Search results for: epistemological functions

Authors: Mark Darius Juszczak

Abstract:

While epistemology, as a sub-field of philosophy, is generally concerned with theoretical questions about the nature of knowledge, the explosion in digital media technologies has resulted in an exponential increase in the storage and transmission of human information. That increase has resulted in a particular non-linear dynamic – digital epistemological functions are radically altering how and what we know. Neither the rate of that change nor the consequences of it have been well studied or taken into account in developing state-level strategies for epistemological functions. At the current time, US Federal policy, like that of virtually all other countries, maintains, at the national state level, clearly defined boundaries between various epistemological agencies - agencies that, in one way or another, mediate the functional use of knowledge. These agencies can take the form of patent and trademark offices, national library and archive systems, departments of education, departments such as the FTC, university systems and regulations, military research systems such as DARPA, federal scientific research agencies, medical and pharmaceutical accreditation agencies, federal funding for scientific research and legislative committees and subcommittees that attempt to alter the laws that govern epistemological functions. All of these agencies are in the constant process of creating, analyzing, and regulating knowledge. Those processes are, at the most general level, epistemological functions – they act upon and define what knowledge is. At the same time, however, there are no high-level strategic epistemological directives or frameworks that define those functions. The only time in US history where a proxy state-level epistemological strategy existed was between 1961 and 1969 when the Kennedy Administration committed the United States to the Apollo program. While that program had a singular technical objective as its outcome, that objective was so technologically advanced for its day and so complex so that it required a massive redirection of state-level epistemological functions – in essence, a broad and diverse set of state-level agencies suddenly found themselves working together towards a common epistemological goal. This paper does not call for a repeat of the Apollo program. Rather, its purpose is to investigate the minimum structural requirements for a national state-level epistemological strategy in the United States. In addition, this paper also seeks to analyze how the epistemological work of the multitude of national agencies within the United States would be affected by such a high-level framework. This paper is an exploratory study of this type of framework. The primary hypothesis of the author is that such a function is possible but would require extensive re-framing and reclassification of traditional epistemological functions at the respective agency level. In much the same way that, for example, DHS (Department of Homeland Security) evolved to respond to a new type of security threat in the world for the United States, it is theorized that a lack of coordination and alignment in epistemological functions will equally result in a strategic threat to the United States.

Keywords: strategic security, epistemological functions, epistemological agencies, Apollo program

Procedia PDF Downloads 51

Authors: Dení Stincer Gómez, Zuraya Monroy Nasr

Abstract:

Pedagogy of science historically has given priority to teaching strategies that mobilize the cognitive mechanisms leaving out emotional. Modern epistemology, cognitive psychology and psychoanalysis begin to argue and prove that emotions are relevant epistemological functions. They are 1) the selection function: that allows the perception and reason choose, to multiple alternative explanation of a particular fact, those are relevant and discard those that are not, 2) heuristic function: that is related to the activation cognitive processes that are effective in the process of knowing; and 3) the function that called carrier content: on the latter it arises that emotions give the material reasoning that later transformed into linguistic propositions. According to these hypotheses, scientific knowledge seems to come from emotions that meet these functions. In this paper I argue that science education should start from the presence of certain emotions in the learner if it is to form citizens with scientific or cultural future scientists.

Keywords: epistemic emotions, science education, formation of citizens and scientists., philosophy of emotions

Procedia PDF Downloads 92

Authors: Lin Zou

Abstract:

This paper explores how the development of science and technology in the recent decades has created new conditions for literature and aesthetics. These are epistemological conditions that not only offer empirical understandings of the human mentality, behavior, emotions, and humanity in general, but reshape how value and the ontological questions are understood and linked with humanity. This paper will discuss the implications of these epistemological conditions for the depiction and interpretation of human subjectivity in literature. The paper will first seek to present the argument that science and technology have created new conditions for literature and aesthetics. It then outlines the implications of these new conditions for literature and aesthetics. The main methodologies used are close reading and case studies.

Keywords: epistemological conditions, literature and aesthetics, science and technology, subjectivity

Procedia PDF Downloads 93

Authors: Bukhari Badamasi, Chidi G. Ononiwu

Abstract:

Globally, educational technology (EdTech) has become a known catalyst for gaining access to education, job creation, and national development of a nation. Howbeit, it is common understanding that higher institutions continue to deploy digital technologies, to help provide access to education, but in most case, it is somehow institutional access not epistemological access especially in sub Saharan African higher institutions. Some scholars, however, lament the fact that studies on educational technology affordances are mostly fragmented because they focus on specific theme or sub aspect of access (i.e., institutional access). Thus, drawing from the Archer Morphogenetic approach, and Gibson Affordance theory, and applying critical realist based Danermark model for explanatory research, the study seeks to conduct a realist case study on underprivileged students in Higher institutions on how they gain epistemological access by enacting educational technology (EdTech) affordances.

Keywords: affordance, epistemological access, educational technology, underprivileged students

Procedia PDF Downloads 50

Authors: Fuad Al Sarari

Abstract:

The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out.

