In computer science , the SatisfiabilityModuloTheories SMT problem is a decision problem for logical formulas with respect to combinations of background Theory mathematical logic theories expressed in classical first order logic with equality. Examples of theories typically used in computer science are the theory of real numbers , the theory of integers , and the theories of various data structure s such as List computing list s, Array data structure arrays , bit vector s and so on. Basic terminology ... Herde Ratschan Schubert 2007 . External links http smtlib.org SMT LIB The SatisfiabilityModuloTheories Library http www.smtcomp.org SMT COMP The SatisfiabilityModuloTheories Competition http ... NP complete problems Category Formal methods Category Electronic design automation Category Satisfiability problems fr SatisfiabilityModuloTheories SMT ru SatisfiabilityModuloTheories ... pub tinelli papers NieOT JACM 06.pdf contribution Solving SAT and SAT ModuloTheories From an Abstract ... is satisfiable. In other words, imagine an instance of the Boolean satisfiability problem ... theory ref http www.csl.sri.com users demoura smt comp introduction.shtml ref . Other theories include the theories of array data structure arrays and List computing list structures useful for modeling ... satisfiability problem Boolean SAT instance in which various sets of variables are replaced by predicate mathematical logic predicate s from a variety of underlying theories. Obviously, SMT formulas ... theories means that the Boolean SAT solver has to work a lot harder than necessary to discover ... theories Most of the common SMT approaches support Decidability logic decidable theories ... an extension of the SMT problem to non linear theories, e.g. determine whether math begin align ... arithmetic theories over the reals are ABsolver Harv Bauer Pister Tautschnig 2007 , which employs ... Routing Approach via Search Based Boolean Satisfiability , IEEE Transactions on Computer Aided ... more details
In mathematical logic , satisfiability and validity are elementary concepts concerning interpretation logic interpretation . A formula is satisfiable with respect to a class of interpretations if it is possible to find an interpretation that makes the formula true ref See, for example, Boolos and Jeffrey, 1974, chapter 11. ref . A formula is valid if all such interpretations make the formula true. These notions can be relativised to satisfiability and validity within an axiomatic Theory mathematical logic theory , where we count only interpretations that make all axioms of that theory true. The opposites of these concepts are unsatisfiability and invalidity , that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false. These four concepts are related to each other in a manner exactly analogous to Aristotle s square of opposition . The four concepts can be raised to apply to whole theories a theory ... of the theory false. Reduction of validity to satisfiability For classical logic s, it is generally possible to reexpress the question of the validity of a formula to one involving satisfiability, because ... positive propositional calculus , the questions of validity and satisfiability may be unrelated ... , the satisfiability problem is trivial, as every formula is satisfiable, while the validity problem is Co NP complete co NP complete . Propositional satisfiability main Propositional satisfiability In the case of classical propositional logic , satisfiability is decidable for propositional formulae. In particular, satisfiability is an NP complete problem, and is one of the most intensively studied problems in computational complexity theory . Satisfiability in first order logic Satisfiability ... validity of a formula is a semi decidable problem. If satisfiability were also a semi decidable problem ... and Logic . Cambridge University Press. See also 2 satisfiability Boolean satisfiability problem Karp ... more details
Wiktionary modulo In the mathematical community, the word modulo jargon modulo is often used informally, in many imprecise ways. Generally, to say A is the same as B modulo C means, more or less, A and B are the same except for differences accounted for or explained by C . In the various branches of mathematics, it may be used in connection with Modular arithmetic , a b mod n Modulo operation , in computing, the remainder after division Ideal ring theory , a special subset of a ring Equivalence relation It also may refer to M dulo , a Brazilian company specializing in IT governance Ferrari Modulo , a concept car from 1970 See also Modulus disambiguation Module disambiguation Up to disambig Category Mathematical terminology ... more details
