Search results for: integral inequality

Authors: Cui Fu, Yi-Zhou Zhuang, Sheng-Zhi Wang

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Full scale tests of six micropiles with different predrilled-hole parameters under low frequency cyclic lateral loading in-sand were carried out using the MTS hydraulic loading system to analyze the seismic performance of micropiles. Hysteresis curves, skeleton curves, energy dissipation capacity and ductility of micropiles were investigated. The experimental results show the hysteresis curves appear like plump bows in the elastic–plastic stage and failure stage which exhibit good hysteretic characteristics without pinching phenomena and good energy dissipating capacities. The ductility coefficient varies from 2.51 to 3.54 and the depth and loose backfill of oversized holes can improve ductility, but the diameter of predrilled-hole has a limited effect on enhancing its ductility. These findings and conclusions could make contribution to the practical application of the semi-integral abutment bridges and provide a reference for the predrilled oversized hole technology in integral abutment bridges.

Keywords: ductility, energy dissipation capacity, micropile with predrilled oversized hole, seismic performance, semi-integral abutment bridge

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: K. Manmi, Q. X. Wang

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This paper investigates microbubble dynamics subject to ultrasound in a weakly viscous fluid near a rigid boundary. The phenomenon is simulated using a boundary integral method. The weak viscous effects are incorporated into the model through the normal stress balance across the bubble surface. The model agrees well with the Rayleigh-Plesset equation for a spherical bubble for several cycles. The effects of the fluid viscosity in the bubble dynamics are analyzed, including jet development, centroid movement and bubble volume.

Keywords: microbubble dynamics, bubble jetting, viscous effect, boundary integral method

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Authors: Lina Wu, Jia Liu, Ye Li

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The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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Authors: Yang Zhong, Mei-Jie Xu

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To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in the single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is an obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. Therefore, the dynamic change of parameter in asphalt mixture should be taken into consideration when the theoretical analysis is taken out.

Keywords: asphalt pavement, dynamic modulus, integral transformation, transfer matrix, thermal stress

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Authors: J. Fernandez de Canete, S. Fernandez-Calvo, I. García-Moral

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This paper presents and discusses the application of the object-oriented modelling software SIMSCAPE to hydraulic systems, with particular reference to multivariable proportional-integral-derivative (PID) control. As a result, a particular modelling approach of a double cylinder-piston coupled system is proposed and motivated, and the SIMULINK based PID tuning tool has also been used to select the proper controller parameters. The paper demonstrates the usefulness of the object-oriented approach when both physical modelling and control are tackled.

Keywords: object-oriented modeling, multivariable hydraulic system, multivariable PID control, computer simulation

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Authors: Amin Khaksar

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The popular music scene is a highly speculative field of cultural production in which eroticism plays an essential role in attracting audiences. The juxtaposition of eroticism and cultural products possibly implies the importance of the representation of cultural values in popular music videos. As with norms in conservative societies, however, there are some types of inequalities, most of which are dominated by institutional inclinations as opposed to socio-cultural inclinations. This paper explores the challenges that increasing structural inequality poses to erotic representations, focusing on Iranian popular music videos. It outlines how eroticism is becoming a leading tool for circumventing institutional inequalities that affect some cultural values. Using the value-based approach, which draws on visual semiotics and content analysis of Iranian popular music videos compared to Western popular music videos, this study contends that the problematic nature of eroticism emerges when sexual representation takes on meaning beyond its commercial purpose. Indeed, erotica has more to say about freedom, social violence, gender discrimination, and, most importantly, values that can be shared and communicated. The concept of eroticism used in this study functions as a shared practice and can be perceived through symbols. Furthermore, the conclusions show that music artists (performers) use eroticism in three ways to represent cultural values: erotic performances, erotic qualities, and erotic narratives. The expected contribution highlights the role that eroticism can play in the encounter with institutional inequality and injustice. Consider a female celebrity whose erotic qualities help her body gain attention.

