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Topic: Autonomous system mathematics

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	Springer Online Reference Works
		in the autonomous system (1) yields the system
		For a Hamiltonian system, a consequence of (3) is the conservation of the phase volume by the phase flow.
		For a linear autonomous system the structure of phase trajectories in a neighbourhood of an equilibrium point is known, since the autonomous system is integrable [5].
	eom.springer.de /a/a014190.htm (951 words)

	truth in mathematics
		Mathematical propositions are not true because they deal in eternal or idealized entities, but because their denial is logically impossible.
		Indeed, mathematics begins with a languageless activity of the mind which moves on from one thing to another but keeps a memory of the first as the empty form of a common substratum of all such moves.
		Mathematics arises out of its practice, and must ultimately be a free creation of the human mind, not an exercise in logic or a discovery of preexisting fundamentals.
	www.poetrymagic.co.uk /literary-theory/truth-in-mathematics.html (930 words)

	Omnipelagos.com ~ article "Autonomous system (mathematics)" (Site not responding. Last check: 2007-10-11)
		In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not depend on the independent variable.
		Many laws in physics, where the independent variable is usually assumed to be time, are expressed as autonomous systems because it is assumed the laws of nature which hold now are identical to those for any point in the past or future.
		It is distinguished from systems of differential equations of the form in which the law governing the rate of motion of a particle depends not only on the particle's location, but also on time; such systems are not autonomous.
	www.omnipelagos.com /entry?n=autonomous_system_(mathematics) (194 words)

	A PRIMARY SCHOOL CURRICULUM TO FOSTER THINKING ABOUT MATHEMATICS (Site not responding. Last check: 2007-10-11)
		On the other hand, some studies in the field of mathematics suggest that there are myths and prejudices about mathematics in primary schools and that the school system is partly responsible for this.
		With regard to the intrinsic interest and motivation to learn mathematics, Dewey states (l967) that as soon as studies in mathematics are dissociated from personal interest and their social utility, that is, when mathematics are presented as a mass of technical relationships and formulas, they become abstract and vain for students.
		It is a global and fundamental education, which encourages students to think critically and creatively about mathematics and which gives them the possibility to articulate the expression of their opinions and contentions concerning personal as well as social or moral problems.
	www.vusst.hr /ENCYCLOPAEDIA/mathematics.htm (5460 words)

	What are Fractal Systems? (Complex Adaptive Systems)
		A period of flux occurs in all the populations in the system until a new balance is established.
		The greater the variety within the system the stronger it is. In fact ambiguity and paradox abound in fractal systems which use contradictions to create new possibilities to co-evolve with their environment.
		The ways in which the agents in a system connect and interact to one another is critical to the survival of the system, because it is from these connections that the patterns are formed and the feedback disseminated.
	www.fractal.org /Bewustzijns-Besturings-Model/Fractal-Systems.htm (1585 words)

	TNE Standards - Mathematics
		By this we mean that prospective teachers should be able to recognize potential connections among ideas in mathematics, recognize the correctness (or incorrectness) of mathematical arguments, and be able to use mathematics successfully to solve a wide range of problems.
		They should also be committed and prepared to help their own pupils gain an understanding of mathematics, to apply their understanding to produce and recognize valid mathematical reasoning, and to solve problems both within and outside of mathematics.
		The precise explanation of a mathematical solution, regardless of the specific problem, starts with definitions and axioms, and builds from there to basic properties, which are then used to obtain desired results.
	www.msu.edu /~tne/math (522 words)

	Aristotle and Mathematics (Stanford Encyclopedia of Philosophy)
		It is not clear why Aristotle thinks one needs to learn mathematical axioms to learn anything, unless he means that one needs to learn them to learn anything in a mathematical subject or that axioms are so basic that they should form the first part of one ‘s learning.
		The objects studied by mathematical sciences are perceptible objects treated in a special way, as a perceived representation, whether as a diagram in the sand or an image in the imagination.
		The parts of a mathematical object which do not occur in the definition of the object, e.g., acute angle is not in the definition of right angle, but is a part of it and so is a non-perceptible material part of the angle (Metaphysics vii.10, 11).
	plato.stanford.edu /entries/aristotle-mathematics (9445 words)