In formal logic , Horn satisfiability , or HORNSAT , is the problem of deciding whether a given set of propositional Horn clause s is satisfiable. A Horn clause is a Clause logic clause with at most one positive literal, called the head of the clause, and any number of negative literals, forming the body of the clause. A Horn formula is a propositional formula formed by logical and conjunction of Horn clauses. The problem of Horn satisfiability is solvable in P complexity polynomial time . A polynomial time algorithm for Horn satisfiability is based on the rule of unit propagation if the formula contains a clause composed of a single literal math l math a unit clause , then all clauses containing math l math are removed, and all clauses containing math neg l math have this literal removed. The result of the second rule may itself be a unit clause, which is propagated in the same manner. The formula is satisfiable if this transformation does not generate a pair of opposite unit clauses math l math and math neg l math . Horn satisfiability is actually one of the hardest or most expressive problems which is known to be computable in polynomial time, in the sense that it is a P complete P complete problem. This algorithm also allows determining a truth assignment of satisfiable Horn formulae all variables contained in a unit clause are set to the value satisfying that unit clause all other literals are set to false. The resulting assignment is the minimal model of the Horn formula, that is, the assignment having a minimal set of variables assigned to true, where comparison is made ... time therefore, the satisfiability of such formulae is in P as it can be solved by first performing this replacement and then checking the satisfiability of the resulting Horn formula. ref cite journal ... also Unit propagation Boolean satisfiability problem 2 satisfiability References references Category Logic in computer science Category P complete problems Category Satisfiability problems comp sci theory ... more details
Infobox Automobile image Image Ferrari modulo.jpg 250px center Ferrari Modulo name Ferrari 512 S Modulo manufacturer Ferrari parent company Fiat Group designer Paolo Martin at Pininfarina production 1970 br 1 unit class Concept car body style semi monocoque layout RMR layout engine 5.0 L V12 engine V12 transmission 5 speed manual transmission manual length 4480 mm 176.4 in width 2040 mm 80.3 in height 935 mm 36.8 in wheelbase 2405 mm 94.7 in weight 900 kg 1984 lb predecessor N A successor N A related Ferrari 512 S The Ferrari 512 S Modulo is a concept car designed by coach maker Pininfarina , unveiled at the 1970 Geneva Motor Show . By January 1970, Ferrari had built a series of twenty five Ferrari 512 Ferrari 512 S racing cars for homologation purposes, just like Porsche had done in 1969 with the Porsche 917 . This meant that dozens of high powered mid engine d race cars were available. Ferrari could not race or sell all of the manufactured cars, and gave chassis number 1046 that means the 23rd to Pininfarina. The Modulo was the last ... V12 engine. The Modulo is a working car, although the limitations of the bodywork prevent it being practical or road legal. gallery Image Ferrari modulo 2.jpg Side view Image Wikipfarina.jpg ... Ferrari Modulo at Pininfarina s web site Italian http www.paolomartindesigner.com gallery.new view.asp?nid 10&cgallery Cars Ferrari Modulo at Paolo Martin s web site http www.ultimatecarpage.com car 153 Ferrari 512 S Modulo.html Ferrari 512 S Modulo at Ultimatecarpage http www.paolomartindesigner.com Paolo Martin s site including Video of Ferrari Modulo driven mostly in a straight line Classicpow auto stub Category Ferrari vehicles Modulo Category Concept automobiles Category Pininfarina de Ferrari Modulo es Ferrari Modulo fa fr Ferrari Modulo it Ferrari Modulo ja pl Ferrari Modulo ... more details
Unreferenced date December 2009 Cleanup date January 2009 The word modulo Latin, with respect to a modulus of is the Latin ablative of wikt modulus modulus which itself means a small measure. It was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. Ever since, however, modulo has gained many meanings, some exact and some imprecise. Usage This usage ... to b modulo n means that a &minus b is a multiple of n , or equivalently, a and b ... , given two numbers either integer or real , a and n , a modulo n is the remainder after numerical Division mathematics division of a by n , under certain constraints. See modulo operation . Two members of a ring mathematics ring or an algebra are congruent modulo an ideal ring theory ideal if the difference ... modulo a normal subgroup if and only if ab sup &minus 1 sup is a member of the normal subgroup. See quotient group and isomorphism theorem . Two subsets of an infinite set are equal modulo finite ... or congruent to b modulo R if aRb . Example Using Gauss s definintion 13 is congruent 63 modulo 10 to mean 13 and 63 differ by a multiple of 10 However, the word modulo has acquired several related ..., to say A is the same as B modulo C means, more or less , as in A and B are the same except ..., using modulo as a term alerting the hearer. The use of the term in modular arithmetic is a special ... by C is that of identifying with each other any two things that are the same modulo C . Here are several ways in which modulo is used. http and https are the same, modulo encryption. means the only ... mean, equal modulo case. indicates that the first speaker s words are true only for a relaxed sense ... students performed equally well on the exam, modulo some minor computational mistakes. means that the two ... is finished modulo testing means this code is finished except for testing . See also Up to DEFAULTSORT Modulo Jargon Category Mathematical terminology de Restklasse nl Restklasse sk Modulo ur ... more details
