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Topic: Invariant (mathematics)

In the News (Fri 18 Apr 14)

  Invariant (mathematics) - Wikipedia, the free encyclopedia
The property of being an invariant is invariance.
One simple example of invariance is that the distance between two points on a number line is not changed by adding the same quantity to both numbers.
The variance of a probability distribution is invariant under translations of the real line; hence the variance of a random variable is unchanged by the addition of a constant to it.
en.wikipedia.org /wiki/Invariant_(mathematics)   (265 words)

 Invariant | World of Mathematics
Thus, magnitude is an invariant property of vectors under the operation of rotation, while both magnitude and direction are invariant properties of a vector under a translation of axes.
An important objective in any branch of mathematics is to identify the invariants of a given operation, as they often lead to a deeper understanding of the mathematics involved, or to simplified analytical procedures.
Still another invariant of the general equation of the conic sections, under a rotation of axes, is the sum of the coefficients of the squared terms (a+c).
www.bookrags.com /sciences/mathematics/invariant-wom.html   (616 words)

 The Mathematics of Face Recognition
To begin with, a recognition system has to be invariant both to external changes, like environmental light, and the person's position and distance from the camera, and internal deformations, like facial expression, aging, and makeup.
It is clear that we are not working under simple invariant theory, such as Lie group invariants, and that different tools are needed.
There are fundamental mathematical results in the literature that try to address these questions and have not yet been fully exploited for face recognition.
www.siam.org /siamnews/04-03/face.htm   (1302 words)

 Publications by Joseph Rosenblatt
Invariant Means and Invariant Ideals in L_infty(G) for a Locally Compact Group G, J.
Invariant Means for the Bounded Measurable Functions in a Non-discrete Locally Compact Group, Mathematische Annalen 220 (1976) 219-228.
Invariant Means on the Continuous Bounded Functions, Transactions AMS 236 (1978) 315-324.
www.math.uiuc.edu /~jrsnbltt/pubs.html   (1443 words)

 Department of Mathematics
The study of Mathematics is essential for all of the sciences, for Computer Science, for Economics, and for the social sciences.
The Mathematics Award is presented to a graduating senior and a junior for excellence in Mathematics and service to the Department.
The Sidney Goldwater Roth Prize in Mathematics is presented to the graduating senior who in the estimation of the Department shows the greatest Mathematical promise and who has been of greatest service to the Department and fellow students.
www.nyu.edu /cas/dept/math.htm   (578 words)

 Canisius College - Per Enflo
Historically, the use of Mathematics was important for progress in areas like Physics and Astronomy, and these areas [and the analytic problems they generated] were important for the development of Mathematics.
His work on the invariant subspace problem was accomplished during the years 1970—1975, so one can see that the late 1960s to the mid 1970s was a period of remarkable brilliance for Enflo.
For example, determining classes of operators that must have invariant subspaces (in the spirit of Lomonosov’s result) is an active area, and, equally, some of the mathematics developed in his solution to the invariant subspace problem have led him to progress in other areas of operator theory.
www.canisius.edu /topos/enflo.asp   (1170 words)

 Jeff Johannes
For a reference on the content of elementary school mathematics, here is the NCTM Principles and Standards for School Mathematics.
Calculus is the culmination of high school mathematics and the entryway to higher level college mathematics.
As the mathematics of change, calculus is widely applicable in all fields of study that have quantifiable change.
www.geneseo.edu /~johannes   (943 words)

 Red Raider Symposium Homepage   (Site not responding. Last check: 2007-08-19)
Classical invariant theory was motivated by the basic problems of equivalence and symmetry of polynomials (forms) under the projective group.
Invariant Theory is a branch of algebra that is more than 150 years old.
We are soliciting applications from senior undergraduate, graduate, post-doctoral students and early-career researchers in Mathematics to participate in the symposium.
www.math.ttu.edu /~mneusel/red04.html   (1473 words)

 Invariant theory - Wikipedia, the free encyclopedia
In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations.
This was a major field of study in the latter part of the nineteenth century, when it appeared that progress in this particular field (out of any number of possible mathematical formulations of invariance with respect to symmetry) was the key algorithmic discipline.
The modern formulation of geometric invariant theory is due to David Mumford, and emphasizes the construction of a quotient by the group action that should capture invariant information through its coordinate ring.
en.wikipedia.org /wiki/Invariant_theory   (566 words)

 Ars Mathematica » Blog Archive » Invariant Subspace Problem
I was recently reminded of the invariant subspace problem in Hilbert spaces: the question of whether every bounded operator on a Hilbert space has a closed invariant subspace.
Of famous open problems in mathematics, this one is perhaps the most surprising.
This entry was posted on Saturday, July 22nd, 2006 at 9:02 pm and is filed under Mathematics.
www.arsmathematica.net /archives/2006/07/22/invariant-subspace-problem   (205 words)

