Search results for: circle theorem

Authors: Mukhtari Hussaini Muhammad, Abba Adamu

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The paper will examine the approaches and solutions that will be offered by Senior Secondary School II Students (Demonstration Secondary School, Azare Bauchi State Northern Nigeria – Hausa/ Fulani predominant area) toward solving exercises related to the circle theorem. The angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of the circumference. The Students will be divided in to 2 groups by given them numbers 1, 2; 1, 2; 1, 2, then all 1s formed group I and all 2s formed group II. Group I will be considered as control group in which the traditional method will be applied during instructions. Thus, the researcher will revise the concept of circle, state the theorem, prove the theorem and then solve examples. Group II, experimental group in which the concept of circle will be revised to the students and then the students will be asked to draw different circles, mark arcs, draw angle at the center, angle at the circumference then measure the angles constructed. The students will be asked to explain what they can infer/deduce from the angles measured and lastly, examples will be solved. During the next contact day, both groups will be subjected to solving exercises in the classroom related to the theorem. The angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of circumference. The solution to the exercises will be marked, the scores compared/analysed using relevant statistical tool. It is expected that group II will perform better because of the method/ technique followed during instructions is more learner-centered. By exploiting the talents of the individual learners through listening to the views and asking them how they arrived at a solution will really improve learning and understanding.

Keywords: circle theorem, control group, experimental group, traditional method

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Authors: Fahad Suleiman, Sammani Abdullahi

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The study depicts that a Wedderburn Artin – theorem for rings is considered to be a semisimple ring R which is isomorphic to a product of finitely many mi by mi matrix rings over division rings Di, for some integers n_i, both of which are uniquely determined up to permutation of the index i. It has been concluded that when R is simple the Wedderburn – Artin theorem is known as Wedderburn’s theorem.

Keywords: Commutativity, Wedderburn theorem, Semisimple ring, R module

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Authors: Orlyn Joyce D. Esquivel

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This study analyzed 50 selected research papers from professional language and linguistic academic journals to portray the differences between Kachru’s (1994) outer circle and expanding circle Englishes. The selected outer circle Englishes include those of Bangladesh, Malaysia, the Philippines, India, and Singapore; and the selected expanding circle Englishes are those of China, Indonesia, Japan, Korea, and Thailand. The researcher built ten corpora (five research papers for each corpus) to represent each variety of Englishes. The corpora were examined under grammatical and lexical features using Modified English TreeTagger in Sketch Engine. Results revealed the distinct grammatical and lexical features through the table and textual analyses, illustrated from the most to least dominant linguistic elements. In addition, comparative analyses were done to distinguish the features of each of the selected Englishes. The Language Change Theory was used as a basis in the discussion. Hence, the findings suggest that the ‘outer circle’ Englishes and ‘expanding circle’ Englishes will continue to drift from International English.

Keywords: applied linguistics, English as a global language, expanding circle Englishes, global Englishes, outer circle Englishes

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Authors: Ayubi Wirara, Ardya Suryadinata

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Improper application of the RSA algorithm scheme can cause vulnerability to attacks. The attack utilizes the relationship between broadcast messages sent to the user with some fixed polynomial functions that belong to each user. Scheme attacks carried out by applying the Chinese Remainder Theorem to obtain a general polynomial equation with the same modulus. The formation of the general polynomial becomes a first step to get back the original message. Furthermore, to solve these equations can use Coppersmith's theorem.

Keywords: RSA algorithm, broadcast message, Chinese Remainder Theorem, Coppersmith’s theorem

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Authors: Mohammed Husein Mohammad Rashid

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For a bounded linear operator T acting on a complex infinite dimensional Hilbert space ℋ, we say that T is ∗-class A operator (abbreviation T∈A*) if |T²|≥ |T*|². In this article, we prove the following assertions:(i) we establish some conditions which imply the normality of ∗-class A; (ii) we consider ∗-class A operator T ∈ ℬ(ℋ) with reducing kernel such that TX = XS for some X ∈ ℬ(K, ℋ) and prove the Fuglede-Putnam type theorem when adjoint of S ∈ ℬ(K) is dominant operators; (iii) furthermore, we extend the asymmetric Putnam-Fuglede theorem the class of ∗-class A operators.

