Search results for: Bernstein Ran

Authors: Tareq Hamadneh, Jochen Merker, Hassan Al-Zoubi

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Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain.

Keywords: Bernstein polynomials, Stability of control functions, numerical optimization, Taylor function

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Erin McKellar, Narelle Yeo

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Gender disparity can be found in the representation of the female characters in Leonard Bernstein’s musical West Side Story. As a postmodern composer, Bernstein was open about his social activism, yet did not consider his compositional portrayal of female characters as part of that activism. Using discretization as an analysis tool, this thesis explores the melodic contours of male and female songs in West Side Story to show differences in complexity between male and female characterisation. The analysis explores the intervallic relationship between the vocal line and melodic color in relation to the accompaniment harmony, taking into consideration the use of consonance and dissonance. West Side Story is commonly known for its distinct use of the tritone motif and its inherent dissonance. It is evident when reviewing the findings of this study that there is a distinct disparity between male-led and female-led music. The male-led numbers consistently adhere to a dissonant aesthetic with the tritone motif implemented in all of the extracted songs. By contrast, the female songs remain consonant with simple intervallic movements. By examining the results of this study through the lens of Equality Feminism, this thesis finds that Bernstein has simplified the characterisations of the female leads. The thesis further proposes that without cognisant consideration of the compositional portrayal of women, the musical theatre will continue to reinforce gender stereotypes, as evident through this study of Bernstein’s West Side Story.

Keywords: music theatre, gender bias, composition, Leonard Bernstein

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Serge Provost, Yishan Zang

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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Johan Buermans, Kristel Crombé, Niek Desmet, Laura Dittrich, Andrei Goriaev, Yurii Kovtun, Daniel López-Rodriguez, Sören Möller, Per Petersson, Maja Verstraeten

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The International Thermonuclear Experimental Reactor (ITER) will rely on three sources of external heating to produce and sustain a plasma; Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRH), and Electron Cyclotron Resonance Heating (ECRH). ECRH is a way to heat the electrons in a plasma by resonant absorption of electromagnetic waves. The energy of the electrons is transferred indirectly to the ions by collisions. The electron cyclotron heating system can be directed to deposit heat in particular regions in the plasma (https://www.iter.org/mach/Heating). Electron Cyclotron Resonance Heating (ECRH) at the fundamental resonance in X-mode is limited by a low cut-off density. Electromagnetic waves cannot propagate in the region between this cut-off and the Upper Hybrid Resonance (UHR) and cannot reach the Electron Cyclotron Resonance (ECR) position. Higher harmonic heating is hence preferred in heating scenarios nowadays to overcome this problem. Additional power deposition mechanisms can occur above this threshold to increase the plasma density. This includes collisional losses in the evanescent region, resonant power coupling at the UHR, tunneling of the X-wave with resonant coupling at the ECR, and conversion to the Electron Bernstein Wave (EBW) with resonant coupling at the ECR. A more profound knowledge of these deposition mechanisms can help determine the optimal plasma production scenarios. Several ECRH experiments are performed on the TOroidally MAgnetized System (TOMAS) to identify the conditions for Electron Bernstein Wave (EBW) heating. Density and temperature profiles are measured with movable Triple Langmuir Probes in the horizontal and vertical directions. Measurements of the forwarded and reflected power allow evaluation of the coupling efficiency. Optical emission spectroscopy and camera images also contribute to plasma characterization. The influence of the injected power, magnetic field, gas pressure, and wave polarization on the different deposition mechanisms is studied, and the contribution of the Electron Bernstein Wave is evaluated. The TOMATOR 1D hydrogen-helium plasma simulator numerically describes the evolution of current less magnetized Radio Frequency plasmas in a tokamak based on Braginskii’s legal continuity and heat balance equations. This code was initially benchmarked with experimental data from TCV to determine the transport coefficients. The code is used to model the plasma parameters and the power deposition profiles. The modeling is compared with the data from the experiments.

