Search results for: folk theorem

Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Hassam Muazzam

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This paper devises an autonomous self-driven vehicle that is capable of taking a disabled person to his/her desired location using three different power sources (gasoline, solar, electric) without any control from the user, avoiding the obstacles in the way. The GPS co-ordinates of the desired location are sent to the main processing board via a GSM module. After the GPS co-ordinates are sent, the path to be followed by the vehicle is devised by Pythagoras theorem. The distance and angle between the present location and the desired location is calculated and then the vehicle starts moving in the desired direction. Meanwhile real-time data from ultrasonic sensors is fed to the board for obstacle avoidance mechanism. Ultrasonic sensors are used to quantify the distance of the vehicle from the object. The distance and position of the object is then used to make decisions regarding the direction of vehicle in order to avoid the obstacles using artificial neural network which is implemented using ATmega1280. Also the vehicle provides the feedback location at remote location.

Keywords: autonomous self-driven vehicle, obstacle avoidance, desired location, pythagoras theorem, neural network, remote location

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Authors: Santiago Guerra Fernández

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Abstract—This study is focused on exploring the conditions for the development of Galician music in the communities of Latin America after the massive arrival of Galician immigrants in the late nineteenth and early twentieth centuries, fleeing from hunger and misery in Spain. Migration would be accentuated after 1936 with the arrival of refugees from the Spanish Civil War due to their Republican political militancy fleeing fascism. The aim of this paper is to investigate the part that miscegenation with other local musical traditions has played within Galician expat music, helping to understand the complexity of contemporary Galician identity. Through archival work, the focus is set on examining the different traditional dances (such as the ‘muiñeira’), folk instruments (bagpipes, ‘pandeireta’), and poetic forms (‘cantiga’, ‘copla’) that were exported to Argentina and Cuba. Although research about migrant Galician music has been conducted in Spanish scholarship, there is a gap in the English literature on the topic that this paper intends to fill in. The results show how these musical traditions have played an essential role in shaping the social life and customs of Galician emigrants. By virtue of its malleability and blending properties, music serves here as an indicator of social cohesion.

Keywords: folk, Galicia, migration, identity

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Authors: Beghdadi Lotfi

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In the present work a numerical method is proposed in order to optimize the thermal performance of finned surfaces. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study, it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. 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. 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, effectiveness

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Authors: Benedict Ita, Peter Okoi

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In this work, the concept of the extended Nikiforov-Uvarov technique is discussed and employed to obtain the exact bound state energy eigenvalues and the corresponding normalized eigenfunctions of the inverse square root potential. With expressions for the exact energy eigenvalues and corresponding eigenfunctions, the expressions for the expectation values of the inverse separation-squared, kinetic energy, and the momentum-squared of the potential are presented using the Hellmann Feynman theorem. For visualization, algorithms written and implemented in Python language are used to generate tables and plots for l-states of the energy eigenvalues and some expectation values. The results obtained here may find suitable applications in areas like atomic and molecular physics, chemical physics, nuclear physics, and solid-state physics.

Keywords: Schrodinger equation, Nikoforov-Uvarov method, inverse square root potential, diatomic molecules, Python programming, Hellmann-Feynman theorem, second order differential equation, matrix algebra

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Authors: Beghdadi Lotfi, Belkacem Abdellah

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In this work, a numerical method is proposed in order to solve the thermal performance problems of heat transfer of fins surfaces. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study, it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. 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. 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: T. J. Stepien, L. T. Stepien

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This abstract concerns an extremely fundamental issue. Namely, the fundamental problem of science is the issue of consistency. In this abstract, we present the theorem saying that the classical calculus of quantifiers is inconsistent in the traditional sense. At the beginning, we introduce a notation, and later we remind the definition of the consistency in the traditional sense. S1 is the set of all well-formed formulas in the calculus of quantifiers. RS1 denotes the set of all rules over the set S1. Cn(R, X) is the set of all formulas standardly provable from X by rules R, where R is a subset of RS1, and X is a subset of S1. The couple < R,X > is called a system, whenever R is a subset of RS1, and X is a subset of S1. Definition: The system < R,X > is consistent in the traditional sense if there does not exist any formula from the set S1, such that this formula and its negation are provable from X, by using rules from R. Finally, < R0+, L2 > denotes the classical calculus of quantifiers, where R0+ consists of Modus Ponens and the generalization rule. L2 is the set of all formulas valid in the classical calculus of quantifiers. The Main Result: The system < R0+, L2 > is inconsistent in the traditional sense.

