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Topic: Modular group

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Dicyclic group

Fundamental region

Young diagram

Partition function (number theory)

Hyperbolic geometry

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	Congruence subgroup (Site not responding. Last check: 2007-11-06)
		In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries.
		Detailed information about the congruence subgroups of the modular group Gamma has proved basic in much research, in number theory, and in other areas such as monstrous moonshine.
		The modular group Λ (also called the theta subgroup) is another subgroup of the modular group Γ.
	www.sciencedaily.com /encyclopedia/congruence_subgroup (603 words)

	Elliptic Curves and Modular Functions
		Modular and elliptic functions are both special cases of the concept of an automorphic function, which is a meromorphic function of 1 or more complex variables defined on a particular complex manifold and invariant under a particular group of analytic transformations (symmetries) of the manifold.
		the modular functions, are essentially the meromorphic functions on D considered as a Riemann surface by its isomorphism with H/ We have stressed this idea of symmetry because of the way it relates the analytic and geometric properties of an object like a Riemann surface to the algebraic properties of a group.
		Modular functions are, then, the automorphic functions on the upper half plane under the action of the modular group.
	www.mbay.net /~cgd/flt/flt05.htm (2994 words)

	Proposal (Site not responding. Last check: 2007-11-06)
		The purpose of a Division sponsored modular railroad is to promote the NMRA and the hobby of model railroading to the general public.
		The modular group should have advance notice for any shows/events that the modules will be on display so that all members should have enough time to participate.
		The modular HO scale layout will be built by individual members who will be responsible for the construction of their modules.
	home.comcast.net /~cjperry3/html/proposal.html (1063 words)

	Extended Glossary
		The founders of modern algebra used groups of isometries of a space to investigate the space itself, that is, they studied groups associated with a space as a means to understand that space.
		The modular group is one of the simplest types of tessellation groups for the hyperbolic context, which makes it the ideal place to begin investigations with novices.
		The modular group is often manifested (not represented) as 2x2 matrices with integer components and such that the determinate of the matrix is equal to one.
	www.xula.edu /math/faculty/McCreary/modularGarden/extendedGlossary.htm (1586 words)

	The Modular Group and Fractals
		The goal here is to establish that these are once again given by the modular group, and that furthermore, these have utility in that they are automorphisms of the unit interval: they are both injective and surjective maps of the unit interval.
		Modular Fractal Measures (PDF) (DVI) (9 pages) points out that the derivative of the Minkowski Question Mark function is given by the distribution of the Farey fractions on the real number line.
		Here, a modular form is a kind of analytic function that is closely related to elliptic functions, and has a certain type of modular group symmetry.
	www.linas.org /math/sl2z.html (1340 words)

	[No title]
		Subject: Modular equations, theta functions and solution of the equation of degree 5, 1/2 Date: Sun, 30 Apr 2000 15:59:18 +0200 Newsgroups: sci.math Summary: [missing] Hi all, Modular equations and theta functions are (could be) used to solve the equation of degree 5.
		Properties of modular equations and theta functions as well as the outline of the solution of the equation of degree 5 are listed in the book "Pi and the AGM of Borwein and Borwein".
		Subject: Modular equations, theta functions and solution of the equation of degree 5, 2/2 Date: Sun, 30 Apr 2000 22:38:38 +0200 Newsgroups: sci.math I had promised we needed one important theorem to formulate and proof "Theorem 4.7 of Pi and the AGM of Borwein and Borwein".
	www.math.niu.edu /~rusin/known-math/00_incoming/modfcn (744 words)

	H. E. A. eddy Campbell, Interesting Open Problems
		The same characterization of a group with a polynomial ring of invariants holds for a non-modular group, that is, a group whose order is not divisible by the characteristic p of the ground field k.
		For arbitrary groups, we know that a polynomial ring of invariants guarantees the group is generated by pseudo-reflections, but this is not sufficient thanks to examples of Nakajima.
		In particular, for an arbitrary group, the ring of invariants is not generated in degrees less than or equal to the order of the group.
	www.mast.queensu.ca /~campbelh/research.html (882 words)

	Seminar: Algebra and its Applications
		The Shafarevich-Tate group of an elliptic curve is an important invariant, measures the failure of the local-to-global principle.
		Modular Forms II This is the second of a series of introductory talks on Modular Forms.
		Introduction to the modular curves X(N) for the congruence subgroups Γ(N) of the Modular group Γ(1).
	www.math.fsu.edu /~ealdrov/seminar/spring2005/algebra.html (581 words)

	Citrus: Modular home group's lawsuit obstructs talks
		The Florida Manufactured Housing Association sued Marion County, which banned modular houses in 1998 from neighborhoods of site-built homes, after feeling frustrated that talks seemed to be at an impasse, FMHA executive director Frank Williams said this week.
		Modular homes meet the same building standards as site-built homes, so Florida law allows them to go anywhere that site-built homes go.
		A model ordinance drafted by Citrus County provides such a solution, allowing counties to spell out in their land use plans which areas are for site-built homes, modular homes or a mix of the two.
	www.sptimes.com /News/040100/news_pf/Citrus/Modular_home_group_s_.shtml (611 words)

