Search results for: special functions

Authors: Lenell D. Walton

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African American families have consistently contended that their child’s special education team does not provide the services necessary to meet their child’s academic goals. Special education teams must guide and mentor African American students and their families through the special education process. This qualitative study examined African American female caregivers' perceptions, experiences, and expectations regarding the special education process. Data collection methods utilized in the study included a survey, semi-structured interviews, and three focus groups. Data were analyzed and compared to identify themes. Three themes emerged from the survey: education and training, participation, and challenges. Six major themes emerged: (a) differences in treatment and cultural disconnect, (b) lack of support and resources, (c) participants’ experiences of the special education process, (d) parent participation, (e) barriers and concerns, and (f) expectations. Implications for policy and practice to improve the special education process are discussed.

Keywords: African American, caregivers, critical race theory, special education

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Authors: P. Y. Tsyba, O. V. Razina, E. Güdekli, R. Myrzakulov

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In this paper, we consider the equation of motion for the F(R,T) gravity on their property of conformal invariance. It is shown that in the general case such a theory is not conformally invariant. Special cases for the functions v and u, in which the properties of the theory can appear, were studied.

Keywords: conformal invariance, gravity, space-time, metric

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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: Aviva Lvan, Lipaz Shamoa-Nir

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Recently, has increased the research interest in modern fatherhood especially, the increasing involvement of fathers in the family. However, there is a little research evidence on fathers to children with special needs. Therefore, the purpose of this study was to examine the effects of stress and coping style on involvement in school among fathers to children with special needs in inclusive education. We compared the fathers to children with special needs (N=72) with fathers to non-special needs children (N = 75), and found that higher stress levels, greater educational involvement and greater use of social support coping style, were found among fathers of children with special needs. In addition, mission coping style and emotional coping style predict involvement in the school and emotional coping style predicts high levels of stress. The above findings contribute to the investigation of changes in the perception of the role of fathers and their involvement in their children's lives especially, among fathers to children with special needs. From the applied aspect, the findings may increase the understanding of the role of fathers and their unique contribution to the social, emotional, and academic development of their children.

Keywords: coping style, educational involvement, special needs, stress

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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: 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: Nefrijanti Sutikno

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This paper highlights puberty and sexuality on children with special needs (SNC) in which they are very vulnerable to child sexual abuse (CSA). By providing sufficient knowledge and skill to teachers, they can synergise with parents to better anticipate, prevent and reduce the possibility of CSA and when it has already happened, together they are able to provide proper support and assistance to the victims of CSA.

Keywords: Special Needs Children (SNC), puberty, sexuality, child sexual abuse (CSA), prevention of CSA, anticipation of CSA

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Authors: T. J. Hasanova, C. N. Imamalieva

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The problem about the movement of the rigid cylinder keeping the vertical position under the influence of running superficial waves in a liquid is considered. The indignation of a falling wave caused by the presence of the cylinder which moves is thus considered. Special decomposition on a falling harmonious wave is used. The problem dares an operational method. For a finding of the original decision, Considering that the image denominator represents a tabular function, Voltaire's integrated equation of the first sort which dares a numerical method is used. Cylinder movement in the continuous environment under the influence of waves is considered in work. Problems are solved by an operational method, thus originals of required functions are looked for by the numerical definition of poles of combinations of transcendental functions and calculation of not own integrals. Using specificity of a task below, Decisions are under construction the numerical solution of the integrated equation of Volter of the first sort that does not create computing problems of the complex roots of transcendental functions connected with search.

Keywords: rigid cylinder, linear interpolation, fluctuations, Voltaire's integrated equation, harmonious wave

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Authors: Kenneth Kapalu Muzata, Dikeledi Mahlo, Pinkie Mabunda Mabunda

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This paper presents results of a study conducted to establish special education teachers’ knowledge and application of curriculum adaptation of the 2013 revised curriculum in Zambia. From a sample of 134 respondents (120 special education teachers, 12 education officers, and 2 curriculum specialists), the study collected both quantitative and qualitative data to establish whether teachers understood and applied the concept of curriculum adaptation in teaching learners with special education needs. To obtain data validity and reliability, the researchers collected data by use of mixed methods. Semi-structured questionnaires and interviews were administered. Lesson Observations and post-lesson discussions were conducted on 12 selected teachers from the 120 sample that answered the questionnaires. Frequencies, percentages, and significant differences were derived through the statistical package for social sciences. Qualitative data were analyzed with the help of NVIVO qualitative software to create themes and obtain coding density to help with conclusions. Both quantitative and qualitative data were concurrently compared and related. The results revealed that special education teachers lacked a thorough understanding of the concept of curriculum adaptation, thus denying learners with special education needs the opportunity to benefit from the revised curriculum. The teachers were not oriented on the revised curriculum and hence facing numerous challenges trying to adapt the curriculum. The study recommended training of special education teachers in curriculum adaptation.