Keywords: classical calculus of quantifiers, classical predicate calculus, generalization rule, consistency in the traditional sense, Modus Ponens

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Authors: Faguna Barmahalia

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Politics of ethnic identity in the north-east India is well-known phenomenon. The ethnic assertion in this region is mostly linguistic and cultural in nature. Most of the ethnic groups in the north-east region have been demanding either autonomous or separate state to maintain their socio-cultural identity. After the Indian Independence, the ethnic groups of people think that they have not developed till. Despite having many natural resources, North East India remained backward in terms of economic, education as well as politics. In this scenario, many educated and middle-class elite people have involved in working for the all-round development of their community. The Bodos are one of the major tribes in North Eeast India. In Assam, the Bodos are assumed by themselves to be exploited and suppressed by the Assamese Hindu society. Consequently, the socio-cultural identity movement has emerged among the Bodos.The main aims of my study are: i. to focus on how the Bodos of Assam are using the folk media in their political movement and iii. To analyse the role of folklore towards serving the ethnic unity and nationalism among the Bodos. Methodology: The study is based on the primary and secondary sources. Interview and observation method was conducted for collecting the primary data. For secondary source, some printed books, magazines and others materials published by the distinguished publishers and websites have been used.

Keywords: media, culture, nationalism, politics

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Authors: Amar Partap Singh Pharwaha, Balkrishan Jindal

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In this paper, a new method is developed for hiding image in a digital image with multilayer security. In the proposed method, the secret image is encrypted in the first instance using a flexible matrix based symmetric key to add first layer of security. Then another layer of security is added to the secret data by encrypting the ciphered data using Pythagorean Theorem method. The ciphered data bits (4 bits) produced after double encryption are then embedded within digital image in the spatial domain using Least Significant Bits (LSBs) substitution. To improve the image quality of the stego-image, an improved form of pixel adjustment process is proposed. To evaluate the effectiveness of the proposed method, image quality metrics including Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), entropy, correlation, mean value and Universal Image Quality Index (UIQI) are measured. It has been found experimentally that the proposed method provides higher security as well as robustness. In fact, the results of this study are quite promising.

Keywords: Pythagorean theorem, pixel adjustment, ciphered data, image hiding, least significant bit, flexible matrix

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Authors: Nazish Iftikhar, Adil Jhangeer, Tayyaba Naz

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The universe is expanding at an accelerated rate. Symmetries are useful in understanding universe’s behavior. Emmy Noether reported the relation between symmetries and conservation laws. These symmetries are known as Noether symmetries which correspond to a conserved quantity. In differential equations, conservation laws play an important role. Noether symmetries are helpful in modified theories of gravity. Time independent plane symmetric spacetime was classified by Noether`s theorem. By using Noether`s theorem, set of linear partial differential equations was obtained having A(r), B(r) and F(r) as unknown radial functions. The Lagrangian corresponding to considered spacetime in the Noether equation was used to get Noether operators. Different possibilities of radial functions were considered. Firstly, all functions were same. All the functions were considered as non-zero constant, linear, reciprocal and exponential respectively. Secondly, two functions were proportional to each other keeping third function different. Second case has four subcases in which four different relationships between A(r), B(r) and F(r) were discussed. In all cases, we obtained nontrivial Noether operators including gauge term. Conserved quantities for each Noether operators were also presented.

Keywords: Noether gauge symmetries, radial function, Noether operator, conserved quantities

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Authors: Johnson-Egemba Helen Amaka

