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APPLICATION OF ORTHOGONALITY ON THE SEMICIRCLE IN SIGNAL PROCESSING
In 1987, in Gautschi W., Landau H.J, Milovanović G.V. Polynomials orthogonal on the semicircle, II. Constr. Approx. 1987;3:389–404. the weighted orthogonality on the semicircle and the corresponding orthogonal polynomials were introduced.. Orthogonality is defined using an integral over the area of the upper unit semicircle centered at the origin, without conjugating the second component. Later, the Gaussian quadrature rule on the semicircle was considered. After a long period of time, the au...
In 1987, in Gautschi W., Landau H.J, Milovanović G.V. Polynomials orthogonal on the semicircle, II. Constr. Approx. 1987;3:389–404. the weighted orthogonality on the semicircle and the corresponding orthogonal polynomials were introduced.. Orthogonality is defined using an integral over the area of the upper unit semicircle centered at the origin, without conjugating the second component. Later, the Gaussian quadrature rule on the semicircle was considered. After a long period of time, the au...
COMPREHENSION OF INTERPOLATION AMONG THIRD-YEAR HIGH SCHOOL STUDENTS TALENTED IN COMPUTER SCIENCE AND INFORMATICS
This paper presents the outcomes of a five year study conducted with third grade students from class for talented students in computer science and informatics at grammar school, within the subject Application of Computers. The research addresses the pedagogical challenge of introducing advanced mathematical concepts, specifically interpolating polynomial, at an early stage of education. The aim was to evaluate both the effectiveness of instructional methods and the depth of student understand...
This paper presents the outcomes of a five year study conducted with third grade students from class for talented students in computer science and informatics at grammar school, within the subject Application of Computers. The research addresses the pedagogical challenge of introducing advanced mathematical concepts, specifically interpolating polynomial, at an early stage of education. The aim was to evaluate both the effectiveness of instructional methods and the depth of student understand...
Numerical differentiation of analytic functions using GAG quadrature rules on the semicircle
As stated in [1], until 1991, the numerical differentiation of analytical functions was discussed in several papers. The corresponding formulas for differentiation were mostly obtained by Cauchy’s integral formula and the application of the trapezoidal rule. In paper [1], new formulas for numerical differentiation were introduced using Gaussian quadrature rules on the semicircle. In [2] generalized averaged Gaussian (GAG) quadrature rule on the semicircle are introduced with aim of better...
As stated in [1], until 1991, the numerical differentiation of analytical functions was discussed in several papers. The corresponding formulas for differentiation were mostly obtained by Cauchy’s integral formula and the application of the trapezoidal rule. In paper [1], new formulas for numerical differentiation were introduced using Gaussian quadrature rules on the semicircle. In [2] generalized averaged Gaussian (GAG) quadrature rule on the semicircle are introduced with aim of better...
σ-orthogonal polynomials on the semicircle
Orthogonal polynomials on the semicircle and the corresponding quadratures of Gaussian type were introduced and studied by Gautschi and Milovanovi´c for the first time in [1]. In the real case quadrature rules with multiple nodes [3] are observed. A special case of polynomials whose zeros are these multiple nodes are given by the so-called s-orthogonality conditions [2]. The s-orthogonal polynomials on the semicircle are considered in [4]. In this paper we introduce σ-orthogonal polynomial...
Orthogonal polynomials on the semicircle and the corresponding quadratures of Gaussian type were introduced and studied by Gautschi and Milovanovi´c for the first time in [1]. In the real case quadrature rules with multiple nodes [3] are observed. A special case of polynomials whose zeros are these multiple nodes are given by the so-called s-orthogonality conditions [2]. The s-orthogonal polynomials on the semicircle are considered in [4]. In this paper we introduce σ-orthogonal polynomial...
Animating Marble : The Spiritual Afterlife of Byzantine Whiteness in the Palatine Chapel in Aachen
This article explores how white marble, as a material charged with theological resonance and imperial symbolism, was strategically employed in the Palatine Chapel of Aachen to construct a sacred space that conveyed both divine presence and political authority. Drawing on the legacy of Byzantine architecture, especially Hagia Sophia and the Church of Sts. Sergius and Bacchus, the study analyzes how Charlemagne’s architects appropriated the aesthetics of Byzantine whiteness to evoke sacred ligh...
This article explores how white marble, as a material charged with theological resonance and imperial symbolism, was strategically employed in the Palatine Chapel of Aachen to construct a sacred space that conveyed both divine presence and political authority. Drawing on the legacy of Byzantine architecture, especially Hagia Sophia and the Church of Sts. Sergius and Bacchus, the study analyzes how Charlemagne’s architects appropriated the aesthetics of Byzantine whiteness to evoke sacred ligh...
