Search results for: social and ecological functions

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: Panpan Feng

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The concept of green infrastructure originated in Europe and the United States. It aims to ensure smart growth of urban and rural ecosystems and achieve sustainable urban and rural ecological, social, and economic development by combining it with gray infrastructure in traditional planning. Based on the literature review of the theoretical origin, value connotation, and measurement methods of green infrastructure, this study summarizes the research content of green infrastructure at different scales from the three spatial levels of region, city, and block and divides it into functional dimensions, spatial dimension, and strategic dimension. The results show that in the functional dimension, from region-city-block, the research on green infrastructure gradually shifts from ecological function to social function. In the spatial dimension, from region-city-block, the research on the spatial form of green infrastructure has shifted from two-dimensional to three-dimensional, and the spatial structure of green infrastructure has shifted from single ecological elements to multiple composite elements. From a strategic perspective, green infrastructure research is more of a spatial planning tool based on land management, environmental livability and ecological psychology, providing certain decision-making support.

Keywords: green infrastructure, multi-scale, social and ecological functions, spatial strategic decision-making tools

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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: Yazhou Zhou, Yong Huang, Guoqin Ge

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In the process of human social development, the coupling and coordinated development among the ecological environment(E), production(P), and living functions(L) is of great significance for sustainable development. This study uses an improved coupling coordination degree model (CCDM) to discover the coordination conflict between E and human settlement environment. The main work of this study is as follows: (1) It is found that in the process of urbanization development of Ya 'an city from 2014 to 2018, the degree of coupling (DOC) value between E, P, and L is high, but the coupling coordination degree (CCD) of the three is low, especially the DOC value of E and the other two has the biggest decline. (2) A more objective weight value is obtained, which can avoid the analysis error caused by subjective judgment weight value.

Keywords: ecological environment, coupling coordination degree, neural network, sustainable development

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Authors: Esmail Sadipour

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The use of social networks is increasing day by day in all societies. The purpose of this research was to know the relationship between the use of social networks (Instagram, WhatsApp, and Telegram) with executive functions and academic performance in first-year female high school students. This research was applied in terms of purpose, quantitative in terms of data type, and correlational in terms of technique. The population of this research consisted of all female high school students in the first year of district 2 of Tehran. Using Green's formula, the sample size of 150 people was determined and selected by cluster random method. In this way, from all 17 high schools in district 2 of Tehran, 5 high schools were selected by a simple random method and then one class was selected from each high school, and a total of 155 students were selected. To measure the use of social networks, a researcher-made questionnaire was used, the Barclay test (2012) was used for executive functions, and last semester's GPA was used for academic performance. Pearson's correlation coefficient and multivariate regression were used to analyze the data. The results showed that there is a negative relationship between the amount of use of social networks and self-control, self-motivation and time self-management. In other words, the more the use of social networks, the fewer executive functions of students, self-control, self-motivation, and self-management of their time. Also, with the increase in the use of social networks, the academic performance of students has decreased.

Keywords: social networks, executive function, academic performance, working memory

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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: 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: Fariha Asif

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The main purpose of this study was to investigate the effectiveness of eclectic approach in teaching of communicative functions. The objectives of the study were to get the information about the use of communicative functions through eclectic approach and to point out the most effective way of teaching functional communication and social interaction with the help of communicative activities through eclectic approach. The next step was to select sample from the selected population. As the research was descriptive so a questionnaire was developed on the basis of hypothesis and distributed to different selected schools of Lahore, Pakistan. Then data was tabulated, analyzed and interpreted through computer by finding percentages of different responses given by teachers to see the results. It was concluded that eclectic approach is effective in teaching communicative functions and communicative functions are better when taught through eclectic approach and communicative activities are more appropriate way of teaching communicative functions. It was found those teachers who were qualified in ELT gave better opinions as compare to those who did not have this degree. Techniques like presentations, dialogues and roleplay proved to be effective for teaching functional communication through communicative activities and also motivate the students not only in learning rules but also in using them to communicate with others.

Keywords: methodology, functions, teaching, ESP

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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: Zahra Yazdani Paraii, Zohreh Yazdani Paraei

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Many urban designers and planners have been involved in the design of environmentally friendly or nature adaptable urban development models due to increase in urban populations in the recent century, limitation on natural resources, climate change, and lack of enough water and food. Ecological city is one of the latest models proposed to accomplish the latter goal. In this work, the existing establishing indicators of the ecological city are used regarding energy, water, land use and transportation issues. The model is used to compare the function of traditional settlements of Iran. The result of investigation shows that the specifications and functions of the traditional settlements of Iran fit well into the ecological city model. It is found that the inhabitants of the old cities and villages in Iran had founded ecological cities based on their knowledge of the environment and its natural opportunities and limitations.

