Search results for: analytic functions

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

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Authors: Muna Tabuni

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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

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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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

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Authors: Fuad Al Sarari

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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

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Authors: Muna Tabuni

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The paper contains an investigation on the special properties of the zeros of the analytic representations of finite quantum systems. These zeros and their paths completely define the finite quantum system. The present paper studies the construction of the analytic representation from its zeros. The analytic functions of finite quantum systems are introduced. The zeros of the analytic theta functions and their paths have been studied. The analytic function f(z) have exactly d zeros. The analytic function has been constructed from its zeros.

Keywords: construction, analytic, representation, zeros

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Authors: Nicolae Pascu

Abstract:

Aside from being a fundamental tool in Complex analysis, Schwarz Lemma-which was finalized in its most complete form at the beginning of the last century-generated an important area of research in various fields of mathematics, which continues to advance even today. We present some properties of analytic functions in the half-plane which satisfy the conditions of the classical Schwarz Lemma (Carathéodory functions) and obtain a generalization of the well-known Aleksandrov-Sobolev Lemma for analytic functions in the half-plane (the correspondent of Schwarz-Pick Lemma from the unit disk). Using this Schwarz-type lemma, we obtain a characterization for the entire class of Carathéodory functions, which might be of independent interest. We prove two monotonicity properties for Carathéodory functions that do not depend upon their normalization at infinity (the hydrodynamic normalization). The method is based on conformal mapping arguments for analytic functions in the half-plane satisfying appropriate conditions, in the spirit of Schwarz lemma. According to the research findings in this paper, our main results give estimates for the modulus and the argument for the entire class of Carathéodory functions. As applications, we give several extensions of Julia-Wolf-Carathéodory Lemma in a half-strip and show that our results are sharp.

Keywords: schwarz lemma, Julia-wolf-caratéodory lemma, analytic function, normalization condition, caratéodory function

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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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

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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: Anas Hourani, Batool Ahmad

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Software applications play an important role inside any institute. They are employed to manage all processes and store entities-related data in the computer. Therefore, choosing the right software product that meets institute requirements is not an easy decision in view of considering multiple criteria, different points of views, and many standards. As a case study, Mutah University, located in Jordan, is in essential need of customized software, and several companies presented their software products which are very similar in quality. In this regard, an analytic hierarchy process (AHP) and a fuzzy analytic hierarchy process (Fuzzy-AHP) models are proposed in this research to identify the most suitable and best-fit software product that meets the institute requirements. The results indicate that both modules are able to help the decision-makers to make a decision, especially in complex decision problems.

Keywords: analytic hierarchy process, decision modeling, fuzzy analytic hierarchy process, software product

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Kunpeng Wang, Hongchun, Wu, Liangzhi Cao, Chuanqi Zhao

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The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions which satisfy the diffusion equation at any point in a triangular-z node for each energy group, and nodes were coupled with each other with both the zero- and first-order partial neutron current moments across all the interfaces of the triangular prism at the same time. Based this method, a code TABFEN has been developed and applied to solve the neutron diffusion equation in a complicated geometry. In addition, after a series of numerical derivation, one can get the neutron adjoint diffusion equations in matrix form which is the same with the neutron diffusion equation; therefore, it can be solved by TABFEN, and the low-high scan strategy is adopted to improve the efficiency. Four benchmark problems are tested by this method to verify its feasibility, the results show good agreement with the references which demonstrates the efficiency and feasibility of this method.

Keywords: analytic basis function expansion method, arbitrary triangular-z node, adjoint neutron flux, complicated geometry

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Authors: Latif Yanar, Muammer Kaçan

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Decision support systems are getting more important in many fields of science and technology and used effectively especially when the problems to be solved are complicated with many criteria. In this kind of problems one of the main challenges for the decision makers are that sometimes they cannot produce a countable data for evaluating the criteria but the knowledge and sense of experts. In recent years, fuzzy set theory and fuzzy logic based decision models gaining more place in literature. In this study, a decision support model to determine a country to build naval base is proposed and the application of the model is performed, considering Turkish Navy by the evaluations of Turkish Navy officers and academicians of international relations departments of various Universities located in Istanbul. The results achieved from the evaluations made by the experts in our model are calculated by a decision support tool named DESTEC 1.0, which is developed by the authors using C Sharp programming language. The tool gives advices to the decision maker using Analytic Hierarchy Process, Analytic Network Process, Fuzzy Analytic Hierarchy Process and Fuzzy Analytic Network Process all at once. The calculated results for five foreign countries are shown in the conclusion.