 Springer Online Reference Works
Integration of functions on a topological group that has a certain invariant property with respect to the group operations.
is called (two-sided) invariant if it is both left- and right-invariant.
Invariant average) is closely related to that of invariant integration.
eom.springer.de /i/i052240.htm   (262 words)

 Cut The Knot! December 1997
To resolve the enigma, suffice it to note that the parity of the number of circles remains invariant under legitimate moves.
In mathematics, all the cards can be put on the table: Nothing has to be taken on faith or on the say-so of some authority figure.
He holds M.S. degree in Mathematics from the Moscow State University and Ph.D. in Applied Mathematics from the Hebrew University of Jerusalem.
www.maa.org /editorial/knot/invariant.html   (774 words)

The Invariant Society was founded in 1936 to 'promote interest in all branches of Mathematics'.
We also organize a few social events, which everybody with an interest in Mathematics is invited to attend, details to be found on the termcard; we also publish a magazine, the 'Invariant'.
All speaker meetings take place at the Mathematical Institute (on the corner of St. Giles' and Keble Road) unless another venue is given in the termcard, and begin at 8.15 p.m.
users.ox.ac.uk /~invar   (208 words)

Maxwell's equations are invariant under the conformal group but there aren't too many other equations that are.
In any event, a quantum field theory that is invariant under all diffeomorphisms of spacetime is called by physicists a "topological quantum field theory," or TQFT.
Chern-Simons theory is the source of the best-understood states of quantum gravity in the loop representation.
math.ucr.edu /home/baez/symmetries.html   (2452 words)

 Welcome to Mathematics at Los Angeles Mission College
To best accommodate the needs of both our full-time and evening students, courses are scheduled throughout the day form 8:00 a.m.
By relating five of the most basic quantities in mathematics this formula becomes one of its most beautiful.
Pi, the ratio of the circumference of a circle to its diameter, is invariant throughout the universe.
www.lamission.edu /math   (215 words)

 Springer Online Reference Works
» Encyclopaedia of Mathematics » H » Haar measure
is called unimodular; in this case a left-invariant Haar measure is also right-invariant and is called (two-sided) invariant.
In particular, every compact or discrete or Abelian locally compact group, and also every connected semi-simple or nilpotent Lie group, is unimodular.
eom.springer.de /H/h046060.htm   (345 words)

 Andrew Leahy
In calculus, I have been looking at mathematicians who were working immediately prior to the time of Leibnitz and Newton -- the two individuals usually credited with the discovery of calculus -- and studying their techniques for finding tangents and rectifying curves.
In algebra, I have been studying the history of 19th century invariant theory.
Invariant theory all but disappeared at the beginning of the 20th century, but was crucial in the development of commutative ring theory and representation history -- two very important branches of modern algebra.
www.knox.edu /aleahy.xml   (259 words)

 Contemporary Mathematics - Meyn, Tweedie, decomposition (ResearchIndex)
Abstract: We establish a group-invariant version of the variational bicomplex that is based on a general moving frame construction.
The main application is an explicit group-invariant formula for the Euler-Lagrange equations of an invariant variational problem.
6 Invariant Euler-Lagrange equations and the invariant variati..
citeseer.ist.psu.edu /meyn93contemporary.html   (528 words)

 Epsilon = Invariant Proportion - Science Forums
This model is too simple to be not immediately understood, it can make hard time only to persons that their abstraction abilities are limited to the agreed formal linear way of written notations.
An inherent and invariant NEXT state prevents the use of a universal quantification, it is simple, and it is right in front of your mind, don't you see it?
Actually, a collection of infinitely many elements cannot exist without the permanent existence of this Epsilon, and this is an amazing thing, because it gives us the deep insight that the existence of infinitely many elements actually depends on the existence of a single element as its inherent permanent NEXT state.
www.scienceforums.net /forums/showthread.php?t=7993   (2777 words)

 Applied Mathematics Colloquium
In this talk I shall illustrate, by means of two examples, an on-going program at Utah State University to create Maple software and Java applets for implementing the solution to various classification problems in mathematics.
The first classification problem to be discussed is Petrov’s remarkable classification of all 4 dimensional local group actions which admit an Lorentz invariant metric.
Petrov’s classification contains over 100 distinct local group actions and associated invariant metrics and thus it is a non-trivial task to identify a given local group action or a given invariant metric in Petrov’s list.
www.apmaths.uwo.ca /upcomingevents/03_10_07.shtml   (272 words)