	Is Society a Self-Organizing System?
		Notions of systems which organize the social process autonomously have been around in social theory, particularly on the marxist side, but these theories were suspect because of their lack of analytical rigor, and consequently of sophistication in empirical design.
		The crucial point is that the system is healthy as long as it communicates what it is supposed to communicate, as long as the subsystems perform their operations at the right moments in time, and as long as each subsystem additionally self-controls its structural organization with reference to its operation.
		As we saw in the paradigm example, in a self-organizing system control flip-flops: the contributors to the genesis and the maintenance of the system are no longer able to control the system's substance, although this substance is logically a result of their interactions.
	users.fmg.uva.nl /lleydesdorff/jses93/index.htm (9026 words)

	The transition through resonance of a nonlinear non-autonomous system (Site not responding. Last check: 2007-10-11)
		An approximate nonlinear perturbation analysis for the re-entry roll resonance model is given.
		The results are used to identify the dynamic process involved, as characterised by terms in the model equations, and to suggest a prudent management rule for this and similar transiently-resonant systems.
		Department of Mathematics, The University of Western Australia, Nedlands, W.A., 6009.
	anziamj.austms.org.au /V34/part1/Chapman.html (90 words)

	NationMaster - Encyclopedia: Main Page
		The immune system is a set of mechanisms that protect an organism from infection by identifying and killing pathogens.
		The immune systems of vertebrates such as humans consist of many types of proteins, cells, organs, and tissues, which interact in an elaborate and dynamic network.
		The immune system is the collection of organs and tissues involved in the adaptive defense of a body against foreign biological material.
	www.nationmaster.com /encyclopedia (3526 words)

	Topology history
		The next step in freeing mathematics from being a subject about measurement was also due to Euler.
		This was a topic which arose from mathematical physics and astronomy, brought about because the methods of classical analysis were somewhat inadequate in tackling certain types of problems.
		Jacob Bernoulli and Johann Bernoulli invented the calculus of variations where the value of an integral is thought of as a function of the functions being integrated.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Topology_in_mathematics.html (1456 words)

	Paul Ernest Paper
		The teacher's conception of the nature of mathematics, is his or her belief system concerning the nature of mathematics as a whole.
		Mathematics is a process of enquiry and coming to know, not a finished product, for its results remain open to revision.
		The model of teaching mathematics is the teacher's conception of the type and range of teaching roles, actions and classroom activities associated with the teaching of mathematics.
	www.people.ex.ac.uk /PErnest/impact.htm (1805 words)

	SATBOT I: Prototype of a Biomorphic Autonomous Spacecraft
		The human nervous system is an analog system which consists of approximately ten trillion neurons,[3] each having the ability to receive, process, and transmit electrochemical signals over complex pathways.
		The efficiency and power vs. frequency were discussed since the the system can operate in different states as an emergent function of the network and as shown the energy dissipated at these higher frequencies decreases.
		The noise immunity of the system is due to the fundamental structure of the neuron, a hysteresis differentiator.
	pw1.netcom.com /~mthorn/satbot00.htm (1018 words)

	Introduction and Motivation
		Therefore, the use of system of differential equations is very useful.
		A solution to this system is the couple of functions (x(t),y(t)) which satisfy both differential equations of the system.
		An equilibrium solution (or critical solution) of an autonomous system is the trajectory of a moving-object with no motion, that is the object is not moving.
	www.sosmath.com /diffeq/system/introduction/intro.html (645 words)

