about numbers where permutations of their digits in some base yield related numbers the number theoretic concept cyclicnumber group theory summary in Repeating decimal Mergefrom Transposable integer discuss Talk CyclicnumberCyclic permutation of integer date September 2009 A cyclicnumber is an integer in which cyclic permutation s of the digits are successive multiples of the number. The most widely known is 142857 number 142857 142857 × 1 142857 142857 × 2 285714 142857 × 3 428571 142857 × 4 571428 142857 × 5 714285 142857 × 6 857142 Details To qualify as a cyclicnumber, it is required that successive multiples be cyclic permutations. Thus, the number 076923 would not be considered a cyclicnumber, even though all cyclic permutations are multiples 076923 ... fractions . A cyclicnumber of length L is the digital representation of 1 L 1 . Conversely, if the digital period of 1 p where p is prime is p &minus 1, then the digits represent a cyclicnumber. For example ... is a Prime number prime that does not Divisor divide b . Primes p that give cyclic numbers are called full reptend prime s or long primes . For example, the case b 10, p 7 gives the cyclicnumber 142857. Not all values of p will yield a cyclicnumber using this formula for example p 13 gives 076923076923 ... is a cyclicnumber. This procedure works by computing the digits of 1 p in base b , by long division ... Note that in ternary b 3 , the case p 2 yields 1 as a cyclicnumber. While single digits may be considered ... digits exist in any numeric base which is a Square number perfect square thus there are no cyclic numbers ... CyclicNumber title CyclicNumber Category Number theory Category Permutations de Zyklische Zahl ... 5 repeated digits, i.e. 555 repeated cyclic numbers, i.e. 142857142857 If leading zeros are not permitted on numerals, then 142857 is the only cyclicnumber in decimal . Allowing leading zeros, the sequence of cyclic numbers begins 142857 6 digits 0588235294117647 16 digits 052631578947368421 18 ... more details
A cyclicnumber ref http www.numericana.com data crump.htm Carmichael Multiples of Odd Cyclic Numbers ref is a natural number n such that n and n are coprime . Here is Euler s totient function . An equivalent definition is that a number n is cyclic iff any group mathematics group of order n is cyclic group cyclic . Any prime number is clearly cyclic. All cyclic numbers are square free integer square free . ref For if some prime square p sup 2 sup divides n , then from the formula for it is clear that p is a common divisor of n and n . ref Let n p sub 1 sub p sub 2 sub p sub k sub where the p sub i sub are distinct primes, then n p sub 1 sub 1 p sub 2 sub 1 p sub k sub 1 . If no p sub i sub divides any p sub j sub 1 , then n and n have no common prime divisor, and n is cyclic. The first cyclic numbers are 1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, OEIS A003277 . References reflist Category Number theory ... more details
There are many terms in mathematics that begin with cyclicCyclic chain rule , for derivatives, used in thermodynamics Cyclic code , linear codes closed under cyclic permutations Cyclic convolution , a method of combining periodic functions Cycle decomposition disambiguation Cyclic extension , a field extension with cyclic Galois group Cycle graph or cyclic graph is a connected, 2 regular graph Cycle graph algebra , a diagram representing the cycles determined by taking powers of group elements Circulant graph , a graph whose adjacency matrix is circulant Cycle graph theory , a nontrivial path from a node to itself Cyclic group , a group generated by a single element Cyclic homology , an approximation of K theory used in non commutative differential geometry Cyclic module , a module generated by a single element Cyclic notation , a way of writing permutations Cyclicnumber , a number such that cyclic permutations of the digits are successive multiples of the numberCyclic order , a binary relation for doubly linked lists Cyclic permutation , a permutation with one nontrivial orbit Cyclic polygon , a polygon which can be given a circumscribed circle Cyclic shift , also known as circular shift Cyclic symmetry , n fold rotational symmetry of 3 dimensional space See also Cycle disambiguation Cycle mathematics Category Mathematics related lists sv Cyklisk matematik ... more details
