Disputed date October 2010 Programming paradigms Modularprogramming is a software design technique that increases ... Haas location http www.about.com publisher About.com title Modularprogramming quote Modularprogramming is a programming style that breaks down program functions into modules, each of which accomplishes .... Modularprogramming is a solution to the problem of very large programs that are difficult to debug ... determine the source of program errors more easily. Object orientated programming languages, such as SmallTalk and HyperTalk, incorporate modularprogramming principles. ref Conceptually, modules represent ... With modularprogramming, separation of concerns concerns are separated such that no or few modules ... between the modules . History Traditional programming languages have been used to support modularprogramming since at least the 1960s. Modularprogramming is a loosely defined concept with no official ... References references http legosoftwareprocess.org O2 Software Process DEFAULTSORT ModularProgramming ... programming language Ada , BlitzMax , COBOL , Component Pascal , D programming language D , Erlang programming language Erlang , F programming language F , Fortran , Haskell programming language Haskell , IBM 360 Assembler for an assembly language Assembler , IBM RPG , Java programming language Java packages are considered modules in the JLS , MATLAB , ML programming language ML , Modula 2 , Modula 3 , Morpho, Oberon programming language Oberon , OCaml , Pascal programming language Pascal , Perl , PL 1 , Python programming language Python , and Ruby programming language Ruby . The IBM System i also uses Modules in AS 400 Control Language CL , COBOL , and IBM RPG RPG when programming in the Integrated Language Environment ILE . Modularprogramming can be performed even where the programming language lacks explicit syntactic features to support named modules. Software tools can create modular ... is the goal Dubious date October 2010 . When creating a modular system, instead of creating ... more details
and to make the manufacturing process more adaptive to change see modularprogramming . ref Baldwin and Clark, 2000 ref Modular design is an attempt to combine the advantages of standardization high ... Function Deployment Modularprogramming Separation of concerns Systems engineering Modular building ...Context date October 2009 Modular design , or modularity in design is an approach that subdivides a system ... to drive multiple functionalities. A modular system can be characterized by the following 1 Functional ... elements 2 Rigorous use of well defined modular interfaces, including object oriented descriptions ... part5 releases 1.3.0 WebHelp glossary m.htm title Glossary Modular Design publisher Net ... module , and exclusion. Examples of modular systems are car s, computers and high rise buildings ... and this depends on the extent of modularity is that modular systems are not optimized for performance ... September 2007 Proper inter modular design Recognizing that excessive inter module dependencies are an indicator ... dependencies. Thus, inter modular design should be easy to work with because modules can .... Modular design in cars Aspects of modular design can be seen in cars or other vehicles to the extent ... of the car. A simple example of modular design in cars is the fact that, while many cars come as a basic ... systems. Modular design in buildings File Flexible Workplace Variability.jpg thumb right 275px Modular workstations Modular design can be seen in certain buildings, especially modular buildings . Modular buildings and also modular homes generally consist of universal parts or modules that are manufactured .... ref cite web url http architecture.about.com cs buildyourhouse g modular.htm title Modular home definition accessdate 2010 08 19 ref Modular buildings can be added to or reduced in size .... Modular buildings can also undergo changes in functionality using the same process of adding or removing modular components. For example, an office building can be built using modular parts ... more details
nordmodularbook nm book toc.html Advanced Programming Techniques for Modular Synthesizers a Nord Modular ...Image Nord Modular.jpg thumb 300px Nord Modular Classic, keyboard version The Clavia Nord Modular series ... Modular series, in common with their sister range the Nord Lead series, are analogue modelling .... Overview The Nord Modular range approximates the much more flexible world of modular synthesizers , offering ... to computer based modular synthesis environments like Reaktor which offer a graphical representation ... The Nord Modular line of synthesizers features a range of modules familiar to users of hardware modulars ... time indeed with some thought and careful programming it is possible to exceed the specified polyphony of the unit by this definition of polyphony at least . Nord Modular G2 Image Nord Modular G2.jpg thumb 300px Nord Modular G2 Clavia introduced the first generation in 1998. The series was discontinued in 2004 upon the release of the next generation Nord Modular G2 series. The G2 is an updated and more powerful version of the original Modular the G2 uses a new version of the Editor software ... in 2009. The original Nord Modular or Classic series Image Nord Modular Rack, G2 Engine.jpg thumb Nord Modular Rack and G2 Engine from the Clavia website The first generation Nord Modular family consists of three hardware models Nord Modular Key, Nord Modular Rack and Nord Micro Modular. They are all built around the same type of electronics and use the same type of DSP. Nord Modular Key and Rack have 4 DSPs as standard can be expanded to 8 with the Nord Modular Voice Expansion Board , and the Nord Micro Modular has 1 DSP non expandable . Nord Modular Key and Rack General Programmable polyphonic modular synthesizer Minimum 4 voices expandable to minimum 8 voices Maximum 32 voices ... sensitive keyboard with octave shift buttons 2 octaves Nord Modular Key MIDI In trig indicator Nord Modular Rack Dimensions Nord Modular Key convert 473 mm in abbr on W x convert 264 mm in abbr on D ... more details