Keywords: electron Bernstein wave, Langmuir probe, plasma characterization, TOMAS

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Authors: Wen Xu

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The expansion of Confucius institutes and Chinese as a Foreign Language (CFL) education is often considered as cultural invasion and part of much bigger, if not ambitious, Chinese central government agenda among Western public opinion. The CFL knowledge and teaching practice inherent in textbooks are also harshly critiqued as failing to align with Western educational principles. This paper takes up these concerns and attempts to articulate that Confucius’s idea of ‘education without discrimination’ appears to have become synonymous with social justice touted in contemporary Australian education and policy discourses. To do so, it capitalises on Bernstein's conceptualization of classification and pedagogic rights to articulate CFL curriculum's potential of drawing in and drawing out curriculum boundaries to achieve educational justice. In this way, the potential useful knowledge of CFL constitutes a worthwhile tool to engage in a peripheral Western country’s education issues, as well as to include disenfranchised students in the multicultural Australian society. It opens spaces for critically theorising CFL curricular justice in Australian educational contexts, and makes an original contribution to scholarly argumentation that CFL curriculum has the potential of including socially and economically disenfranchised students in schooling.

Keywords: curriculum justice, Chinese as a Foreign Language curriculum, Bernstein, equity

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Authors: Martin Bloomfield

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This paper examines frictions that lie at the heart of any pragmatist conception of religion and moral progress. I take moral progress to require the ability to correctly analyse social problems, provide workable solutions to these problems, and then rationally justify the analyses and solutions used. I take religion here to involve, as a minimal requirement, belief in the existence of God, a god, or gods, such that they are recognisable to most informed observers within the Western tradition. I take pragmatism to belong to, and borrow from, the philosophical traditions of non-absolutism, anti-realism, historicism, and voluntarism. For clarity, the relevant brands of each of these traditions will be examined during the paper. The friction identified in the title may be summed up as follows: those who, like Cornel West (and, when he was alive, Hilary Putnam), are theistic pragmatists with an interest in realising moral progress, have all been aware of a problem inherent in their positions. Assuming it can be argued that religion and moral progress are compatible, a non-absolutist, anti-realist, historicist position nevertheless raises problems that, as Leon Wieseltier pointed out, the pragmatist still believes in a God who isn’t real, and that the truth of any religious statement (including “God exists”) is relative not to any objective reality but to communities of engaged interlocutors; and that, where there are no absolute standards of right and wrong, any analysis of (and solution to) social problems can only be rationally justified relative to one or another community or moral and epistemic framework. Attempts made to universalise these frameworks, notably by Dewey, Gadamer, and Bernstein, through democracy and hermeneutics, fall into either a vicious and infinite regress, or (taking inspiration from Habermas) the problem of moral truths being decided through structures of power. The paper removes this friction by highlighting the work of Christian pragmatist Cornel West through the lens of the philosopher of religion Eleanore Stump. While West recognises that for the pragmatist, the correctness of any propositions about God or moral progress is impossible to rationally justify to any outside the religious, moral or epistemic framework of the speakers themselves without, as he calls it, a ‘locus of truth’ (which is itself free from the difficulties Dewey, Gadamer and Bernstein fall victim to), Stump identifies routes to knowledge which provide such a locus while avoiding the problems of relativism, power dynamics, and regress. She describes “Dominican” and “Franciscan” knowledge (roughly characterised as “propositional” and “non-propositional”), and uses this distinction to identify something Bernstein saw as missing from Gadamer: culture-independent norms, upon which universal agreement can be built. The “Franciscan knowledge” Stump identifies as key is second-personal knowledge of Christ. For West, this allows the knower to access vital culture-independent norms. If correct, instead of the classical view (religion is incompatible with pragmatism), Christianity becomes key to pragmatist knowledge and moral-knowledge claims. Rather than being undermined by pragmatism, Christianity enables pragmatists to make moral and epistemic claims, free from troubling power dynamics and cultural relativism.