. The processes by which cyclic peptides are formed in cells are not yet fully understood. One interesting property of cyclic peptides, however, is that they tend to be extremely resistant to the process ... makes cyclic peptides attractive to designers of protein based drugs that may be used as scaffolds ... pmid 16543448 External links http www.cybase.org.au Cybase MeshName Cyclic Peptides Category ... more details
A cyclic permutation or circular permutation is a permutation built from one or more Set mathematics sets of elements in cyclic order . The notion cyclic permutation is used in different, but related ways Definition 1 image 050712 perm 1.png right mapping of permutation A permutation P over a Set mathematics set S with k elements is called a cyclic permutation with offset t if and only if the elements of S may be total order ordered c 1 c 2 ... c k and the mapping of P may be written as p c i c i t for i 1, 2, ..., k &minus t , and p c i c i t &minus k for i k &minus t 1, k &minus t 2, ..., k . Note Every cyclic permutation of definition type 1 will be constructed with exactly greatest common divisor gcd k , t disjoint cycles of equal length see cycles and fixed points . Cyclic permutations of definition type 1 are also called rotations , or circular shifts . Example math begin pmatrix 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 3 & 4 & 5 & 7 & 6 & 1 & 8 & 2 end pmatrix begin pmatrix 1 & 2 & 3 & 4 & 5 & 7 & 6 & 8 3 & 4 & 5 & 7 & 6 & 8 & 1 & 2 end pmatrix 1356 2478 math is a cyclic permutation with offset 2. It may be constructed with gcd ... perm 2.png right mapping of permutation A permutation is called a cyclic permutation if and only ... is a cyclic permutation of definition type 2 if and only if it is a cyclic permutation of definition ... A permutation is called a cyclic permutation if and only if only one of the constructing cycles will have length 1. Note Every cyclic permutation of definition type 3 may be seen as an union mathematics union of a cyclic permutation of definition type 2 and some fixed point mathematics fixed points . Every cyclic permutation of definition type 2 may be seen as a cyclic permutation of definition type ... end pmatrix 146837 2 5 math See also Cyclic permutation of integer Cycle notation Cycles and fixed points Stirling number Caesar cipher Category Abstract algebra Category Permutations eo Cikla permuto ... more details
In homological algebra , cyclic homology and cyclic cohomology are co homology theories for associative algebra s introduced by Alain Connes around 1980, which play an important role in his noncommutative ... Tsygan, Loday, Quillen , and others. Hints about definition The first definition of the cyclic ... to cyclic homology using a notion of cyclic object in an abelian category , which is analogous to the notion of simplicial object . In this way, cyclic homology and cohomology may be interpreted ... of the striking features of cyclic homology is the existence of a long exact sequence connecting Hochschild and cyclic homology. This long exact sequence is referred to as the periodicity sequence. Case of commutative rings Cyclic cohomology of the commutative algebra A of regular functions on an affine ..., cyclic cohomology of A are expressed in terms of the de Rham cohomology of V as follows math ... was extensively developed by Connes. Variants of cyclic homology One motivation of cyclic homology ... complex . Cyclic cohomology is in fact endowed with a pairing with K theory , and one hopes this pairing to be non degenerate. There has been defined a number of variants whose purpose is to fit ... than on algebras without additional structure. Since, on the other hand, cyclic homology degenerates on C algebras, there came up the need to define modified theories. Among them are entire cyclic homology due to Alain Connes , analytic cyclic homology due to Ralf Meyer or asymptotic and local cyclic homology due to Michael Puschnigg. The last one is very near to K theory as it is endowed with a bivariant Chern character from KK theory . Applications One of the applications of cyclic homology ... geometry . Inst. Hautes tudes Sci. Publ. Math. No. 62 1985 , 257 360. Jean Louis Loday, Cyclic ... 0 External links http mathsci.kaist.ac.kr jinhyun note cyclic cyclic.pdf A personal note on Hochschild and Cyclic homology DEFAULTSORT Cyclic Homology Category Homological algebra fr Cohomologie cyclique ... more details