Keywords: decision support system, analytic hierarchy process, fuzzy analytic hierarchy process, analytic network process, fuzzy analytic network process, naval base, country selection, international relations

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Authors: Cristina-Maria Păcurar

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The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

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Authors: X. L. Nguyen, T. Y. Chou, F. Y. Min, F. C. Lin, T. V. Hoang, Y. M. Huang

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In Vietnam, land use planning is utilized as an efficient tool for the local government to adjust land use. However, planned locations are facing disapproval from people who live near these planned sites because of environmental problems. The selection of these locations is normally based on the subjective opinion of decision-makers and is not supported by any scientific methods. Many researchers have applied Multi-Criteria Analysis (MCA) methods in which Analytic Hierarchy Process (AHP) is the most popular techniques in combination with Fuzzy set theory for the subject of rationality assessment of land use planning locations. In this research, the Fuzzy set theory and Analytic Network Process (ANP) multi-criteria-based technique were used for the assessment process. The Fuzzy Analytic Hierarchy Process was also utilized, and the output results from two methods were compared to extract the differences. The 20 planned landfills in Hung Ha district, Thai Binh province, Vietnam was selected as a case study. The comparison results indicate that there are different between weights computed by AHP and ANP methods and the assessment outputs produced from these two methods also slight differences. After evaluation of existing planned sites, some potential locations were suggested to the local government for possibility of land use planning adjusts.

Keywords: Analytic Hierarchy Process, Analytic Network Process, Fuzzy set theory, land use planning

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Authors: Darius Danesh, Michael J. Ryan, Alireza Abbasi

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Project Portfolio Management (PPM) is an essential component of an organisation’s strategic procedures, which requires attention of several factors to envisage a range of long-term outcomes to support strategic project portfolio decisions. To evaluate overall efficiency at the portfolio level, it is essential to identify the functionality of specific projects as well as to aggregate those findings in a mathematically meaningful manner that indicates the strategic significance of the associated projects at a number of levels of abstraction. PPM success is directly associated with the quality of decisions made and poor judgment increases portfolio costs. Hence, various Multi-Criteria Decision Making (MCDM) techniques have been designed and employed to support the decision-making functions. This paper reviews possible option to improve the decision-making outcomes in the organisational portfolio management processes using the Analytic Hierarchy Process (AHP) both from academic and practical perspectives and will examine the usability, certainty and quality of the technique. The results of the study will also provide insight into the technical risk associated with current decision-making model to underpin initiative tracking and strategic portfolio management.

Keywords: analytic hierarchy process, decision support systems, multi-criteria decision making, project portfolio management

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Authors: Derya Duran, Christine Jacknick

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Despite a growing body of research on classroom, especially language classroom interactions, much more is yet to be discovered on how interaction is organized in higher education settings. This study investigates how the discourse marker 'I mean' in teacher questioning turns functions as a resource to promote student participation as well as to enhance collective understanding in whole-class discussions. This paper takes a conversation analytic perspective, drawing on 30-hour video recordings of classroom interaction in an English as a medium of instruction university in Turkey. Two content classrooms (i.e., Guidance) were observed during an academic term. The course was offered to 4th year students (n=78) in the Faculty of Education; students were majoring in different subjects (i.e., Early Childhood Education, Foreign Language Education, Mathematics Education). Results of the study demonstrate the multi-functionality of discourse marker 'I mean' in teacher questioning turns. In the context of English as a medium of instruction classrooms where possible sources of confusion may occur, we found that 'I mean' is primarily used to indicate upcoming adjustments. More specifically, it is employed for a variety of interactional purposes such as elaboration, clarification, specification, reformulation, and reference to the instructional activity. The study sheds light on the multiplicity of functions of the discourse marker in academic interactions and it uncovers how certain linguistic resources serve functions to the organization of repair such as the maintenance of understanding in classroom interaction. In doing so, it also shows the ways in which participation is routinely enacted in shared interactional events through linguistic resources.

