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Topic: Atom (measure theory)

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	Atom (disambiguation) - Wikipedia, the free encyclopedia
		Atom refers to smallest possible particle of ordinary matter.
		The narrator of The History and Adventures of an Atom, a satire by Tobias Smollett
		Atomic number, the number of protons found in the nucleus of an atom
	en.wikipedia.org /wiki/Atom_(disambiguation) (229 words)

	Measure Theory. (Site not responding. Last check: 2007-10-20)
		When it is meaningful to say, of the values taken by the measure, that they lie between 0 and 1, with the measure of the entire space being 1: then we refer to the measure as a probability measure.
		The common case of this has the measure taking values in the real interval [0, 1]; however, entirely similar structure is to be found if one has a measure taking values in some commuting sub-algebra of the hermitean projectors of some Hilbert space.
		If a meaningful tensor product can be operated between the domain in which the measure takes value and the domains in which the functions to be integrated take their values, then one may use the measure to integrate functions.
	www.bgnett.no /~eddy/math/measure.html (258 words)

	Quantum field theory - Wikipedia, the free encyclopedia
		Relativistic quantum field theories are indispensable in particle physics (see the standard model), although they are known to arise as effective field theories in condensed matter physics.
		A gauge theory is a theory which admits a symmetry with a local parameter.
		For example, in every quantum theory the global phase of the wave function is arbitrary and does not represent something physical, so the theory is invariant under a global change of phases (adding a constant to the phase of all wave functions, everywhere); this is a global symmetry.
	en.wikipedia.org /wiki/Quantum_field_theory (4227 words)

	Search Results for measure*
		A measure of her research activity during this period is that from 1918 to 1932 Wrinch published twenty papers on pure and applied mathematics, and sixteen papers on scientific methodology and the philosophy of science.
		Ancient measurement of length was based on the human body, for example the length of a foot, the length of a stride, the span of a hand, and the breadth of a thumb.
		Measurements of the ruins of the buildings which have been excavated show that these units of length were accurately used by the Harappans in their construction.
	www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=measure*&CONTEXT=1 (15820 words)

	[No title]
		atom +------------------------------------------------------------ An atom is a measurable set Y of positive measure in a measure space such that every subset Z of Y has either zero or the same measure.
		Denote by L,L^+ the set of measureable maps from a measure space (X,A,mu) to the real line (R,B), where B is the Borel sigma-algebra on R,R^+.
		measure space +------------------------------------------------------------ sigma-additive: a real-valued function on a set A of subsets of X is called sigma-additive if for all disjoint Y_n in A, one has mu(bigcup_n Y_n) = sum_n mu(Y_n).
	www.math.harvard.edu /~knill/sofia/data/measuretheory.txt (702 words)

	[No title]
		For the author the term "harmonic analysis" means those parts of analysis in which the action of a locally compact group plays an essential role: more specifically, the theory of unitary representations of locally compact groups, and the analysis of functions on such groups and their homogeneous spaces.
		Chapter III is devoted to the central components of representation theory, such as the theory of characters and of class functions, and Fourier analysis.
		Nevertheless it can be done, as we are witnessing here with a new book on applications of group theory in physics where modern mathematics is nicely intertwined with physics, from classical crystallography to fullerenes and from symmetry properties of atoms and molecules to quarks.
	www.math.niu.edu /~rusin/known-math/99/haar (3713 words)

	Interpretations of Probability
		The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought.
		The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.
		A long-run propensity theory is one in which propensities are associated with repeatable conditions, and are regarded as propensities to produce in a long series of repetitions of these conditions frequencies which are approximately equal to the probabilities.
	plato.stanford.edu /entries/probability-interpret (15163 words)

	Science Timeline (Site not responding. Last check: 2007-10-20)
		Consequently, when the Pythagoreans developed the theory of geometric magnitudes, by which they were able to compare two surfaces' ratio, they were led, for lack of a system which could handle irrational numbers, to the 'incommensurability problem': Applying the side of a square to the diagonal, no common rational measure is discoverable.
		He also produced two major concepts in the history of ideas concerning the brain--that thought was situated there and, anticipating the nervous system, that psychic atoms constituted the material basis of its communication with the rest of the body and the world outside.
		Assuming the earth is a sphere, the measured angle between the sites is seven degrees and the circumference is about 50 times 800 km., or about 40,000 km.
	www.sciencetimeline.net /prehistory.htm (6591 words)

	The Continuum Economy
		Aumann's choice of technique, measure theory, went beyond the mathematical toolbox of the average economist of the time.
		During this time, core theory, perhaps more than any other area of economics, was the preferred habitat of mathematically-inclined economists and a specimen upon which sparkling new mathematical tools could be applied.
		A different measure must be used, which nonetheless captures the idea that relatively "big" coalitions have larger measures than relatively "small" coalitions.
	homepage.newschool.edu /het/essays/edgew/continuum.htm (5388 words)

	The Mathematics of Boolean Algebra
		The study of Boolean algebras has several aspects: structure theory, model theory of Boolean algebras, decidability and undecidability questions for the class of Boolean algebras, and the indicated applications.
		These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent.
		Much of the deeper theory of Boolean algebras, telling about their structure and classification, can be formulated in terms of certain functions defined for all Boolean algebras, with infinite cardinals as values.
	plato.stanford.edu /entries/boolalg-math (2064 words)

	Read This: Ergodic Theory of Numbers
		Ergodic theory requires an understanding of measure theory, so the authors jump from decimal expansions to the measure theory apparatus.
		A heuristic introduction to Lebesgue measure is followed by a more careful treatment of various standard analysis topics (generating sigma- and semi-algebras, complete measure spaces, measurable functions).
		A prime example is the presentation of measure theory topics following a gentle introduction to decimal expansions in chapter 1.
	www.maa.org /reviews/ergodicnt.html (3054 words)