groups to study and a number of nice properties are known. Given a cyclic group G of order ... property, see cyclicnumber group theory cyclicnumber . The direct product of groups direct ... cyclic group is a group of the form Z p sup k sup Z where p is a prime number . The fundamental theorem ... is called virtually cyclic if it contains a cyclic subgroup of finite index group theory index the number ...Groups In group theory , a cyclic group is a group mathematics group that can be generating set of a group ... is a power of g a multiple of g when the notation is additive . Definition File Cyclic group.svg right thumb 150px The six 6th complex roots of unity form a cyclic group under multiplication ... sup 2 sup . A group G is called cyclic if there exists an element g in G such that G < g > g sup ... is cyclic. For example, if G g sup 0 sup , g sup 1 sup , g sup 2 sup , g sup 3 sup , g sup 4 sup , g sup 5 sup is a group, then g sup 6 sup g sup 0 sup , and G is cyclic. In fact, G is essentially the same ... defined by g sup i sup i. For every positive integer n there is exactly one cyclic group up to isomorphism whose Order group theory order is n , and there is exactly one infinite cyclic group the integers under addition . Hence, the cyclic groups are the simplest groups and they are completely classified. The name cyclic may be misleading it is possible to generate infinitely many elements ... one infinitely long cycle. A group generated in this way is called an infinite cyclic group ... are uncountable is not a cyclic group a cyclic group always has countable elements. Since the cyclic ..., this notation can be problematic for number theory number theorists because it conflicts with the usual notation for p adic number p adic number rings or localization of a ring localization ... 2 sup in C sub 5 sub , whereas 3 4 2 in Z 5 Z . Properties The fundamental theorem of cyclic groups states that if G is a cyclic group of order n then every subgroup of G is cyclic. Moreover, the order ... more details
Cyclic succession is a pattern of vegetation change in which in a small number of species tend to replace ... of cyclic replacement have provided evidence against traditional Frederic Clements Clementsian views of an end state climax community with stable species compositions. Cyclic succession is one of several kinds of ecological succession , a concept in community ecology . When used narrowly, cyclic ... Blackwell. ISBN 0865423504, 9780865423503 ref . However, broader cyclic processes can also be observed ... frame right Graphic Model of Cyclic Succession These examples differ from the classic cases of cyclic succession discussed below in that entire species groups are exchanged, as opposed to one species for another. On geologic time scales, climate cycles can result in cyclic vegetation changes ... . Cyclic climate and vegetation change in the late Miocene of Western Bulgaria. Palaeogeography, Palaeoclimatology, Palaeoecology serial online . pp. 272 1 2 99 114. ref . History The cyclic model ... mosaic of species, whose cyclic behavior can be characterized by patch dynamics . Based on the current ... cited in scientific ecology. Modeling cyclic succession Image CyclicMatrix.png thumb 200px right Cyclic Succession Matrix The cyclic model of succession can be displayed in terms of a transition matrix ... Associates, Inc., pp. 180 186. ISBN 978 0 87893 318 1 ref . The three states in the simplest cyclic ... tolerance tolerance models of succession, the key feature of the cyclic model is that A and B are not autosuccession ... can remain open or become occupied by either A or B. This configuration results in a cyclic scheme of species dominance ecology dominance . Mechanisms Cyclic succession is a descriptive phenomenon that can ..., a cyclic pattern of succession is observed. Exogenous factors, such as depredation by herbivores, can also be indirect drivers for cyclic succession if they differentially modulate plant life history .... 651 656. http www.jstor.org stable 2259156. ref . Watt noted that cyclic fluctuations in mortality ... more details
