Search results for: folk theorem

Authors: Chananart Meenanan

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The composition Isan Symphonic Variations for Chorus and Orchestra is a musical composition inspired by Isan Folk music tunes. The composer has created the well crafted melodic variations and cultural sound character of the piece based on the Klon Lum Tang Isan Keaw (Green Isan’s short poems). Meanwhile, the poetic lyric has been motivatedly recreated to bring the abundance of Northeastern Thailand region’s sentiment back to life. Moreover, the sound of xylophone (Ponglang), the instruments of the orchestra and the chorus were blended in order to present Isan folk music’s character via the Western musical idiom. The 3 movement of this composition is divided as following: In Movement I (Allegro), the introduction has been represented the uniqueness in Isan folk music’s liveliness by expressing it through the sound of chorus and orchestra. The composer also added the melodious sound flavor by utilizing the variety of the muting sound style on trumpets and horns. In Movement II (Moderato), the aspect of the heterophonic approach music has been implied to the main idea of the entire movement whereby its formatted transformation worked effectively through chorus and the orchestra. In Movement III (Allegretto) the harmonic chromaticism was modified and applied as the symbolic icon of the entire movement. The transparence of Isan cultural sound was perfectly designed to be the highlight of this spectacular episode.

Keywords: Isan, symphonic variations, chorus, orchestra

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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: D. S. Palimkar

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Random fixed point theory has received much attention in recent years, and it is needed for the study of various classes of random equations. The study of random fixed point theorems was initiated by the Prague school of probabilistic in the 1950s. The existence and uniqueness of fixed points for the self-maps of a metric space by altering distances between the points with the use of a control function is an interesting aspect in the classical fixed point theory. In a new category of fixed point problems for a single self-map with the help of a control function that alters the distance between two points in a metric space which they called an altering distance function. In this paper, we prove the results of existence of random common fixed point and its uniqueness for a pair of random mappings under weakly contractive condition for generalizing alter distance function in polish spaces using Random Common Fixed Point Theorem for Generalized Weakly Contractions.

Keywords: Polish space, random common fixed point theorem, weakly contractive mapping, altering function

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Authors: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Ather Saeed, Arif Khan, Jeffrey Gosper

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Sensor devices are prone to errors and sudden node failures, which are difficult to detect in a timely manner when deployed in real-time, hazardous, large-scale harsh environments and in medical emergencies. Therefore, the loss of data can be life-threatening when the sensed phenomenon is not disseminated due to sudden node failure, battery depletion or temporary malfunctioning. We introduce a set of partial differential equations for localizing faults, similar to Green’s and Maxwell’s equations used in Electrostatics and Electromagnetism. We introduce a node organization and clustering scheme for self-stabilizing sensor networks. Green’s theorem is applied to regions where the curve is closed and continuously differentiable to ensure network connectivity. Experimental results show that the proposed GTFD (Green’s Theorem fault-detection and Self-stabilization) protocol not only detects faulty nodes but also accurately generates network stability graphs where urgent intervention is required for dynamically self-stabilizing the network.

Keywords: Green’s Theorem, self-stabilization, fault-localization, RSSI, WSN, clustering

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Authors: Ruining Wu, Na Song

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Paper-cut, as one of the Chinese traditional folk decoration art, has become a unique visual aesthetic characteristics of the Chinese nation in the long-term evolution of cultural symbols. Chinese paper-cut art is the treasure-house for product design in natural resources. This paper first analyzed Chinese folk art of historical origin, cultural background, cultural values, aesthetic value, style features of Chinese paper cut art, then analyzed the design thought and design cases of paper-cut art application in different areas, such as clothing design, logo design and product design areas. Through the research of Chinese paper-cut art culture and design elements, this paper aims to build a household product design concept of Chinese traditional culture.