Keywords: Cornel West, Cultural Relativism, Gadamer, Philosophy of Religion, Pragmatism

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Authors: Bernstein Ran, Shafir Tal, Tsachor Rachelle, Studd Karen, Schuster Assaf

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Laban Movement Analysis (LMA), developed in the dance community over the past seventy years, is an effective method for observing, describing, notating, and interpreting human movement to enhance communication and expression in everyday and professional life. Many applications that use motion capture data might be significantly leveraged if the Laban qualities will be recognized automatically. This paper presents an automated recognition method of Laban qualities from motion capture skeletal recordings and it is demonstrated on the output of Microsoft’s Kinect V2 sensor.

Keywords: Laban movement analysis, multitask learning, Kinect sensor, machine learning

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Authors: A. Preetha Priyadharshini, S. B. M. Priya

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In this paper, we consider the MU-MISO downlink scenario, under imperfect channel state information (CSI). The main issue in imperfect CSI is to keep the probability of each user achievable outage rate below the given threshold level. Such a rate outage constraints present significant and analytical challenges. There are many probabilistic methods are used to minimize the transmit optimization problem under imperfect CSI. Here, decomposition based large deviation inequality and Bernstein type inequality convex restriction methods are used to perform the optimization problem under imperfect CSI. These methods are used for achieving improved output quality and lower complexity. They provide a safe tractable approximation of the original rate outage constraints. Based on these method implementations, performance has been evaluated in the terms of feasible rate and average transmission power. The simulation results are shown that all the two methods offer significantly improved outage quality and lower computational complexity.

Keywords: imperfect channel state information, outage probability, multiuser- multi input single output, channel state information

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Authors: Prabal Singh Verma

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Electrostatic Waves in plasma have emerged as a new source for the acceleration of charged particles. The accelerated particles have a wide range of applications, for example in cancer therapy to cutting and melting of hard materials. The maximum acceleration can only be achieved when the amplitude of the plasma wave stays below a critical limit known as wave-breaking amplitude. Beyond this limit amplitude of the wave diminishes dramatically as the coherent energy of the wave starts to convert into random kinetic energy. In this work, spatiotemporal evolution of non-relativistic electrostatic waves in a cold plasma has been studied in the wave-breaking regime using a 1D particle-in-cell simulation (PIC). It is found that plasma gets heated after the wave-breaking but a fraction of initial energy always remains with the remnant wave in the form of Bernstein-Greene-Kruskal (BGK) mode in warm plasma. Another interesting finding of this work is that the frequency of the resultant BGK wave is found be below electron plasma frequency which decreases with increasing initial amplitude and the acceleration mechanism after the wave-breaking is also found to be different from the previous work. In order to explain the results observed in the numerical experiments, a simplified theoretical model is constructed which exhibits a good agreement with the simulation. In conclusion, it is shown in this work that electrostatic waves get shower after the wave-breaking and a fraction of initial coherent energy always remains with remnant wave. These investigations have direct relevance in wakefield acceleration experiments.

Keywords: nonlinear plasma waves, longitudinal, wave-breaking, wake-field acceleration

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Authors: Tien-Hui Chiang

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The code theory, proposed by Basil Bernstein, indicates that framing can be viewed as the core element in constituting the phenomenon of cultural reproduction because it is able to regulate the transmission of pedagogical information. Strong framing increases the social relation boundary between a teacher and pupils, which obstructs information transmission, so that in order to improve underachieving students’ academic performances, teachers need to reduce to strength of framing. Weak framing enables them to transform academic knowledge into commonsense knowledge in daily life language. This study posits that most teachers would deliver strong framing due to their belief mainly confined within the aspect of instrumental rationality that deprives their critical minds. This situation could make them view the normal distribution bell curve of students’ academic performances as a natural outcome. In order to examine the interplay between framing, instrumental rationality and pedagogical action, questionnaires were completed by over 5,000 primary school teachers in Henan province, China, who were stratified sample. The statistical results show that most teachers employed psychological concepts to measure students’ academic performances and, in turn, educational inequity was legitimatized as a natural outcome in the efficiency-led approach. Such efficiency-led minds made them perform as the agent practicing the mechanism of social control and in turn sustaining the phenomenon of cultural reproduction.

Keywords: code, cultural reproduction, framing, instrumental rationality, social relation and interaction

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