Keywords: fuglede-putnam theorem, normal operators, ∗-class a operators, dominant operators

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Authors: Gloria Chen

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In the past, when we complimented someone who had a good command of English, we would say ‘She/He speaks/writes standard English,’ or ‘His/Her English is standard.’ However, with English has becoming a ‘global language,’ many scholars and English users even create a plural form for English as ‘world Englishes,’ which indicates that national/racial varieties of English not only exist, but also are accepted to a certain degree. Now, a question will be raised when it comes to English teaching and learning: ‘What variety/varieties of English should be taught?’ This presentation will first explore Braj Kachru’s well-known categorization of the inner circle, the outer circle, and the expanding circle of English users, as well as inner circle varieties such as ‘Ebonics’ and ‘cockney’. The presentation then will discuss the purposes and contexts of English learning, and apply different approaches to different purposes and contexts. Three major purposes of English teaching/learning will be emphasized and considered: (1) communicative competence, (2) academic competence, and (3) intercultural competence. This presentation will complete with the strategies of ‘code switch’ and ‘register switch’ in teaching English to non-standard English speakers in both speaking and writing.

Keywords: world Englishes, standard and non-standard English, inner, outer, expanded circle communicative, academic, intercultural competence

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Authors: Kishor J. shinde

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We determine the values of k and p such that the Sturm-Liouville differential operator τu=-(d^2 u)/(dx^2) + kx^p u is in limit point case or limit circle case at infinity. In particular it is shown that τ is in the limit point case when (i) for p=2 and ∀k, (ii) for ∀p and k=0, (iii) for all p and k>0, (iv) for 0≤p≤2 and k<0, (v) for p<0 and k<0. τ is in the limit circle case when (i) for p>2 and k<0.

Keywords: limit point case, limit circle case, Sturm-Liouville, infinity

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Authors: Zhuoran Shan, Li Wan, Xianchun Zhang

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With an increasing trend of regionalization and polycentricity in Chinese contemporary big cities, “sub-region life circle” turns to be an effective method on rational organization of urban function and spatial structure. By the method of questionnaire, network big data, route inversion on internet map, GIS spatial analysis and logistic regression, this article makes research on characteristic and formation mechanism of “sub-region life circle” based on human high-probability daily activity in Chinese big cities. Firstly, it shows that “sub-region life circle” has been a new general spatial sphere of residents' high-probability daily activity and mobility in China. Unlike the former analysis of the whole metropolitan or the micro community, “sub-region life circle” has its own characteristic on geographical sphere, functional element, spatial morphology and land distribution. Secondly, according to the analysis result with Binary Logistic Regression Model, the research also shows that seven factors including land-use mixed degree and bus station density impact the formation of “sub-region life circle” most, and then analyzes the index critical value of each factor. Finally, to establish a smarter “sub-region life circle”, this paper indicates that several strategies including jobs-housing fit, service cohesion and space reconstruction are the keys for its spatial organization optimization. This study expands the further understanding of cities' inner sub-region spatial structure based on human daily activity, and contributes to the theory of “life circle” in urban's meso-scale.

Keywords: sub-region life circle, characteristic, formation mechanism, human activity, spatial structure

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Authors: Abdulrahman Abdulrahman, Abir Abdulrahman

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The stability of slopes of earthen embankments is usually examined by Swedish slip circle method or the slices method. The factor of safety against sliding using Fellenius procedure depends upon the angle formed by the arc of sliding at the center ψ and the radius of the slip circle r. The values of both mentioned parameters ψ and r aren't precisely predicted because they are measured from the drawing. In this paper, analytical formulae were derived for finding the exact values of both ψ and r. Also this paper presents the different conditions of intersections the slip circle with the body of an earthen dam and the coordinate of intersection points. Numerical examples are chosen for demonstration the proposed solution

Keywords: earthen dams stability, , earthen embankments stability, , Fellenius method, hydraulic structures, , side slopes stability, , slices method, Swedish slip circle

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Authors: Siyuan Cai

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COVID-19 has triggered the planning circles to think about how to improve the city's ability to respond to public health emergencies. From the perspective of the community, this article reviews the risk cases in Wuhan Chenjiadun Community and other communities under the epidemic, and analyzes the response to public health emergencies such as infectious disease outbreaks in the excellent cases of resilient epidemic prevention communities. Then, combined with the planning of the living circle, it demonstrates the necessity of integrating the concept of resilience into the 15-minute community living circle to make up for the shortcomings of infectious disease prevention. Finally, it is proposed to strictly control the source and tail of the epidemic in the layout of the living circle, daily health and epidemic emergency should be taken into account in planning, community medical resources should be decentralized in management, and the application of smart technologies in the planning of living circle should be fully emphasized, so as to improve the community's ability to respond to public health emergencies.

