioning error of the grating scale is less than 15um/10m and the accuracy of the machine tool is significant improved.

Keywords: thermal expansion error of grating scale, error compensation, machine tools, integral method

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Authors: Ibrahim Cicek, Melike Nikbay

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Electrically propelled vehicles, either road or aerial vehicles are studied on contemporarily for their robust maneuvers and cost-efficient transport operations. The main power generating systems of such vehicles electrified by selecting proper components and assembled as e-powertrain. Generally, e-powertrain components selected considering the target performance requirements. Since the main component of propulsion is the drive unit, e-motor control system is subjected to achieve the performance targets. In this paper, the optimization of e-motor control parameters studied by Integral Squared Method (ISE). The overall aim is to minimize power consumption of such vehicles depending on mission profile and maintaining smooth maneuvers for passenger comfort. The sought-after values of control parameters are computed using the Optimal Control Theory. The system is modeled as a closed-loop linear control system with calibratable parameters.

Keywords: optimization, e-powertrain, optimal control, electric vehicles

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Authors: Benalia Nadia, Zerzouri Nora, Ben Si Ali Nadia

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Abstract: Among the many different modern heuristic optimization methods, genetic algorithms (GA) and the particle swarm optimization (PSO) technique have been attracting a lot of interest. The GA has gained popularity in academia and business mostly because to its simplicity, ability to solve highly nonlinear mixed integer optimization problems that are typical of complex engineering systems, and intuitiveness. The mechanics of the PSO methodology, a relatively recent heuristic search tool, are modeled after the swarming or cooperative behavior of biological groups. It is suitable to compare the performance of the two techniques since they both aim to solve a particular objective function but make use of distinct computing methods. In this article, PSO and GA optimization approaches are used for the parameter tuning of the power system stabilizer and Proportional integral derivative regulator. Load angle and rotor speed variations in the single machine infinite bus bar system is used to measure the performance of the suggested solution.

Keywords: SMIB, genetic algorithm, PSO, transient stability, power system stabilizer, PID

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Authors: Anupoju Rajeev, Joanne Mathew, Amit Shelke

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In the current study, a new type of Composite Structural Insulated Panels (CSIPs) is developed and investigated its performance against shock loading which can replace the conventional wooden structural materials. The CSIPs is made of Fibre Cement Board (FCB)/aluminum as the facesheet and the expanded polystyrene foam as the core material. As tornadoes are very often in the western countries, it is suggestable to monitor the health of the CSIPs during its lifetime. So, the composite structure is installed with three smart sensors located randomly at definite locations. Each smart sensor is fabricated with an embedded half stainless phononic crystal sensor attached to both ends of the nylon shaft that can resist the shock and impact on facesheet as well as polystyrene foam core and safeguards the system. In addition to the granular crystal sensors, the accelerometers are used in the horizontal spanning and vertical spanning with a definite offset distance. To estimate the health and damage of the CSIP panel using granular crystal sensor, shock wave loading experiments are conducted. During the experiments, the time of flight response from the granular sensors is measured. The main objective of conducting shock wave loading experiments on the CSIP panels is to study the effect and the sustaining capacity of the CSIP panels in the extreme hazardous situations like tornados and hurricanes which are very common in western countries. The effects have been replicated using a shock tube, an instrument that can be used to create the same wind and pressure intensity of tornado for the experimental study. Numerous experiments have been conducted to investigate the flexural strength of the CSIP. Furthermore, the study includes the damage detection using three smart sensors embedded in the CSIPs during the shock wave loading.

Keywords: composite structural insulated panels, damage detection, flexural strength, sandwich structures, shock wave loading

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Authors: Najib K. Dankadai, Ahmad 'Athif Mohd Faudzi, Khairuddin Osman, Muhammad Rusydi Muhammad Razif, IIi Najaa Aimi Mohd Nordin

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Researches in soft actuators are now growing rapidly because of their adequacy to be applied in sectors like medical, agriculture, biological and welfare. This paper presents system identification (SI) and control of the force generated by a two chambers pneumatic soft actuator (PSA). A force mathematical model for the actuator was identified experimentally using data acquisition card and MATLAB SI toolbox. Two control techniques; a predictive functional control (PFC) and conventional proportional integral and derivative (PID) schemes are proposed and compared based on the identified model for the soft actuator flexible mechanism. Results of this study showed that both of the proposed controllers ensure accurate tracking when the closed loop system was tested with the step, sinusoidal and multi step reference input through MATLAB simulation although the PFC provides a better response than the PID.

