Search results for: folk theorem

Authors: Yoshifumi Hino

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An infinitely repeated prisoner’s dilemma is a typical model that represents teamwork situation. If both players choose costly actions and contribute to the team, then both players are better off. However, each player has an incentive to choose a selfish action. We analyze the game under costly observation. Each player can observe the action of the opponent only when he pays an observation cost in that period. In reality, teamwork situations are often costly observation. Members of some teams sometimes work in distinct rooms, areas, or countries. In those cases, they have to spend their time and money to see other team members if they want to observe it. The costly observation assumption makes the cooperation difficult substantially because the equilibrium must satisfy the incentives not only on the action but also on the observational decision. Especially, it is the most difficult to cooperate each other when the stage-game is prisoner's dilemma because players have to communicate through only two actions. We examine whether or not players can cooperate each other in prisoner’s dilemma under costly observation. Specifically, we check whether symmetric Pareto efficient payoff vectors in repeated prisoner’s dilemma can be approximated by sequential equilibria or not (efficiency result). We show the efficiency result without any randomization device under certain circumstances. It means that players can cooperate with each other without any randomization device even if the observation is costly. Next, we assume that public randomization device is available, and then we show that any feasible and individual rational payoffs in prisoner’s dilemma can be approximated by sequential equilibria under a specific situation (folk theorem). It implies that players can achieve asymmetric teamwork like leadership situation when public randomization device is available.

Keywords: cost observation, efficiency, folk theorem, prisoner's dilemma, private monitoring, repeated games.

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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: Wongwarit Nipitwittaya

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The objectives of this research is bringing folk song with the teaching of Western music were to examine to investigate, to compare, develop the skill, technique, knowledge of Thai folk song and to preserve folk song of Thailand to be known more widely also learn Thai culture from Thai folk song. Study by bringing Thailand folk song is widely known for learning with Western music in course brass performance. Bringing the melody of Thai folk music and changing patterns to western music notes for appropriate on brass performance. A sample was selected from brass students, using research by assessment of knowledge from test after used Thai folk song lesson. The lesson focus for scales and key signature in western music by divided into two groups, the one study by used research tools and another one used simple lesson and a collection of research until testing. The results of the study were as follows: 1. There are good development skill form research method 2. Sound recognition can be even better. The study was a qualitative research and data collection by observation.

Keywords: Thai folk song, brass instrument, key signature, western music

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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: Jyoti Brahma

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Folk epics of India are found in various Indian languages. The study of folk epics and its importance in folkloristic study in India came into prominence only during the nineteenth century. The British administrators and missionaries collected and documented folk epics from various parts of the country. The paper is an attempt to investigate how colonial outpost appears to penetrate the interiors of Indian land and society and triggered off the Indian Renaissance. It takes into account the compositions of the epics of India and the attention it received during the nineteenth century, which in turn gave, rise to the national consciousness shaping the culture of India. Composed as oral traditions these folk epics are now seen as repositories of historical consciousness whereas in earlier times societies without literacy were said to be without history. So, there is an urgent need to re-examine the British impact on Indian literary traditions. The Bhakti poets through their nuanced responses in their efforts to change the behavior of Indian society gives us the perfect example of deferment in the clear cut distinction between the folk and the classical in the context of India. It evades a pure categorization and classification of the classical and constitutes part of the folk traditions of the cultural heritage of India. Therefore, the ethical question of what is ontologically known as ordinary discourse in the case of the “folk” forms metaphors and folk language gains importance once more. The paper also thus seeks simultaneously to outline the significant factors responsible for shaping the destiny of folklore in South India particularly the four political states of the Indian Union: Andhra Pradesh, Karnataka, Kerala and Tamil Nadu, what could be termed as South Indian “cultural zones”.

Keywords: colonial, folk, folklore, tradition

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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: Dani Karmakar

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In India, the journey of street theatre was started with Indian peoples Theatre Association (IPTA) as a tool for anti-establishment that was categorized as by the people and for the people. It has expressed common people’s feelings, problems, day to day life. It has brought a social change that is downtrodden. By its nature, it is based on communist ideology. Street theatre is a theatre of protest. In India, many folk theatres translate directly ‘Street Theatre’, those are Veedhi Natakam in Andhra Pradesh and Therukoothu in Tamil Nadu. But they do not covey to common definition of street theatre. There are different folk theatres of different regions in India. All folk theatres have individual characteristic, criteria, taste and flavor that can render distinctive each others. In festivals or special occasions, whole communities come together to enjoy collectively and express their feelings. The Veedhi Natakam means 'street theatre'. Theru koothu is a traditional street theatre in the northern districts of Tamilnadu. Folk theatre has potential to deliver strong messages. It has a socially significant role. At Veedhi Natakam, Vidhushaka takes part for social criticism. Gambhira is also a socio-political folk drama presentation in West Bengal.