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Music is emotional in the sense that it controls people’s feelings. The way and manner people react to music at a point in time depend on the type of music that is playing. Music can make someone to march or dance, to cry or laugh, to be happy or sad, to fight or make peace and so on. It therefore makes someone o exhibit some kind of behaviours, either positive or negative. Even dangerous animals have been found to be controlled by music. In the psychiatric homes, mad people are always found to be dancing to music. During funeral ceremony, music singing and dancing are sources of comfort to the bereaved. As a background to the study, Tarok ethnic group in Plateau State was used. The Tarok comprise of Langtang North and South Local Government Areas. The ethnic group of Tarok integrates music in almost all the activities of their lives. A total of six (6) types of folk songs were identified. These songs range from marriages, funeral, royalty, togetherness, war, rituals, festivals, and farming. This paper points out the significance of basic responsiveness of the Tarok people towards the folk songs, their reaction generally whether positive or negative. The methods of data collection employed in this work include oral interview approach, recording of various types of Tarok folk songs, consulting of journals, magazines and textbooks. The researcher used oral interview as her primary source of information which is found to be the most effective procedure in carrying out this task. The songs were textually analyzed with a view to unveiling their meanings, thought processes, and conveying their direction and functions within the context of their rendition. The major findings of the study are that music in Tarok culture covers the physical, mental, emotional and social experiences. The physical aspect is the motor skills, which include dancing and demonstration of the songs. The mental experiences are intellectual levels which include construction and manufacturing of musical instruments, composing songs, teaching and learning etc. Furthermore, this research provided in addition to musical activities, the literature, history and culture of the Tarok communities.

Keywords: cultural, music, practice, responsiveness

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Authors: A. U. Haque, W. Asrar, A. A Omar, E. Sulaeman, J. S. M. Ali

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Buoyancy force applied on deformable symmetric bodies can be estimated by using Archimedes Principle. Such bodies like ellipsoidal bodies have high volume to surface ratio and are isometrically scaled for mass, length, area and volume to follow square cube law. For scaling up such bodies, it is worthwhile to find out the scaling relationship between the other physical quantities that represent thermodynamic, structural and inertial response etc. So, dimensionless similarities to find an allometric scale can be developed by using Bukingham π theorem which utilizes physical dimensions of important parameters. Base on this fact, physical dependencies of buoyancy system are reviewed to find the set of physical variables for deformable bodies of revolution filled with expandable gas like helium. Due to change in atmospheric conditions, this gas changes its volume and this change can effect the stability of elongated bodies on the ground as well as in te air. Special emphasis was given on the existing similarity parameters which can be used in the design of experiments of such bodies whose shape is affected by the external force like a drag, surface tension and kinetic loads acting on the surface. All these similarity criteria are based on non-dimensionalization, which also needs to be consider for scaling up such bodies.

Keywords: Bukhigham pi theorem, similitude, scaling, buoyancy

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Authors: Genevieve Jorolan-Quintero

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The recording as well as the preservation of indigenous literature is an important task as it deals with a significant heritage of pre-colonial culture. The beliefs and traditions of a people are reflected in their oral narratives, such as the folk epic, which must be written down to insure their preservation. The epic poem for instance, known as dawot among the Mandaya, one of the indigenous communities in the southern region of the Philippines, narrates the customs, the ways of life, and the adventures of an ancient people. Nabayra, an expert on Philippine folkloric studies, stresses that still extant after centuries of unknown origin, the dawot was handed down to the magdadawot (bard) by word of mouth, forming the greatest bulk of Mandaya oral tradition. Unhampered by modern means of communication to distract her/him, the magdadawot has a sharp memory of the intricacies of the ancient art of chanting the panayday (verses) of the epic poem. The dawot has several hullubaton (episodes), each of which takes several nights to chant . The language used in these oral traditions is archaic Mandaya, no longer spoken or clearly understood by the present generation. There is urgency to the task of recording and writing down what remain of the epic poem since the singers and storytellers who have retained the memory and the skill of chanting and narrating the dawot and other forms of oral tradition in their original forms are getting fewer. The few who are gifted and skilled to transmit these ancient arts and wisdom are old and dying. Unlike the other Philippine epics (i.e. the Darangen, the Ulahingan, the Hinilawod, etc.), the Mandaya epic is yet to be recognized and given its rightful place among the recorded epics in Philippine Folk Literature. The general aim of this study was to put together and preserve an intangible heritage, the Mandaya hullubaton (episodes of the dawot), in order to preserve and promote appreciation for the oral traditions and cultural legacy of the Mandaya. It was able to record, transcribe, and translate four hullubaton of the folk epic into two languages, Visayan and English to insure understanding of their contents and significance among non-Mandaya audiences. Evident in the contents of the episodes are the cultural practices, ideals, life values, and traditions of the ancient Mandaya. While the conquests and adventures of the Mandaya heroes Lumungtad, Dilam, and Gambong highlight heroic virtues, the role of the Mandaya matriarch in family affairs is likewise stressed. The recording and the translation of the hullubaton and the dawot into commonly spoken languages will not only promote knowledge and understanding about their culture, but will also stimulate in the members of this cultural community a sense of pride for their literature and culture. Knowledge about indigenous cultural system and philosophy derived from their oral literature will serve as a springboard to further comparative researches dealing with indigenous mores and belief systems among the different tribes in the Philippines, in Asia, in Africa, and other countries in the world.