Keywords: pandemic, resilient cities, resilient community, 15-minute community life circle

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Authors: T. J. Jemi Jeya, V. Sriram

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Pile Supported Caisson breakwater is an ecofriendly breakwater very useful in coastal zone protection. The model is developed by considering the advantages of both caisson breakwater and pile supported breakwater, where the top portion is a vertical or quarter circle caisson and the bottom portion consists of a pile supported breakwater defined as Vertical Pile Supported Breakwater (VPSCB) and Quarter-circle Pile Supported Breakwater (QPSCB). The study mainly focuses on comparison of run up over VPSCB and QPSCB under oblique waves. The experiments are carried out in a shallow wave basin under different water depths (d = 0.5 m & 0.55 m) and under different oblique regular waves (0⁰, 15⁰, 30⁰). The run up over the surface is measured by placing two run up probes over the surface at 0.3 m on both sides from the centre of the model. The results show that the non-dimensional shoreward run up shows slight decrease with respect to increase in angle of wave attack.

Keywords: Caisson breakwater, pile supported breakwater, quarter circle breakwater, vertical breakwater

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Authors: Bo Ram Choi, Ji Su Kim, Juyeon Cho, Hyukjin Lee

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Food contaminated by bacteria (E.coli), causes food poisoning, which occurs to many patients worldwide annually. We have introduced an application of rolling circle amplification (RCA) as a versatile biosensor and developed a diagnostic platform composed of capillary tube and microbeads for rapid and easy detection of Escherichia coli (E. coli). When specific mRNA of E.coli is extracted from cell lysis, rolling circle amplification (RCA) of DNA template can be achieved and can be visualized by beads aggregation in capillary tube. In contrast, if there is no bacterial pathogen in sample, no beads aggregation can be seen. This assay is possible to detect visually target gene without specific equipment. It is likely to the development of a genetic kit for point of care testing (POCT) that can detect target gene using microbeads.

Keywords: rolling circle amplification (RCA), Escherichia coli (E. coli), point of care testing (POCT), beads aggregation, capillary tube

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: Ji Su Kim, Bo Ram Choi, Ju Yeon Cho, Hyukjin Lee

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Epidermal growth factor receptor (EGFR) 19 deletion mutation gene is over-expressed in carcinoma patient. EGFR 19 deletion mutation is known as typical biomarker of non-small cell lung cancer (NSCLC), which one section in the coding exon 19 of EGFR is deleted. Therefore, there have been many attempts over the years to detect EGFR 19 deletion mutation for replacing conventional diagnostic method such as PCR and tissue biopsy. We developed a simple and facile detection platform based on Rolling Circle Amplification (RCA), which provides highly amplified products in isothermal amplification of the ligated DNA template. Limit of detection (~50 nM) and a faster detection time (~30 min) could be achieved by introducing RCA.

Keywords: EGFR19, cancer, diagnosis, rolling circle amplification (RCA), hydrogel

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Authors: M. H. M. Rashid

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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge transform

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Authors: Jennifer Nutton, Gayle Ployer, Ky Scott, Jenny Morgan

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Working in a circle within higher education creates a decolonial space of mutual respect, responsibility, and reciprocity that facilitates collaborative learning and deep connections among learners and instructors. This approach is beyond simply facilitating a group in a circle but opens the door to creating a sacred space connecting each member to the land, to the Indigenous peoples who have taken care of the lands since time immemorial, to one another, and to one’s own positionality. These deep connections not only center human knowledges and relationships but also acknowledges responsibilities to land. Working in a circle as a relational pedagogical praxis also disrupts institutional power dynamics by creating a space of collaborative learning and deep connections in the classroom. Inherent within circle work is to facilitate connections not just academically but emotionally, physically, culturally, and spiritually. Recent literature supports the use of online talking circles, finding that it can offer a more relational and experiential learning environment, which is often absent in the virtual world and has been made more evident and necessary since the pandemic. These deeper experiences of learning and connection, rooted in both knowledge and the land, can then be shared with openness and vulnerability with one another, facilitating growth and change. This process of beginning with the land is critical to ensure we have the grounding to obstruct the ongoing realities of colonialism. The authors, who identify as both Indigenous and non-Indigenous, as both educators and learners, reflect on their teaching and learning experiences in circle. They share a relational pedagogical praxis framework that has been successful in educating future social workers, environmental activists, and leaders in social and human services, health, legal and political fields.