Keywords: folk theatre, Gambhira, politics, street theatre

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Authors: Meseret Berhanie Menkir

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The present study explores folk dance, one of the folklore texts, its symbols, and its therapeutic role. As a case, the study concentrates on Astrio-Mariam and Merkorios Bera, celebrated on January 30 and February 3 at Deresgie-Mariam Church in Ethiopia. By taking a qualitative stance, the study analyses the meaning of folk dance, explains its role, and describes its types. The data gathered through observation, interview, and focus group discussion techniques are documented in field notes, audio, and video. The data obtained is analyzed using structural-functionalism, psychoanalysis, and semiotics. Accordingly, community members of all ages (mainly the Ethiopian Orthodox Tewahedo Church followers) participate in the performance. While the folk dance is a type of small group dance and group dance, the group has no feature of using men and women performing together. The folk dance's role is a form of healing and spiritual fulfilment besides entertainment. The folk dance also has sword dance characteristics; the study confirmed this feature in content and form. Moreover, the folk dance characterized by frequent shoulder and hand movements Wancha likleka (Horn-mug spin), Doro metet (Chicken drink), and sword dance depict wealth, heroism, and warfare. The instruments used in the performances are also alive, with religious symbols reaching from the drum, incense, and cross to the suffering of Jesus Christ from Hanna to Qeyafa, and references to the 12 Apostles.

Keywords: folk dance, festival, ritual, symbol, therapeutic

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Authors: Violeta Kostadinova, Emilia Tsankova

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The purpose of this research is to explore and analyze the integration of the younger generation with Bulgarian folklore through various innovative forms, methods and approaches. A survey was conducted among students to evaluate its success. The results prove the relevance of the problem as well and the necessity of innovation to keep the national and promotion of Bulgarian folklore. Innovation in music education is a good way to create positive motivation and raise interest in folk art, which is especially pronounced when the folk songs have contemporary arrangement. Modern interpretation of Bulgarian folk music makes the music more approachable to young people and makes it more likely that folk music will become an integral part of our modern culture. The research would help the implementation of appropriate innovations for more effective training and upgrading for music students in all middle and high schools in the country.

Keywords: Bulgarian folklore, innovative forms, methods and approaches, motivation, music education

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Authors: Ms Yaowaluck Ruampol

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The research on the development of using folk tales based on performance activities aimed to (1) study the development of speaking skill for early-childhood students, (2) evaluate the development of speaking skill before and after speaking activities. Ten students of Kindergarten level 2, who have enrolled in the subject of the research for speaking development of semester 2 in 2013, were purposively selected as the research cohort. The research tools were lesson plans for speaking activities and pre-posttest for speaking development that were approved for content validity and reliability (IOC=.66-1.00,0.967). The research found that the development of speaking skill of the research samples before using performance activities on folk tales in developing speaking skill was in the normal high level. Additionally, the results revealed that the preschoolers after applying speaking skill on performance activities also imaginatively created their speaking skill.

Keywords: speaking development, folk tales, performance activities, communication engineering

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Authors: Dina Sabirova, Madina Moldagali

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The rapid development of new media, especially the Internet, has led to major changes in folk culture. The net space is increasingly becoming a creation of the ‘folk’ imagination, saturated with multimedia stories with collective authorship, like traditional folklore. Moreover, the Internet picks up and changes old folklore traditions, such as the form of publication, the way of storytelling, or gave a new morality to the ‘old tales’. In this article, the similarities and differences between Internet folklore/ cyber-folklore/ digital folklore and oral folk art were examined by using the material of modern Kazakh authors. The relationship between tradition and innovation was studied in order to interpret the sequence of the authors' research taking into account the realities. The material of the article was the prose texts of Kazakh writers published in internet magazines and social networks. An immanent and intertextual analysis of the text was carried out. Thus, the new forms of Internet folklore lead to new forms of expression and social morality in society