In mathematics, a modular invariant may be A modular invariant of a group acting on a vector space of positive characteristic The elliptic modular function , giving the modular invariant of an elliptic curve. mathdab ... more details
wave triangle , and sawtooth wave sawtooth waveforms The modular synthesizer is a type of synthesizer ... often requires converters. Some standard modules found on almost any modular synth are VCO Voltage ... by modular synthesizers include white noise white , pink noise pink , and low frequency noise. VCF ... modular synthesizers have voltage driven inputs, it is possible to connect almost any kind of control ... falling on a sensor. Modular synthesizers can be bulky and expensive, and there is a steep learning ... to play live. In the late 1980s, modular synthesizers were largely replaced by highly ... at the height of their 1970 s peak popularity. Historic manufacturers of modular synthesizer hardware Image Moog Modular 55 img2.jpg thumb A Moog 55 c. 1972 to c. 1981 The earliest commercial modular ... lines of simple DIY modular synthesizer systems. Modern manufacturers of modular hardware synthesizers ... Synton http mmm.sevcom.com Mattson Mini Modular http www.metalbox.com Metalbox http www.metasonix.com ... modular systems use a volts octave system, sometimes termed linear voltage control some such as Korg .... Modular software synthesizers alphabetical There are also software synthesizers for personal ..., where the modules simulate hardware functionality. Some of them are also virtual modular systems, which simulate real historical modular synthesizers. Alsa Modular Synthesiser http alsamodular.sourceforge.net ARP 2600 by ARP Instruments, Inc AudioMulch Bidule By plogue ChucK CreamwareAudio Modular ... Kyma by Symbolic Sound Corporation Moog Modular V by Bob Moog Pure Data Reaktor http www.rollosonic.com Pages RolloSONIC Intro.html RolloSONIC SpiralSynthModular SuperCollider programming language SuperCollider http www.sonicspot.com syncmodular syncmodular.html SynC Modular http www.synthedit.com ... s, software modular synthesizers offer the infinite variations and visual patching at a more affordable ... Studio Technology VST may be combined in a modular fashion. Semi modular synthesizers A modular synthesizer ... more details
Unreferenced date December 2009 In mathematics , in the field of group theory , a modular subgroup is a subgroup that is a modular lattice modular element in the lattice of subgroups , where the meet operation is defined by the intersection and the join operation is defined by the subgroup generating set of a group generated by the union of subgroups. By the Modular Property of Groups , every quasinormal subgroup that is, a subgroup that permutes with all subgroups is modular. In particular, every normal subgroup is modular. DEFAULTSORT Modular Subgroup Category Subgroup properties ... more details
, as implemented in many programming language s and calculator s, is an application of modular ...In mathematics , modular arithmetic sometimes called clock arithmetic is a system of arithmetic for integer ... samplings feature column fcarc eulers formula ref Modular arithmetic was further advanced by Carl Friedrich ... right Time keeping on this clock uses arithmetic modulo 12. A familiar use of modular arithmetic is in the 12 .... Congruence relation This section is linked from RSA algorithm Modular arithmetic can be handled mathematically ... of a ring mathematics ring . Remainders The notion of modular arithmetic is related to that of the remainder ... residue , the least non negative member of an equivalence class. When working with modular arithmetic ... science , it is the remainder operator that is usually indicated by either e.g. in C programming language C , Java programming language Java , Javascript , Perl and Python programming language Python or mod e.g. in Pascal programming language Pascal , BASIC , SQL , Haskell programming language Haskell ... residue rather than a remainder e.g. in Ruby programming language Ruby . Parentheses are sometimes dropped ... system modulo 4. Applications Modular arithmetic is referenced in number theory , group theory ... algebra. Modular arithmetic is often used to calculate checksums that are used within identifiers ... input errors in bank account numbers. In cryptography, modular arithmetic directly underpins public ... Algorithm IDEA , and RC4 . In computer science, modular arithmetic is often applied in bitwise ... by hand. It is based on modular arithmetic modulo 9, and specifically on the crucial property that 10 ... 7 arithmetic. More generally, modular arithmetic also has application in disciplines such as law ... part of the analysis. Computational complexity Since modular arithmetic has such a wide range of applications ... arithmetic operations, such as multiplication and Modular exponentiation exponentiation modulo n , to be performed efficiently on large numbers. Solving a system of non linear modular arithmetic ... more details