Keywords: ecological city, traditional city, urban design, environment

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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: Revaz Gvelesiani

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Nowadays, social inequality increasingly strengthens the trend from business entrepreneurship to social entrepreneurship. It can be said that business entrepreneurs, according to their interests, move towards social entrepreneurship. Effectively operating markets create mechanisms, which lead to 'good' behavior. This is the most important feature of the rationally functioning society. As for the prospects of social entrepreneurship, expansion of entrepreneurship concept at the social arena may lead to such an outcome, when people who are skeptical about business, become more open towards entrepreneurship as a type of activity. This is the way which by means of increased participation in entrepreneurship promotes fair distribution of wealth. Today 'entrepreneurship for all' is still a dream, although the one, which may come true.

Keywords: social entrepreneurship, business entrepreneurship, functions of entrepreneurship, social inequality, social interests, interest groups, interest conflicts

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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: 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: Hu Changjuan, Gong Cong, Long Hao

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Although urban ecological policies and the public's aspiration for livable environments have expedited the pace of ecological revitalization, historic districts that have evolved through natural ecological processes often become obsolete and less habitable amid rapid urbanization. This raises a critical question about historic districts inherently incapable of being ecological and livable. The thriving concept of ‘intrinsic ecology,’ characterized by its ability to transform city-district systems into healthy ecosystems with diverse environments, stable functions, and rapid restoration capabilities, holds potential for guiding the integration of ancient and modern ecological wisdom while supporting the dynamic involvement of cultures. This study explores the intrinsic ecology of historic districts from three aspects: 1) Population Density: By comparing the population density before urban population expansion to the present day, determine the reasonable population density for historic districts. 2) Building Density: Using the ‘Space-mate’ tool for comparative analysis, form a spatial matrix to explore the intrinsic ecology of building density in Chinese historic districts. 3) Green Capacity Ratio: By using ecological districts as control samples, conduct dual comparative analyses (related comparison and upgraded comparison) to determine the intrinsic ecological advantages of the two-dimensional and three-dimensional green volume in historic districts. The study inform a density optimization strategy that supports cultural, social, natural, and economic ecology, contributing to the creation of eco-historic districts.

Keywords: eco-historic districts, intrinsic ecology, suitable density, green capacity ratio.

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Authors: Tulin Coskun

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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: Taehyun Kim, Hyunjoo Park, Taehyun Kim

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Since the rapid economic development, Korea has recently entered a period of low growth due to population decline and aging. Due to the urbanization around the metropolitan area and the hollowing of local cities, the ecological capacity of a city is decreasing while ecological footprints are increasing, requiring a compact space plan for maintaining urban functions. The purpose of this study is to analyze the relationship between urban spatial structure and residents' ecological footprints for sustainable spatial planning. To do this, we try to analyze the relationship between intra-urban spatial structure, such as net/gross density and service accessibility, and resident ecological footprints of food, housing, transportation, goods and services through survey and structural equation modeling. The results of the study will be useful in establishing an implementation plan for sustainable development goals (SDGs), especially for sustainable cities and communities (SDG 11) and responsible consumption and production (SDG 12) in the future.

Keywords: ecological footprint, structural equation modeling, survey, sustainability, urban spatial structure

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Authors: Sisi Xia, Dezhuan Tao

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Urban Double Reform is an effective means to improve the quality of ecological space, based on improving the living environment and urban functions and promoting the organic integration of the city and nature. This paper takes the design of Qinyang Wetland Park in Jiaozuo, Henan Province, as an example, attempting to closely link the ecological restoration of wetland with the urban culture and to extend the urban spirit of the ancient county of Qinyang while purifying the ecological water system. This design uses ecological technology to repair underwater forests and underwater turf, rapidly improving the quality of urban water without biological side effects. The ecological grass slope is used to create multiple bank forms, combining with a number of hydrophilic platforms to provide a good view of the public. Through the placement of ecological education bases, urban cultural exhibition halls, and other means, the cultural value of wetland parks will be enhanced, and the citizens will return to nature and experience the ecology and appreciate the charm of urban culture in the ecological space. Repair the ecosystem, sculpt the urban culture, let the public return to nature, experience the ecology, and experience the charm of urban culture in the ecological space.

Keywords: urban double reform, ecological space, improvement strategy, wetland park design

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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: C. C. Liang

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MSN used to be the most popular application for communicating among social networks, but Facebook chat is now the most popular. Facebook and MSN have similar characteristics, including usefulness, ease-of-use, and a similar function, which is the exchanging of information with friends. Facebook outperforms MSN in both of these areas. However, the adoption of Facebook and abandonment of MSN have occurred for other reasons. Functions can be improved, but users’ willingness to use does not just depend on functionality. Flow status has been established to be crucial to users’ adoption of cyber applications and to affects users’ adoption of software applications. If users experience flow in using software application, they will enjoy using it frequently, and even change their preferred application from an old to this new one. However, no investigation has examined choice behavior related to switching from Facebook to MSN based on a consideration of flow experiences and functions. This investigation discusses the flow experiences and functions of social-networking applications. Flow experience is found to affect perceived ease of use and perceived usefulness; perceived ease of use influences information ex-change with friends, and perceived usefulness; information exchange influences perceived usefulness, but information exchange has no effect on flow experience.