Keywords: curriculum adaptation, special education, learners with special education needs, special education teachers

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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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

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Authors: Haoshu Li, Shaolong Wan

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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

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Authors: Kassim A. Jassim

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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

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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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

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Authors: Megan Chaney

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In the United States, research continues to show school administrators do not view themselves as adequately prepared in the area of special education. Often, special education is an omitted topic of study for school administrator preparation programs. The majority of special education teachers do not view their principals as well-prepared to support them in the educational context. Administrator preparation in the area of special education may begin at the foundational levels of understanding but is fundamentally an equity issue when serving individuals from marginalized populations with an urgent need to increase inclusionary practices. Special education and building-level administrators have a direct impact on teacher quality, instructional practices, inclusion, and equity with the opportunity to shape positive school culture. The current study was situated within an innovative IHE/LEA partnership pathway implemented with current K-12 administrators earning a Mild/Moderate Education Specialist Credential or coursework equivalent. Specifically, the study examined administrator’s perception of the Special Education Laws and Ethics’ course value and impact on the capacity to serve children with exceptionalities within the comprehensive school site context.

Keywords: special education laws and ethics, school adminstrator perspectives, school administrator training, inclusive practices

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Authors: Anthonia Emmanuel Inaja

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The role of the counseling services by Special Educators, Guidance Counsellors and psychologists alike to Families and Parents of children with special needs cannot be over-emphasized. This paper examined the vital role of counseling services and its impact on the emotional and physical readiness of parents to initiate and support the education and rehabilitation needs of their children. The paper considered the importance of counseling, when counseling services are best required preparing the mindset of parents and family members as well as the immediate community of the social needs child.

Keywords: counseling, families, special, needs, children, problems, prospect

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Authors: Shih-Chieh Liao, Jen-Ying Ma

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Dual protagonists game always bring a unique experience compared to the other games. This research wants to discuss whether the dual protagonists have the moving ability and special ability or not; it will affect the preference of the players. This research will focus on the single-player dual protagonists game. After the observation, we found that when players control the dual protagonists, the moving ability and special ability are a great point defining the preference of players. When players control the character, which is lack of moving ability, they often feel impatient with the inconvenient mechanism and then reduce the will to play with the character or even the game. Furthermore, the special ability is also important in the situation that there is another character to compare with. When the character is too powerful, players tend not to use the weaker one. In addition, gender is a big deal in the games. It surprisingly controls the will of play occasionally. In view of these, this research makes a single-player dual protagonists game and the dual protagonists are limited to male and female. The experiment content detected with Electrodermal Activity (EDA) includes seven different situations. (1) male and females both have the moving ability and special ability. (2) male and female both have a special ability, but female does not have the moving ability. (3) male and females both have a special ability, but the male does not have the moving ability. (4) male and female both have the moving ability, but the male does not have special ability (5) male and female both have the moving ability, but female does not have a special ability (6) male-only has the moving ability and female-only has a special ability (7) male-only has a special ability and female only has the moving ability. The experiment will evaluate the emotional changes of the subjects in those situations. The result sorted by the significance of player preference is (6)>(4)>(1)>(2)>(5)>(3)>(7). The result demonstrates that players prefer females with special abilities or males with moving abilities. The game developer could design the ability of dual protagonists based on this research. Therefore, players may have a better experience.

Keywords: biofeedback, dual protagonists, emotional responses, psychology, user experience

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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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: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Jareeluk Ratanaphan

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The purposed of this research were; 1. To survey the teacher’s needs on knowledge about special education management for special needs student 2. Development of distance training packages for teacher on special education management for special needs student 3. to study the effects of using the packages on trainee’s achievement 4. to study the effects of using the packages on trainee’s opinion on the distance training packages. The design of the experiment was research and development. The research sample for survey were 86 teachers, and 22 teachers for study the effects of using the packages on achievement and opinion. The research instrument comprised: 1) training packages on special education management for special needs student 2) achievement test 3) questionnaire. Mean, percentage, standard deviation, t-test and content analysis were used for data analysis. The findings of the research were as follows: 1. The teacher’s needs on knowledge about teaching for a learner with learning disability, mental retardation, autism, physical and health impairment and research in special education. 2. The package composed of special education management for special needs student document and manual of distance training packages. The document consisted by the name of packages, the explanation for the educator, content’s structure, concept, objectives, content and activities. Manual of distance training packages consisted by the explanation about a document, objectives, explanation about using the package, training schedule, and evaluation. The efficiency of packages was established at 79.50/81.35. 3. The results of using the packages were the posttest average scores of trainee’s achievement were higher than the pretest. 4. The trainee’s opinion on the package was at the highest level.

Keywords: distance training package, teacher, learner with special needs

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

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In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: NFV, resource allocation, virtual routing function, minimum power consumption

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Authors: Yamin Sayyari

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In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Anna K. Johnson

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Technology can provide endless opportunities for students with special needs. Virtual learning, particularly virtual charter schools in the US, provides opportunities for students with special needs for alternative education besides Brick and Mortar schools. Virtual schools have proven to be successful in the way they are able to provide quality education for their students. Virtual schools, just like Brick and Mortar schools, are not for everybody. This research is designed to look at the effectiveness of online charter schools, so parents can make decisions based on data. This article explains what inclusion is and how inclusion is addressed in the virtual environment. Often, students with special needs have limited options for schooling, and new charter schools provide that alternative education for students who don’t fit in the local brick-and-mortar school.