In Graph mathematics graph theory , the modular decomposition is a decomposition of an undirected graph ... to them, and the first description of modular quotients and the graph decomposition they give ... of nested modules, of which the modular decomposition is an example, can be used to guide the recursive ... graph s, a further generalization of modular decomposition, called the split decomposition , is especially ... subseteq M math . Modular quotients and factors If math X math and math Y math are disjoint modules ... between these two extremes can exist. Because of this, modular partitions of math V math where each partition class is a module are of particular interest. Suppose math P math is a modular partition. Since ... below, vertex 1, vertices 2 through 4, vertex 5, vertices 6 and 7, and vertices 8 through 11 are a modular ... V and math x x in V math are the trivial modular partitions . math G V math is just the one ... X math and the one elements subsets of math V backslash X math are a nontrivial modular partition of math V math . Thus, the existence of any nontrivial modules implies the existence of nontrivial modular ... modular partition, then G P is a compact representation of all the edges that have endpoints ... is a factor of a modular quotient G P , it is possible that G X can be recursively decomposed into factors ... one way of recursively decomposing factors of an initial modular partition into smaller modular ... different ways of decomposing it recursively. Some ways may be more useful than others. The modular ... represents all ways of decomposing it this is the modular decomposition. It is itself a way of decomposing ... of the root of the modular decomposition tree, and its full modular decomposition tree series nodes ... the modular decomposition If X is a module of G and Y is a subset of X , then Y is a module of G , if and only if it is a module of G X . In Gallai, 1967 , Gallai defined the modular decomposition ... modular decomposition is a single tree node. Gallai showed that if G is connected and so is its ... more details
speed benefit over both of the previous two algorithms. In programming languages Because modular ... Math BigInt.html bmodpow 28 29 to perform modular exponentiation Go programming language Go s tt ...Modular exponentiation is a type of exponentiation performed over a modular arithmetic modulus . It is particularly useful in computer science , especially in the field of cryptography . Doing a modular ... with the property 0 c < m . Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm . That is br ... m math Modular exponentiation problems similar to the one described above are considered easy to do ... e given b , c , and m is believed to be difficult. This one way function behavior makes modular ... straightforward method of calculating a modular exponent is to calculate b sup e sup directly, then to take ... O notation O e multiplications to complete. Memory efficient method A second method to compute modular ... in this method. In pseudocode, this method can be performed the following way function modular pow ... required to perform modular exponentiation. It is a combination of the previous method and a more ... , and modulus correspond to b , e , and m in the equations given above. function modular pow ... see above that are much faster than simply exponentiating and then taking the remainder, many programming languages and arbitrary precision integer libraries have a dedicated function to perform modular exponentiation Python programming language Python s built in tt pow tt exponentiation function http ... to modulo by Java programming language Java s tt java.math.BigInteger tt class has a Javadoc SE name modPow java math BigInteger modPow java.math.BigInteger, 20java.math.BigInteger method to perform modular ... http www.php.net manual en function.bcpowmod.php to perform modular exponentiation The GNU Multiple ... Integer Exponentiation.html to perform modular exponentiation See also Montgomery reduction , for calculating ... more details
Unreferenced stub auto yes date December 2009 In theoretical physics , modular invariance is the invariance under the group mathematics group such as SL 2,Z of large diffeomorphism s of the torus . The name comes from the classical name modular group of this group, as in modular form theory. In string theory , modular invariance is an additional requirement for one loop diagram s. This helps in getting rid of some global anomaly global anomalies such as the gravitational anomaly gravitational anomalies . DEFAULTSORT Modular Invariance Category Symmetry Category Article Feedback 5 Physics stub es Invariancia modular fr Invariance modulaire ... more details