. In computing , the modulo operation finds the remainder of division mathematics division of one number by another. Given two positive numbers, math a the dividend and math n the divisor , a modulo ... theory . TOC clear Remainder calculation for the modulo operation class wikitable style float right margin left 1em margin right 0 width 30 Integer modulo operators in various programming languages ... tt Mod tt Divisor rowspan 2 Fortran tt mod tt Dividend tt modulo tt Divisor Game Maker Language ... language Scheme tt modulo tt Divisor tt remainder tt Dividend rowspan 2 Scheme programming language ... 2 SenseTalk tt modulo tt Divisor tt rem tt Dividend Smalltalk tt tt Divisor SQL SQL 1999 tt mod x,y ... language tt MODULO x,y tt Divisor class wikitable style float right clear right margin left 1em margin right 0 width 30 Floating point modulo operators in various programming languages Language Operator ... constitutes the result of a modulo operation depends on the programming language and or the underlying .... See the table for details. a modulo 0 is undefined in the majority of systems, although ... 1985 Rounding floating point numbers round to nearest convention . Common pitfalls When the result of a modulo ... is equal to 1 source lang c bool is odd int n return n 2 1 source But in a language where modulo has ... Modulo operation expression Some calculators have a mod function button, and many programming languages ... that use , mod , or Mod as a modulo or remainder operator, such as code a n code or code a mod ... issues Modulo operations might be implemented such that a division with a remainder is calculated each time. For special cases, there are faster alternatives on some hardware. For example, the modulo ... than modulo, these alternative forms can result in faster calculations. Compiler optimization ... performance. Note This will not work for the languages whose modulo have the sign of the dividend including C , because if the dividend is negative, the modulo will be negative however, code expression ... more details
on Satz SAT solver Satz , IncMaxSatz, IUT MaxSatz, WBO. Satisfiability based SAT4J, QMaxSat. Unsatisfiability based msuncore, WPM1, PM2. See also Boolean satisfiability problem Boolean Satisfiability Problem Constraint satisfaction SatisfiabilityModuloTheories External links http users.ecs.soton.ac.uk ...Context date October 2009 In computational complexity theory , the Maximum Satisfiability problem , or MAX SAT , is the problem of determining the maximum number of clauses, of a given Propositional formula Boolean formula, that can be satisfied by some assignment. The MAX SAT problem is NP hard , since its solution easily leads to the solution of the boolean satisfiability problem , which is NP complete .In particular math O NP log math for unweighted, and math O NP NP math for weighted. From another point of view, it is also APX complete, and thus does not admit a Polynomial time approximation scheme PTAS unless P NP. ref Mark Krentel. The Complexity of Optimization Problems. 1986. ACM. ref ... 2004. ref MAX SAT is one of the optimization extensions of the boolean satisfiability problem , which ... at most 2 literals, as in 2 satisfiability , we get the MAX 2SAT problem. If they are restricted to at most 3 literals per clause, as in 3 satisfiability , we get the MAX 3SAT problem. Related problems There are several extensions to MAX SAT The weighted maximum satisfiability problem Weighted ... clauses. The partial maximum satisfiability problem PMAX SAT asks for the maximum number of clauses ... be satisfied. The soft satisfiability problem soft SAT , given a set of SAT problems, asks for the maximum ... . In Journal of Heuristics 12 4 pp. 375 392. Springer, 2006. ref . The minimum satisfiability ... presented in the well known conference on the boolean satisfiability problem and related problems ... pseudo boolean satisfiability problem and the quantified boolean formula problem. Solvers There are several ... science Category Combinatorial optimization Category Satisfiability problems ... more details
article. The theories of the etiology of dyslexia have and are evolving with each new generation of dyslexia researchers, and the more recent theories of dyslexia tend to enhance one or more of the older theories as understanding of the nature of dyslexia evolves. Theories of Developmental Dyslexia The following theories should not be viewed as competing, but viewed as theories trying to explain .... ref name theories Cite journal author Ramus F, Rosen S, Dakin SC title Theories of developmental ... cgi pmidlookup?view long&pmid 12615643 ref ref name theories ref Cite journal author ... relationships when reading text. ref name theories ref Cite journal author Stoodley CJ, Stein ... . ref name theories ref Cite journal author Ray NJ, Fowler S, Stein JF title Yellow filters ... annals.1325.027 url ref Naming speed deficit and double deficit theories The speed with which an individual ... the graphic letter symbols and speech sounds which they represent. ref name theories Rapid auditory ... name theories Visual theory The visual theory represents a traditional perspective of dyslexia, as being ... causes of dyslexia ref name theories References Reflist 2 Dyslexia DEFAULTSORT Theories Of Dyslexia ... Theories of dyslexia ... more details