Keywords: convolution conditions, subordination, Janowski functions, starlike functions, convex functions

Procedia PDF Downloads 41

Authors: A. V. Varfolomeeva, N. S. Tkachenko, A. G. Tishchenko

Abstract:

The problem of violation of internal validity in studies of psychological structures is considered. The role of epistemological attitudes of researchers in the planning of research within the methodology of the system-evolutionary approach is assessed. Alternative programs of psychological research involving representatives of different biological species are presented. On the example of the results of two research series the variants of solving the problem are discussed.

Keywords: epistemological attitudes, experimental design, validity, psychological structure, learning

Procedia PDF Downloads 89

Authors: Muna Tabuni

Abstract:

The paper contains an investigation of the behavior of the Zeros of Bargmann functions for one and two-mode systems. A brief introduction to Harmonic oscillator formalism for one and two-mode is given. The Bargmann analytic representation for one and two-mode has been studied. The zeros of Bargmann analytic function for one-mode are considered. The Q Husimi functions are introduced. The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros are discussed. The zeros of Bargmann analytic functions for two-mode are introduced. Various examples have been given.

Keywords: Bargmann functions, two-mode, zeros, harmonic oscillator

Procedia PDF Downloads 541

Authors: Melike Aydoğan, Dürdane Öztürk

Abstract:

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

Procedia PDF Downloads 494

Authors: Faride Crespo Razeg, Beatriz Eugenia Rivera Pedroza

Abstract:

While Colombian’s society has changed, the way that Colombian’s civil society participates has changed too. Thus, the social movements as a form of participation should be research to understand as the society structure as the groups’ interactions. In fact, in the last decades, the social movements in Colombia have been transformed in three categories: actors, spaces, and demands. For this reason, it is important to know from what perspectives have been researched this topic, allowing to recognize an epistemological and ontological reflections of it. The goal of this research has been characterizing the social movements of Cali – Colombia between 2002 and 2016. Cali is the southwest largest Colombian city; for this reason, it could be considered as a representative data for the social dynamic of the region. Qualitative methods as documental analysis have been used, in order to know the way that the research on social movements has been done. Thus taking into account this methodological technique, it has been found the goals that are present in most of the studies, which represents what are the main concerns around this topic. Besides, the methodology more used, to understand the way that the data was collected, its problems and its advantages. Finally, the ontological and epistemological reflections are important to understand which have been the theory and conceptual approach of the studies and how its have been contextualized to Cali, taking into account its own history.

Keywords: social movements, civil society, forms of participation, collective actions

Procedia PDF Downloads 248

Authors: Alicia C. Sanchez

Abstract:

This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice.

Keywords: automatic navigation control, lateral control, lane-keeping control, RAFU approximation

Procedia PDF Downloads 250

Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

Procedia PDF Downloads 264

Authors: İbrahim Aktaş, Árpád Baricz

Abstract:

In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

Procedia PDF Downloads 248

Authors: Tulin Coskun

Abstract:

We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

Procedia PDF Downloads 313

Authors: Chahid K. Ghaddar

Abstract:

The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

Procedia PDF Downloads 309

Authors: Irfan Ahmed Rind

Abstract:

Science education has recently become the top priority of government of Pakistan. Number of schemes has been initiated for the improvement of science teaching and learning at primary and secondary levels of education, most importantly training in-service science teachers on inquiry based teaching and learning to empower students and encourage creativity, critical thinking, and innovation among them. Therefore, this approach has been promoted in the recent continuous professional development trainings for the in-service teachers. However, the follow ups on trained science teachers and educators suggest that these teachers fail to implement the inquiry based teaching and learning in their classes. In addition, these trainings also fail to bring any significant change in students’ science content knowledge and understanding as per the annual national level surveys conducted by government and independent agencies. Research suggests that science has been taught using scientific positivism, which supports objectivity based on experiments and mathematics. In contrary, the inquiry based teaching and learning are based on constructivism, which conflicts with the positivist epistemology of science teachers. It was, therefore, assumed that science teachers struggle to implement the inquiry based teaching approach as it conflicts with their basic epistemological beliefs. With this assumption, this research aimed to (i) understand how science teachers conceptualize the nature of science, and how this influence their understanding of learning, learners, their own roles as teachers and their teaching strategies, (ii) identify the conflict of science teachers’ epistemological beliefs with the inquiry based teaching approach, and (iii) find the ways in which science teachers epistemological beliefs may be developed from positivism to constructivism, so that they may effectively use the inquiry based teaching approach in teaching science. Using qualitative case study approach, thirty six secondary and higher secondary science teachers (21 male and 15 female) were selected. Data was collected using interviewed, participatory observations (sixty lessons were observed), and twenty interviews from students for verifications of teachers’ responses. The findings suggest that most of the science teacher were positivist in defining the nature of science. Most of them limit themselves to one fix answer that is provided in the books and that there is only one 'right' way to teach science. There is no room for students’ or teachers’ own opinion or bias when it comes to scientific concepts. Inquiry based teaching seems 'no right' to them. They find it difficult to allow students to think out of the box. However, some interesting exercises were found to be very effective in bringing the change in teachers’ epistemological beliefs. These will be discussed in detail in the paper. The findings have major implications for the teachers, educators, and policymakers.

