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Topic: Homogeneous (mathematics)

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In the News (Mon 22 Jul 19)

  Clay Mathematics Institute
The 2007 Clay Research Summer School on Homogeneous Flows, Moduli Spaces and Arithmetic was held June 11 - July 6 at the Centro di Ricerca Matematica more....
The Clay Mathematics Institute announced the appointment of four Research Fellows.
The Clay Mathematics Institute announced the recipients of the Clay Research Award for 2007.
www.claymath.org   (383 words)

Homogenization is intensive mixing of mutually insoluble phases (sometimes with addition of surfactants) to obtain a soluble suspension or emulsion, for example homogenizing milk so that the cream doesn't separate out.
In physical chemistry, homogeneous describes a single-phase system as opposed to a heterogeneous system.
In the context of procurement/purchasing, homogeneous is used to describe goods that do not vary in their essential characteristic irrespective of the source of supply.
www.brainyencyclopedia.com /encyclopedia/h/ho/homogeneous.html   (254 words)

 Institute of Mathematics and Computer Science University of Latvia - Department of Mathematics
A special class of exact solutions for the nonlinear wave equations has been constructed, and geometrical properties of these solutions are described (V.Gudkov).
In the field of mathematical modeling main efforts are devoted to elaboration of mathematical models, difference schemes and programs for describing electro-kinetic processes, flows of gas and liquid matter in non-homogeneous media with rapidly varying coefficients, and phase transitions.Transport kinetic models are based on nonlinear Fokker-Planck,diffusion-absortion, advection-diffusion, Schrodinger and master equations.
Nonlinear mathematical models and non-classical boundary value problem for ordinary differential equations.
www.lumii.lv /math.htm   (629 words)

 homogeneous - Search Results - MSN Encarta
For various specialized meanings, see: Homogeneous (mathematics), a variety of meanings; In statistics homogeneity can refer to
For other meanings, see homogeneous (mathematics) In mathematics, a homogeneous polynomial is a polynomial whose terms are monomials all having the same total degree ; or are elements of the same...
The differential equation is homogeneous if the function f (x, y) is homogeneous, that is-
encarta.msn.com /homogeneous.html   (207 words)

 Mathematics Awareness Month - April 2007
The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics announce that the theme for Mathematics Awareness Month 2007 is Mathematics and the Brain.
Mathematics plays a vital role in the research to understand the mechanisms and function of the human brain, from its smallest components to the brain itself:
Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area.
www.mathaware.org /mam/07/press-release.html   (298 words)

 Index page for Daniel W. VanArsdale
Explicit n-dimensional expressions for homogeneous matrix representations of familiar geometric transformations including projection, dilation, reflection, shear, strain, and rotation.
These are extracted from my article "Homogeneous Transformation Matrices for Computer Graphics," Computers and Graphics, Vol.
This is a companion article to "Homogeneous Transformation Matrices" and provides methods sufficient to derive all the matrices presented there.
www.silcom.com /~barnowl   (721 words)

 Elements of the Premise
Consequently, it must be strongly evidenced here that fundamental particles such as the electron possess a structure that can most logically be seen as deriving from the imponderable but omnipresent substratum, rather than from "nothingness", or the spatial vacuum, as thought earlier by physics.
Charles Bueker is well educated in fields of math useful to a mechanical engineer whose specialties lie in the area of satellite design.
Such Field consists of homogeneous motion whose dynamic energy remains in a single state of intensity.
www.metaparticles.com /page3-9.htm   (892 words)

  Mathematics Program at Bard College | Program Overview
Mathematics is at the core of human civilization and is the cornerstone of all modern science and technology.
For example, when each senior mathematics major engages in a year-long research program for her senior project, she is not required to work on whatever interests the professor— contrast to student research at many other colleges and universities.
At Bard all senior projects in mathematics are individually tailored to meet the interests of the students; indeed, the topics for senior projects are often suggested by the students themselves, with guidance from the faculty.
math.bard.edu /math/overview   (458 words)