WARNINGS ONLY AFTER THE OMISSION HAS BEEN ADDRESSED. USER ANDRIES 17 MARCH 2008 Theory Theories of religion can be divided into substantive theories focusing on what religion is and functional or reductionism reductionist theories focusing on what it does . Influential substantive theories have been proposed by Theories of religion Edward Burnett Tylor and James George Frazer Tylor and Frazer focusing on the explanatory value of religion for its adherents , by the theology theologian Theories ... experiences that are both fascinating and terrifying , Theories of religion Mircea Eliade ... for patterns in mythology in various religions . Influential functional theories have been proposed by Theories of religion Karl Marx Karl Marx focusing on the economic background , Theories of religion ... beliefs , and Theories of religion mile Durkheim and functionalism mile Durkheim focusing on the social function of religions . Theories of religion Max Weber Max Weber did not so much propose ..., the anthropology anthropologists Theories of religion E. E. Evans Pritchard E. E. Evans Pritchard and Theories of religion Clifford Geertz Clifford Geertz performed detailed ethnography ethnographical studies of primitive cultures, and came to the conclusion that earlier theories had been one sided at best. Geertz denied that it would ever be possible to propose a general theory of religion. The Theories ... theories have been proposed since presocratic times. ref name Robert A page 49 Segal 2005, p. 49 ... advocated comparative religion . ref Pals, page 3 ref Later serious doubts were raised, by Theories ... only treats influential theory theories about religion that are open for empirical verification or falsifications i.e. attempts to scientific theories. This means that most religious views will not be treated here. Theories of religion can be classified into. ref Pals, page 12 ref Substantive or essentialist theories that focus on the contents of religions and the meaning the contents has for people ... more details
There are a number of theories attempting to address technology , which tend to be associated with the disciplines of Science and Technology Studies science and technology studies STS and communication studies . Most generally, the theories attempt to address the relationship between technology and society and prompt questions about Structure and agency agency , Technological Determinism determinism autonomy , and teleonomy . Essay like date January 2010 If forced, one might categorize them into social and group theories. Additionally, one might distinguish between descriptive and critical theories. Descriptive theories attempt to address the definition and substance of technology, how does it emerge, change, and, of course, what is its relation to the human social sphere? More substantively, to what extent is technology autonomous and how much force does it have in determining social structure or human practice? Critical theories of technology often take a descriptive theory as their basis ... from one another and of course build upon seminal theorists that preceded them. Social theories ... autonomy. Key authors include Thomas P. Hughes 1992 and Luhmann 2000 . Critical theories ... so as to critique and or emphasize aspects of technology as addressed by the mainline theories. For example ... of technology including Gilbert Simondon and Andr Leroi Gourhan . Group theories There are also a number of technology related theories that address how media technology affects group processes. Broadly, these theories are concerned with the social effects of communication media. Some e.g. ... . Other theories social presence, SIDE, media naturalness are concerned with the consequences of those ... effects based on theories of social identity e.g., Turner et al., 1987 . The SIDE ... towards a goal , support affective and well being norms and roles . Analytic theories Finally, there are theories of technology which are not defined or claimed by a proponent, but are used ... more details
Aether theories in early modern physics proposed the existence of a medium, the aether also spelled ether , from the Greek word Polytonic , meaning upper air or pure, fresh air ref name aetherDict , a space filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic waves. The assorted aether theories embody the various conceptions of this Medium optics medium and Substance theory substance . This early modern aether has little in common with the Aether classical element aether of classical elements from which the name was borrowed. Theories Although hypotheses of the aether vary somewhat in detail they all have certain characteristics in common. In 19th century theories, aether is considered to be a physical medium occupying every point in space, including within material bodies. A second essential feature is that aether s properties give rise to the electric and magnetic phenomena and determines the propagation velocity of their effects. Therefore the speed of light and all other propagating effects are determined by the physical properties of the aether at the relevant location, analogous to the way that gaseous, liquid and solid media affect the propagation of sound waves. The aether is considered the overall reference frame for the universe and thus velocities are all absolute relative to its rest frame. Therefore, in this view, any physical consequences of those velocities are considered as having an absolute ... of proposed Aether drag hypothesis aether dragging theories could explain the null result but these were ... from E. T. Whittaker s A History of the Theories of Aether and Electricity . PDF format Maxwell, James ... Whittaker, Edmund Taylor year 1910 title A History of the theories of aether and electricity edition ... Citation author Schaffner, Kenneth F. year 1972 title Nineteenth century aether theories ... , Encyclop dia Britannica , Thirteenth Edition 1926 . Category Aether theories de ther Physik ... more details
