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A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
In this paper, we introduce a natural classification of bar and joint frameworks that possess symmetry. This classification establishes the mathematical foundation for extending a variety of results in rigidity, as well as infinitesimal or…
Dynamic manipulation, such as robot tossing or throwing objects, has recently gained attention as a novel paradigm to speed up logistic operations. However, the focus has predominantly been on the object's landing location, irrespective of…
In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
We prove a Kotake-Narasimhan type theorem in general ultradifferentiable classes given by weight matrices. In doing so we simultaneously recover and partially generalize the known results for classes given by weight sequences and weight…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However,…
In this report it is approched the Contest dynamics as mathematical theory, therefore applicable to all contest sports. Starting with the physical definition of Athlete and Couple of Athlete systems and after singling out the interaction…
We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric…
Due to the non-commutative nature of quaternions we introduce the concept of left and right action for quaternionic numbers. This gives the opportunity to manipulate appropriately the $H$-field. The standard problems arising in the…
It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding…
We give a $C^1$-perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain recurrence class of a periodic point. The technique is first…
We introduce discrete and p-adic continuous versions of the FitzHugh-Nagumo system on the one-dimensional p-adic unit ball. We provide criteria for the existence of Turing patterns. We present extensive simulations of some of these systems.…
The article describes basic principles of the theory which unites thermodynamics of reversible and irreversible processes also extends them methods on processes of transfer and transformation of any forms of energy
In this paper we strengthen the relationship between Yoneda structures and KZ doctrines by showing that for any locally fully faithful KZ doctrine, with the notion of admissibility as defined by Bunge and Funk, all of the Yoneda structure…
To represent motions from a mechanical point of view, this paper explores motion embedding using the motion taxonomy. With this taxonomy, manipulations can be described and represented as binary strings called motion codes. Motion codes…
We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability…
Despite its apparent simplicity, Newtonian Mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtleties concern fundamental issues such as, e.g., the number of independent laws needed…
The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.