Keywords: paper-cut art, culture, household products, design

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Authors: Romy Martinez

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This paper focuses on the use of the indigenous language Guarani in Paraguayan popular song and on some key interpreters born between the 1930s and 1980s. It analyses two representative musical genres of Paraguay, the Polka Paraguaya and Guarania. The lyrics of these genres follow one of four poetic-linguistic forms: to be entirely in Guarani, entirely in Spanish, bilingual (alternating verses in Guarani and Spanish), or in Jopará; the last being a form where words of both languages may be mixed in a single verse. Through these forms, the lyrics alternate and combine the indigenous voice with the one introduced with colonisation, in turn reflecting how Guarani seems to constantly transit, to and from, between a position of disdain and of value within Paraguayan society. Through analysing recordings of Polkas, Paraguayas, and Guaranias, it identifies three styles of singing adopted by female singers who include these genres in their repertoires, namely Paraguayan classical folk, Paraguayan folk, and Paraguayan pop-folk. This analysis is informed by a pilot study which consisted of online interviews with several Paraguayan artists, revealing significant aspects of their backgrounds and musical influences. In addition, it draws on autoethnographic approaches, building on the experience of the music researcher and singer. From a decolonising perspective, the paper brings together the distinctive voices and sounds expressed in popular songs from a marginalised country, language, and gender.

Keywords: female singers, Guarani, Paraguayan song, performance

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: Muhammad Sufian Jusoh, Mesliza Mohamed

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In this paper, we investigate the existence of positive solutions for a Dirichlet second order boundary value problem by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.

Keywords: Krasnosel'skii fixed point theorem, positive solutions, Dirichlet boundary value problem, Dirichlet second order boundary problem

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Authors: Li-Jun Zheng

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The use of drums as an accompanying instrument is a common phenomenon in traditional Chinese folk rituals and musical culture. Especially, some folk rituals construct ritual-related sounds and give them ritual-specific symbolic and meaningful systems through the combination and use of multiple percussion instruments. The Yue drum(岳鼓), an asymmetrically shaped thin waist drum, is currently used in Han Chinese Shigong（师公）rituals in Guangxi, China, and is an important ritual instrument in Shigong rituals. This paper examines the use of the Yue drum and other percussion instruments in Han Chinese Shigong rituals in Guangxi, China, and shows the current status of combining instrumental accompaniment forms with human voices in Shigong rituals. Through further analysis of the musical and dance forms of Han Chinese Shigong rituals, this paper shows how Han Chinese Shigong ritual performers construct the ritual field through "sound-human-dance" and further explains the relationship between the existing and fictitious performance fields in the rituals. In addition, this paper demonstrates the relationship between Han Chinese Shigong rituals and the religious beliefs they involve, such as Taoism and Buddhism. And it further explores how performers in Han Chinese Shigong rituals use Yue drums for the dual purpose of "entertaining the gods" and "entertaining the people".

Keywords: sound research, the Han Chinese Shigong ritual, the thin waist drum, folk beliefs, ritual music

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Authors: Anas M. Fares

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Reinforced concrete shear walls are the most frequently used forms of lateral resisting structural elements. These walls may take many forms due to their functions and locations in the building. In Palestine, the most lateral resisting forces construction forms is the cantilever shear walls system. It is thus of prime importance to study the rigidity of these walls. The virtual work theorem is used to derive the total lateral deflection of cantilever shear walls due to flexural and shear deformation. The case of neglecting the shear deformation in the walls is also studied, and it is found that the wall height to length aspect ratio (H/B) plays a major role in calculating the lateral deflection and the rigidity of such walls. When the H/B is more than or equal to 3.7, the shear deformation may be neglected from the calculation of the lateral deflection. Moreover, the walls with the same material properties, same lateral load value, and same aspect ratio, shall have the same of both the lateral deflection and the rigidity. Finally, an equation to calculate the total rigidity and total deflection of such walls is derived by using the virtual work theorem for a cantilever beam.

Keywords: cantilever shear walls, flexural deformation, lateral deflection, lateral loads, reinforced concrete shear walls, rigidity, shear deformation, virtual work theorem

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Authors: Eveline Muika Kabongo, Peter Delobelle, Ferdinand Mukumbang, Edward Nicol