Keywords: special education, virtual school, online, inclusion

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Authors: Jennifer Duffy, Liz Fleming

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Teacher shortage in special education is an American educational problem. Due to the implementation of The No Child Left Behind Act (2001) and The Individuals with Disabilities Education Improvement Act (2004), there has been an increase in the number of students requiring special education services. Consequently, there has been an influx to hire more special education teachers. However, the historic challenge of hiring certified special education teachers has been intensified with this the profession’s increasing demand of positions to fill. Efforts to improve recruitment and entry into the field must be informed by an understanding of the factors that initially inspire special education teachers to choose this career pathway. Hence, an understanding of reasons why teachers select special education as a profession is needed. The purpose of this study was to explore personal, academic, and professional motivations that lead to the selection of special education as a career choice. Using the grounded theory approach, this research investigation examined the factors that were most instrumental in influencing applicants to select special education as a career choice. Over one hundred de-identified graduate school applications to Bay Path University’s Graduate Special Education Programs from 2014- 2017 were qualitatively analyzed. Grounded coding was used to discover themes that emerged in applicants’ admissions essays explaining why he/she was pursuing a career in special education. The central themes that were most influential in applicants’ selection of special education as a career trajectory were (a) personal/familial connections to disability, (b) meaningful paraprofessional experiences working with disabled children, (c) aptitudes for teaching, and (d) finding personal rewards and professional fulfillment by advocating for vulnerable children. Implications from these findings include educating family members of children with disabilities about possible career tracks in special education, designing programs for paraprofessionals to become certified teachers, exposing prospective teacher candidates to the field of special education, and recruiting professionals from the human services field who seek to improve the quality of life and educational opportunities for children with special needs.

Keywords: career choice, professional pathways to teaching children with disabilities, special education, teacher recruitment

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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Authors: Shih-Ching Wang, Mark Lang

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This paper examines the secondary effects and consequences of special displays on subsequent shopping behavior. Special displays are studied as a prominent form of in-store or shopper marketing activity. Two experiments are performed using special value and special quality-oriented displays in an online simulated store environment. The impact of exposure to special displays on mindsets and resulting product choices are tested in a shopping task. Impact on store image is also tested. The experiments find that special displays do trigger shopping mindsets that affect product choices and shopping basket composition and value. There are intended and unintended positive and negative effects found. Special value displays improve store price image but trigger a price sensitive shopping mindset that causes more lower-priced items to be purchased, lowering total basket dollar value. Special natural food displays improve store quality image and trigger a quality-oriented mindset that causes fewer lower-priced items to be purchased, increasing total basket dollar value. These findings extend the theories of product categorization, mind-sets, and price sensitivity found in communication research into the retail store environment. Findings also warn retailers to consider the total effects and consequences of special displays when designing and executing in-store or shopper marketing activity.

Keywords: special displays, mindset, shopping behavior, price consciousness, product categorization, store image

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Authors: Lucia Hrebeňárová, Jarmila Žolnová, Veronika Palková

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Inclusive education of students with special educational needs has been on the increase in the Slovak Republic, facing many challenges. Preparedness of teachers for inclusive education is one of the most frequent issues; teachers lack skills when it comes to the use of effective instruction depending on the individual needs of students, improvement of classroom management and social skills, and support of inclusion within the classroom. Social support is crucial for the school success of students within inclusive settings. The aim of the paper is to analyse perception of the frequency and importance of peer social support by students with special educational needs in inclusive education. The data collection tool used was the Child and Adolescent Social Support Scale (CASSS). The research sample consisted of 953 fourth grade students – 141 students with special educational needs educated in an inclusive setting and 812 students of the standard population. No significant differences were found between the students with special educational needs and the students without special educational needs in an inclusive setting when it comes to the perception of frequency and importance of social support of schoolmates and friends. However, the perception of frequency and importance of a friend’s social support was higher than the perception of frequency and importance of a classmate’s social support in both groups of students.

Keywords: inclusive education, peer social support, peer, student with special eEducational needs

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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

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In the search of potential models applied in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf) for displacing and modifying the shape of the potential under study. In order to transcend the scope of hyperbolic functions, in this work, a kind of generalized q-deformed hyperbolic functions (g q-dhf) is presented. By a suitable transformation, through the q deformation parameter, it is shown that these g q-dhf can be expressed in terms of their corresponding standard ones besides they can be reduced to the sc q-dhf. As a useful application of the proposed approach, and considering a class of exactly solvable multi-parameter exponential-type potentials, some new q-deformed quantum interactions models that can be used as interesting alternative in quantum physics and quantum states are presented. Furthermore, due that quantum potential models are conditioned on the q-dependence of the parameters that characterize to the exponential-type potentials, it is shown that many specific cases of q-deformed potentials are obtained as particular cases from the proposal.

Keywords: diatomic molecules, exponential-type potentials, hyperbolic functions, q-deformed potentials

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Authors: Smita Sonker

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Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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