	MILLROCK™ Stationery & Greeting, Foodservice, Audio & Video, Retail Fixtures. Grow Your Brand™
		When using the Millrock name solely as a reference to the company, Millrock a division of Modular Brand Group (fully spelled out) may be used as a noun and no TM symbol is needed.
		It generally appears at the end of a document or on the back of a package, but it may be placed elsewhere, such as inside the front cover of documentation, or the bottom of a web page.
		Modular Brand Group uses a standard trademark legend that does not change except to add the marks that are referenced in the text, which is set forth as follows: "Millrock, Modular Brand Group, and the Millrock Logo are trademarks or registered trademarks of Modular Brand Group, LLC in the United States and/or other countries."
	www.millrock.com /termsconditions.shtml (1385 words)

	Murillo Modular (Site not responding. Last check: 2007-11-06)
		Murillo Modular Group, Ltd was formed by two principals who collectively boast 25 years experience in virtually all aspects of the modular building industry including modular design, construction, structure transportation, and installation.
		On August 17, 2004 the Group's principals had their first meeting with personnel from the Army Corps of Engineers and the White House (three individuals from the Office of White House Services were present because it was assigned to oversee the project).
		Once the Group went to work, the 8,100 square foot facility was finished on schedule 90 days from the Group's first meeting with the Corps and 75 days from the Notice to Proceed.
	www.murillomodular.com /about.php (834 words)

	Chapter 3 - The Minkowski Question Mark and the Modular Group (Site not responding. Last check: 2007-11-06)
		This enumeration will help cement that the modular group is the symmetry group of a broad range of fractal curves (the de Rham curve and its various expressions).
		This group can be presented as a free group of a pair of generators, and there are many different possible choices of generators.
		of the modular group, and showed that it was a semigroup, and that it had a representation as a set of intervals.
	linas.org /math/chap-minkowski/chap-minkowski.html (5943 words)

	AREA_GROUP
		Area groups with a compression factor are not affected by the -c option.
		When used in modular designs, all routing that connects only members of an area group will be constrained to lie within the range.
		You can also specify a TNM group name, or the name of a user group defined by a TIMEGRP statement (but note that edge qualifiers used in the TIMEGRP definition are ignored when determining area group membership).
	toolbox.xilinx.com /docsan/xilinx6/books/data/docs/cgd/cgd0058_11.html (2490 words)

	conjugacy equivalence (Site not responding. Last check: 2007-11-06)
		It is easy to show that all order two elements in the modular group are conjugate equivalent.
		This follows from how the modular group tessellation is constructed.
		Each triangular shaped region is the image of a single triangular shaped fundamental region that is acted on, in succession, by each modular group element.
	www.xula.edu /math/faculty/McCreary/modularGarden/conjugacyEquivalence.htm (296 words)

	Research in Algebra \| Matrix Groups
		A group of this type consists of n-by-n matrices defined over some ring, R, and its structure is determined by both n and R. For a given R, the groups tend to be more complicated structure when n is "low".
		Lower dimensional groups however are also important.The study of such groups began in the 19th century when mathematicians were searching for functions (of a complex variable) which would generalize the classical trigonometric and elliptic functions.
		Roughly speaking such groups are matrix groups defined over one of the "basic" rings of number theory, for example the integers, Z. Much of the study of these groups has concentrated on the so-called congruence subgroups which are defined arithmetically.
	www.maths.gla.ac.uk /research/groups/algebra/matgrp.htm (553 words)

	Crystall Project (Site not responding. Last check: 2007-11-06)
		However, the implementation of group communication with process crashes and unpredictable communication delay is a difficult task.
		Therefore, we are interested in the semantic foundations (or models) of group communication and implementations of group communication that would correspond closely to the model, thus making it easier to understand the system's behaviour and verify its correctness.
		In this project, we design and implement group communication using a modular approach that is based on implementing group communication services as separate protocols, and then combining selected protocols using a protocol framework.
	lsrwww.epfl.ch /Research/Crystall (949 words)

	Genesis Systems Group - Versa Modular System Workcells - Robotics Online
		Founded in 1974, RIA is the only trade group in North America organized specifically to serve the robotics industry.
		The Modular components are placed together in a ''building block'' fashion, interacting with one another to comprise a cohesive and complete robotic welding system.
		Genesis Systems Group is an industry leader in the design, manufacture and building of robotic systems for welding and cutting applications.
	www.roboticsonline.com /buyers_guide/newproducts/details.cfm?id=77 (345 words)