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Introduction: Studies have been conducted to establish the effect of the MomConnect program in South Africa, but these studies did not focus on the stakeholders' and implementers' perspectives and the underlying program theory of the MomConnect initiative program. We strived to obtain stakeholders’ perspectives and assumptions on the MomConnect program and develop an initial program theory (IPT) of how the MomConnect initiative was expected to work. Methods: A realist-informed explanatory design used. The interviewer was performed with 10 key informants selected purposively among MomConnect key informants at the a national level of NDoH South Africa. The interview was done via zoom and lasted for 30 to 60 minutes. Introduction and abduction inferencing approaches were applied. The deductive and inductive approaches were performed during the analysis. ICAMO hereustic framework was used to analysed the data in order to get key informants expectations on how the MomConnect will work or not. Results: We developed three folk’s theories illustrating how the key informants’ expected the MomConnect to work. These theories showed that the MomConnect intended to provide users with health information and education that will empower and motivate them with knowledge which will allow the improvement of health services delivery among HCPs and improvement of the uptake of MCH services among pregnant women and mothers and decrease the rate of maternal and child mortality in the country. The lack of an updated mechanism to link women to the outcome was an issue. Another problem enlightened was the introduction of the WhatsApp program instead of SMS messaging, which was free of charge to women. Conclusion: The Folk’s theory developed from this study provided an insight into how the MomConnect was expected to work and what did not work. The folk’s theory will be merged with information from candidate theories on synthesis review and document review to develop our initial program theory of the MomConnect initiative.

Keywords: mHealth, MomConnect program, realist evaluation, maternal and child health, maternal and child health services, introduction, theory-driven

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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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: Lavina N. Bhaskar, Ashima Tiwari

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In the endeavour of connecting culture to stories, textile to narratives and people to material, authors analyse the impact of narratives in two popular Indian textiles namely - Mata Ni Pachedi and Pabuji Ki Phad. These textiles narrate people’s tale or Folk tale. Each textile has a style or format in which the story is told (and it is visual). Mata Ni Pachedi, when translated into the English language literally means behind the mother goddess. Mata Ni Pachedi is an Indian textile from the province of Gujarat which constitutes an entire temple of the goddess, with the idol herself in it. On the other hand, Pabuji ki Phad is scroll painting of folk deities of Rajasthan, narrated by Bhopas (the Priest singers of Rajasthan). These textiles narrate stories of ordinary people with extraordinary courage, of social reform, and people’s belief in the divine. Authors take to task their years of craft-cluster study conducted in the past and use existing literature to map their journey in the preliminary phase of research. And then carried out an ethnographic study by visiting the origins of these textiles in Rajasthan and Gujrat (in India), met artisans and their families who are still practicing these dying art form, in order to understand the format and impact of textile story-telling. This research paper talks about the narrative in Indian textiles; the stories in them, artisans and their life as metaphorical representations of the People in Mata Ni Pachedi and Pabuji Ki Phad.

Keywords: cultural derivatives, folk-tale, Indo-Narratives, Indology

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Authors: Peter Akayuure, Michael Johnson Nabie

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Similar to many colonized nations in the world, one indelible mark left by colonial masters after Ghana’s independence in 1957 has been the fact that many contexts used to teach statistics and probability concepts are often alien and do not resonate with the social domain of our indigenous Ghanaian child. This has seriously limited the understanding, discoveries, and applications of mathematics for national developments. With the recent curriculum demands of making the Ghanaian child mathematically literate, this qualitative study involved video recordings and mathematical analysis of play sessions of an indigenous girl game called Ampe with the aim to demystify the concepts in probability theorem, which is applied in mathematics related fields of study. The mathematical analysis shows that the game of Ampe, which is widely played by school girls in Ghana, is suitable for learning concepts of the probability theorems. It was also revealed that as a girl game, the use of Ampe provides good lessons to educators, textbook writers, and teachers to rethink about the selection of mathematics tasks and learning contexts that are sensitive to gender. As we undertake to transform teacher education and student learning, the use of indigenous games should be critically revisited.

Keywords: Ampe, mathematical analysis, probability theorem, Ghanaian girl game

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Authors: Zainab Magaji Musa, Nordin M. A. Rahman, Julaily Aida Jusoh

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The web services applications for digital reference service (WSDRS) of LIS model is an informal model that claims to reduce the problems of digital reference services in libraries. It uses web services technology to provide efficient way of satisfying users’ needs in the reference section of libraries. The formal WSDRS model consists of the Z specifications of all the informal specifications of the model. This paper discusses the formal validation of the Z specifications of WSDRS model. The authors formally verify and thus validate the properties of the model using Z/EVES theorem prover.