Keywords: inequality, value- based economics, eroticism, popular music video

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Authors: Chitsanzo Isaac

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Across the world, the ongoing Covid-19 pandemic has challenged urban systems and policy frameworks, highlighting societal vulnerabilities and systemic inequities among many communities. Measures of confinement and social distancing to contain the Covid-19 virus have fragmented the physical and social fabric of cities. This has caused urban dwellers to reassess how they engage with their urban surroundings and maintain social ties. Urbanists have presented strategies that would allow communities to survive and even thrive, in extraordinary times of crisis like the pandemic. Tactical Urbanism, particularly the 15-Minute City, has gained popularity. It is considered a resilient approach in the global north, however, it’s transferability to the global south has been called into question. To this end, this paper poses the question: to what extent is the 15-Minute City framework integral sustainable design, and are there processes that make it adoptable by cities in the global south? This paper explores four issues using secondary quantitative data analysis and convergence analysis in the Paris and Blantyre urban regions. First, it questions how the 15-Minute City has been defined and measured, and how it impacts urban dwellers. Second, it examines the extent to which the 15-minute city performs under the lens of frameworks such as Wilber’s integral theory and Fleming’s integral sustainable design theory. Thirdly this work examines the processes that can be transferred to developing cities which foster community resilience through the perspectives of experience, behaviors, cultures, and systems. Finally, it reviews the principal ways in which a multi-perspective reality can be the basis for resilient community design and sustainable urban development. This work will shed a light on the importance of a multi-perspective reality as a means of achieving sustainable urban design goals in developing urban areas.

Keywords: 15-minute city, developing cities, global south, community resilience, integral sustainable design, systems thinking, complexity, tactical urbanism

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Authors: Saeed Otarod

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

Keywords: explicit, linear, differential, closed form

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Authors: Wen-Bao Qiao, Jean-Charles Créput

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To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: parallel 2-opt, double links, large scale TSP, GPU

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Authors: Vassilis C. Moulianitis, Evgenios Scourboutis, Ilias Katsanis, Paraskevas Papanikos, Nikolas Zacharopoulos

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This paper presents the conceptual design of an automated biomethane potential measurement system. First, the design specifications for the BMP system and the basic components of the system will be presented. Three concepts that meet the design specifications will be presented. The basic characteristics of each concept will be analyzed in detail. The concepts will be evaluated using a set of design criteria that includes flexibility, cost, size, complexity, aesthetics, and accessibility in order to determine the best solution. The evaluation will be based on the discrete Choquet integral.

Keywords: automated biomethane test, conceptual mechatronics design, concept evaluation, Choquet integral

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Authors: Manana Chumburidze

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We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Kanyarat Bussaban, Siriporn Poolsuwan

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This study is conducted with the objective to prove how the distorted distribution of welfare affects the quality of school-age children lives differently in the case of an urban community in Bangkok. 334 samples are households from Suan Oi and Ratchapatubtim communities. The study of sample communities found the difference between two community areas that are close. The people of Suan Oi community are economically better off people than the people of the Ratchapatubtim community. They share the benefits of using most services except the welfare of a child’s education. The resulting analysis of the variability in quality of life of the school age children indicate that heads of the households are women looking for quality of life benefits when the compulsory school age is less. A study of the two communities suggests that the inequality in income distribution currently affects the quality of life of school-age children.

Keywords: inequality, income distribution, quality of school-age children lives, welfare state

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Authors: V. Rekha, Rama Pal

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The study examines the degree and magnitude of wealth-based inequalities in child health and its determinants in India. Despite making strides in economic growth, India has failed to secure a better nutritional status for all the children. The country currently faces the double burden of malnutrition as well as the problems of overweight and obesity. Child malnutrition, obesity, unsafe water, sanitation among others are identified as the risk factors for Non-Communicable Diseases (NCDs). Eliminating malnutrition in all its forms will catalyse improved health and economic outcomes. The assessment of the distributive dimension of child health across various segments of the population is essential for effective policy intervention. The study utilises the fourth round of District Level Health Survey for 2012-13 to analyse the inequalities among children in the age group 0-14 years in Maharashtra, a state in the western region of India with a population of 11.24 crores which constitutes 9.3 percent of the total population of India. The study considers the extent of health inequality by state, districts, sector, age-groups, and gender. The z-scores of four child health outcome variables are computed to assess the nutritional status of pre-school and school children using WHO reference. The descriptive statistics, concentration curves, concentration indices, correlation matrix, logistic regression have been used to analyse the data. The results indicate that magnitude of inequality is higher in Maharashtra and child health inequalities manifest primarily among the weaker sections of society. The concentration curves show that there exists a pro-poor inequality in child malnutrition measured by stunting, wasting, underweight, anaemia and a pro-rich overweight inequality. The inequalities in anaemia are observably lower due to the widespread prevalence. Rural areas exhibit a higher incidence of malnutrition, but greater inequality is observed in the urban areas. Overall, the wealth-based inequalities do not vary significantly between age groups. It appears that there is no gender discrimination at the state level. Further, rural-urban differentials in gender show that boys from the rural area and girls living in the urban region experience higher disparities in health. The relative distribution of undernutrition across districts in Maharashtra reveals that malnutrition is rampant and considerable heterogeneity also exists. A negative correlation is established between malnutrition prevalence and human development indicators. The findings of logistic regression analysis reveal that lower economic status of the household is associated with a higher probability of being malnourished. The study recognises household wealth, education of the parent, child gender, and household size as factors significantly related to malnutrition. The results suggest that among the supply-side variables, child-oriented government programmes might be beneficial in tackling nutrition deficit. In order to bridge the health inequality gap, the government needs to target the schemes better and should expand the coverage of services.