about the History of Science book Theory of everything disambiguation Orphan date February 2009 Infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name Theories for Everything title orig translator image image caption author Bruce Stutz, John Langone and Andrea Gianopoulos illustrator cover artist country language series genre publisher National Geographic Society release date 2006 english release date media type Print Leather Cover and Hard Cover versions pages 408 Deluxe Version isbn 0 7922 3912 1 dewey 509 22 congress Q125 .L29 2006 oclc 70232302 preceded by followed by Theories for Everything subtitled An Illustrated History of Science, From the Invention of Numbers to String Theory is a book, published by the National Geographic Society which details the history of science from its earliest beginnings to the latest discoveries. Available in two versions, Deluxe and Standard, it was available through order to National Geographic members and on the online shop. It was co authored by Bruce Stutz, Andrea Gianopoulos and John Langone to whom it was dedicated to. The book is subdivided into six chapters, each focusing on a specific area of science and highlights the achievements of past scientists. Chapters Introduction Bruce Stutz The Heavens Andrea Gianopoulos The Human Body John Langone Matter and Energy Bruce Stutz Life Itself Bruce Stutz Earth and Moon Andrea Gianopoulos Mind and Behaviour John Langone category Science books Category 2006 books Category National Geographic Society books ... more details
Various theories of victimology exist, each with the aim of explaining why certain people become victims of crimes, and why others do not. Some people view some theories in a negative light, believing that to conjecture as to the causes of victimisation is tantamount to victim blaming blaming the victim for crime, at least partly. ref name web Cite web title Victimology Theory accessdate 2010 09 03 url http faculty.ncwc.edu mstevens 300 300lecturenote01.htm ref Abuse in general The lifestyle exposure theory is one theory of victimology which examines how the lifestyle of a person contributes to the likelihood that he will become the victim of a crime. ref name web Abuse towards women The interpersonal model describes violence against women as a consequence of individual psychology and abnormal interpersonal relations. ref name rosenberg124 Rosenberg 1991 , pg. 124 ref The family violence model explains the phenomenon more in terms of socioeconomic and educational factors. ref name rosenberg124 Finally, the gender politics model is an attempt to schematise abuse of women as attempts by males in general to maintain their position of power over females. ref name rosenberg124 See also Abuse Victimology References references Bibliography Cite book publisher Oxford University Press US isbn 9780195064377 last Rosenberg first Mark L. coauthors Mary Ann Fenley title Violence in America a public health approach date 1991 Category Victimology Criminology stub ... more details
Unreferenced date December 2009 Orphan date December 2009 Modulo N code is a lossy compression algorithm used to compress correlated data sources using modulo arithmetic . Compression When applied to two nodes in a computer networking network whose data are in close range of each other Modulo N code requires one node say odd to send the coded data value as the raw data math M o D o math the even node is required to send the coded data as the math M e D e mod N math . Hence the name Modulo N code. Since it is known that for a number K, at least math log 2 K math bits are required to represent it in binary. So the modulo coded data of the two nodes requires totally math log 2 M o log 2 M e math . As we can generally expect math log 2 M e le log 2 M o math always, because math M e le N math . This is the how compression is achieved. A compression ratio achieved is math C.R frac log 2 M o log 2 M e 2log 2 M o math . Decompression At the receiver by joint decoding we may complete the process of extracting the data and rebuilding the original values. The code from the even node is reconstructed by the assumption that it must be close to the data from the odd node. Hence the decoding algorithm retrieves even node data as BR math CLOSEST M o,N.k M e math . The decoder essentially finds the closest match to math M o simeq N.k M e math and the decoded value is declared as math N.k M e math Example For a mod 8 code, we have Encoder D o 43,D e 47 M o 43,M e 47 mod 8 7, Decoder M o 43,M e 47 mod 8 7, D o 43,D e CLOSEST 43,8.k 7 math 43 simeq 8.5 7 math D o 43,D e 47 Modulo N decoding is similar to phase unwrapping and has the same limitation If the difference from one node to the next is more than N 2 if the phase changes from one sample to the next more than math pi math , then decoding leads to an incorrect value. See also DISCUS is a more sophisticated technique for compressing ... designed for correlated data sources. DEFAULTSORT Modulo N Code Category Information theory Category ... more details