 CiteULike: Tag mathematics   (Site not responding. Last check: 2007-08-19)
Mathematics Success and Failure Among African-American Youth: The Roles of Sociohistorical Context, Community Forces, School Influence, and Individual...
Responses to “Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn
“Theoretical mathematics”: Toward a cultural synthesis of mathematics and theoretical physics
www.citeulike.org /tag/mathematics   (687 words)

 Amazon.com: Invariant Manifolds for Physical and Chemical Kinetics (Lecture Notes in Physics): Books: Alexander N. ...   (Site not responding. Last check: 2007-08-19)
Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.
Some of current research projectsConstructive Methods of Invariant Manifolds for Kinetic Problems (1989-present);Cluster structure of Genome (2000-present);Molecular Individualism: Theory, computational models, applications (2003-present).Iliya Karlin obtained the doctral degree in physics in 1992 for his thesis "Methods of invariant manifolds in physical kinetics".
His current research projects include constructive methods of invariant manifolds, theory of polymer dynamics and turbulence modeling.
www.amazon.com /Invariant-Manifolds-Physical-Chemical-Kinetics/dp/3540226842   (904 words)

 [No title]   (Site not responding. Last check: 2007-08-19)
In short, we are taught to arbitrarily uphold Lorentz invariance of the descriptive equations and Lorentz symmetry of the circuit, as if such were absolutely required by nature.
The adherence to Lorentz symmetry and to Lorentz invariant equations makes the mathematics and the systems simpler, and therefore much easier to solve, but it also produces and describes only COP< 1.0 electrical power systems taking their energy from the vacuum.
Yes, a small and determined group of physicists are pushing to try to break through the “Lorentz invariance barrier”, but they have a very hard row to hoe and they also take a real professional beating (or undergo a lack of advancement, etc.).
www.cheniere.org.cob-web.org:8888 /correspondence/120504.htm   (4064 words)

 Tribute to Invariance: Mathematics Education and Mathematical Games
After the secret is revealed, its verification still provides an entertaining and purposeful exercise in counting much removed from the customary rote.
Guided by a well-prepared teacher, students can conduct their own experiments, make their own discoveries, and uncover many of the basic principles without being told.
Quotations and an argument that combine to foster the idea that presently children are not given instruction in abstract when they need it most.
www.cut-the-knot.org /ctk/invariant.shtml   (711 words)

 invariant - OneLook Dictionary Search
Tip: Click on the first link on a line below to go directly to a page where "invariant" is defined.
Phrases that include invariant: lorentz invariant, algebraic invariant, fully invariant subgroup, invariant chain, invariant subgroup, more...
Words similar to invariant: changeless, constant, steady, unvarying, more...
www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=invariant   (222 words)

 Amazon.ca: An Extension of Casson's Invariant. (Am-126): Books: Kevin Walker   (Site not responding. Last check: 2007-08-19)
This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case.
The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l.
It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M. Customer Reviews
www.amazon.ca /Extension-Cassons-Invariant-Am-126/dp/0691025320   (245 words)

 Rich Stankewitz   Associate Professor of Mathematics
B.S. in Mathematics from the University of Michigan in 1991
Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign with thesis advisor Professor Aimo Hinkkanen in 1998
Assistant Professor of Mathematics at Penn State University at Erie from 2000-2002
www.bsu.edu /web/rstankewitz   (200 words)

 Mathematical Institutions in the UK
Mathematical Institutions in the UK Links to Mathematics Faculties, Departments, Institutes, Societies, Schools and Centres in the United Kingdom.
Bristol: See also Basic Research Institute in the Mathematical Sciences and University of the West of England
A list of mathematics departments in Ireland is available, covering both Eire and Northern Ireland.
users.ox.ac.uk /~invar/departments.html   (270 words)

 Amazon.com: Invariant theory (Mathematics lecture note series): Books: John Fogarty   (Site not responding. Last check: 2007-08-19)
This item is not eligible for Amazon Prime, but over a million other items are.
Invariant theory (Mathematics lecture note series) (Unknown Binding)
Keep connected to what's happening in the world of books by signing up for Amazon.com Books Delivers, our monthly subscription e-mail newsletters.
www.amazon.com /exec/obidos/ASIN/B0006DXEOA   (617 words)

 Amazon.com: Invariant Forms on Grassmann Manifolds (Annals of Mathematics Studies): Books: Wilhelm Stoll   (Site not responding. Last check: 2007-08-19)
Amazon.com: Invariant Forms on Grassmann Manifolds (Annals of Mathematics Studies): Books: Wilhelm Stoll
Invariant Forms on Grassmann Manifolds (Annals of Mathematics Studies) (Paperback)
Publish Mathematics Research Online — For only $60 all Mathematics papers, projects, presentations, theses, dissertations, art, etc. Can now be published at the Internet's original academic network.
www.amazon.com /Invariant-Grassmann-Manifolds-Mathematics-Studies/dp/0691081999   (751 words)

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