Keywords: Dawot, epic poem, Mandaya, Philippine folk literature

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Authors: Niroshi Senevirathne

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The history of Pasan Gee (Passion Songs) relates back to the Portuguese Colonial period (1505-1658) in Sri Lanka. It is about chants on the passion of Christ during the Lent period which is repentance for Christians lasting for 40 days. Among the other villages in Sri Lanka, Wahakotte, which is situated in Matale district, Central Province is famous for their traditional Pasan melodies. It is a village where both Christians and Buddhists live. King Rajasinghe II of Kandy, who fought against the Portuguese, allowed the captives to settle down in Wahakotte. These people fairer in complexion have assimilated themselves with locals. Pasan singing in Wahakotte is a significant event and it is influenced by traditional folk music melodies such as “Nelum Gee” (harvesting songs) sung by farmers of Matale, Welapum Gee (Lamantation songs) sung at funerals in Sri Lanka and Buddhist Pirith chanting melodies. Prose of Pasan verses are included in the book named “Deshana namaye Pasan potha” (Nine Sermon Passion Book), written by Fr. Jacome Gonsalvez. The verses are composed with Sinhala and with some Tamil words. These songs are transmitted from generation to generation in an oral tradition. Today, chanting of Pasan is not heard in many Catholic areas during the lent season. Some of them have been recorded in cassette form. This research should aim to protect these traditional Passion songs unique to village Wahakotte of Sri Lanka without changing its character and original melodies.

Keywords: influence of folk melodies, passion songs, preserving traditional passion songs, traditional passion melodies

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Authors: Yuyang Cheng, Marcos Escobar-Anel

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This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in Grasselli (2017). Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market.

Keywords: stochastic covariance process, 4/2 stochastic volatility model, stochastic co-volatility movements, characteristic function, expected utility theory, verication theorem

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Authors: Damir Latypov

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A closed-form solution for 4-D double surface integrals arising in boundary integrals equations of a potential theory is obtained for arbitrary coplanar polygonal surfaces. The solution method is based on the construction of exact differential forms followed by the application of Stokes' theorem for each surface integral. As a result, the 4-D double surface integral is reduced to a 2-D double line integral. By an appropriate change of variables, the integrand is transformed into a separable function of integration variables. The closed-form solutions to the corresponding 1-D integrals are readily available in the integration tables. Previously closed-form solutions were known only for the case of coincident triangle surfaces and coplanar rectangles. Solutions for these cases were obtained by surface-specific ad-hoc methods, while the present method is general. The method also works for non-polygonal surfaces. As an example, we compute in closed form the 4-D integral for the case of coincident surfaces in the shape of a circular disk. For an arbitrarily shaped surface, the proposed method provides an efficient quadrature rule. Extensions of the method for non-coplanar surfaces and other than 1/R integral kernels are also discussed.

Keywords: boundary integral equations, differential forms, integration, stokes' theorem

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Khrystyna Zai

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This research delves into the profound impact of Ukrainian musical traditions on the life and works of the renowned composer Sergei Prokofiev. Sergei Prokofiev's formative years in Ukraine, particularly in Sontsivka(Eastern Ukraine), allowed him to immerse himself in the local music. He encountered Ukrainian folk songs and dances, which left an indelible mark on his musical sensibilities. With a focus on the early 20th century, a period of significant cultural transformation in both Ukraine and Europe, this study examines how Prokofiev's exposure to Ukrainian folk music, its melodic motifs, and rhythmic patterns influenced his compositions. Prokofiev’s works showcase his deliberate efforts to fuse Ukrainian elements with his distinctive modernist style. This study analyzes Prokofiev's engagement with Ukrainian themes in his music, such as the "Semen Kotko”, “The Love of Three Oranges”, “On the Dnieper”, “Scythian Suite”, “Sinfonia Concertante" for cello and orchestra, "Sonata No. 9,", “Partisans in the steppes of Ukraine” (where Prokofiev uses texts in Ukrainian). The scientific work mentions his interactions and collaborations with Ukrainian musicians and cultural figures during Prokofiev’s career. Notably, his association with Ukrainian pianist Sviatoslav Richter and conductor Kirill Karabits led to interpretations of his compositions with a Ukrainian perspective. This research illuminates the nuances of cross-cultural influences in Prokofiev's oeuvre, contributing to a deeper understanding of the interplay between national identities and artistic expression during a pivotal period in history, based on the fact that the composer himself considered Ukraine to be his homeland, calling himself “steppe boy”.

