Papers by Angeliki Stamati Ph. D.
Real world applications have the potential to bring learning mathematics to a new, exciting, even... more Real world applications have the potential to bring learning mathematics to a new, exciting, even authentic level for students. Based on the tenets of experiential learning theory students learn through meaningful and collaborative experiences with the dimensions, usage, regulations, and design of local parking lots. Initially conducted with a small group of students, the resulting enthusiasm from students and teachers, additional ideas and activities were created. The activities outlined here use arithmetic, algebra, geometry, trigonometry, and statistics into studies of architecture, engineering, and other areas that depend on mathematics at their core. The premise of these activities comes from a creative approach of teaching students, using an actual structure to understand how mathematics was used to design it and how mathematics can be applied to improve it. At each stage, the process goes from data to knowledge, to information, and finally to wisdom. Students from middle scho...
Journal of Education and Practice, 2017
Every object we think of or encounter, whether a natural or human-made, has a regular or irregula... more Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object’s geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is also an important part of daily life. However, geometry is challenging for some students, even high-achieving students. One way to help students understand geometry and its relevance in life is to engage students to discover them cognitively, then to research and identify them in real world examples and then to relate them to past, present, and future innovations that improved our way of thinking about ourselves and the world around us. This interdisciplinary activity uses the Developmental Awareness Approach of Teaching and Learning (DAATL) to help students discover principles, acquire knowledge, and learn mathematical concepts includin...
Asymptotic stability criteria of time-varying systems via averaging
Σκοπός της Διατριβής είναι η εδραίωση ικανών συνθηκών για ασυμπτωτική ευστάθεια χρονικώς μεταβαλλ... more Σκοπός της Διατριβής είναι η εδραίωση ικανών συνθηκών για ασυμπτωτική ευστάθεια χρονικώς μεταβαλλομένων συστημάτων, των οποίων τα δυναμικά είναι μη φραγμένα ως προς τον χρόνο. Μεταξύ άλλων, εδραιώνονται μέθοδοι averaging για ασυμπτωτική ευστάθεια, οι οποίες αποτελούν γενικεύσεις των αρκετά γνωστών μεθοδολογιών που έχουν υιοθετηθεί στην βιβλιογραφία, για συστήματα των οποίων τα δυναμικά είναι μη φραγμένα ως προς τον χρόνο. Τα πρώτα δύο κεφάλαια (Κεφάλαιο ΙΙ και ΙΙΙ) είναι αφιερωμένα στα χρονικά μεταβαλλόμενα συστήματα συνεχούς χρόνου. Στο Κεφάλαιο ΙΙ εδραιώνεται ένα νέο κριτήριο τύπου-Lyapunov για ασυμπτωτική ευστάθεια που αφορά χρονικά μεταβαλλόμενα συστήματα με διαταραχές καθώς επίσης μία γενίκευση της μεθόδου averaging για αργά χρονικά μεταβαλλόμενα συστήματα, των οποίων τα δυναμικά ως τώρα ήταν φραγμένα ως προς τον χρόνο. Στο Κεφάλαιο III, εδραιώνεται ένα νέο Θεώρημα Αντίστροφης Εκθετικής Ευστάθειας για συστήματα συνεχούς χρόνου των οποίων τα δυναμικά είναι εν γένει μη φραγμένα ω...
Averaging Criteria for Asymptotic Stability of Time-Varying Systems
IEEE Transactions on Automatic Control, 2014
ABSTRACT
Local Asymptotic Stability via Averaging for Time-Varying Systems With Unbounded Dynamics With Respect to Time
IEEE Transactions on Automatic Control, 2009
ABSTRACT
IEEE Transactions on Automatic Control, 2011
The purpose of this paper is to establish sufficient conditions for local asymptotic stability an... more The purpose of this paper is to establish sufficient conditions for local asymptotic stability and feedback stabilization for discrete-time systems with time depended dynamics. Our main results constitute generalizations of those developed by same authors in a recent paper, for the case of continuoustime systems. Notations: We adopt the following notations. For x ∈ R n , |x| denotes its usual Euclidean norm. Given a matrix A ∈ R n×m we denote by |A| := sup x =0 (|Ax| / |x|)its induced norm. By S[0,R] we denote the sphere of radius R > 0 around zero 0 ∈ R n. N denotes the set of all C 0 functions φ : R + → R + and K is the set of all functions φ ∈ N which are strictly increasing and vanishing at zero. K ∞ denotes the subset of K that constitutes by all φ ∈ K with φ (t) → ∞ as t → ∞.
Asymptotic stability criteria for time-varying systems via averaging
The purpose of this thesis is to provide sufficient conditions for asymptotic stability for time-... more The purpose of this thesis is to provide sufficient conditions for asymptotic stability for time-varying systems, whose dynamics are in general unbounded with respect to time. Among other things, averaging approaches are established for asymptotic stability that constitute generalizations of the well-known methodologies adopted in the literature for systems, whose dynamics are bounded with respect to time. The first two chapters (Chapter II and III) are devoted to continuous time-varying systems. In Chapter II, a new Lyapunov like criterion is established for asymptotic stability concerning time-varying systems with disturbances along with a generalization of the averaging approach for slow time-varying systems, which until now was used for bounded in time systems. In Chapter III, a new converse theorem is established concerning exponential stability for continuous time-varying systems whose dynamics are in general unbounded in time. This result is used to derive a new partial avera...
Κριτήρια ασυμπτωτικής ευστάθειας χρονικώς μεταβαλλομένων συστημάτων με χρήση μεθόδων προσέγγισης δυναμικών
From Theory to Life
Handbook of Research on K-12 Blended and Virtual Learning Through the i²Flex Classroom Model
Today, more than ever, academic institutions need to identify ways to inspire their students to a... more Today, more than ever, academic institutions need to identify ways to inspire their students to acquire mathematics skills and competencies which are essential for becoming critical thinkers, innovators, and decision makers. Therefore, there is a need for a new trajectory in the teaching and learning of mathematics in particular in the k-12 environment. The Mathematics Morfosis Educational Philosophy that has been successfully applied to ACS Athens transforming the teaching of high school mathematics is an authentic, unbounded, and exciting educational model for the instruction of mathematics that is preparing students for complex and ambiguous future needs.
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Papers by Angeliki Stamati Ph. D.