Keywords: validation, verification, formal, theorem prover

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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: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Beghdadi Lotfi, Bouziane Abdelhafid

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A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: Ching-Yi Wang

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The purpose of this study is to explore strategies for integrate Minhsiung environments and cultural resources for Infernal Lord Festival. Minhsiung Infernal Lord Festival is one of the famous religious event in Chia-Yi County, Taiwan. This religious event and the life of local residents are inseparable. Minhsiung Infernal Lord Festival has a rich cultural ceremonies meaning and sentiment of local concern. This study apply field study, document analysis and interviews to analyze Minhsiung Township’s featured attractions and folklore events. The research results reveal the difficulties and strategies while incorporating culture elements into culture tourism. This study hopes to provide innovative techniques for the purpose of prolonging the feasibility of future development of the tradition folk culture.

Keywords: Taiwan folk culture, Minhsiung Infernal Lord Festival, religious tourism, folklore, cultural tourism

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Authors: W. Promprom, W. Chatan

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Leguminosae is a large plant family and its members are important for local people utilization in the Northeast of Thailand. This research aimed to survey medicinal plants in this family in Kantharalak Community forest. The plant collection and exploration were made from October 2017 to September 2018. Folk medicinal uses were studied by interviewing villagers and folk medicine healers living around the community forest by asking about local names, using parts, preparation and properties. The results showed that 65 species belonging to 40 genera were found. Among these, 30 species were medicinal plant. The most used plant parts were leaf. Decoction and drinking were mostly preparation method and administration mode used. All medicinal plants could be categorized into 17 diseases/symptoms. Most plant (56.66%) were used for fever. The voucher specimens were deposited in Department of Biology, Faculty of Science, Mahasarakham University, Thailand. Therefore, the data from this study might be widely used by the local area and further scientific study.

Keywords: ethnobotany, ethnophamacology, medicinal plant, taxonomy, utilization

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Authors: Sonia Wahengbam, Natasha Elangbam

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Female impersonation has existed through the length of human civilization and the breadth of its cultures. Transvestism and drag queen cultures have created multi-sited spaces where in the shadow of art, one can cross the gender barrier and express one’s hidden identity. This paper will explore a dynamic cultural space that exists in Manipur, a state in the northeastern region of India, where the female impersonators (nupi shabis) of a folk theater (Shumang Leela) are using this traditional and popular art form to claim social acceptance of their homosexual identities through the medium of entertainment. It will highlight how by crossing the gender boundary, this third gender group has carved out a unique socio-economic niche where they have exploited their sexual identities to their advantage. The paper will trace the expanding cultural ‘’borderland’’ of Manipur where there is an increasing sense of ‘becoming’, belonging and sharing” of identities through the interweaving of old and new media. The research will be based on interviews with the nupi shabis, cultural critics and other experts.

Keywords: transvestism, Manipur, female impersonators (nupi shabis), Shumang Leela, gender

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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Jenn-Yih Chen, Bean-Yin Lee, Yuan-Chuan Hsu, Jui-Cheng Lin, Kuang-Chyi Lee

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In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.

Keywords: adaptive law, passivity theorem, permanent magnet synchronous motor, sliding mode control

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Authors: Jia-Jane Shuai

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Purpose of this research aims to improve understanding of the nature of online religion by examining the religious social websites. What motivates individual users to use the online religious social websites, and which factors affect those motivations. We survey various online religious social websites provided by different religions, especially the Taiwanese folk religion. Based on the theory of the Content Analysis and Social Network Analysis, religious social websites and religious web activities are examined. This research examined the folk religion websites’ presentation and contents that promote the religious use of the Internet in Taiwan. The difference among different religions and religious websites also be compared. First, this study used keywords to examine what types of messages gained the most clicks of “Like”, “Share” and comments on Facebook. Dividing the messages into four media types, namely, text, link, video, and photo, reveal which category receive more likes and comments than the others. Meanwhile, this study analyzed the five dialogic principles of religious websites accessed from mobile phones and also assessed their mobile readiness. Using the five principles of dialogic theory as a basis, do a general survey on the websites with elements of online religion. Second, the project analyzed the characteristics of Taiwanese participants for online religious activities. Grounded by social network analysis and text mining, this study comparatively explores the network structure, interaction pattern, and geographic distribution of users involved in communication networks of the folk religion in social websites and mobile sites. We studied the linkage preference of different religious groups. The difference among different religions and religious websites also be compared. We examined the reasons for the success of these websites, as well as reasons why young users accept new religious media. The outcome of the research will be useful for online religious service providers and non-profit organizations to manage social websites and internet marketing.