 The Effects of Homogeneous Groupings in Mathematics. ERIC/CSMEE Digest.
The practice of homogeneous grouping, which is quite widespread in the United States, uses a model that typically groups students together on ability or achievement as the deciding variable.
The persistence of homogeneous grouping is particularly troubling given the long-term effects on female and minority students, both groups of whom are dramatically underrepresented in the mathematics and science areas.
Recent assessments in mathematics achievement suggest students in the United States are not generally strong in mathematics, with too few students, especially minority and female, studying higher level mathematics.
www.ericdigests.org /1993/groupings.htm   (2008 words)

 Homogeneity - Wikipedia, the free encyclopedia
Homogenetic or homoplastic, in biology, applied both to animals and plants, of having a resemblance in structure, due to descent from a common progenitor with subsequent modification [1]
Homogenization is intensive mixing of mutually insoluble phases (sometimes with addition of surfactants) to obtain a soluble suspension or emulsion, for example homogenizing milk so that the cream doesn't separate out.
In the context of procurement/purchasing, homogeneous is used to describe goods that do not vary in their essential characteristic irrespective of the source of supply.
en.wikipedia.org /wiki/Homogeneous   (204 words)

MATH112 is not open to Mathematics and Mathematics Education majors except by permission of the chairperson.
This seminar has featured such topics as the study of the history of mathematics, the impact and potential effects of computers upon society, and the study of mathematics as it occurs with society in the forms of puzzles, games, and other types of recreation.
Mathematical logic, set theory, relevant topological and algebraic properties together with proof techniques are heavily utilized throughout the course.
www.lhup.edu /academic/acad_affairs/MATHEMATICS.htm   (1870 words)

 ABRHS Program of Studies   (Site not responding. Last check: 2007-10-29)
The goal of the Mathematics Department is to teach mathematical structure, theory, concepts and skills to develop student self-confidence and positive attitudes towards mathematics.
Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.
Technology is an essential tool in a mathematics education and all students should gain facility in using it where advantageous.
ab.mec.edu /abrhs/POS/math.html   (2275 words)

 Math Department
The primary objective of the mathematics department is to have all students increase their problem solving skills and abstract reasoning ability in order to prepare them for a rapidly changing society.
There are two tracks: the pure mathematics must include 322, 324 and 411 and three electives above the 200 level; the computer emphasis track must include 272, 305, 361 and 362 and two electives above 200.
One independent study topic in the field of algebra, number theory, or geometry, to be done beginning the spring term of the junior year or fall term of the senior year and terminating with development of the honors project will be required.
www.erskine.edu /academics/math   (971 words)

 Sterling College Catalog: Mathematics
This course is designed to provide the opportunity to understand mathematics and mathematical processes for both prospective teachers as well as the general liberal arts students.
Students provide assistance to the college, a local church, school, or non-profit organization in mathematics related areas such as: installation and evaluation of mathematical software, tutoring or assisting the teaching of developmental mathematics for one semester, or tutoring GED candidates in mathematics.
A study of the mathematical basis of probability theory, including sample spaces, elementary theorems of probability, random variables, distributions, moments and their generating functions, conditional and marginal distributions, and the Central Limit Theorem.
www.sterling.edu /academics/catalog/current/majors/math.cfm   (995 words)

 Homogeneous Equations   (Site not responding. Last check: 2007-10-29)
You learn very early in your study of mathematics that, many times, the best way to solve a new problem is to reduce it, in some way, into the form of a problem that you already know how to solve.
If you recognize the fact that an equation is homogeneous you can, in some cases, perform a substitution which will allow you to use separation of variables to solve the equation.
The homogeneity of the function in the next example is not as easy to determine by inspection.
homepage.mac.com /nshoffner/nsh/ODE/Homog.htm   (1023 words)