Keywords: circle work, relational pedagogies, decolonization, distance education

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Authors: Deng Tingting

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The coordinated and integrated development of regions is an inevitable requirement for China to move towards high-quality, sustainable development. As one of the regions with the best economic foundation and the strongest economic strength in western China, it is a typical area with national importance and strong network connection characteristics in terms of the comprehensive effect of linking the inland hinterland and connecting the western and national urban networks. The integrated development of the Chengdu-Chongqing economic circle is of great strategic significance for the rapid and high-quality development of the western region. In the context of new urbanization, this paper takes 16 urban units within the economic circle as the research object, based on the 5-year panel data of population, regional economy, and spatial construction and development from 2016 to 2020, using the entropy method and Theil index to analyze the three target layers, and cause analysis. The research shows that there are temporal and spatial differences in the Chengdu-Chongqing economic circle, and there are significant differences between the core city and the surrounding cities. Therefore, by reforming and innovating the regional coordinated development mechanism, breaking administrative barriers, and strengthening the "polar nucleus" radiation function to release the driving force for economic development, especially in the gully areas of economic development belts, not only promote the coordinated development of internal regions but also promote the coordinated and sustainable development of the western region and take a high-quality development path.

Keywords: Chengdu-Chongqing economic circle, new urbanization, coordinated regional development, Theil Index

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Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu

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Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC_4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC₃ cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC_4,6 cryptosystem than LUC₃ and LUC cryptosystems. Current study concludes that LUC_4,6 cryptosystem is more secure than LUC and LUC₃ cryptosystems in sustaining against Lenstra’s attack.

Keywords: Lucas sequence, Dickson polynomial, faulty signature, corresponding signature, congruence

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Authors: Siyuan Cai

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This paper takes community segregation during major infectious diseases as the background, based on the physiological needs and safety needs of citizens during home segregation, and based on the selection of convenient facilities and medical facilities as the main research objects. Based on the POI data of public facilities in Chongqing, the spatial distribution characteristics of the convenience and medical facilities in the 15-minute living circle centered on three neighborhoods in Shapingba, namely Shengwei Community, Anju Commmunity and Fengtian Garden Community, were explored by means of GIS spatial analysis. The results show that the spatial distribution of convenience and medical facilities in this area has significant clustering characteristics, with a point-like distribution pattern of "dense in the west and sparse in the east", and a grouped and multi-polar spatial structure. The spatial structure is multi-polar and has an obvious tendency to the intersections and residential areas with dense pedestrian flow. This study provides a preliminary exploration of the distribution of medical and convenience facilities within the 15-minute living circle of a segregated community, which makes up for the lack of spatial research in this area.

Keywords: ArcGIS, community segregation, convenient facilities; distribution pattern, medical facilities, POI, 15-minute community life circle

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Authors: Aji Budi Rinekso, Revika Niza Artiyana, Lisa Widayanti

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English is one of the international languages in the world. People use this language to communicate with each other in the international forums, international events or international organizations. As same as other languages, English has a rule which is called grammar. Grammar is the part of english which has a role as the language systems. In grammar, there are tenses which provide a time period system for past, present and future. Sometimes it is difficult for some English learner to remember all of the tenses completely. Especially for those with special needs or exceptional children with vision restrictiveness. The aims of this research are 1) To know the design of Special Grammar Circle (Spegraci) as the media for blind people to learn english grammar. 2) To know the work of Special Gramar Circle (Spegraci) as the media for blind people to learn english grammar. 3) To know the function of this device in increasing tenses ability for blind people. The method of this research is Research and Development which consists of several testing and revision of this device. The implementation of Special Grammar Circle (Spegraci) is to make blind people easily to learn the tenses. This device is easy to use. Users only roll this device and find out the tense formula and match to the name of the formula in braille. In addition, this device also enables to be used by normal people because normal written texts are also provided.

Keywords: blind people, media innovation, spegraci, tenses

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Authors: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: positive solution, boundary value problem, fixed point theorem, cone

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Crank-Nicolson scheme, Lax-Richtmyer theorem, stability, consistency, Peclet number, Greschgorin circle

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Authors: Tiantian Feng

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There is a dearth of research on the literary circle as a teaching strategy in English as a Foreign Language (EFL) classes in Chinese colleges and universities and even fewer empirical studies on its impacts. In this one-quarter, design-based project, the researcher aims to increase students’ engagement, cooperation, and, on top of that, reading comprehension performance by utilizing a researcher-developed, adapted reading circle model in an EFL reading course at a Chinese college. The model also integrated team-based learning and portfolio assessment, with an emphasis on the specialization of individual responsibilities, contributions, and outcomes in reading projects, with the goal of addressing current issues in EFL classes at Chinese colleges, such as passive learning, test orientation, ineffective and uncooperative teamwork, and lack of dynamics. In this quasi-experimental research, two groups of students enrolled in the course were invited to participate in four in-class team projects, with the intervention class following the adapted literature circle model and team members rotating as Leader, Coordinator, Brain trust, and Reporter. The researcher/instructor used a sequential explanatory mixed-methods approach to quantitatively analyze the final grades for the pre-and post-tests, as well as individual scores for team projects and will code students' artifacts in the next step, with the results to be reported in a subsequent paper(s). Initial analysis showed that both groups saw an increase in final grades, but the intervention group enjoyed a more significant boost, suggesting that the adapted reading circle model is effective in improving students’ reading comprehension performance. This research not only closes the empirical research gap of literature circles in college EFL classes in China but also adds to the pool of effective ways to optimize reading comprehension performance and class performance in college EFL classes.