Keywords: internet literature, modern Kazakhstani authors, net folklore, oral folk art

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Authors: Yaowaluck Ruampol, Suthakorn Wasupokin

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The research on the development of speaking using folk tales based on performance activities aimed to (1) study the development of speaking skill for early- childhood students, and (2) evaluate the development of speaking skill before and after speaking activities. Ten students of Kindergarten level 2, who have enrolled in the subject of the research for speaking development of semester 2 in 2013 were purposively selected as the research cohort. The research tools were lesson plans for speaking activities and pre-post test for speaking development that were approved as content validity and reliability (IOC=.66-1.00,α=0.967). The research found that the development of speaking skill of the research samples before using performance activities on folk tales in developing speaking skill was in the normal high level. Additionally, the results appeared that the preschoolers after applying speaking skill on performance activities also imaginatively created their speaking skill.

Keywords: speaking development, folk tales, performance activities, early-childhood students

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Authors: Supalak Fakkhum, Wannita Pochanakul

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This research is qualitative research that aims to study the application of local wisdom in health care of early childhood at Ban Nam Chieo Community, Laem Ngop, Trat Province. The target is one folk medicine healer and 45 parents who have children or grandchildren aged between 0-5 years. The folk medicine healer was interviewed and observed during early childhood health care practice. Parents were interviewed. The results showed that local wisdom in health care of early childhood are as follows: 1. Local wisdom about early childhood diseases: It is believed that the disease was determined while the child was still in the womb, in the third month of pregnancy. When a child is born, they will have La, La-ong and Saang diseases, which are URI (upper respiratory infection) and DI (diarrhea) diseases. Supernatural aspect is also considered. 2. The treatment is chosen to match the symptoms of the disease. Caring for early childhood includes psychological therapy by rituals and spells. 3. For local wisdom concerning prevention and health promotion, parents normally bring their child to folk medicine healers for “throat paint” as an act of protection and health promotion. Folk healers often prescribe food according to belief and local wisdom.

Keywords: local wisdom, early childhood, folk medicine, healer

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Authors: Yu Lu

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Fixed point theory is a basic tool for the study of the existence of Nash equilibria in game theory. This paper presents a significant generalization of the Veinott-Zhou fixed point theorem for increasing correspondences, which serves as an essential framework for investigating the existence of Nash equilibria in supermodular and quasisupermodular games. To establish our proofs, we explore different conceptions of multivalued increasingness and provide comprehensive results concerning the existence of the largest/least fixed point. We provide two distinct approaches to the proof, each offering unique insights and advantages. These advancements not only extend the applicability of the Veinott-Zhou theorem to a broader range of economic scenarios but also enhance the theoretical framework for analyzing equilibrium behavior in complex game-theoretic models. Our findings pave the way for future research in the development of more sophisticated models of economic behavior and strategic interaction.

Keywords: fixed-point, Tarski’s fixed-point theorem, Nash equilibrium, supermodular game

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Authors: Ahmed Mousa, Huda Mazeed

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The research aims to determine the appropriate songs and artistic indications for the kindergarten child. In addition, it aims to use the songs of folk to develop expressive visual drawings with artistic connotations for the kindergarten child. The current research used a one group semi-experimental approach to identify the impact of songs on expressive children's drawings. The research community is represented in the educational administration in Giza Governorate for the academic year (2018 - 2019). The sample was taken from the kindergarten of Gamal Abdel Nasser School of Dokki Educational Administration in Giza Governorate. The study was applied to the second level children sample (5-6 years), where they numbered 20 children, males and females. The research results show that there are statistically significant differences between the average scores of the children of the experimental group in the pre and post-measurements on the observation card for children after hearing the songs of social and national folk in favor of post measurement. Moreover, the results demonstrate that there are no statistically significant differences between the average scores of children in the experimental group in the measurements, the post and follow-up, on the observation card of children's drawings for social and national folk.