mergefrom Laughter in literature date December 2010 There are many theories of humour which attempt to explain what humour is, what social function it serves, and what would be considered humorous. It would be very difficult to explain humor to a hypothetical person who did not have a sense of humour already. In fact, to such a person humor would appear to be quite strange if not outright irrational behavior. Among the prevailing types of theories that attempt to account for the existence of humour there are psychology psychological theories, the vast majority of which consider humour to be very healthy behavior there are Spiritualism beliefs spiritual theories which may, for instance consider humor to be a gift from God there are also theories that consider humour to be an unexplainable mystery, very much like a mysticism mystical experience . ref Raymond Smullyan , The Planet Without Laughter , This Book Needs No Title ref Sense of humor, sense of seriousness One must have a sense of humor and a sense of seriousness to distinguish what is supposed to be taken literally or not. An even more keen sense is needed when humor is used to make a serious point. ref name SRF cite news title Seriousness Redeemed by Frivolity Ayckbourn s Intimate Exchanges work Journal of Modern Drama volume 53 issue 4 year 2010 pages 447 470 author Bernard F. Dukore url http utpjournals.metapress.com content n522p1833t225j18 ref ref When Congress makes a joke Congressional Humor as Serious and Purposeful Communication , International Journal of Humor Research. Volume 14, Issue 4, Pages 359 394, Nov ... recent development in the theory of laughter. ref Salvatore Attardo 1994 Linguistic Theories of Humor ... seemingly disparate theories of humor to predict that humor occurs when three conditions are satisfied ... Humor Theory Website Philosophy topics Use dmy dates date November 2010 DEFAULTSORT Theories Of Humor Category Humor research Category Theories of aesthetics uk ... more details
electromagnetism Theories of cloaking discusses various theories based on science and research , for producing an electromagnetic cloak of invisibility. Theories presented employ metamaterial cloaking transformation optics , event cloaking , dipolar scattering cancellation , tunneling light transmittance , sensors and active sources , and acoustic metamaterials acoustic cloaking . A cloaking device is one where the purpose of the transformation is to hide something, so that a defined region of space is invisibility invisibly isolated from passing electromagnetic fields see Metamaterial cloaking ref name Eng space Cite journal last Kildishev first A.V. coauthors and Shalaev, V.M. title Engineering space for light via transformation optics journal Optics Letters volume 33 issue 1 pages 43 45 publisher Optical Society of America date 2007 12 18 2008 01 01 url http cobweb.ecn.purdue.edu shalaev Publication list files OL 2033 20 1 20January 202007.pdf doi 10.1364 OL.33.000043 accessdate 2010 02 14 ref ref name TLTC 1 or sound waves. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself. Along with this basic cloak of invisibility invisibility cloak , other related concepts have been proposed in peer review ed, scientific article s, and are discussed here. Naturally, some of the theories discussed here also employ metamaterials, either metamaterial electromagnetic or acoustic metamaterials acoustic , although often in a different manner than the original demonstration and its successor, the broad band cloak . The first electromagnetic cloak The first electromagnetic cloaking device was produced in 2006, using produced with gradient index metamaterial s. This has led to the burgeoning field of transformation ... Electromagnetic wormholes, as an optical device not gravitational are derived from cloaking theories ... sonar is also part of these theories. Up to this point, only mathematical theoretical solutions have ... more details
DISPLAYTITLE Primitive root modulo n In modular arithmetic , a branch of number theory , a primitive root modulo n is any number g with the property that any number coprime to n is Modular arithmetic Congruence relation congruent to a power of g modulo n . In other words, g is a generator of the multiplicative group of integers modulo n . That is, if g is a primitive root modulo n , then for every ... n . Such k is called the index or discrete logarithm of a to the base g modulo n . Carl Friedrich ... 55 is Constructive proof constructive . Elementary example The number 3 is a primitive root modulo ... modulo 7 is 6. The remainders in the period, which are 3, 2, 6, 4, 5, 1, form a rearrangement of all nonzero remainders modulo 7, implying that 3 is indeed a primitive root modulo 7. Curiously, permutations ... group with multiplication Modular arithmetic modulo n as the operation it is denoted by Z sub n sub sup × sup and is called the group of units modulo n or the group of primitive classes modulo n . As explained in the article multiplicative group of integers modulo n multiplicative group of integers modulo n , this group is cyclic group cyclic if and only if n is equal ref Gauss, DA, arts 82 ... . A generating set of a group generator of this cyclic group is called a primitive root modulo n ... mod n is called the multiplicative order of a modulo n . In other words, for a to be a primitive root modulo n , n has to be the smallest power of a which is 1 mod n . Take for example n 14. The elements ... 