Keywords: content analysis, online religion, social network analysis, social websites

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Authors: Hashem Sazegar

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In 1937, Vinograd of Russian Mathematician proved that each odd large number can be shown by three primes. In 1973, Chen Jingrun proved that each odd number can be shown by one prime plus a number that has maximum two primes. In this article, we state one proof for Goldbach’conjecture. Introduction: Bertrand’s postulate state for every positive integer n, there is always at least one prime p, such that n < p < 2n. This was first proved by Chebyshev in 1850, which is why postulate is also called the Bertrand-Chebyshev theorem. Legendre’s conjecture states that there is a prime between n2 and (n+1)2 for every positive integer n, which is one of the four Landau’s problems. The rest of these four basic problems are; (i) Twin prime conjecture: There are infinitely many primes p such that p+2 is a prime. (ii) Goldbach’s conjecture: Every even integer n > 2 can be written asthe sum of two primes. (iii) Are there infinitely many primes p such that p−1 is a perfect square? Problems (i), (ii), and (iii) are open till date.

Keywords: Bertrand-Chebyshev theorem, Landau’s problems, twin prime, Legendre’s conjecture, Oppermann’s conjecture

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Authors: Kailash Pattanaik, Giribala Mohanty

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Dhanujatra is a folk performance of ODISHA, India, that transports the participants, on lookers and all alike into a mythical atmosphere for eleven days and nights as well. In this performance the whole town becomes stage. The uniqueness of the festival lies in the fact that all the episodes of this Jatra enacted in different parts of the town making it the largest open air theatre in the world. The paper would emphasize on the uniqueness and the impact of this performance.Different episodes are enacted at different places in the regime. So, Dhanujatra does not confine itself to a fixed static or dead stage, as in case of other Jatra’s; it rather becomes the stage for the world at large. For that, it is said that, Worlds biggest open air theatre held in the tiny town called Bargarh in the western part of Orissa. The play moves sequentially day after day and the audience moves from locale to locale. Here it is analogues to the Ramleela of Ramnagar of Benars. Parallal enactment is a significant feature of this Jatra. From the second day, parallal performances take place in both Bargarh town and Ambapalli epitomising ‘Mathura’ and ‘Gokul’ respectively. Krishna is born in the prison on the second day of the jatra. Basudeb exchanges the child with the Nanda’s newborn baby in Gokul. In this way, parallal performances go on both in Mathura and Gokul. The ordinary persons who act as the mythological characters, or become historical heroes or the legendary Saints or Bhaktas in a Jatra in the evening, lead the lives of ordinary persons during day time. The dramatic personas of those individuals are shed with the end of the Jatra. On the contrary, the persons who act as the main characters of Dhanujatra are exceptions in this regard. They are identified as the characters they enact for the whole period of performance, both in the evenings and during daytime. It is worth mentioning that generally in the folk performances there is an ample scope to touch upon or interpret or comment or satirize the issues of contemporary relevance with the sole purpose to convey some specific message. Dhanujatra is no exception to that.

Keywords: folk performance, Jatra, parallel enactment, open-air stage, Odisha

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Authors: Jiaqi Huang, Yuheng Wang

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Premises selection, the task of selecting a set of axioms for proving a given conjecture, is a major bottleneck in automated theorem proving. An array of deep-learning-based methods has been established for premises selection, but a perfect performance remains challenging. Our study examines the inaccuracy of deep neural networks in premises selection. Through training network models using encoded conjecture and axiom pairs from the Mizar Mathematical Library, two potential biases are found: the network models classify more premises as necessary than unnecessary, referred to as the ‘positive bias’, and the network models perform better in proving conjectures that paired with more axioms, referred to as ‘length bias’. The ‘positive bias’ and ‘length bias’ discovered could inform the limitation of existing deep neural networks.

Keywords: automated theorem proving, premises selection, deep learning, interpreting deep learning

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