Unreferenced date December 2009 Wikify date December 2009 Modular Classrooms are prefabricated buildings constructed off site in a factory. Most modular classrooms are portable, and are sometimes called temporary classrooms or relocatable classrooms, but permanent modular classrooms are becoming a common option. Modular classrooms are also built to all the same codes and specifications as site built structures. Modular classrooms are frequently used by schools in need of additional rooms or in emergencies. Benefits Modular construction is performed in a factory where workers and materials are protected ... are a benefit. The greatest advantage of modular construction is time savings, typically 30 to 60 faster than traditional site built construction. A modular project does not need to wait until the foundation has cured before starting building construction. Since modular buildings are constructed off site, modular units can be built and prepared for shipment before the foundation is poured. The nearly ... term or permanent use. Strength Modular buildings are also sturdier than the stereotype that mobile trailers would suggest. Because modular buildings often travel along the road at high speeds during delivery, they are built as sturdy as site built structures, often sturdier. Modular buildings are usually ... on top of the first module. Usage Use of modular classrooms is a more rapid way of replacing ... within a tight time frame. Modular classrooms also add flexibility. Since modular classrooms are constructed in modules, it is easier to disassemble a modular classroom and move it to another site, or to reconfigure the building for other purposes. Some modular classrooms are indistinguishable ... to help preserve our environment. Modular Green classrooms offer energy efficiency, can be built ... Modular Building Institute International trade association representing non residential modular construction professionals http www.triumphmodular.com blog Design & Build Modular Blog discussing ... more details
About modular connectors the registered jack RJ wiring standard registered jack Refimprove date October 2010 Image rjxx.jpg thumb Left to right, modular connectors 8P8C plug, 6P6C plug, 6P4C plug, 4P4C plug, 6P6C jack. Image Uncrimped rj 45 connector close up.jpg thumb An 8P8C modular plug. This is the common ... Modular connector is the name given to a family of electrical connector s originally used in telephone ... expensive connector have now migrated to modular connectors. Probably the most well known applications of modular connectors are for telephone jacks and for Ethernet jacks, both of which are nearly always modular connectors. Modular connectors were originally used with the registered jack system .... TIA EIA 568 is a standard for data circuits wired on modular connectors. Other systems exist for assigning signals to modular connectors physical interchangeability of plugs and jacks does not ensure interoperation, nor protection from electrical damage to circuits. For example, modular cables .... Nomenclature Main Registered jack naming confusion Modular connectors also go by the names modular phone jack plug , RJ connector, and Western jack plug. The term modular connector ... modular. This includes the 4P4C handset connector which is sometimes called an RJ9 or an RJ22 but such RJ ... to refer to the physical connector itself for instance, the 8P8C modular connector type is often called ... used with different signals, such as for Ethernet over twisted pair . History Modular connectors ... and larger 3 and 4 pin telephone jacks in buildings. Gender Modular connectors have Gender of connectors ... cables, cables with a modular plug on one end and a jack on the other are rare. Instead, cables .... Latching tab and orientation Modular connectors are designed to latch together. A spring loaded tab .... The modular connector suffers from a design flaw however, as the fragile tab easily snags on other ... Image Rj45plug 8p8c.png thumb 8P8C modular plug pin numbering Image Rj 45 male compare.jpg thumb ... more details
Image Smallest nonmodular lattice 1.svg thumb right Hasse diagram of N sub 5 sub , the smallest non modular lattice. In the branch of mathematics called order theory , a modular lattice is a lattice order lattice that satisfies the following self dual condition Modular law x b implies x .... Modular lattices arise naturally in algebra and in many other areas of mathematics. For example, the subspaces of a vector space and more generally the submodules of a module over a ring form a modular lattice. Every distributive lattice distributive lattice is modular. In a not necessarily modular lattice, there may still be elements b for which the modular law holds in connection with arbitrary elements a and x b . Such an element is called a modular element . Even more generally, the modular law may hold for a fixed pair a , b . Such a pair is called a modular pair , and there are various ... . Introduction The modular law can be seen and memorized as a restricted associativity associative ... x a b in every lattice. Therefore the modular law can also be stated as Modular law variant x b implies x a b x a b . By substituting x with x b , the modular law can be expressed as an equation that is required to hold unconditionally, as follows Modular identity x b a b x b a b . This shows that, using terminology from universal algebra , the modular lattices form a subvariety of the variety universal ... of modular lattices are again modular. The smallest non modular lattice is the pentagon lattice ... to x or to b . For this lattice x a b x 0 x b 1 b x a b holds, contradicting the modular law. Every non modular lattice contains a copy of N sub 5 sub as a sublattice. Modular lattices are sometimes called Dedekind lattices after Richard Dedekind , who discovered the modular identity. Diamond isomorphism theorem For any two elements a , b of a modular lattice, one can consider the intervals a b ... , b that are defined by x x a and x x b . gallery heights 180px widths 225px Image Modular pair.svg ... more details