6 of them. Here is a table of their powers modulo 14 code x x, x sup 2 sup , x sup 3 sup , ... mod ... and 5 are the primitive roots modulo 14. For a second example let n 15. The elements of Z sub 15 sub ... roots modulo 15. Table of primitive roots This is Gauss s table of the primitive roots from the Disquisitiones ... 100 the second column is a primitive root modulo that number. The columns are labelled with the primes less than 97. The entry in row p column q is the index of q modulo p for the given root. blockquote ... more details
DISPLAYTITLE Root of unity modulo n In mathematics, the k th root of unity modulo n for positive integer ... such exponent for given x , then x is called a primitive k th root of unity modulo n ... title Roots of unity and nullity modulo n journal Proceedings of the American Mathematical Society ... gerg papers downloads RUNM.pdf accessdate 2011 02 20 ref Do not confuse this with a Primitive root modulo n primitive element modulo n , where the primitive element must generate all Unit ring theory ... roots and primitive roots of unity modulo n for n 2, but for some n there is no primitive element modulo n . Being a root or a primitive root modulo n always depends on the exponent k and the modulus n , whereas being a primitive element modulo n only depends on the modulus n &ndash ... math th roots of unity modulo math n math by math f n,k math . It satisfies several interesting laws ... of unity Properties The maximum possible radix exponent for primitive roots modulo math n math is math ... of a widely accepted symbol, we denote the number of primitive math k math th roots of unity modulo ... k th root of unity modulo n By Exponentiation by squaring fast exponentiation you can check ... text prime x k p not equiv 1 pmod n math . Finding a primitive k th root of unity modulo n Among the primitive ... k th roots modulo n Once you have a primitive math k math th root of unity math x math , every power ... are coprime, there exists an inverse math l 1 math of math l math modulo math k math . This yields ... k th root of unity modulo n You may want to know, in what integer residue class ring s you ... to divide by math k math , that is math k math shall also be a unit modulo math n math . A simple ... appropriate moduli. Finding an n with multiple primitive roots of unity modulo n If you want to have ... k m math th roots of unity modulo math n math , the following theorem reduces the problem to a simpler ... modulo math n math if and only if there is a primitive math mathrm lcm k 1, ..., k m math th root ... more details
multiple issues orphan May 2008 Theories on the causes of poverty are the foundation upon which poverty reduction strategies are based. While in developed nations poverty is often seen as either a personal or a structural defect, in developing nations the issue of poverty is more profound due to the lack of governmental funds. Some theories on poverty in the developing world focus on cultural characteristics as a retardant of further development. Other theories focus on social and political aspects that perpetuate poverty perceptions of the poor has a significant impact on the design and execution of programs to alleviate poverty. Causes of poverty in the United States Poverty as a personal failing When it comes to poverty in the United States , there are two main lines of thought. The most common line of thought within the U.S. is that a person is poor because of personal traits. ref name rank full harvnb Rank Yoon Herschl 2003 pp full 3 29 . ref These traits in turn have caused the person to fail. Supposed traits range from personality characteristics, such as laziness, to educational levels. Despite this range, it is always viewed as the individual s personal failure not to climb out of poverty. This thought pattern stems from the idea of meritocracy and its entrenchment within U.S. thought. Meritocracy, according to Katherine S. Newman is the view that those who are worthy are rewarded and those who fail to reap rewards must also lack self worth. ref harvnb Newman 1999 p 16 . ref This does not mean that all followers of meritocracy believe that a person in poverty deserves their low standard of living. Rather the underlying ideas of personal failure show in the resistance to social and economic programs such as welfare a poor individual s lack of prosperity shows a personal failing and should not be compensated or justified by the state. Poverty as a structural failing CITEREFRankYoonHershl2003 Rank, Yoon, and Herschl 2003 present a contrary argument to the idea ... more details
or math mathbb Z n math i.e., the ring of integers modulo the Ideal ring theory ideal .... math Structure Powers of 2 Modulo 2 there is only one relatively prime congruence class, 1, so math mathbb Z 2 mathbb Z times cong 1 math is trivial. Modulo 4 there are two relatively prime congruence ... elements. Modulo 8 there are four relatively prime classes, 1, 3, 5 and 7. The square of each of these is 1, so math mathbb Z 8 mathbb Z times cong C 2 times C 2, math the Klein four group . Modulo 16 ... a generator is called a primitive root modulo n . Since all the math mathbb Z n mathbb Z times ... maths MultiGrpModN.html Calculator by Shing Hing Man MathWorld title Modulo Multiplication Group ... vi Nh m nh n c c s nguy n modulo n zh n ... more details