Keywords: child health, inequality, malnutrition, obesity

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Authors: Nur R. Daut

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The objective of this paper is to offer an insight on how political power inequality has contributed and exacerbated the political violence towards the Rohingya ethnic group in Myanmar. In particular, this paper attempts to illustrate how power inequality in the country has prevented Myanmar’s leader Aung San Suu Kyi from taking effective measures on the issue. The research centers on the question of why Aung San Suu Kyi has been seen as not doing enough to stop the persecution of the Rohingya ethnic group ever since she was appointed the State Counsellor to the Myanmar government. As a Nobel Peace Prize laureate, Suu Kyi’s lack of action on the matter has come under severe criticism by the international community. Many have seen this as Suu Kyi’s failure to establish democracy and allowing mass killing to spread in the country. The real question that many perhaps should be asking, however, is how much power Suu Kyi actually holds within the government which is still heavily controlled by the military or Tatmadaw. This paper argues that Suu Kyi’s role within the government is limited which hinders constructive and effective measures to be taken on the Rohingya issue. Political power in this research is being measured by 3 factors: control over events such as burning of Rohingya villages, control over resources such as land ownership and media and control over actors such the Tatmadaw, police force and civil society who are greatly needed to ease and resolve the conflict. In order to illustrate which individuals or institution have control over all the 3 above factors, this paper will first study the constitution of Myanmar. The constitution will also be able to show the asymmetrical power relations as it will provide evidence as to how much political power Suu Kyi holds within the government in comparison to other political actors and institutions. Suu Kyi’s role as a state counsellor akin to a prime minister is a newly created position as the current constitution of Myanmar bars anyone with a foreign spouse from holding the post of a president in the country. This is already an indication of the inequality of political power between Suu Kyi and the military. Apart from studying the constitution of Myanmar, Suu Kyi’s speeches and various interviews are also studied in order to answer the research question. Unfortunately, Suu Kyi’s limited political power also involves the Buddhist monks in Myanmar who have held significant influence throughout the history of the country. This factor further prevents Suu Kyi from preserving the sanctity of human rights in Myanmar.

Keywords: Aung San Suu Kyi, constitution of Myanmar, inequality, political power, political violence, Rohingya, Tatmadaw

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator 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 Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. 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 analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Arbolino R., Boffardi R., L. De Simone

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The success of a development policy requires the definition of a proper investment planning on behalf of policymakers. Such planning should consider both tangible and intangible features characterizing a territory and, moreover, evaluate both state of place and an ideal situation to be achieved, that represents the final goal of the policy. The aim of this research is to propose a methodological approach to implement this ideal solution or the best solution appliable to the Italian regions. It consists of two steps: the first one is a measure of regional inequality through building a composite indicator for analyzing the level of development and compare the differences among the regions. It is constructed by means of a principal component analysis. Ranking regions according to the scores achieved is useful as benchmark, to identify a best solution towards which other regions should strive. Thus, this distance is measured through a revised Sen index that allows to assign a weight on which calculate the financing resource programming. The results show that this approach is a good instrument to fairly and efficiently allocate public funds, in order to reduce regional inequalities.