Orphan date February 2009 Modular additions are usually side and 2nd story additions to homes that are pre fabricated at the facilities. General characteristics of a modular home apply. For a 2nd story modular addition the existing house should have a sound structure as modular rooms are 30 heavier than the same stick built. Modular additions are built in the facility, brought to the site and dropped by crane on the new location. It is necessary to have a general contractor to supervise the project as there is always some work to tie new rooms into an existing house. Even though it is assumed that modular additions are less expensive than traditional stick built this is rarely true when compared by square footage. The buyer would generally get more wood and better insulation plus benefits of controlled environment but total cost of the contract would be about the same. See also Prefabricated home Manufactured housing Stick built home NTA Inc Third Party Inspection Design Review Agency References reflist External links http www.modularcouncil.org National Modular Housing Council The national trade organization representing all segments of the modular housing industry. http www.modularhousing.com Modular Building Systems Association The national trade association representing the legislative and regulatory interests of the modular housing industry. http www.ntainc.com NTA, Inc. Modular housing engineering design http www.bergenremodeling.com modular.html Truth and Myth of Modular Additions br Category Building engineering Category House types ... more details
Infobox Album See Wikipedia WikiProject Albums Name Miss Modular Type ep Artist Stereolab Cover MissModular.jpg Released 1997 Recorded March 1997 August 1997 Genre Post rock Length Label Duophonic Records Duophonic small United Kingdom UK small Producer Reviews Allmusic Rating 4 5 Allmusic class album id r342648 pure url yes link Miss Modular is an Extended play EP by the post rock band Stereolab , released in 1997. It was produced in collaboration with the group Mouse on Mars . All four of its tracks were later re released on the Oscillons from the Anti Sun compilation. Track listing Miss Modular 4 16 Allures 3 29 Off On 5 26 Spinal Column 2 53 References cite web url Allmusic class album id r342648 pure url yes publisher All Media Guide All Music work Stereolab title Miss Modular & 91 EP& 93 accessdate 2007 05 05 cite web url http www.stereolab.co.uk discography ?no 31 publisher Stereolab work Stereolab Official Site title miss modular accessdate 2007 05 05 Stereolab Category 1997 EPs Category Stereolab EPs es Miss Modular fr Miss Modular ... more details
thumb 240px Two story modular dwelling Modular buildings and modular homes are sectional prefabricated ... residential building using either a crane or trucks. Modular buildings are considerably different from mobile home s or manufactured homes. Off frame modular dwellings differ from mobile homes largely ... by means of flat bed truck s however, some modular dwellings are built on a steel frame on frame modular that can be used for transportation to the site. Many modular homes have multiple levels. Homes are often set in place using a crane machine crane . Uses Image Bd 3.jpg thumb right Modular home in Sutton, Alaska Modular buildings have a variety of uses. They may be used for long term, temporary ... housing, and industrial facilities. Modular buildings are used in remote and rural areas where conventional ... food restaurants and cruise ship construction. Construction process Modular components are typically .... Once assembled, modular buildings are essentially indistinguishable from typical site built structures. While mobile manufactured buildings often decrease in value over time, a well built modular building ... Image Bulk Material Stored In A Modular Home Factory.jpg Bulk materials Image Interior Walls Set On Modular Home Floor System.jpg Walls attached to floor Image Roof and Ceiling are built and drywalled.jpg ... Ready for delivery to site gallery Advantages Modular buildings are very affordable ... Modular Homes Make Sense Building Systems A1854.html title Modular homes make sense accessdate 2007 ... Speed of construction faster return on investment . Modular construction allows for the building ... built house in a remote area or an area experiencing a construction boom such as mining towns. Modular ... several large dumpsters, construction of a modular dwelling generates much less waste. ref cite web url http www.housingzone.com probuilder article CA6349844.html title Modular and Green accessdate 2006 09 15 ref Environmentally friendly construction process . Modular construction reduces waste and site ... more details
A modular bill of materials modular BOM is type of bill of materials BOM and a critical element in defining the product structure of an end item . Modular BOMs define the component materials, documents, parts and engineering drawings needed to complete a sub assembly. While the terms BOM and modular BOM are most commonly used in association with physical products, the concept can be used in a variety of industries e.g. software, medical records . Modular BOMs are used by modern information systems to serve a variety of purposes, such as defining the components needed to produce a sub assembly, and providing cost information for each component and rolled up cost information for the overall sub assembly. For option based, configurable products e.g. automobiles, PCs companies needed to plan every combination and permutation of options to ensure they could fulfill customer demands. With a modular BOM structure, companies can plan the demand for each module independent of the end item demand by estimating the popularity of the module sub assembly. See also Bill of materials BOM Configurable BOM CBOM Material requirements planning MRP Manufacturing resource planning MRP II Enterprise resource planning ERP Product data management PDM References Refimprove date June 2007 Category Production and manufacturing Category Enterprise resource planning terminology engineering stub ... more details
