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Experimental Characterization of Steel and Concrete as Construction Materials: State-of-the-Art Methods and Advances Beyond Standardized Testing
Construction materials like steel and concrete have been used for thousands of years; however, their industrial-scale production began relatively recently in the 19th century. These materials are still being improved as the drive to build taller buildings, longer bridges, larger dams, and similar engineering marvels keeps pushing boundaries and re-quirements to previously unimaginable values. Yet, testing and characterization of con-struction materials that make all that progress possible are...
Construction materials like steel and concrete have been used for thousands of years; however, their industrial-scale production began relatively recently in the 19th century. These materials are still being improved as the drive to build taller buildings, longer bridges, larger dams, and similar engineering marvels keeps pushing boundaries and re-quirements to previously unimaginable values. Yet, testing and characterization of con-struction materials that make all that progress possible are...
RECURSION AS A BRIDGE BETWEEN MATHEMATICS AND COMPUTER SCIENCE
Recursion is a technique in which a function calls itself during the process of solving a problem, thereby reducing complex tasks to simpler, selfsimilar instances until a base case is reached. This approach to problem-solving plays a significant role in both mathematics and computer science, particularly in algorithmic modeling and the mathematical formalization of problems. The aim of this paper is to demonstrate how recursive models can be methodically adapted for teaching purposes, ...
Recursion is a technique in which a function calls itself during the process of solving a problem, thereby reducing complex tasks to simpler, selfsimilar instances until a base case is reached. This approach to problem-solving plays a significant role in both mathematics and computer science, particularly in algorithmic modeling and the mathematical formalization of problems. The aim of this paper is to demonstrate how recursive models can be methodically adapted for teaching purposes, ...
PROMOTION OF MATHEMATICS THROUGH THE INTEGRATION OF THE MATHEMATICAL KANGAROO COMPETITION, A STUDENT JOURNAL, A WEB PLATFORM, AND A YOUTUBE CHANNEL
This paper presents an innovative approach to the promotion of mathematics based on the integration of the Mathematical Kangaroo competition, the student magazine "Matematički list", an educational web platform, and a YouTube channel featuring video solutions to mathematical problems. The primary objective of this approach is to increase students' interest in learning mathematics, encourage autonomous study, and develop mathematical literacy by combining formal and informal educational ...
This paper presents an innovative approach to the promotion of mathematics based on the integration of the Mathematical Kangaroo competition, the student magazine "Matematički list", an educational web platform, and a YouTube channel featuring video solutions to mathematical problems. The primary objective of this approach is to increase students' interest in learning mathematics, encourage autonomous study, and develop mathematical literacy by combining formal and informal educational ...
INTEGRATING NOTEBOOKLM IN MATHEMATICS EDUCATION USING THE FLIPPED CLASSROOM APPROACH
The flipped classroom model integrates two complementary segments: computer-assisted independent instruction outside the school setting and collaborative learning within the classroom. This process can be examined through three distinct chronological stages: pre-class, in-class, and post-class activities. During the preparatory phase (prior to in-class instruction), students are provided with carefully designed or curated digital learning materials – such as video lectures, podcasts, or...
The flipped classroom model integrates two complementary segments: computer-assisted independent instruction outside the school setting and collaborative learning within the classroom. This process can be examined through three distinct chronological stages: pre-class, in-class, and post-class activities. During the preparatory phase (prior to in-class instruction), students are provided with carefully designed or curated digital learning materials – such as video lectures, podcasts, or...
BEYOND RIGHT AND WRONG: A WEB PLATFORM FOR LEARNING MATHEMATICS THROUGH THE ANALYSIS OF CORRECT AND INCORRECT PROBLEM SOLUTIONS
This paper presents the web platform Beyond Right and Wrong, developed with the aim of supporting mathematics teaching and learning through the analysis of offered problem solutions. The platform is based on an approach according to which students are not only required to recognize the correct solution, but also to identify, analyze, and evaluate errors in incorrect procedures, which corresponds to higher cognitive levels of learning in Bloom’s taxonomy. In this way, students develop cr...
This paper presents the web platform Beyond Right and Wrong, developed with the aim of supporting mathematics teaching and learning through the analysis of offered problem solutions. The platform is based on an approach according to which students are not only required to recognize the correct solution, but also to identify, analyze, and evaluate errors in incorrect procedures, which corresponds to higher cognitive levels of learning in Bloom’s taxonomy. In this way, students develop cr...
DYNAMIC VISUALIZATION OF MATHEMATICAL CONCEPTS USING THE MANIM TOOL
The development of educational technologies has opened up new possibilities for improving mathematics teaching, particularly in the visualization of abstract concepts and processes. This paper examines the use of Manim as a tool for creating mathematically precise animations that can play a significant didactic role in the teaching process. Special emphasis is placed on the possibility of dynamically presenting various types of content whose understanding often requires more than a stat...
The development of educational technologies has opened up new possibilities for improving mathematics teaching, particularly in the visualization of abstract concepts and processes. This paper examines the use of Manim as a tool for creating mathematically precise animations that can play a significant didactic role in the teaching process. Special emphasis is placed on the possibility of dynamically presenting various types of content whose understanding often requires more than a stat...
Shift-invariant subspaces of Sobolev type
This paper has the characteristics of a review paper in which results of shift-invariant subspaces of Sobolev type are summarized without proofs. The structure of shift-invariant spaces $V_s$, $s\in\mathbb{R}$, generated by at most countable family of generators, which are subspaces of Sobolev spaces $H^s(\mathbb{R}^n)$, are announced in \cite{aap} and Bessel sequences, frames and Riesz families of such spaces are characterized. With the Fourier multiplier $\left(1-\fracΔ{4π^2}\right)^{s/2}f=...
This paper has the characteristics of a review paper in which results of shift-invariant subspaces of Sobolev type are summarized without proofs. The structure of shift-invariant spaces $V_s$, $s\in\mathbb{R}$, generated by at most countable family of generators, which are subspaces of Sobolev spaces $H^s(\mathbb{R}^n)$, are announced in \cite{aap} and Bessel sequences, frames and Riesz families of such spaces are characterized. With the Fourier multiplier $\left(1-\fracΔ{4π^2}\right)^{s/2}f=...
Sensor fault estimation in Markov jump linear system: A Bayesian perspective
Existing fault estimation methods for Markov jump linear systems, particularly the interacting multiple model approaches, heavily rely on pre-defined fault model banks. This reliance renders them ineffective against faults with unknown or time-varying dynamics. Conversely, emerging Bayesian estimation approaches are typically confined to single-mode systems and fail to accommodate stochastic mode switching. To bridge this gap, this paper proposes a novel Bayesian framework for the real-time j...
Existing fault estimation methods for Markov jump linear systems, particularly the interacting multiple model approaches, heavily rely on pre-defined fault model banks. This reliance renders them ineffective against faults with unknown or time-varying dynamics. Conversely, emerging Bayesian estimation approaches are typically confined to single-mode systems and fail to accommodate stochastic mode switching. To bridge this gap, this paper proposes a novel Bayesian framework for the real-time j...
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...
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