 Behind the scenes
Its mathematical origin is the work of Gaspard Monge, a French geometer, who developed, around 1795, a method called descriptive geometry for representing spatial configurations by planar perspective drawings.
Many mathematical theories find their broadest, most elegant and most economic setting when they are formulated over the complex numbers.
It is an elegant and consistent mathematical approach to measurements that combines Projective Geometry and complex numbers.
www.unl.edu /tcweb/fowler/Documentation/Texts/Mathematics.html   (5045 words)

 Hiram Mathematics Courses
Contemporary mathematical thinking is used to seek connections between mathematics and modern society.
This course examines the historical development of major mathematical concepts, with special emphasis on the period through the invention of the calculus in the late seventeenth century.
Selected topics are chosen from the mathematics of the eighteenth, nineteenth, and twentieth centuries.
home.hiram.edu /www/math/courses.html   (1009 words)

 Doklady. Mathematics, 2002; 66 (3)
Mathematics - Application of the Cyclic Properties of Dynamical Systems to the Study of the Boundary Limits of Arbitrary Functions / Pavicevic, Z / Susic, E
Mathematics - Localization Riesz Means of Spectral Expansions in a Piecewise Homogeneous Half-Space / Bavrin, I I / Yaremko, O E
Mathematics - On a Boundary Control at One End of a Process Described by the Telegraph Equation / Il'in, V A / Moiseev, E I
www.ucm.es /BUCM/compludoc/W/10302/10645624_1.htm   (738 words)

 Frequently Asked Questions
The average sixth-grade CAT Mathematics percentiles for the CPMP students and those in the traditional curriculum are similar as shown in Table 2, so these two groups were well-matched on mathematical achievement prior to high school.
The Mathematics Placement Test, compiled from a bank of items developed by the Mathematical Association of America, that is presently used at a major university was administered in several field-test schools in May 1999 at the end of CPMP Course 4 and traditional Precalculus courses.
The mathematics courses are 105/110 (precalculus), 115 (calculus I), 116 (calculus II), 215 (calculus III), 216 (introduction to differential equations), and honors (all honors math courses open to freshmen).
www.wmich.edu /cpmp/cpmpfaq.html   (8364 words)

 CSMEE Digest 93-6   (Site not responding. Last check: 2007-10-29)
At the high school level, this practice is most prevalent in mathematics, where students are placed in vocational, general, or college-preparatory mathematics courses (McPartland, Coldiron, & Braddock, 1987; Oakes, 1985, 1990a, 1990b; Slavin, 1990).
While it is true that tracking at earlier grade levels may limit the numbers of students eligible to take college-preparatory mathematics coursework, the end result is that many students are denied access to important mathematics experiences which prepares them to pursue the study of mathematics and science beyond high school.
Here, the research has been inconclusive, with several studies of regrouping for mathematics instruction showing that homogeneous regrouping had positive effects on mathematics achievement when materials appropriate for the student's level of performance were used (Provus, 1960; Morris,1969).
www.stemworks.org /digests/dse93-6.html   (2003 words)

 Doklady. Mathematics, 2000; 61 (3)   (Site not responding. Last check: 2007-10-29)
Mathematics - On the Properties of Operators of a Class Related to a Fischer Pair in the Space of Analytic Functions / Napalkov, V V / Komarov, A V
Mathematics - Theorems on the Reducibility of a Pair of Matrices as Rational Criteria / Al'pin, Yu A / Ikramov, Kh D
Mathematics - The Generalized Hardy-Titchmarsh Transform in the Space of Summable Functions / Kilbas, A A / Saigo, M / Borovko, A N
www.ucm.es /BUCM/compludoc/W/10001/10645624_4.htm   (763 words)

 [No title]   (Site not responding. Last check: 2007-10-29)
] Pertaining to a group of mathematical symbols of uniform dimensions or degree.
] An equation that can be rewritten into the form having zero on one side of the equal sign and a homogeneous function of all the variables on the other side.
] A polynomial all of whose terms have the same total degree; equivalently it is a homogenous function of the variables involved.
www.accessscience.com /Dictionary/H/H18/DictH18.html   (1147 words)