In mathematics , a modular equation is an algebraic equation satisfied by moduli , in the sense of moduli problem . That is, given a number of functions on a moduli space , a modular equation is an equation holding between them, or in other words an identity mathematics identity for moduli. The most frequent use of the term modular equation is in relation with the moduli problems for elliptic curve s. In that case the moduli space itself is of dimension 1. That implies that any two rational function s F and G , in the function field of an algebraic variety function field of the modular curve, will satisfy a modular equation P F , G 0 with P a non zero polynomial of two variables over the complex number s. For suitable non degenerate choice of F and G , the equation P X , Y 0 will actually define the modular curve. One should qualify that by saying that P , in the worst case, will be of high degree and the plane curve it defines will have Mathematical singularity singular points and the coefficient s of P may be very large numbers. Further, the cusps of the moduli problem, which are the points of the modular curve not corresponding to honest elliptic curves but degenerate cases, may be difficult to read off from knowledge of P . That all being said, in that sense a modular equation becomes the equation of a modular curve . Such equations first arose in the theory of multiplication of elliptic function s geometrically, the n sup 2 sup fold covering map from a 2 torus to itself given by the mapping x n x on the underlying group expressed in terms of complex analysis . References unreferenced date August 2008 Category Moduli theory ... more details
In mathematics , a modular form is a complex analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs ... with number theory . Modular forms appear in other areas, such as algebraic topology and string theory . A modular function is a modular form, without the condition that f z be holomorphic at infinity. Instead, modular functions are meromorphic at infinity. Modular form theory is a special case of the more ... part of a rich theory of discrete group s. Modular forms for SL sub 2 sub Z A modular form of weight ... math f 1 z z k f z , math and math f z 1 f z , math respectively. Since S and T generate the modular ... in terms of lattices or elliptic curves A modular form can equivalently be defined as a function ..., by its values on lattices of the form math langle 1, omega rangle math , where H . Modular functions When the weight k is zero, the only modular forms are constant functions, as can be shown. However, relaxing the requirement that f be holomorphic leads to the notion of modular functions . A function f H C is called modular iff it satisfies the following properties f is meromorphic function meromorphic in the open upper half plane H . For every matrix mathematics matrix M in the modular group Gamma modular group &Gamma , f M f . f is required to be meromorphic at the cusp . This means ... ref http www.msri.org about computing docs magma html text600.htm Elliptic and Modular Functions ... to phrase the definition of modular functions is to use elliptic curve s every lattice determines ... is obtained from the other by multiplying by some non zero complex number . Thus, a modular function ... elliptic curves, is a modular function. More conceptually, modular functions can be thought of as functions on the moduli problem moduli space of isomorphism classes of complex elliptic curves. A modular ... of f at i . Modular forms for more general groups The functional equation, i.e., the behavior of f ... more details
In number theory and algebraic geometry , a modular curve Y is a Riemann surface , or the corresponding ... plane H by the group action action of a congruence subgroup of the modular group of integral 2 2 matrices SL 2, Z . The term modular curve can also be used to refer to the compactified modular ... . The points of a modular curve moduli problem parametrize isomorphism classes of elliptic curve ... to give a purely algebraic definition of modular curves, without reference to complex numbers, and, moreover, prove that modular curves are field of definition defined either over the field Q of rational ... in number theory. Analytic definition The modular group SL 2, Z acts on the upper half plane by fractional linear transformation s. The analytic definition of a modular curve involves a choice ... H to obtain a noncompact Riemann surface commonly denoted Y . Compactified modular curves ... with the subgroups N , sub 0 sub N , and sub 1 sub N . The modular curve X 5 has genus 0 it is the Riemann .... This group is a simple group of order 60 isomorphic to A sub 5 sub and PSL 2,5 . The modular curve ... classical model for X sub 0 sub N , the classical modular curve this is sometimes called the modular curve. The definition of N can be restated as follows it is the subgroup of the modular group which is the kernel of the reduction Modular arithmetic modulo N . Then sub 0 sub N is the larger ... they play an important role in arithmetic geometry . The level N modular curve X N is the moduli ... 0 sub N can be defined over Q . The equations defining modular curves are the best known examples of modular ... s connecting pairs of modular curves. Remark quotients of H that are compact do occur for Fuchsian group s other than subgroups of the modular group a class of them constructed from quaternion ... for the genus of the modular curve X N of any level N that involves divisors of N . Relation with the Monster group Unreferenced section date August 2009 Modular curves of genus mathematics genus 0, which ... more details