Keywords: public economics, inequalities, growth, development

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Authors: Fatihin Khoirul, Muhammad Muqorrobin Ist

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Bojonegoro Regency is one of the districts that use the concept Agropolitan as the Territorial Development Policy. Three sub-district designated as Area Development District of Agropolitan are Kapas, Dander, and Kalitidu or commonly called KADEKA. Current policy has been shown results, but there was an inequality of results in some areas. One of them occurred in the Ngringinrejo village with the main commodities is Starfruit and Wedi village with the main commodities is Salak fruit. Therefore, a comparative study is used to search for causal factors of inequality result of the policy by using the 5 aspects compared, namely: (1) Management Development Agropolitan; (2) Physical Condition agropolitan Region; (3) Implementing Agency at the Village Level; (4) Village Government Support; and (5) Community support. Based on the discussion of qualitative analysis, it was found that five aspects have their respective roles in creating inequality of outcomes that occur in both villages. But beyond that, there are conditions where the two villages experienced the same condition that is when the initial implementation of the policy. The condition is referred to as 'the phenomenon of price trap.' The condition is caused by lower commodity prices, causing the village government's commitment in implementing policies too low, followed by public awareness in support of the policy is also low, so care for commodities is also low, and the quality is too low lead and eventually back causing low price. However, the difference is that the village Ngringinrejo able to get out of this condition with 'the new culture of administration' at the end of 2013. While the conditions in the village of Wedi compounded by not respected request assistance by the irrigation district.

Keywords: comparative policy analysis, qualitative comparative, inequallity, price trap, new culture of administration

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Authors: Sheren H. Salah, Ahmed Y. Ben Sasi

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The inverted pendulum system is a classic control problem that is used in universities around the world. It is a suitable process to test prototype controllers due to its high non-linearities and lack of stability. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. This paper presents the possibility of balancing an inverted pendulum system using sliding mode control (SMC). The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart's position. Therefore, proportional-integral-derivative (PID) is used for comparison. Results have proven SMC control produced better response compared to PID control in both normal and noisy systems.

Keywords: inverted pendulum (IP), proportional-integral derivative (PID), sliding mode control (SMC), systems and control engineering

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Authors: Arnaud Nougues

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This paper describes a two-stage methodology derived from internal model control (IMC) for tuning a proportional-integral-derivative (PID) controller for levels or other integrating processes in an industrial environment. Focus is the ease of use and implementation speed which are critical for an industrial application. Tuning can be done with minimum effort and without the need for time-consuming open-loop step tests on the plant. The first stage of the method applies to levels only: the vessel residence time is calculated from equipment dimensions and used to derive a set of preliminary proportional-integral (PI) settings with IMC. The second stage, re-tuning in closed-loop, applies to levels as well as other integrating processes: a tuning correction mechanism has been developed based on a series of closed-loop simulations with model errors. The tuning correction is done from a simple closed-loop step test and the application of a generic correlation between observed overshoot and integral time correction. A spin-off of the method is that an estimate of the vessel residence time (levels) or open-loop process gain (other integrating process) is obtained from the closed-loop data.

Keywords: closed-loop model identification, IMC-PID tuning method, integrating process control, on-line PID tuning adaptation

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Antonio Abatemarco, Francesca Stroffolini

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In the economic literature, Rawls’ Theory of Justice is usually interpreted in a two-stage setting, where a priority to the worst off individual is imposed as a distributive value judgment. In this paper, instead, we model Rawls’ Theory in a three-stage setting, that is, a separating line is drawn between the original position, the educational stage, and the working life. Hence, in this paper, we challenge the common interpretation of Rawls’ Theory of Justice as Fairness by showing that this Theory goes well beyond the definition of a distributive value judgment, in such a way as to embrace efficiency issues as well. In our model, inequalities are shown to be permitted as far as they stimulate a greater effort in education in the population, and so economic growth. To our knowledge, this is the only possibility for the inequality to be ‘bought’ by both the most-, and above all, the least-advantaged individual as suggested by the Difference Principle. Finally, by recalling the old tradition of ‘universal ex-post efficiency’, we show that a unique optimal social contract does not exist behind the veil of ignorance; more precisely, the sole set of potentially Rawls-optimal social contracts can be identified a priori, and partial justice orderings derived accordingly.

Keywords: justice, Rawls, inequality, social contract

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Authors: Mónica Arroyo

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South America shows increasing decline in regional export values in the last years, after a strong growth of trade flows especially with China up to 2013. This change is due to the end of the commodity price boom, the slowing of the Chinese economy and the effects of the 2008 economic crisis. This paper examines the integration of regional economies in this context, particularly the situation in Brazil and Argentina. Based on transformations over the last two decades, the analysis is focused on the spatial circuits of production linked to foreign markets, contributing to the understanding of the different uses of territory and the within-country inequality. The South American regional exports, consisting basically of raw materials, are concentrated in a few companies. Large areas are intended for the production of agriculture and mining commodities, under the command of major economic groups, both domestic and foreign, relegating the local population to less productive places or, in most cases, forcing them to change their activity and to migrate to other regions in search of some source of income. On the other hand, the dynamics of these commodities’ spatial circuits of production print requirements in territories in terms of infrastructure and regulation. Capturing this movement requires understanding businesses and government’s role in territorial regulation, and consequently how regional systems are changing – for instance, economic specialisation, growing role of services, investment in roads, railways, ports, and airports. This paper aims to highlight topics for discussion on regional economic dynamics and their different degrees of internationalisation. The intention is to contribute to the debate about the relations between trade, globalization, and development.