	Mathematics Course Descriptions
		Topics surveyed may include aspects of algebra and geometry, the mathematics of finance, probability and statistics, exponential growth, and other topics chosen from traditional and contemporary mathematics which do not employ the calculus.
		The course may be taken to meet the mathematical proficiency requirement, but may not be used as a prerequisite for other mathematics courses.
		A study of the logic of mathematics by the axiomatic method, with a development of the propositional calculus and restricted predicate calculus emphasizing its application to the foundations of mathematics.
	www.umsl.edu /bulletin/98_99/body_mathematics_course_description.html (3462 words)

	Autonomous Agents and Multi-Agent Systems - Artificial Intelligence (incl. R...Journals, Books & Online Media \| Springer
		The emergence of autonomous agents and multi-agent technology is one of the most exciting and important events to occur in computer science during the 1990s.
		While a range of submissions are welcome, from purely theoretical to application-oriented, all submissions should indicate both the consequences of their results for the development of agent systems and the significance of their results for other researchers and practitioners within the field.
		Macro-level aspects of multi-agent systems, including cooperation, coordination, conflict detection and resolution, negotiation, organizational structuring and design for multi-agent systems, computational market systems, self-organization, emergent functionality and swarm intelligence, multi-agent learning, languages for cooperation and coordination, agent communication languages, and issues of overall performance of multi-agent systems.
	springer.com /10458 (542 words)

	Qualitative Analysis
		Very often it is almost impossible to find explicitly of implicitly the solutions of a system (specially nonlinear ones).
		Draw the nullclines for the autonomous system and the velocity vectors along them.
		For most of the nonlinear autonomous systems, it is impossible to find explicitly the solutions.
	www.sosmath.com /diffeq/system/qualitative/qualitative.html (880 words)

	GLOBAL ATTRACTORS OF NON-AUTONOMOUS DISSIPATIVE DYNAMICAL SYSTEMS
		The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations.
		This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor.
		Intended for experts in qualitative theory of differential equations, dynamical systems and their applications, this accessible book can also serve as an important resource for senior students and lecturers.
	www.worldscibooks.com /mathematics/5643.html (258 words)

	MIT OpenCourseWare \| Mathematics \| 18.03 Differential Equations, Spring 2006 \| Syllabus
		Utilize Delta functions to model abrupt phenomena, compute the unit impulse response, and express the system response to a general signal by means of the convolution integral.
		Recreate the phase portrait of a two-dimensional linear autonomous system from trace and determinant.
		Determine the qualitative behavior of an autonomous nonlinear two-dimensional system by means of an analysis of behavior near critical points.
	ocw.mit.edu /OcwWeb/Mathematics/18-03Spring-2006/Syllabus/index.htm (966 words)

	The Novamente software system is an ambitious attempt to achieve the holy grail of AI research: true autonomous, ...
		The Novamente software system is an ambitious attempt to achieve the holy grail of AI research: true autonomous, creative computational intelligence, via the integration of multiple interacting cognitive processes.
		Among the many aspects of the psynet model of mind -- the conceptual foundation of the Novamente system – there is a theory of the relation between learning and mind that contrasts with the most common perspectives expressed in the AI literature.
		In Phase 2, the conscious theater of the global-brain-mediating AGI system is composed of ideas built by numerous individual humans – or ideas emergent from ideas built by numerous individual humans – and it conceives ideas that guide the actions and thoughts of individual humans, in a way that is motivated by its own goals.
	www.goertzel.org /dynapsyc/2003/mindplex.htm (6403 words)

	34: Ordinary differential equations
		Using the asymptotics on an ODE to determine the asymptotic behaviour of its solutions.
		System of DEs which model highly oscillatory motion on a sphere.
		Rolling balls: a nearly-linear system of 3 first-order differential equations.
	www.math.niu.edu /~rusin/known-math/index/34-XX.html (771 words)

	math lessons - Autonomous system (mathematics)
		In differential equations, an autonomous system is an equation of the form
		It is distinguished from systems of differential equations of the form
		algebra arithmetic calculus equations geometry differential equations trigonometry number theory probability theory applied mathematics mathematical games mathematicians
	www.mathdaily.com /lessons/Autonomous_system_(mathematics) (90 words)