Keywords: literature circle, EFL teaching, college english reading, reading comprehension

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Authors: Paola Cattabriga

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According to Gödel’s first incompleteness argument it is possible to construct a formally undecidable proposition in Principia mathematica, a statement that, although true, turns out to be neither provable nor refutable for the system, making therefore incomplete any formal system suitable for the arithmetic of integers. Its features and limitation effects are today widespread basics throughout whole scientific thought. This article brings Gödel’s achievement into question by the definition of the refutability predicate as a number-theoretical statement. We develop proof of invalidity of Theorem VI in Gödel’s 1931, the so-called Gödel’s first incompleteness theorem, in two steps: defining refutability within the same recursive status as provability and showing that as a consequence propositions (15) and (16), derived from definition 8.1 in Gödel’s 1931, are false and unacceptable for the system. The achievement of their falsity blocks the derivation of Theorem VI, which turns out to be therefore invalid, together with all the depending theorems. This article opens up thus new perspectives for mathematical research and for the overall scientific reasoning.

Keywords: Gödel numbering, incompleteness, provability predicate, refutability predicate

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Authors: Hao-Hsi Tseng, Hsin-Yun Lee

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The Most Advantageous Tender (MAT) has been criticized for its susceptibility to dictatorial situations and for its processing of same score, same rank issues. This study applies the four criteria from Arrow's Impossibility Theorem to construct a mechanism for revealing illegitimate scores in scoring methods. While commonly be used to improve on problems resulting from extreme scores, ranking methods hide significant defects, adversely affecting selection fairness. To address these shortcomings, this study relies mainly on the overall evaluated score method, using standardized scores plus normal cumulative distribution function conversion to calculate the evaluation of vender preference. This allows for free score evaluations, which reduces the influence of dictatorial behavior and avoiding same score, same rank issues. Large-scale simulations confirm that this method outperforms currently used methods using the Impossibility Theorem.

Keywords: Arrow’s impossibility theorem, cumulative normal distribution function, most advantageous tender, scoring method

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Authors: Hemant Kumar Pathak

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In 1994, Matthews (S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197) introduced the concept of a partial metric as a part of the study of denotational semantics of data flow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory. In this paper, we introduce the concept of almost partial Hausdorff metric. We prove a fixed point theorem for multi-valued mappings on partial metric space using the concept of almost partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. In the sequel, we derive a homotopy result as an application of our main result.

Keywords: fixed point, partial metric space, homotopy, physical sciences

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Authors: J. Leige Lopes, L. Aparecida Bastos, R. Monteiro da Silva

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The objective of this paper is to study the work of children and adolescents and the vicious circle of poverty from the perspective of Guinar Myrdal’s Theory of Circular Cumulative Causation. The objective is to show that if a person starts working in the juvenile phase of life they will be classified as poor or extremely poor when they are adult, which can to be observed in the case of Brazil, more specifically in the north and northeast. To do this, the methodology used was statistical and econometric analysis by applying a probit model. The main results show that: if people reside in the northeastern region of Brazil, and if they have a low educational level and if they start their professional life before the age 18, they will increase the likelihood that they will be poor or extremely poor. There is a consensus in the literature that one of the causes of the intergenerational transmission of poverty is related to child labor, this because when one starts their professional life while still in the toddler or adolescence stages of life, they end up sacrificing their studies. Because of their low level of education, children or adolescents are forced to perform low-paid functions and abandon school, becoming in the future, people who will be classified as poor or extremely poor. As a result of poverty, parents may be forced to send their children out to work when they are young, so that in the future they will also become poor adults, a process that is characterized as the "vicious circle of poverty."

Keywords: children, adolescents, Gunnar Myrdal, poverty, vicious circle

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Authors: Ti-Jun Xiao, Zhe Xu

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Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem.

Keywords: evolutional control system, controllability, boundary control, existence and uniqueness

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Authors: P. W. Tsai, J. W. Chen, C. W. Chen, C. Y. Chen

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In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method

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