homology and cohomology theories in algebraic topology that are defined on the categories of CW complex es or spectrum homotopy theory spectra . For other sorts of homology theories see the See also ... product of two spectra. If X is a spectrum, then it defines generalized homology and cohomology theories ... of Y Ordinary homology theories These are the theories satisfying the dimension axiom of the Eilenberg ... numbers, or the integers mod a prime p . The cohomology functors of ordinary cohomology theories are represented by Eilenberg MacLane space s. On simplicial complexes, these theories coincide with singular .... These are the easiest of all homology theories. The homology groups HQ sub n sub X are often .... K theories The simpler K theory K theories of a space are often related to vector bundle s over the space, and different sorts of K theories correspond to different structures that can be put ... p . Other K theories can also be given coefficients. Self conjugate K theory Spectrum KSC Coefficient ... Ph.D. dissertation, A new cohomology theory . Connective K theories Spectrum ku for connective K ... sub 1 sub sup 4 sup in dimension 8, the periodicity generator, modulo the relations that 2 0 ..., from which many of the other K theories can be derived. Bordism and cobordism theories Cobordism ... of some generalized cohomology theory. There are many such theories, corresponding roughly to the different structures that one can put on a manifold. The functors of cobordism theories are often represented ... spectra . In other words the corresponding homology and cohomology theories are no more powerful than ... F sub p sub v sub n sub , v sub n sub sup 1 sup , where v sub n sub has degree 2 p sup n sup 1 . These theories ... ring Theories related to elliptic curve s Elliptic cohomology Spectrum Ell Expand section date ... 1 Category Algebraic topology Category Cohomology theories Category Mathematics related lists Cohomology theories ... more details
facts about the &sigma structure. There are two common ways to specify theories List or describe ... are all true by the completeness theorem , satisfiability is equivalent to consistency be complete ... theories . be superstable have an atomic model mathematical logic atomic model have a prime model have a saturated model Pure identity theories The signature of the pure identity theory is empty ... theories in this language as follows. Any theory is either the theory of all sets of cardinality ... is not in N , for some finite or infinite subset N of the non negative integers. There are no theories .... The complete theories are the theories of sets of cardinality n for some finite n , and the theory ... is not necessarily true. Theories of equivalence relations are not all that difficult or interesting ... are sometimes used to produce examples of theories with certain spectrum of a theory spectra in fact by applying them to a small number of explicit theories T one gets examples of complete countable theories with all possible uncountable spectra. If T is a theory in some language, we define ..., but not categorical for any uncountable cardinal. There are 3 other very similar theories the theory ... of Boolean algebras. So the possible complete theories are The trivial algebra if this is allowed sometimes 0&ne 1 is included as an axiom. The theory with m &infin The theories with m a natural ... of degree n have a root, plus axioms fixing the characteristic. The classical examples of complete theories ... DF sub p sub of differential fields of characteristic p and similarly with the other theories below ... theories described above can be extended to complete recursively enumerable consistent theories. This is no longer true for most of the following theories they can usually encode both multiplication ... that G del s incompleteness theorem applies and the theories can no longer be both complete and recursively ... mathematics . Set theories The usual signature of set theory has one binary relation , no constants ... more details
The received view of theories is a position in the philosophy of science that identifies a scientific theory with a set of propositions which are considered to be linguistic objects, such as axiom axioms . Frederick Suppe describes the position of the received view by saying that it identifies scientific theories with an axiomatic calculi in which theoretical terms are given a partial observation interpretation by mean of correspondence rules. ref Suppe, Frederick 1989 , The Semantic Conception of Theories and Scientific Realism. Urbana University of Illinois Press. p. 33 ref The received view is generally associated with the logical positivism logical empiricists . Recently, the received view of theories has been displaced by the semantic view of theories as the dominant position in theory formulation in the philosophy of science. Notes references philosophy of science philo stub Category Metatheory of science ... more details
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