Keywords: folk songs, visual expressive, artistic connotations, early childhood

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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: Gokul G. Kshirsagar

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Native folk theatre and folk songs have a significant influence on the origin and development of Indian cinema. Therefore, the presence of songs and music has been an integral part and special characteristics of Indian cinema which is popularly known as Bollywood. An Indian cinema without songs, either in Hindi or other regional languages, is simply unimaginable. The present paper, in the first part, attempts to explain the use and need of musical songs and also the psychology of Indian audience in this respect with reference to some of the films which give primary importance to songs. In the second part, the paper tries to situate the present study in the context by referring to the Hindi language drama film Teesari Kasam directed by Basu Bhattacharys. The film is based on the Hindi novelist Phanishwarnath Renu’s short story Teesari Kasam (Mare Gaye Gulfam) in this adapted film, the director has made use of eight songs, but these songs are the extensive versions of the songs as used in the original story. Thus, the main aim of the paper is to underscore the fact that through artistic use of the musical, the director has succeeded in transforming the central feelings conveyed in the original story. Eventually, through the present study of the film adaptation, the relevance of songs in films will be illustrated and understood.

Keywords: Bollywood, folk theatre, folk songs, film adaptation

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Authors: Shiv Kumar

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In the shifting scenario of postmodern age that foregrounds the multiplicity of meanings and discourses, the present research article seeks to investigate various paradigm shift of contemporary performances concerning Haryanvi Saangs, so-called folk plays, which are being performed widely in the regional territory of Haryana, a northern state of India. Folk arts cannot be studied efficiently by using the tools of literary criticism because it differs from the literature in many aspects. One of the most essential differences is that literary works invariably have an author. Folk works, on the contrary, never have an author. The situation is quite clear: either we acknowledge the presence of folk art as a phenomenon in the social and cultural history of people, or we do not acknowledge it and argue it is a poetical or art of fiction. This paper is an effort to understand the performative tradition of Saang which is traditionally known as Saang, Swang or Svang became a popular source for instruction and entertainment in the region and neighbouring states. Scholars and critics have long been debating about the origin of the word swang/svang/saang and their relationship to the Sanskrit word –Sangit, which means singing and music. But in the cultural context of Haryana, the word Saang means ‘to impersonate’ or ‘to imitate’ or ‘to copy someone or something’. The stories they portray are derived for the most part from the same myths, tales, epics and from the lives of Indian religious and folk heroes. Literally, the use of poetic sense, the implication of prose style and elaborate figurative technique are worthwhile to compile the productivity of a performance. All use music and song as an integral part of the performance so that it is also appropriate to call them folk opera. These folk plays are performed strictly by aboriginal people in the state. These people, sometimes denominated as Saangi, possess a culture distinct from the rest of Indian folk performances. The concerned form is also known with various other names like Manch, Khayal, Opera, Nautanki. The group of such folk plays can be seen as a dynamic activity and performed in the open space of the theatre. Nowadays, producers contributed greatly in order to create a rapidly growing musical outlet for budding new style of folk presentation and give rise to the electronic focus genre utilizing many musicians and performers who had to become precursors of the folk tradition in the region. Moreover, the paper proposes to examine available sources relative to this article, and it is believed to draw some different conclusions. For instance, to be a spectator of ongoing performances will contribute to providing enough guidance to move forward on this root. In this connection, the paper focuses critically upon the major performative aspects of Haryanvi Saang in relation to several inquiries such as the study of these plays in the context of Indian literary scenario, gender visualization and their dramatic representation, a song-music tradition in folk creativity and development of Haryanvi dramatic art in the contemporary socio-political background.

Keywords: folk play, indigenous, performance, Saang, tradition

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Authors: Walter Beck

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Jharkhand is newly constituted 28th State in the eastern part of India which is known for the oldest settlement of the indigenous people. In the State of Jharkhand in which broadly three language family are found namely, Austric, Dravidian, and Indo-European. Ex-Mundari, kharia, Ho Santali come from the Austric Language family. Kurukh, Malto under Dravidian language family and Nagpuri Khorta etc. under Indo-European language family. There are 32 Indigenous Communities identified as Scheduled Tribe in the State of Jharkhand. Santhal, Munda, Kahria, Ho and Oraons are some of the major Tribe of the Jharkhand state. Jharkhand has a Rich Cultural heritage which includes Folk art, folklore, Folk Dance, Folk Music, Folk Songs for which diversity can been seen from place to place, season to season and all traditional Culture and practices. The languages as well as the songs are vulnerable to dominant culture and hence needed to be protected. The collection and documentation of these songs in their natural setting adds significant contribution to the conservation and propagation of the cultural elements. This paper reflects to bring out the Originality of the Collected Songs from remote areas of the plateau of Sothern Jharkhand as a rich intangible Cultural heritage of the Country. The research was done through participatory observation. In this research project more than 100 songs which were never documented before.