Keywords: consumer behavior, social media, technology acceptance model, flow experience

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Authors: Luiz F. J. Maia

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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

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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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

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

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sᵩ 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

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Authors: Xinyi Huang

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As a former British colony and one of the most famous world financial centers today, Hong Kong attracts countless businessmen and tourists to visit or settle down every year. Hong Kong is a land that leads western culture to blossom in Asia, and in the meantime, it inherits the unique charm of Chinese traditional culture. The Chinese-English bilingual phenomenon can be seen everywhere in Hong Kong. The public presentation, code choice, and practical use of these two languages can also reflect the economic and social status, population distribution, and individual identity construction of a specific area. This paper mainly compares the linguistic landscape of two areas with different social functions in Hong Kong: Tsim Sha Tsui, a large commercial center in Kowloon, and Tai Wai, a residential area in New Territories. By adopting the methodology of the Walking Tour, the bilingual data of 75 photos are collected unintentionally during the field trip in the two areas. Through the methods of quantitative analysis and linguistic landscape studies, this paper deeply analyzes the similarities and differences in language distribution and the respective social functions of two languages in the two places.

Keywords: bilingualism, linguistic landscape, identity construction, commodification

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Authors: Khosrow Maleknejad, Yaser Rostami

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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

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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

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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

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Authors: Sandra Cecilia Bautista-Rodríguez, Vladimir Melgarejo

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Climate change, loss of ecosystems, increasing poverty, increasing marginalization of rural communities and declining food security are global issues that require urgent attention. In this regard, a great deal of research has focused on how agroecosystems respond to these challenges as they provide ecosystem services (ES) that lead to higher levels of resilience, adaptation, productivity and self-sufficiency. Hence, the valuing of ecosystem services plays an important role in the decision-making process for the design and management of agroecosystems. This paper aims to define the link between ecosystem service valuation methods and ES value dimensions in agroecosystems from ecological economics and agroecology. The method used to identify valuation methodologies was a literature review in the fields of Agroecology and Ecological Economics, based on a strategy of information search and classification. The conceptual framework of the work is based on the multidimensionality of value, considering the social, ecological, political, technological and economic dimensions. Likewise, the valuation process requires consideration of the ecosystem function associated with ES, such as regulation, habitat, production and information functions. In this way, valuation methods for ES in agroecosystems can integrate more than one value dimension and at least one ecosystem function. The results allow correlating the ecosystem functions with the ecosystem services valued, and the specific tools or models used, the dimensions and valuation methods. The main methodologies identified are multi-criteria valuation (1), deliberative - consultative valuation (2), valuation based on system dynamics modeling (3), valuation through energy or biophysical balances (4), valuation through fuzzy logic modeling (5), valuation based on agent-based modeling (6). Amongst the main conclusions, it is highlighted that the system dynamics modeling approach has a high potential for development in valuation processes, due to its ability to integrate other methods, especially multi-criteria valuation and energy and biophysical balances, to describe through causal cycles the interrelationships between ecosystem services, the dimensions of value in agroecosystems, thus showing the relationships between the value of ecosystem services and the welfare of communities. As for methodological challenges, it is relevant to achieve the integration of tools and models provided by different methods, to incorporate the characteristics of a complex system such as the agroecosystem, which allows reducing the limitations in the processes of valuation of ES.

Keywords: ecological economics, agroecosystems, ecosystem services, valuation of ecosystem services

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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: Marcia Figueira

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Context: Positivist transformations in agriculture were responsible for top-down – often coercive – mechanisms of uniformed modernization that weathered local diversities and agency. New development pathways need to now shift according to comprehensive integrations of knowledge - scientific, indigenous, and local, and to be sustained on political interventions, bottom-up change, and social learning if climate goals are to be met – both in mitigation and adaptation. Objectives The objectives of this research are to understand how social-ecological and socio-technical systems characterisation can be nested to bridge scientific research/knowledge into a local context and knowledge system; and, with it, stem sustainable innovation. Methods To do so, we conducted a scoping review to explore theoretical and empirical works linked to Ostrom’s Social-Ecological Systems framework and Geels’ multi-level perspective of socio-technical systems transformations in the context of agriculture. Results As a result, we were able to identify key variables and connections to 1- understand the rules in use and the community attributes influencing resource management; and 2- how they are and have been shaped and shaping systems innovations. Conclusion Based on these results, we discuss how to leverage action research for mutual learning toward a replicable but highly place-based agriculture transformation frame.

Keywords: agriculture systems innovations, social-ecological systems, socio-technical systems, action research

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