Keywords: regional inequality, international trade, developing world, South America

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: S. Houcine Habib, B. Elkhalil Hachi, Mohamed Guesmi, Mohamed Haboussi

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In this paper, dynamic fracture behaviors of cracked orthotropic structure are modeled using extended finite element method (X-FEM). In this approach, the finite element method model is first created and then enriched by special orthotropic crack tip enrichments and Heaviside functions in the framework of partition of unity. The mixed mode stress intensity factor (SIF) is computed using the interaction integral technique based on J-integral in order to predict cracking behavior of the structure. The developments of these procedures are programmed and introduced in a self-software platform code. To assess the accuracy of the developed code, results obtained by the proposed method are compared with those of literature.

Keywords: X-FEM, composites, stress intensity factor, crack, dynamic orthotropic behavior

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Authors: Brahim Berbaoui

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In this paper, a new particle swarm optimization (PSO) based method is proposed for the implantation of optimal harmonic power flow in power systems. In this algorithm approach, proportional integral controller for reference compensating currents of active power filter is performed in order to minimize the total harmonic distortion (THD). The simulation results show that the new control method using PSO approach is not only easy to be implanted, but also very effective in reducing the unwanted harmonics and compensating reactive power. The studies carried out have been accomplished using the MATLAB Simulink Power System Toolbox.

Keywords: shunt active power filter, power quality, current control, proportional integral controller, particle swarm optimization

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Authors: Azadeh Jafari, Farzin Ghanadi, Matthew J. Emes, Maziar Arjomandi, Benjamin S. Cazzolato

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The turbulence within the atmospheric boundary layer induces highly unsteady aerodynamic loads on structures. These loads, if not accounted for in the design process, will lead to structural failure and are therefore important for the design of the structures. For an accurate prediction of wind loads, understanding the correlation between atmospheric turbulence and the aerodynamic loads is necessary. The aim of this study is to investigate the effect of turbulence within the atmospheric boundary layer on the surface pressure on a flat plate over a wide range of turbulence intensities and integral length scales. The flat plate is chosen as a fundamental geometry which represents structures such as solar panels and billboards. Experiments were conducted at the University of Adelaide large-scale wind tunnel. Two wind tunnel boundary layers with different intensities and length scales of turbulence were generated using two sets of spires with different dimensions and a fetch of roughness elements. Average longitudinal turbulence intensities of 13% and 26% were achieved in each boundary layer, and the longitudinal integral length scale within the three boundary layers was between 0.4 m and 1.22 m. The pressure distributions on a square flat plate at different elevation angles between 30° and 90° were measured within the two boundary layers with different turbulence intensities and integral length scales. It was found that the peak pressure coefficient on the flat plate increased with increasing turbulence intensity and integral length scale. For example, the peak pressure coefficient on a flat plate elevated at 90° increased from 1.2 to 3 with increasing turbulence intensity from 13% to 26%. Furthermore, both the mean and the peak pressure distribution on the flat plates varied with turbulence intensity and length scale. The results of this study can be used to provide a more accurate estimation of the unsteady wind loads on structures such as buildings and solar panels.

Keywords: atmospheric boundary layer, flat plate, pressure coefficient, turbulence

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Authors: S. Aizikovich, L. Krenev, Y. Tokovyy, Y. C. Wang

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An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical indentation of a flat cylindrical punch into an arbitrarily non-homogeneous elastic half-space is constructed by making use of the bilateral asymptotic method. The key point of this method lies in evaluation of the ker¬nels in the obtained integral equations by making use of a numerical technique. Once the structure of the kernel is defined, it then is approximated by an analytical expression of special kind so that the solution of the integral equation can be achieved analytically. This fact allows for construction of the solution in an analytical form, which is convenient for analysis of the mechanical effects concerned with arbitrarily presumed non-homogeneity of the material.

Keywords: contact problem, circular punch, arbitrarily-nonhomogeneous halfspace

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Authors: Yang Zhong, Meijie Xu

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The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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