Image Cyclic adenosine monophosphate 2D skeletal.png thumb Cyclic adenosine monophosphate Image CGMP.png thumb Cyclic guanosine monophosphate A cyclic nucleotide is any nucleotide in which the phosphate group is bonded to two of the sugar s hydroxyl groups, forming a cyclical or ring structure. These include cyclic AMP cyclic GMP cyclic ADP ribose These function as second messenger s associated with G protein s and calcium signaling . External links MeshName Nucleotides, Cyclic Nucleobases, nucleosides, and nucleotides Category Nucleotides Biochem stub et Ts klilised nukleotiidid nl Cyclisch nucleotide no Syklisk nukleotid sr Cikli ni nukleotid ... more details
A cyclic flower is a flower type formed out of a series of Whorl botany whorls ref name Swartz cite book page 136 title Collegiate Dictionary of Botany last Swartz first Delbert publisher The Ronald Press Company location New York year 1971 ref sets of identical organs attached around the axis at the same point. Most flowers consist of a single whorl of sepal s termed a Calyx botany calyx a single whorl of petal s termed a corolla flower corolla one or more whorls of stamen s together termed the androecium and a single whorl of carpel s termed the gynoecium . This is a cyclic arrangement. Some flowers contain flower parts with a spiral arrangement. Such flowers are not cyclic. However in the common case of spirally arranged sepals on an otherwise cyclic flower, the term hemicyclic may be used ref name Jackson cite book page 174 title A Glossary of Botanic Terms with their Derivation and Accent last Jackson first Benjamin Daydon edition fourth publisher Gerald Duckworth & Co. Ltd. location London year 1928 url http www.archive.org details glossaryofbotani1928jack ref . The suffix cyclic is used to denote the number of number of whorls contained within a flower. The most common case is the pentacyclic flower, which contains five whorls ref cite book page 271 title A Glossary of Botanic Terms with their Derivation and Accent last Jackson first Benjamin Daydon edition fourth publisher Gerald Duckworth & Co. Ltd. location London year 1928 url http www.archive.org details glossaryofbotani1928jack ref a calyx, a corolla, two whorls of stamens, and a single whorl of carpels. Another common case is the tetracyclic flower, which contains only one whorl of stamens, and therefore only four whorls in total. Tricyclic flowers also occur, generally where there is a single undifferentiated Petal perianth . Flowers with more than five whorls are also not uncommon. The greatest variation ... Morphology of Flowers and Inflorescences , p. 11. DEFAULTSORT Cyclic Flower Category Plant morphology ... more details
In coding theory , cyclic codes are linear code linear block error correcting codes that have convenient ... a cyclic code , if for every codeword c c sub 1 sub ,..., c sub n sub from C , the word c sub n sub , c sub 1 sub ,..., c sub n 1 sub in math GF q n math obtained by a circular shift cyclic right ... &minus 1 left shifts and vice versa. Therefore the linear code math mathcal C math is cyclic precisely when it is invariant under all cyclic shifts. Cyclic Codes have some additional structural ... because of which the encoding and decoding algorithms for cyclic codes are computationally efficient. Algebraic structure Cyclic codes can be linked to ideals in certain rings. Let math R A x x n 1 math be a polynomial ring over the finite field math A GF q math . Identify the elements of the cyclic ... 0 c 1x cdots c n 1 x n 1 math thus multiplication by x corresponds to a cyclic shift. Then C is an Ideal ... g . ref van Lint, p.76 ref This must be a divisor of math x n 1 math . It follows that every cyclic ... code is a cyclic code in which the code, as an ideal, is minimal in R , so that its generator is an irreducible ... contained in the 1,1,0 cyclic code is precisely math 0,0,0 , 1,1,0 , 0,1,1 , 1,0,1 , math . It corresponds ... 0,1,1 . Trivial examples Trivial examples of cyclic codes are A sup n sup itself and the code containing ... GF 2 this must always be a factor of math x n 1 math . Quasi cyclic codes and shortened codes Before delving into the details of cyclic codes first we will discuss quasi cyclic and shortened codes which are closely related to the cyclic codes and they all can be converted into each other. Definition Quasi cyclic codes An math n,k math quasi cyclic code is a linear block code such that, for some math ... i x i math . Definition Shortened codes An math n,k math linear code is called a proper shortened cyclic code if it can be obtained by deleting math b math positions from an math n b, k b math cyclic ... end can be reinserted. To convert math n,k math cyclic code to math n b,k b math shortened code ... more details