Echoes of Empire, Contemporary Challenges: A Transnational Path to Preserving Mateič (the Black Mountain Monastery)
Рад се бави културно-историјским значајем манастира Матеич (Скопска Црна Гора) код Кумановa у Северној Македонији, наглашавајући његов статус као споменика изузетне уметничке и духовне вредности који припада наслеђу из времена династије Немањића. Посебан акценат је стављен на могућност транснационалне номинације овог споменика за Листу светске баштине Унеска, што би омогућило бољу заштиту и под- стицање билатералне сарадње између Републике Србије и Републике Се- верне Македоније. У рад...
Рад се бави културно-историјским значајем манастира Матеич (Скопска Црна Гора) код Кумановa у Северној Македонији, наглашавајући његов статус као споменика изузетне уметничке и духовне вредности који припада наслеђу из времена династије Немањића. Посебан акценат је стављен на могућност транснационалне номинације овог споменика за Листу светске баштине Унеска, што би омогућило бољу заштиту и под- стицање билатералне сарадње између Републике Србије и Републике Се- верне Македоније. У рад...
Ка генеричком HTR моделу за српске средњовековне рукописе
This paper presents the process of training and evaluating a general-purpose HTR (Handwritten Text Recognition) model designed for the automatic transcription of Serbian medieval manuscripts written in various forms of Cyrillic script, utilizing the Transkribus software platform. The primary practical outcome of this research is the development of the first version of a generic HTR model for Serbian medieval manuscripts, named Miroslav 1.0, in honor of the Miroslav Gospel, the most repre...
This paper presents the process of training and evaluating a general-purpose HTR (Handwritten Text Recognition) model designed for the automatic transcription of Serbian medieval manuscripts written in various forms of Cyrillic script, utilizing the Transkribus software platform. The primary practical outcome of this research is the development of the first version of a generic HTR model for Serbian medieval manuscripts, named Miroslav 1.0, in honor of the Miroslav Gospel, the most repre...
Relevance-Theoretic Model for the Analysis of Multimodal Communication
The paper examines the interpretation procedure of multimodal messages from a relevance-theoretic perspective. The aim is to test the potential of the RT apparatus to various types of multimodal messages – advertisements, political posters and memes. The chosen modes of communication have the objective of providing genre diversity for the sample analysis conducted in this paper. Our analysis has the following specific goals: 1) analyzing the explicit content of the message (visual a...
The paper examines the interpretation procedure of multimodal messages from a relevance-theoretic perspective. The aim is to test the potential of the RT apparatus to various types of multimodal messages – advertisements, political posters and memes. The chosen modes of communication have the objective of providing genre diversity for the sample analysis conducted in this paper. Our analysis has the following specific goals: 1) analyzing the explicit content of the message (visual a...
Искуство изгнанства и мотив куге у песми „Једном, сањала сам кугу” Ане Ристовић
The second collection of poems by Ana Ristović, entitled Sand rope (1997), discreetly connects the cultural phenomenon of exile with the motif of the plague, thus introducing the reader to the space of an unusual quarantine to which all those to whom this world is given in different forms, in every sense, are condemned. The work focuses on the poem „Once, I dreamed of the plague”, which opens the collection with its oneirism. The collection’s basic inspiration, related to the distant expans...
The second collection of poems by Ana Ristović, entitled Sand rope (1997), discreetly connects the cultural phenomenon of exile with the motif of the plague, thus introducing the reader to the space of an unusual quarantine to which all those to whom this world is given in different forms, in every sense, are condemned. The work focuses on the poem „Once, I dreamed of the plague”, which opens the collection with its oneirism. The collection’s basic inspiration, related to the distant expans...
Influence of lactation period and ketosis on blood ammonia in cows
Ammonia is a central component in ruminant nitrogen metabolism and serves as a sensitive indicator of the dynamic balance between nitrogen intake, rumen microbial activity, and hepatic detoxification efficiency. Once mproduced in the rumen, ammonia is absorbed into the bloodstream and must be rapidly cleared by the liver via the urea cycle. As such, blood ammonia concentration reflects both the rate of ammonia production and the liver’s detoxification capacity, making it a valuable marker for...
Ammonia is a central component in ruminant nitrogen metabolism and serves as a sensitive indicator of the dynamic balance between nitrogen intake, rumen microbial activity, and hepatic detoxification efficiency. Once mproduced in the rumen, ammonia is absorbed into the bloodstream and must be rapidly cleared by the liver via the urea cycle. As such, blood ammonia concentration reflects both the rate of ammonia production and the liver’s detoxification capacity, making it a valuable marker for...
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