Keywords: conversation analysis, discourse marker, English as a medium of instruction, repair

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Authors: Hanoch Yerushalmi

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One of the transformational therapeutic experiences is the therapeutic dyad's immersion in and recovery from shared regressive states that are often provoked by an awakened childhood fear of breakdown. the suggest that the supervisory dyad has parallel transformational experiences―the shared regressive states that follow continuous incomprehension of the unfolding therapeutic reality. Moreover, when the supervisory partners immerse themselves in a shared regressive state, a unique, inclusive, embodied, unsymbolized, and procedural understanding-without-reflection emerges spontaneously. Analytic writers describe such an understanding as unconscious knowledge, and existentialist writers describe it as prereflective consciousness. Before translating this unique understanding into a therapeutic narrative, the supervisor needs to recover from the regressive state and organize it according to discursive and logical analytic principles. From this perspective, the already existing experiential and analytic theoretical knowledge serves as a platform for creating new perceptions and analytic discourses.

Keywords: supervision, existentialism, prereflective consciousness, regressive states

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Authors: Pin-Ju Juan, Peng-Yu Juan, Yi-Shan Chen

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The main purpose of this paper is to present a fuzzy Analytic Network Process (ANP) model for the hostel organizational performance selection. In this article, we created 39 criteria for selecting hostel organizational performance acquired from literature's review and experts method practical investigations, and the methods of fuzzy analytic network process are used to consolidate decision-makers’ assessments about criteria weightings. Finally, we selected organizational performance of a hostel in Taiwan to determine the effectiveness of the proposed evaluation model in this paper.

Keywords: Fuzzy ANP, hostel, organizational performance, strategy management

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: asymptotics, continuous spectrum, difference equations, eigenvalues, jost functions, spectral singularities

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Authors: Gebreegziabher Hailu Gebrecherkos

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This study explores the derivatives of functions defined by I-functions of two variables and their connections to generalized M-series. We begin by defining I-functions, which are generalized functions that encompass various special functions, and analyze their properties. By employing advanced calculus techniques, we derive new formulas for the first and higher-order derivatives of I-functions with respect to their variables; we establish some derivative formulae of the I-function of two variables involving generalized M-series. The special cases of our derivatives yield interesting results.

Keywords: I-function, Mellin-Barners control integral, generalized M-series, higher order derivative

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Authors: Berhane Tewelday Weldhiwot

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This research investigates the pivotal role of modular forms in modern cryptographic systems, particularly focusing on their applications in secure communications and data integrity. Modular forms, which are complex analytic functions with rich arithmetic properties, have gained prominence due to their connections to number theory and algebraic geometry. This study begins by outlining the fundamental concepts of modular forms and their historical development, followed by a detailed examination of their applications in cryptographic protocols such as elliptic curve cryptography and zero-knowledge proofs. By employing techniques from analytic number theory, the research delves into how modular forms can enhance the efficiency and security of cryptographic algorithms. The findings suggest that leveraging modular forms not only improves computational performance but also fortifies security measures against emerging threats in digital communication. This work aims to contribute to the ongoing discourse on integrating advanced mathematical theories into practical applications, ultimately fostering innovation in cryptographic methodologies.

Keywords: modular forms, cryptography, elliptic curves, applications, mathematical theory

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Authors: Te Wen Tu, Sen Yung Lee

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An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition

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Authors: Alicia C. Sanchez

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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

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Authors: İbrahim Aktaş, Árpád Baricz

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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

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Authors: Ashwin Belle, Bryce Benson, Mark Salamango, Fadi Islim, Rodney Daniels, Kevin Ward