	Heroes of Cyberspace: Claude Shannon
		The immediate benefit of information theory is that it gives engineers the math tools needed to figure out channel capacity--how much information can go from A to B without errors.
		Usually entropy is measured in "bits per symbol" or a similar relation--if you are using a set of symbols to transmit your message, the entropy is how many bits it will take to represent one symbol.
		Other researchers are using the tools of information theory to measure the capacity of nerve tissue.
	www.skypoint.com /~gimonca/shannon.html (2291 words)

	By my desk (Site not responding. Last check: 2007-10-20)
		If you could stop every atom in its position and direction and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future.
		Last time I studied Measure theory, it was to develop a theory on integration with no mention of how it adds up to Probability theory.
		Apparently they have also writtem a book on probability and measure theory which is a standard text in quant programs.
	nitishranjan.blogspot.com (1504 words)

	Electron Physics Group Publication List (Site not responding. Last check: 2007-10-20)
		Trapping and Moving Atoms on Surfaces, R. Celotta and J. Stroscio, in Advances in Atomic, Molecular, and Optical Physics, edited by H. Stroke, New York:Elsevier, 2005 pp.
		Artifacts in Ballistic Magnetoresistance Measurements, W.F. Egelhoff, Jr., L.
		Magneto-Optical Trapping of Chromium Atoms, C.C. Bradley, J.J. McClelland, W.R. Anderson, and R.J. Celotta, Phys.
	www.physics.nist.gov /Divisions/Div841/Gp3/Pubs/pub.html (1855 words)

	"Maxwell, Molecules, and Evolution" by Charles Petzold
		No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction.
		Herschel discusses the discovery that atoms of a particular type are always exactly the same, and asserts that these discoveries “effectually destroy the idea of an eternal self-existent matter” such as is implicit in the atomism of Epicurus and Lucretius.
		He strongly opposed the theory of evolution, and was easily able to develop a rigorous mathematical refutation of the famous “nebular hypothesis” of the French atheist LaPlace.
	www.charlespetzold.com /etc/MaxwellMoleculesAndEvolution.html (10391 words)

	atom - OneLook Dictionary Search
		Atom-, Atom (nt), atom : AllWords.com Multi-Lingual Dictionary [home, info]
		Phrases that include atom: gram atom, bohr atom, rutherford atom, excited atom, atom like, more...
		Words similar to atom: mote, particle, speck, molecule, bit, iota, modicum, monad, scintilla, smidgen, whit, more...
	www.onelook.com /?w=atom (414 words)

	Nanotechnology Glossary N
		If the nanotube is calibrated (i.e., its spring constant known), it is possible to measure the mass of the attached particle." A nanobalance "could be useful for determining the mass of other objects on the femtogram to picogram size range." See Weighing The Very Small.
		Single atoms caged inside nanocrystals gives you a "quantum confined atom", or QCA, "with potential uses ranging from clear-glass sunglasses to bio-sensors to optical computing and just about anything optical in between." See Nanocrystals Technology Shines New Light on Optics, A Good Look at Nanocrystals, and Researchers Turn Scrap to Strength with Nanocrystals.
		The force required to press a sharp diamond indenter into a material is measured as a function of indentation depth.
	www.nanotech-now.com /nanotechnology-glossary-N.htm (3544 words)

	if:book
		I've become all but unable to think of the objects around me except in terms of Actor-Network theory, as sort of depositions or instantiations of a great deal of matter, energy and information moving through the world.
		And of course, a book is nothing but a snapshot in that regard; you have to do a lot of extra work if you want to prise out and examine the flows it is a part of, or even those it has set up.
		The book as the principal mode of discourse and cultural ideal of intellectual achievement may indeed be headed for gradual decline, but we believe the network has the potential to keep it in play far longer than the techno-determinists might think.
	www.futureofthebook.org /blog (10263 words)

	Table of contents for The quantum in chemistry
		The Role of Theory in the Physical Sciences 1.0 Introduction 1.1 What is the role of theory in science?
		Comparison of Bohr's model with experiment 2.7.3 Further development of Bohr's theory 2.8 de Broglie's proposal 2.9 The Schrödinger equation 2.9.1 Eigenfunctions and eigenvalues 2.10 Bibliography and further reading Boxes 2.1 and 2.2 Problems Chapter 3.
		The Covalent Chemical Bond 6.0 Introduction 6.1 The binding energy of the hydrogen molecule 6.2 The Hamiltonian operator for the hydrogen molecule 6.3 The Born-Oppenheimer approximation 6.4.
	www.loc.gov /catdir/toc/ecip0510/2005009405.html (345 words)

	Planet Swhack
		If the theory behind the diet is correct, however, this just isn't so.
		Drawing on the results of a number of studies with rats, his own experiments on himself, and the best research on nutrition and weight loss, he's developed a theory of how the body decides what it feels like eating.
		Although clearly rushed, the book has an appendix of scientific studies using rats to back up its arguments about theory and happily features the stories of people who tried the diet and found it didn't work along with those who tried the diet and found it did.
	planet.swhack.com (11435 words)

	Jason Santa Maria \| Design Archive
		When I was younger I used to help out my grandfather (who was a carpenter) on the job building houses.
		I had my own tool belt and hammer, as well as a tape measure and a pocket full of 10 penny nails.
		I spent years in school learning about design history, theory, promotional ideas and creative thinking to sit back and blindly throw darts at a wall.
	www.jasonsantamaria.com /archive/category/design (15890 words)

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