custom papers Modular origami , or unit origami , is a origami paperfolding technique which uses ... that holds the model together. Definition and restrictions Image Modular Origami.jpg thumb right Examples of modular origami made up of Sonobe units Modular origami can be classified as a sub set of multi ... of the sheet of paper is not generally acceptable in modular origami. The additional restrictions that distinguish modular origami from other forms of multi piece origami are using many ... to complete the model. There is a common misconception that treats all multi piece origami as modular ... to modular origami The first historical evidence for a modular origami design comes from a Japanese ... of traditional origami models, one of which is a modular cube . The cube is pictured twice from ... module forms one face of the finished cube. There are several other traditional Japanese modular origami ..., rather inaccurately, used to describe any three dimensional modular origami structure resembling a ball. There are also a few modular designs in the Chinese paperfolding tradition, notably the Pagoda ... piece and the possibilities inherent in the modular origami idea were not explored further until ... by Mitsonobu Sonobe in Japan. Since then the modular origami technique has been popularized .... Types of modular origami Modular origami forms may be flat or three dimensional. Flat forms are usually ... to be polyhedron regular polyhedra or tessellations of simple polyhedra. There are some modular origami that are approximations of fractals , such as Menger s sponge . Macro modular origami is a form of modular origami in which finished assemblies are themselves used as the building blocks to create ... Transformations Japan Publications ISBN 0 87040 852 6 published in 1990 Notable modular ... and artist network. http www.origamitube.com OrigamiTube.com Watch, fold, and show off your modular ... http www.cs.utk.edu plank plank pics origami penultimate intro.html James S. Plank s Penultimate Modular ... more details
A modular stadium ref cite web url http www.dailycommercialnews.com article id38724 title Daily Commercial News Temporary BC Lions stadium the first of its kind in North America date accessdate 2011 03 28 ref ref cite web url http www.journalofcommerce.com article id39401 title Journal of Commerce Overlay work wraps up Empire Field construction in Vancouver date accessdate 2011 03 28 ref ref cite web url http www.vancouversun.com sports Welcome Empire Field Lions fans 3162075 story.html?tab PHOT title Vancouver Sun Welcome to Empire Field, Lions Fans accessdate 2011 03 28 ref ref cite web url http www.worldstadiums.com stadium pictures europe germany hessen wiesbaden brita.shtml title Modular Stadium Brita Arena, Germany accessdate 2011 03 28 ref ref cite web url http www.fussballtempel.net caf LBA Hugo Chavez.html title Modular Stadium Hugo Ch vez Stadium, Baninah accessdate 2011 03 28 ref is a sports facility that is constructed of modular components. In contrast to a temporary stadium, modular stadiums are not time limited constructions, but rather permanent ones. The actual structure is thereby built without the use of concrete. The focus here is on the steel construction . Individual elements are used for modular construction, making it possible to enlarge or downsize even after actual completion. Due to this method, the structures remain flexible, reusable, and when necessary, can be adapted to new requirements with minimal effort for instance, when a soccer club advances ... sports facilities when the athletes have moved on. Even though modular stadiums are built for permanent ... they are quickly and cost efficiently built with prefabricated modules. The modular construction also has another great benefit, which will become even more significant in the future Suppose that a modular ... World Cup 2022 , there have already been design concepts created for the construction of modular stadiums and even plans submitted for modular extensions of existing sports facilities. ref cite web url ... more details