Keywords: predictive functional control (PFC), proportional integral and derivative (PID), soft actuator, system identification

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Authors: Jin Hwa Yang, Hwang Bae, Sung Uk Ryu, Byong Guk Jeon, Sung Jae Yi, Hyun Sik Park

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Experimental studies using a large-scale thermal-hydraulic integral test facility, System–integrated Modular Advanced Reactor Integral Test Loop (SMART-ITL), have been carried out to validate the performance of the prototype, SMART. After Fukushima accident, the passive safety systems have been dealt as important designs for retaining of nuclear safety. One of the concerned scenarios for evaluating the passive safety system is a Complete Loss of Coolant Flow (CLOF). The flowrate of coolant in the primary system is maintained by Reactor Coolant Pump (RCP). When the supply of electric power of RCP is shut off, the flowrate of coolant decreases sharply, and the temperature of the coolant increases rapidly. Therefore, the reactor trip signal is activated to prevent the over-heating of the core. In this situation, Passive Residual Heat Removal System (PRHRS) plays a significant role to assure the soundness of the SMART. The PRHRS using a two-phase natural circulation is a passive safety system in the SMART to eliminate the heat of steam generator in the secondary system with heat exchanger submarined in the Emergency Cooling Tank (ECT). As the RCPs continue to coast down, inherent natural circulation in the primary system transfers heat to the secondary system. The transferred heat is removed by PRHRS in the secondary system. In this paper, the progress of the CLOF accident is described with experimental data of transient condition performed by SMART-ITL. Finally, the capability of passive safety system and inherent natural circulation will be evaluated.

Keywords: CLOF, natural circulation, PRHRS, SMART-ITL

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: Bhavini Pandya

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This paper considers Hη: T2 → T2 the Perturbed Cerbelli-Giona map. That is a family of 2-dimensional nonlinear area-preserving transformations on the torus T2=[0,1]×[0,1]= ℝ2/ ℤ2. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments which define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated, and compared with the distribution of periodic points of the system.

Keywords: feed forward, gradient descent, neural network, integral equation

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Authors: Yang Zhong, Meijie Xue

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The purpose of this paper is to investigate the stresses and excess pore fluid pressure induced by the moving wheel pressure on saturated asphalt pavements, which is one of the reasons for a damage phenomenon in flexible pavement denoted stripping. The saturated asphalt pavement is modeled as multilayered poroelastic half space exerted by a wheel pressure, which is moving at a constant velocity along the surface of the pavement. The governing equations for the proposed analysis are based on the Biot’s theory of dynamics in saturated poroelastic medium. The governing partial differential equations are solved by using Laplace and Hankel integral transforms. The solutions for the stresses and excess pore pressure are expressed in the forms of numerical inversion Laplace and Hankel integral transforms. The numerical simulation results clearly demonstrate the induced deformation and water flow in the asphalt pavement.

Keywords: saturated asphalt pavements, moving loads, excess pore fluid pressure, stress of pavement, biot theory, stress and strain of pavement

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Authors: Abdelhak Bouchakour, Mustafa Brahami, Layachi Zaghba

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The use of photovoltaic energy offers an inexhaustible supply of energy but also a clean and non-polluting energy, which is a definite advantage. The geographical location of Algeria promotes the development of the use of this energy. Indeed, given the importance of the intensity of the radiation received and the duration of sunshine. For this reason, the objective of our work is to develop a data-processing tool (software) of calculation and optimization of dimensioning of the photovoltaic installations. Our approach of optimization is basing on mathematical models, which amongst other things describe the operation of each part of the installation, the energy production, the storage and the consumption of energy.

Keywords: solar panel, solar radiation, inverter, optimization

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Authors: K. K. Riabchenko, T. V Rybitskaya, A. A. Starostenko

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Sper Charm-Tau Factory is a double ring e+e- collider to be operated in the center-of-mass energy range from 2 to 6 GeV, with a peak luminosity of about 1035 cm-2s-1 (Crab Waist collision) and with longitudinally polarized electrons at the IP (interaction point). One of the important elements of the cτ-factory is the superconducting two-aperture quadrupole of the final focus. It was decided to make a full-scale prototype quadrupole. The main objectives of our study included: 1) 3D modeling of the quadrupole in the Opera program, 2) Optimization of the geometry of the quadrupole lens, 3) Study of the influence of magnetic properties and geometry of a quadrupole on integral harmonics. In addition to this, the ways of producing unwanted harmonics have been studied. In the course of this work, a 3D model of a two-aperture iron superconducting quadrupole lens was created. A three-dimensional simulation of the magnetic field was performed, and the geometrical parameters of the lens were selected. Calculations helped to find sources of possible errors and methods for correcting unwanted harmonics. In addition to this, calculations show that there are no obstacles to the production of a prototype lens.

Keywords: super cτ-factory, final focus, twin aperture quadrupole lens, integral harmonics

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Authors: Anand Kishore Kola, G. Uday Bhaskar Babu, Kotturi Ajay Kumar

Abstract:

The modern dynamic systems used in industries are complex in nature and hence the fractional order controllers have been contemplated as a fresh approach to control system design that takes the complexity into account. Traditional integer order controllers use integer derivatives and integrals to control systems, whereas fractional order controllers use fractional derivatives and integrals to regulate memory and non-local behavior. This study provides a method based on the maximumsensitivity (Ms) methodology to discover all resilient fractional filter Internal Model Control - proportional integral derivative (IMC-PID) controllers that stabilize the closed-loop system and deliver the highest performance for a time delay system with a Smith predictor configuration. Additionally, it helps to enhance the range of PID controllers that are used to stabilize the system. This study also evaluates the effectiveness of the suggested controller approach for minimum phase system in comparison to those currently in use which are based on Integral of Absolute Error (IAE) and Total Variation (TV).

Keywords: modern dynamic systems, fractional order controllers, maximum-sensitivity, IMC-PID controllers, Smith predictor, IAE and TV

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