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A reliable, real-time, and non-invasive system that can identify patients at risk for hemodynamic instability is needed to aid clinicians in their efforts to anticipate patient deterioration and initiate early interventions. The purpose of this pilot study was to explore the clinical capabilities of a real-time analytic from a single lead of an electrocardiograph to correctly distinguish between rapid response team (RRT) activations due to hemodynamic (H-RRT) and non-hemodynamic (NH-RRT) causes, as well as predict H-RRT cases with actionable lead times. The study consisted of a single center, retrospective cohort of 21 patients with RRT activations from step-down and telemetry units. Through electronic health record review and blinded to the analytic’s output, each patient was categorized by clinicians into H-RRT and NH-RRT cases. The analytic output and the categorization were compared. The prediction lead time prior to the RRT call was calculated. The analytic correctly distinguished between H-RRT and NH-RRT cases with 100% accuracy, demonstrating 100% positive and negative predictive values, and 100% sensitivity and specificity. In H-RRT cases, the analytic detected hemodynamic deterioration with a median lead time of 9.5 hours prior to the RRT call (range 14 minutes to 52 hours). The study demonstrates that an electrocardiogram (ECG) based analytic has the potential for providing clinical decision and monitoring support for caregivers to identify at risk patients within a clinically relevant timeframe allowing for increased vigilance and early interventional support to reduce the chances of continued patient deterioration.

Keywords: critical care, early warning systems, emergency medicine, heart rate variability, hemodynamic instability, rapid response team

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Authors: Jungeun Cho

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Social finance has received increasing attention as a means to promote the growth of regional economies. Despite the plenty of research discussed their critical role and functions in regional economic development such as the financing and promotion of co-operatives or social enterprises and the offering credit to the financially excluded in the region, however, rarely are efforts made to measure the contribution of social finance in the regional economy. It is essential to establish an evaluation model in order to encourage social finance institutions to perform their supposed role and functions on regional economic development. The objective of this paper is to formulate an evaluation model of the contribution of social finance to the regional economy through an analytic hierarchy process (AHP) approach. This study is expected to provide useful guidelines for social finance institutions’ strategies and the policies of local or central government regarding social finance.

Keywords: social finance, regional economy, social economy, policies of local or central government

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Authors: Chahid K. Ghaddar

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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

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Authors: S. J. Yune, S. Y. Lee, S. J. Im, B. S. Kam, S. Y. Baek

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This study aimed to determine the reliability of clinical performance assessments, having been emphasized by ability-based education, and professors overall assessment methods. We addressed the following problems: First, we try to find out whether there is a difference in what we consider to be the main variables affecting the clinical performance test according to the evaluator’s working period and the number of evaluation experience. Second, we examined the relationship among the global rating score (G), analytic global rating score (Gc), and the sum of the analytical checklists (C). What are the main factors affecting clinical performance assessments in relation to the numbers of times the evaluator had administered evaluations and the length of their working period service? What is the relationship between overall assessment score and analytic checklist score? How does analytic global rating with 6 components in OSCE and 4 components in sub-domains (Gc) CPX: aseptic practice, precision, systemic approach, proficiency, successfulness, and attitude overall assessment score and task-specific analytic checklist score sum (C) affect the professor’s overall global rating assessment score (G)? We studied 75 professors who attended a 2016 Bugyeoung Consortium clinical skills performances test evaluating third and fourth year medical students at the Pusan National University Medical school in South Korea (39 prof. in OSCE, 36 prof. in CPX; all consented to participate in our study). Each evaluator used 3 forms; a task-specific analytic checklist, subsequent analytic global rating scale with sub-6 domains, and overall global scale. After the evaluation, the professors responded to the questionnaire on the important factors of clinical performance assessment. The data were analyzed by frequency analysis, correlation analysis, and hierarchical regression analysis using SPSS 21.0. Their understanding of overall assessment was analyzed by dividing the subjects into groups based on experiences. As a result, they considered ‘precision’ most important in overall OSCE assessment, and ‘precise accuracy physical examination’, ‘systemic approaches to taking patient history’, and ‘diagnostic skill capability’ in overall CPX assessment. For OSCE, there was no clear difference of opinion about the main factors, but there was for CPX. Analytic global rating scale score, overall rating scale score, and analytic checklist score had meaningful mutual correlations. According to the regression analysis results, task-specific checklist score sum had the greatest effect on overall global rating. professors regarded task-specific analytic checklist total score sum as best reflecting overall OSCE test score, followed by aseptic practice, precision, systemic approach, proficiency, successfulness, and attitude on a subsequent analytic global rating scale. For CPX, subsequent analytic global rating scale score, overall global rating scale score, and task-specific checklist score had meaningful mutual correlations. These findings support explanations for validity of professors’ global rating in clinical performance assessment.

Keywords: global rating, clinical performance assessment, medical education, analytic checklist

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