Keywords: cultural heritage, India, indigenous people, songs, languages

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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: Fang Tang

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A major Confucian masterpiece and the earliest-known poetry anthology (composed approximately 1046-771 BCE), The Classic of Poetry, reflects different cultures in ancient China. It is regarded as a Chinese classic and one of the world’s most significant written works, an essential part of our global cultural heritage. This paper explores how the ancient Chinese classic became transformed into part of popular culture, found in folk songs circulated in Fangxian county, a mountainous location in Hubei province in central mainland China. It is the hometown of one of the most well-known authors of The Classic of Poetry, whose name is Yin Jifu. Local villagers process, refine, and recreate these poems into popular folk songs, which have been handed down from generation to generation. The folk songs based on The Classic of Poetry vividly reflect local customs, life styles, and various cultural activities. After thousands of years of singing these traditional songs, the region has become an important area to maintain part of Chinese cultural heritages; here, the original high culture is converted into a popular culture that is absorbed into people’s daily life. Based on a year’s field research and many interviews with local singers, this paper explores the ways in which locals have transformed the contents of The Classic of Poetry. It examines how today these popular folk songs become part of much-treasured culture heritage, illustrating the transformation of traditional high culture into popular culture. The paper argues that the modern adaptations of the traditional poems of The Classic of Poetry combine both oral and written cultural heritage and reflects the interaction between ancient Chinese official literature and folk literature. The paper also explores the reasons why the folk songs of The Classic of Poetry are so popular in the area, including the influences of its author Yin Jifu, the impact of ancient diasporic culture from the political centre to remote rural areas, and the interactions of local cultures (famous as Chu culture) and Chinese mainstream cultural policies.

Keywords: high/low culture, The Classic of Poetry, the functions of media, cultural policy

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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: 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: Iqra Khan, Ghousia Saeed, Salman Jamil

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Fashion is the soul of styles. People of all times want to look trendy, eye catching and unique among all. For this reason, people always adopt different flairs in their outfits including their clothes, shoes, bags and other accessories. However, unfortunately, there is lack of opportunity for accommodating the fashion exposure activities expressed with the folk dances of different regions so as to exhibit the fashion of Pakistan to the world. The paper focuses on the vibrant setting of the whole building according to the social patterns, folk and local trends and existing environment of Lahore. This is done by studying each of the aspect obtained from objectives through research questions evolved from the objectives. The answers to these questions are found through case studies and the existing theories in the world in relevance to the topic. The paper finds out how the geometry of dance works with design principles to create transparent geometry of fashion building. This all creates the fiesta environment taken from the locality of the region from the local and cultural lifestyles of the locals and then assembling it together to create a full festivity experience throughout the building.

Keywords: fashion, folk dance, geometry, local trends, social patterns, transparent

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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: 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: Salmin Alshalmani, Ghazall M Benhusein, Ebtisam Alhadi Absomaha, Marwa I. Meshri, Hamdoon A. Mohammed, Jamal Mezogi

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Eight wild medicinal plants used by Libyan and growing in Al-Jebel Al-Akhdar, Libya were suspected to estimate the antioxidant activity using 2,2-Diphenyl-1-Picrylhydrazyl stable free radical (DPPH). Incidences of purple colour reduction of the DPPH by testing extracts in addition to quercetin and vitamin C as positive controls reflect its ability to scavenge free radicals. All testing plants extract showed noticeable strength as antioxidant regarding its abilities to scavenge DPPH with an especial regards to Sarcopoterium spinosum.

Keywords: antioxidant, scavenging activity, folk medicine, methanol extracts

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Authors: Eudjen Cinc

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Common Byzantine origins of church music of Serbs and Romanians are certainly not the only reason for great similarities between the ways of singing of the two nations, especially in the region of Banat. If it was so, the differences between the interpretation of church music in this part of Orthodox religion and the one specific for other parts where Serbs or Romanians live could not be explained. What is it that connects church signing of two nations in this peaceful part of Europe to such an extent that it could be considered a comprehensive corpus, different from other 'Serbian' or 'Romanian' regions? This is the main issue dealt with in the text according to examples and comparative processing of material. The main aim of the paper is representation of the new and interesting, while its value lies in its potential to encourage the reader or a future researcher to investigate and search further.

Keywords: folk influences, melody, melodic models, ethnomusicology

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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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