	SAND - Society for Autonomous NeuroDynamics
		You have reached the Society for Autonomous NeuroDynamics, a multi-disciplinary group interested in the origins of emergent dynamics in neural networks and the relation between autonomous neurodynamics, autonomous behaviour and epilepsy.
		Emerging techniques in complexity sciences and neural modelling provide the tools to explore dynamics in such systems but have yet to explain how daily computational tasks are accomplished in a continuous and autonomous fashion.
		The issue of increasing freedom in systems is at the foundations of cognitive and social sciences.
	www.utoronto.ca /sand (371 words)

	Topology enters mathematics (Site not responding. Last check: 2007-10-11)
		The collection of methods developed by Poincaré was built into a complete topological theory by Brouwer in 1912.
		E Scholtz Topology : Geometric, algebraic, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 927-938.
		J W Dauben, Topology : Invariance of dimension, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 939-949.
	www.math.columbia.edu /~psorin/u_topology/history/Topology_in_mathematics.html (1580 words)

	ScienceDaily: Autonomous Rendezvous Spacecraft Arrives At Vandenberg
		Science Daily — July 14, 2004 -- The Demonstration for Autonomous Rendezvous Technology (DART) flight demonstrator, a spacecraft developed to prove technologies to locate and maneuver near an orbiting satellite, today arrived at Vandenberg Air Force Base, Calif., in preparation for a fall 2004 launch.
		The DART project is funded by NASA's Office of Exploration Systems and managed by the Marshall Space Flight Center.
		A new computer-based system gives physical therapists real-time, objective measures of the motion of each joint in the patient's body.
	www.sciencedaily.com /releases/2004/07/040715081725.htm (814 words)

	Web Dictionary of Cybernetics and Systems
		The original texts were compiled and converted to hypertext by Francis Heylighen, helped by An Vranckx.
		This dictionary is provided as part of Cybernetics and Systems Theory in the Principia CyberneticaWeb, which contains additional definitions of some concepts not found here.
		More general dictionaries, including a Non-linearity and Complexity Glossary, an extensive Dictionary of Computing terms, Mathematical Programming Glossary and Dictionary of Cell Biology, are available elsewhere on the Web.
	pespmc1.vub.ac.be /ASC/indexASC.html (174 words)

	Lucky Net - Internet Service Provider, Ukraine
		- You can register your autonomous system if you are connected to at least two different providers (ASes) and you need to switch between them from time to time.
		That is, AS is granted to multihomed organisations which need to define their own routing policy.
		Even the fact that you are connected to two providers doesn't guarantee that you will get your own AS (like in mathematics: mandatory, but insufficient condition).
	www.lucky.net /eng/noc/index.shtml (803 words)

	Institute for System Programing
		The mathematical models of neuron and neural network in autonomous adaptive control methodology
		The use of an autonomous adaptive control conception in the angular movement system of the automatic space device Spectr-RG
		Parallel programming of systems with distributed memory in Java environment.
	www.ispras.ru /publications/publications.html (2055 words)

	Rediscover Ancient Egypt - Electronic Articles about Ancient Egypt - its civilization, metaphysics, religion, pyramids, ...
		Egypt as a colony of eastern caliphates; as an autonomous state - Resisting the Arab Rule - The Fatimid Locusts Destroy Egypt - Ayyubids - Mamluks - Ottomans - Arab Republic of Egypt.
		In order to understand the episode of Hatshepsut and Twthomosis III, we must start with his father, Twthomosis II.
		General - International Reputations - Medical Profession (The Physicians - The Conduct and Practice) - The Medical Library (Edwin Smith Papyrus - Ebers Medical Papyrus - Berlin Papyrus - The Hearst Papyrus) - Cures and Prescriptions - Dentistry.
	www.egypt-tehuti.org /articles/electronic-articles.html (1146 words)

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