Keywords: science teachers, epistemology, metacognition, inquiry based teaching

Procedia PDF Downloads 120

Authors: Luiz F. J. Maia

Abstract:

This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

Procedia PDF Downloads 410

Authors: Paula Verdugo-Hernandez, Patricio Cumsille

Abstract:

We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of mathematical working spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: convergence, graphical representations, mathematical working spaces, paradigms of real analysis, real number sequences

Procedia PDF Downloads 113

Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

Abstract:

In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

Procedia PDF Downloads 523

Authors: Maitreyee Datta

Abstract:

Buddhist lakṣaņa of pratyakṣa pramā is not the result of the causal analysis of the genesis of it. Naiyāyikas, on the other hand, has provided the lakṣaņa of pratyakṣa in terms of the causal analysis of it. Thus, though in these two philosophical systems philosophers have discussed in detail the nature of pratyakṣa pramā (perception), yet their treatments and understanding of it vary according to their respective understanding of pramā and prmāņa and their relationship. In Nyāya school, the definition (lakṣņa) of perception (pratyakṣa) has been given in terms of the process by virtue of which it has been generated. Thus, Naiyāyikas were found to provide a causal account of perception (pratyakṣa) by virtue of their lakṣaņa of it. But in Buddhist epistemology perception has been defined by virtue of the nature of perceptual knowledge (pratyakṣa pramā) which is devoid of any vikalpa or cognition. These two schools differed due to their different metaphysical presuppositions which determine their epistemological pursuits. The Naiyāyikas admitted pramā and pramāņa as separate events and they have taken pramāņa to be the cause of pramā. These presuppositions enabled them to provide a lakṣaņa of pratyakṣa pramā in terms of the causes by which it is generated. Why did the Buddhist epistemologists define perception by the unique nature of perceptual knowledge instead of the process by which it is generated? This question will be addressed and dealt with in the present paper. In doing so, the unique purpose of Buddhist philosophy will be identified which will enable us to find out an answer to the above question. This enterprise will also reveal the close relationship among some basic Buddhist presuppositions like pratityasamutpādavāda and kṣaņikavāda with Buddhist epistemological positions. In other words, their distinctive notion of pramā (knowledge) indicates their unique epistemological position which is found to comply with their basic philosophical presuppositions. The first section of the paper will present the Buddhist epistemologists’ lakṣaņa of pratyakṣa. The analysis of the lakṣaņa will be given in clear terms to reveal the nature of pratyakṣa as an instance of pramā. In the second section, an effort will be made to identify the uniqueness of such a definition. Here an articulation will be made in which the relationship among basic Buddhist presuppositions and their unique epistemological positions are determined. In the third section of the paper, an effort will be made to compare Nyāya epistemologist’s position regarding pratyakṣa with that of the Buddhist epistemologist.

Keywords: laksana, prama, pramana, pratyksa

Procedia PDF Downloads 112

Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

Abstract:

It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

Procedia PDF Downloads 26

Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

Procedia PDF Downloads 423

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

Procedia PDF Downloads 219

Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

Abstract:

The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

Procedia PDF Downloads 235

Authors: Yilmaz Simsek

Abstract:

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

Procedia PDF Downloads 238

Authors: K. A.Tharanga, K. H. H. Damayanthi

Abstract:

Perception is an epistemological concept discussed in Philosophy. Perception, in other word, vision, is one of the ways that human beings get empirical knowledge after five senses. However, we face innumerable problems when achieving knowledge from perception, and therefore the knowledge gained through perception is uncertain. what we see in the external world is not real. These are the major issues that we face when receiving knowledge through perception. Sometimes there is no physical existence of what we really see. In such cases, the perception is relative. The following frames will be taken into consideration when perception is analyzed illusions and delusions, the figure of a physical object, appearance and the reality of a physical object, time factor, and colour of a physical object. seeing and knowing become vary according to the above conceptual frames. We cannot come to a proper conclusion of what we see in the empirical world. Because the things that we see are not really there. Hence the scientific knowledge which is gained from observation is doubtful. All the factors discussed in science remain in the physical world. There is a leap from ones existence to the existence of a world outside his/her mind. Indeed, one can suppose that what he/she takes to be real is just a massive deception. However, depending on the above facts, if someone begins to doubt about the whole world, it is unavoidable to become his/her view a scepticism or nihilism. This is a certain reality.

Keywords: empirical, perception, sceptisism, nihilism

Procedia PDF Downloads 103

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

Procedia PDF Downloads 290

Authors: Haoshu Li, Shaolong Wan

Abstract:

The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

Procedia PDF Downloads 110

Authors: Kassim A. Jassim

Abstract:

In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).

Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product

Procedia PDF Downloads 307

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

Procedia PDF Downloads 170

Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

Procedia PDF Downloads 122