Keywords: florida atlantic university, ukrainian music, ukrainian composer, sergei prokofiev

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Authors: Ying-Ming Su

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Fujian earthen building which was known as a classic for ecological buildings was listed on the world heritage in 2008 (UNESCO) in China. Its design strategy can be applied to modern architecture planning and design. This study chose two different cases (Round Atrium: Er-Yi Building, Double Round Atrium: Zhen-Chen Building) of earthen building in Fu-Jian to compare the ventilation effects of different atrium forms. We adopt field measurements and computational fluid dynamics (CFD) simulation of temperature, humidity, and wind environment to identify the relationship between external environment and atrium about comfort and to confirm the relationship about atrium H/W (height/width). Results indicate that, through the atrium convection effect, it makes the natural wind guides to each space surrounded and keeps indoor comfort. It illustrates that the smaller the ratio of the H/W which is the relationship between the height and the width of an atrium is, the greater the wind speed generated within the street valley. Moreover, the wind speed is very close to the reference wind speed. This field measurement verifies that the value of H/W has great influence of solar radiation heat and sunshine shadows. The ventilation efficiency is: Er-Yi Building (H/W =0.2778) > Zhen-Chen Building (H/W=0.3670). Comparing the cases with the same shape but with different H/W, through the different size patios, airflow revolves in the atriums and can be brought into each interior space. The atrium settings meet the need of building ventilation, and can adjust the humidity and temperature within the buildings. It also creates good ventilation effect.

Keywords: traditional folk houses, atrium, tulou, ventilation, building microclimate

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Authors: David M. Lucas, Charles W. Jarrett

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In the culture of Thailand, the Yak serve as a mediated icon representing strength, power, and mystical protection not only for the Buddha, but for population of worshipers. Originating from the forests of China, the Yak continue to stand guard at the gates of Buddhist temples. The Yak represents Thai culture in the hearts of Thai people. This paper presents a qualitative study regarding the curious mix of media, culture, and religion that projects the Yak of Thailand as a larger than life message throughout the political, cultural, and religious spheres. The gate guardians, or gods as they are sometimes called, appear throughout the religious temples of Asian cultures. However, the Asian cultures demonstrate differences in artistic renditions (or presentations) of such sentinels. Thailand gate guards (the Yak) stand in front of many Buddhist temples, and these iconic figures display unique features with varied symbolic significance. The temple (or wat), plays a vital role in every community; and, for many people, Thailand’s temples are the country’s most endearing sights. The authors applied folk-nography as a methodology to illustrate the importance of the Thai Yak in serving as meaningful icons that transcend not only time, but the culture, religion, and mass media. The Yak represent mythical, religious, artistic, cultural, and militaristic significance for the Thai people. Data collection included interviews, focus groups, and natural observations. This paper summarizes the perceptions of the Thai people concerning their gate sentries and the relationship, communication, connection, and the enduring respect that Thai people hold for their guardians of the gates.

Keywords: communication, culture, folknography, icon, image, media, protection, religion, yak

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Authors: Hashem Sazegar

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Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Nazneen Khan, Vakeel A. Khan

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In this article we introduce the Paranorm Zweier I-convergent sequence spaces, for a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem and study some inclusion relations on these spaces.