	Modular Building Group: mobile and modular buildings, portable buildings, office trailers, mobile offices, portable ...
		The Modular Building Group is committed to professionalism, quality and providing their customers the information that they need to make sound modular building decisions.
		The Modular Building Group has a diverse portfolio of factory-built products from storage containers to large office complexes, including mobile offices, portable classrooms, modular buildings, office trailers and custom design-build buildings.
		The Modular Building Institute, a national organization, has recognized these companies many times throughout the years with numerous awards for their work in the industry.
	www.modularbuildinggroup.com (211 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		First let me comment that the Moebius group may be described either as PGL(2,C) or PSL(2,C): given complex coefficients, one may normalize to assume that the determinant is 1.
		Thus every element of PGL(2,Z) may be uniquely written either as a (reduced) word in F and G or as such a word times H. This applies in particular to words in H and K: they fall into the two classes according as the number of H's is even or odd.
		Discussions occur throughout the mathematical literature: in group theory, complex analysis, Riemann surfaces, elliptic curves, and number theory.
	www.math.niu.edu /~rusin/known-math/97/PSL2Z (517 words)

	The Moduli Space of the Modular Group in Complex Hyperbolic Geometry - Falbel, Parker (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		This is the rst Fuchsian group for which the entire complex hyperbolic deformation space has been constructed.
		Falbel and J. Parker, The Moduli Space of the Modular Group in Complex Hyperbolic Geometry, Math.
		1 A circle of Modular groups in PU - Falbel, Kosele
	citeseer.ist.psu.edu /477393.html (404 words)

	MILLROCK™ Stationery & Greeting, Foodservice, Audio & Video, Retail Fixtures. Grow Your Brand™
		Modular Brand Group is honored to announce the continued leadership of Marty Liebmann, David Stackhouse and Spencer Liebmann, the former MILLROCK owners.
		Modular Development, LLC is actively interviewing professional manufacturers' representatives to launch licensed dealerships.
		Today, we are proud to say Modular Brand Group has nearly 250 high-caliber professional group members, achieved our founding goals, and continue to excel within our core competencies of services and manufacturing.
	www.millrock.com /news.shtml (462 words)

	Efficient Average-Case Algorithms for the Modular Group - Cai, Fuchs, Kozen, Liu (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: The modular group occupies a central position in many branches of mathematical sciences.
		In this paper we give average polynomial-time algorithms for the unbounded and bounded membership problems for finitely generated subgroups of the modular group.
		1 Introduction 1.1 The Modular Group The modular group \Gamma is a remarkable mathematical object.
	citeseer.ist.psu.edu /35940.html (607 words)

	Welcome to the Modular Home Group
		The Modular Home Group, has over 15 years experience in building custom, affordable modular homes primarily in New Jersey.
		Using existing modular plans or plans that you may have seen, we at the modular home group look forward to helping you solve your new home descisions, and can walk you through every step of the new home buying process.
		If you have any questions or would like to speak with a Modular Home Group representative, please e-mail us at info@modularhomegroup.com or call us at 732-774-5119.
	www.homesibs.com (162 words)

	Oldcastle Precast Modular Group beats the Learning Curve
		Designed around a new school building system developed by Oldcastle Precast Modular Group (OPMG), an 8,820-sq.-ft. addition to East Hampton's Springs Union Free School provided four general classrooms, a science laboratory, and multipurpose space in addition to retrofits to the existing facility.
		OPMG representatives note that using the NT32 school modules — designed, engineered, produced off-site and erected by a single source — reduced the project's overall cost by 12 percent and the construction schedule by an estimated five months.
		The modular building system, they emphasize, provided a durable, low-maintenance, thoroughly insulated and structurally integrated facility while decreasing labor costs, on-site construction, erection and finish work by more than half with minimal interruption to school routine.
	concreteproducts.com /mag/concrete_oldcastle_precast_modular/index.html (886 words)

	Fläkt Woods Group Global - Modular Air Handling Unit
		Modular air handling unit offer full flexibility allowing different sizes and functions to be combined to meet virtually any air handling requirement.
		Our modular product range is modern and highly-specified, designed for customers with high demand on quality and energy efficiency.
		The EUMM is a modular air conditioning unit for marine applications.
	www.flaktwoods.ru /169/2568/1/aea47896-1b7b-4d02-a331-f698b68ce86d (177 words)

	Modular approach [OCLC - Group Services]
		Using a modular approach, your library group selects and tailors the most appropriate modules to design a custom solution.
		Group catalogs leverage the investment your libraries have made with their cataloging efforts.
		Every library in the group can have unlimited access to OCLC resource sharing services, including loan and photocopy requests and mediated or unmediated requests.
	www.oclc.org /groupservices/about/modular (619 words)

	Modular building: Custom built modular buildings for your modular project needs.
		Modular building - We offer custom built modular buildings of your modular project.
		Modular building group builds modular buildings to meet your modular project needs.
		From a single modular unit to a large complex, the seasoned team at US Modular Group can deliver the perfect modular building to solve your space problems.
	www.usmodulargroup.com (232 words)

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