Infobox record label name Modular Recordings image image bg white parent Universal Music founded 1998 founder Steve Pavlovic distributor Universal Music genre Rock music Rock , Electronica , Electropop country Australia location Sydney url http www.modularpeople.com Modular Records is an Australia n record label . It was established by Sydney based music promoter Steve Pavlovic as a joint venture with EMI , but is now distributed and half owned by Universal Music in Australia. Modular has released recordings by local artists such as Eskimo Joe , Ben Lee , The Avalanches , Wolfmother , Cut Copy , The Bumblebeez , Van She , Rocket Science band Rocket Science , Ghostwood band Ghostwood , The Presets and Tame Impala , as well as local releases of international artists including Dom band Dom , Yeah Yeah Yeahs , Chromeo , Colder , Klaxons The EP Xan Valleys , Ladyhawke , New Young Pony Club , MSTRKRFT , and Softlightes . History Founded in 1998 by Sydney concert promoter Steve Pavlovic . ref name lotd cite web url http www.smh.com.au news entertainment music lord of the dance 2008 12 04 1228257191327.html?page fullpage contentSwap1 title Lord of the Dance accessdate 2008 12 08 author Palathingal ... of regular Modular parties and tours the label began to grow and Modular came to prominence ... 2005. http www.themusic.com.au im m archive 2005 050830 470 eliezer.php Mid 2006 modular signed ... of new acts including Ghostwood , Plug In City and The Whitest Boy Alive . Selected discography Modular Presents Leave Them All Behind 2005 Modular Presents Leave Them All Behind 2 2007 Modular Presents ... 09 16 . We Heart Modular . New Music Press , pp. 16 17. refend reflist External links http www.modularpeople.com Official Modular website http www.myspace.com modularpeople Official Modular US MySpace page Navbox name Modular Recordings title Modular Recordings artists titlestyle background pink list1 ... de Modular Recordings ... more details
Dablink For a group whose lattice of subgroups is modular see Iwasawa group . In mathematics , the modular ... , and many other areas of advanced mathematics. The modular group can be represented as a group mathematics group of geometric transformations or as a group of matrix math matrices . Definition The modular ... operation is the usual matrix multiplication multiplication of matrices . Some authors define the modular group to be PSL 2, Z , and still others define the modular group to be the larger group SL 2, Z . However, even those who define the modular group to be PSL 2, Z use the notation of SL 2, Z , with the understanding ... and quad s cp dq. math Elements of the modular group provide a symmetry on the two dimensional period ..., such as elliptic functions , possess a modular group symmetry. The action of the modular group ... from the origin the action of the modular group on a fraction never takes a visible irreducible ... to Pell s equation . In both cases, the numbers can be arranged to form a semigroup subset of the modular group. Group theoretic properties Presentation The modular group can be shown to be generating ... z 1 math so that every element in the modular group can be represented in a non unique way by the composition ... October 2011 that these are a complete set of relations, so the modular group has the presentation ... describes the modular group as the rotational triangle group 2,3, as there is no relation on T , and it thus ... that the modular group is isomorphic to the free product of the cyclic group s C sub 2 sub and C sub 3 sub math Gamma cong C 2 C 3 math Braid group File Braid modular group cover.svg thumb 376px The braid group B sub 3 sub is the universal central extension of the modular group. The braid group B sub 3 sub is the universal central extension of the modular group, with these sitting as lattices ... mathbf R math . Further, the modular group has trivial center, and thus the modular group is isomorphic ... for all Hurwitz surface s. Relationship to hyperbolic geometry See also PSL2 R The modular group is important ... more details
Infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name The Modular Man title orig translator image File The Modular Man.jpg image caption author Roger MacBride Allen illustrator cover artist country flag USA language English language English series genre Science fiction publisher Bantam Books release date 1992 english release date media type Print pages 306 pp isbn 0 553 29559 4 preceded by followed by The Modular Man is a science fiction novel by American writer Roger MacBride Allen . It is the fourth in the Next Wave series. Plot summary The novel concerns the issue of personhood and what it takes to be considered a member of the moral universe. There are three main characters Herbert the vacuum cleaner, who is modified by his owner, David Jantille, a scientist who specializes in figuring out how to mindload . Mindloading is the act of a human downloading their mind into a machine. A successful mindload entailss the death of the human. It is a way for humans to become immortal, if only in the form of vacuum cleaner. ref The Modular Man by Roger MacBride Allen, Bantam Books, Copyright 1996. ref The book begins with the arrest of Herbert, the vacuum cleaner, for David s murder . David s wife, Suzanne Jantille, is a trial attorney who is a quadriplegic as a result of a car crash that also paralyzed her husband. She lives through a Remote person who has all human senses except for the ability to feel by touch. She can guide the remote person through a helmet attached to her bio body , and retrieves all video and audio signals through the remote. She can function as a whole human being, but the outside world notices that she is a remote, does not approve. Suzanne defends Herbie, with the help of an astute journalist and a police officer who has access to documents that she wouldn t otherwise. The book ends with a recognition of David s humanity ..., her ultimate death. References reflist DEFAULTSORT Modular Man, The Category 1992 novels ... more details
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