 PlanetMath: differential equation
This type of equations comes up often in many different branches of mathematics.
in the domain of interest), then the equation is said to be homogeneous.
Otherwise it is said to be nonhomogeneous (or inhomogeneous).
planetmath.org /encyclopedia/Homogeneous.html   (432 words)

 Homogeneous Functions
The situation, where one parameter appears superfluous, is quite common to the class of homogeneous functions.
All terms in the latter are homogeneous of order a.
For example, all kinds of means are symmetric and naturally homogeneous of order 1.
www.cut-the-knot.org /Generalization/homo.shtml   (317 words)

 Read This: The Mathematics Of Plato's Academy
The early Pythagoreans based their mathematics on commensurable magnitudes (or on rational numbers, or on common fractions m/n), but their discovery of the phenomenon of incommensurability (or the irrationality of the square root of 2) showed that this was inadequate.
A modern mathematician moves almost effortlessly from a definition of proportion ("A is to B as C is to D") to the definition of ratio as a kind of equivalence class.
Fowler's approach takes both history and mathematics seriously in the way it makes an effort to think in a different way, to shed the biases and concerns of our time and try to reconstruct the questions and issues of the ancient Greeks.
www.maa.org /reviews/mpa.html   (2046 words)

 Earliest Known Uses of Some of the Words of Mathematics (H)   (Site not responding. Last check: 2007-10-29)
A relatively recent example is the use of the letter H (for Hamiltonian) in The Mathematical Theory of Optimal Processes (1961) by L. Pontryagin, V. Boltyanskii, R. Gamrelidze and E. Mishchenko.
According to Richard Zach’s Hilbert’s program, the program “calls for a formalization of all of mathematics in axiomatic form, together with a proof that this axiomatization of mathematics is consistent.“ A JSTOR search found "Hilbert program" in 1934 in Alonzo Church's "The Richard Paradox," American Mathematical Monthly, 41, p.
HOMOGENEOUS DIFFERENTIAL EQUATION is found in 1868 in A Treatise on the Differential and Integral Calculus: And on the Calculus of Variations by Edward Henry Courtenay: "Prop.
members.aol.com /jeff570/h.html   (5875 words)

 [No title]
] The property whereby a mathematical system is well behaved (in the context of the given system) with regard to addition and scalar multiplication.
The mathematical approximation of a nonlinear system, whose departures from linearity are small, by a linear system corresponding to small changes in the variables about their average values.
] Quantities that satisfy a homogeneous linear equation in which at least one of the coefficients is not zero.
www.accessscience.com /Dictionary/L/L14/DictL14.html   (1137 words)

MATH 318 Linear Algebra (3) NW Introduction to the mathematical concepts, arguments, and proofs that occur in linear algebra.
MATH 420 History of Mathematics (3) NW Survey of the development of mathematics from its earliest beginnings through the first half of the twentieth century.
Issues in the teaching and learning of college mathematics, such as discovering and working with student background and expectations, increasing student engagement with course material, and evaluating student achievement.
www.washington.edu /students/crscat/math.html   (5102 words)

 Does Homogeneous = Separable?
But it looks like it could be homogeneous non-linear (if such a thing exists, I don't know???).
that is "homogeneous" in this sense: P(x) dy/dx+ Q(x)y= 0 is trivially seperable: dy/y= -(Q(x)/P(x))dx.
A(x,y)dx+ B(x,y)dy= 0 is "homogeneous" if and only if B(andlamda;x,andlamda;y)/A(andlambda;x, andlambda;y)= B(x,y)/A(x,y) (essentially that means that the total exponent of x and y in each term is the same).
www.physicsforums.com /showthread.php?t=42820   (631 words)

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