Keywords: ideal, filter, I-convergence, I-nullity, paranorm

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Authors: Ganiyat Soliu, Glen Bright, Chiemela Onunka

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Performance optimization plays a key role in controlling the waiting time during manufacturing in an advanced manufacturing environment to improve productivity. Queuing mathematical modeling theory was used to examine the performance of the multi-stage production line. Robotics as a disruptive technology was implemented into a virtual manufacturing scenario during the packaging process to study the effect of waiting time on productivity. The queuing mathematical model was used to determine the optimum service rate required by robots during the packaging stage of manufacturing to yield an optimum production cost. Different rates of production were assumed in a virtual manufacturing environment, cost of packaging was estimated with optimum production cost. An equation was generated using queuing mathematical modeling theory and the theorem adopted for analysis of the scenario is the Newton Raphson theorem. Queuing theory presented here provides an adequate analysis of the number of robots required to regulate waiting time in order to increase the number of output. Arrival rate of the product was fast which shows that queuing mathematical model was effective in minimizing service cost and the waiting time during manufacturing. At a reduced waiting time, there was an improvement in the number of products obtained per hour. The overall productivity was improved based on the assumptions used in the queuing modeling theory implemented in the virtual manufacturing scenario.

Keywords: performance optimization, productivity, queuing theory, robotics

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Jorge Gonzalez-Camus

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

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

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Sheikh Z. Ul Abidin, Raees Khan, Rainer W. Bussmann, Mushtaq Ahmad, Shayan Jamshed, Humera Jabeen, Ajmal Khan

Abstract:

Gastropathic disorders are increasing rapidly and millions patients are reported every years across the world. Herbal medicines and traditional phytotherapies are very effective for many diseases including gastropathic ailments. Many communities and study region have their own unique remedies for such diseases. The current study was aimed to investigate and document high valued medicinal plants and folk remedies for different gastropathic disorders among the three ethnic groups of three regions in South West Pakistan. A total of 104 semi-structured interviews involving experts of traditional knowledge in 21 localities of the three regions (D.I. Khan, Zhob and Mianwali) were conducted. The interviews were especially focused on the documentation of folk herbal remedies. The collected data was analyzed using different quantitative methods. The highly effective plants from all localities were identified with the help of local interviewers and collected for proper taxonomic identification. A total of 56 medicinal plants and 33 effective recipes for 12 gastropathic diseases were documented from all the three ethnic groups in 21 localities. Fabaceae and Asteraceae were most prominently used for different gastropathic diseases. Diarrhea, vomiting and dysentery were the most commonly diseases treated with herbal remedies. It was observed that the three communities shared knowledge about the use of medicinal plants, 35 species were commonly reported from all three areas. However, each community had also their own unique uses of medicinal plants, e.g. 23 plants species were only used in Zhob, 20 plant species were only reported in D.I. Khan and 16 species in Mianwali. The present study reveals that different communities and ethnic groups share some traditional knowledge and also have their own unique knowledge of plants utilization. Gastropathic disorder is increasing very rapidly and the traditional cross-cultural knowledge of medicinal plants use can be very effective for its cure.

Keywords: cross cultural, ethnic groups, gastropathy, phytotherapies, South West Pakistan

Procedia PDF Downloads 295

Authors: Saeed Poormoaied

Abstract:

Perishability and developing an intelligent control policy for perishable items are the major concerns of marketing managers in a supply chain. In this study, we address a two-echelon supply chain problem for perishable items with a single vendor and a single buyer. The buyer adopts an aged-based continuous review policy which works by taking both the stock level and the aging process of items into account. The vendor works under the warehouse framework, where its lot size is determined with respect to the batch size of the buyer. The model holds for a positive and fixed lead time for the buyer, and zero lead time for the vendor. The demand follows a Poisson process and any unmet demand is lost. We provide exact analytic expressions for the operational characteristics of the system by using the renewal reward theorem. Items have a fixed lifetime after which they become unusable and are disposed of from the buyer's system. The age of items starts when they are unpacked and ready for the consumption at the buyer. When items are held by the vendor, there is no aging process which results in no perishing at the vendor's site. The model is developed under the centralized framework, which takes the expected profit of both vendor and buyer into consideration. The goal is to determine the optimal policy parameters under the service level constraint at the retailer's site. A sensitivity analysis is performed to investigate the effect of the key input parameters on the expected profit and order quantity in the supply chain. The efficiency of the proposed age-based policy is also evaluated through a numerical study. Our results show that when the unit perishing cost is negligible, a significant cost saving is achieved.

Keywords: two-echelon supply chain, perishable items, age-based policy, renewal reward theorem

Procedia PDF Downloads 144