In mathematics, a cyclic polytope , denoted C n , d , is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in R sup d sup , where n is greater than d . These polytopes were studied by Constantin Carath odory , David Gale , Theodore Motzkin , Victor Klee , and others. They play an important role in polyhedral combinatorics according to the Upper Bound Conjecture , proved by Peter McMullen and Richard P. Stanley Richard Stanley , the boundary &Delta n , d of the cyclic polytope C n , d maximizes the number f sub i sub of i dimensional faces among all simplicial sphere s of dimension d &minus 1 with n vertices. Definition For any 2 &le d n , the convex hull of n distinct points on the rational normal curve math t,t 2, ldots,t d math in R sup d sup the moment curve is called a cyclic polytope and denoted C n , d . The combinatorial structure of this polytope is independent of the points chosen, and the resulting polytope has dimension d and n vertices. Its boundary is a d &minus 1 dimensional simplicial polytope denoted &Delta n , d . The upper bound conjecture The number of i dimensional faces of &Delta n , d is given by the formula math f i Delta d,n binom n i 1 quad textrm for quad 0 leq i left frac d 2 right math and math f 0, ldots,f frac d 2 1 math completely determine math f frac d 2 , ldots,f d 1 math via the Dehn Sommerville equations . The Upper Bound Conjecture states that if &Delta is a simplicial sphere of dimension d &minus 1 with n vertices , then math f i Delta leq f i Delta n,d quad textrm for quad i 0,1, ldots,d 1. math The Upper Bound Conjecture for simplicial polytopes was proposed by Motzkin in 1957 and proved by McMullen in 1970. A key ingredient in his proof was the following reformulation in terms of h vector h vectors math h i Delta leq tbinom n d i 1 i quad textrm for quad 0 leq i left frac d 2 right . math Victor Klee suggested that the same statement should hold for all simplicial spheres and this was indeed ... more details
In mathematics , more specifically in ring theory , a cyclic module is a module mathematics module over a ring which is generated by one element. The term is by analogy with cyclic group s, that is groups which are generated by one element. Definition A left R module M is called cyclic if M can be generated by a single element i.e. M x R x rx r &isin R for some x in M . Similarly, a right R module N is cyclic, if N y R for some y &isin N . Examples Every cyclic group is a cyclic Z module. Every simple module simple R module M is a cyclic module since the submodule generated by any nonzero element x of M is necessarily the whole module M . If the ring R is considered as a left module over itself, then its cyclic submodules are exactly its left principal ideal s as a ring. The same holds for R as a right R module, mutatis mutandis . If R is F x , the ring over polynomials over a field F , and V is an R module which is also a finite dimensional vector space over F, then the Jordan block s of x acting on V are cyclic submodules. The Jordan blocks are all isomorphic to F x x &lambda sup n sup there may also be other cyclic submodules with different annihilators see below. Properties Given a cyclic R module M which is generated by x then there exists a canonical isomorphism between M and R Ann sub R sub x , where Ann sub R sub x denotes the Annihilator ring theory annihilator of x in R . See also cyclic group finitely generated module References cite book author B. Hartley authorlink Brian Hartley coauthors T.O. Hawkes title Rings, modules and linear algebra publisher Chapman and Hall year 1970 isbn 0 412 09810 5 pages 77,152 Pages 147 149 of Lang Algebra edition 3 algebra stub Category Module theory sv Cyklisk modul fr Module monog ne ... more details
Chembox ImageFile Cyclic ozone 3D balls.png Watchedfields changed PIN Cyclic ozone SystematicName Trioxirane Section1 Chembox Identifiers PubChem 16206854 PubChem Ref Pubchemcite InChIKey XQOAKYYZMDCSIA UHFFFAOYAK ChemSpiderID 13375217 ChemSpiderID Ref Chemspidercite InChI 1 O3 c1 2 3 1 SMILES O1OO1 StdInChI 1S O3 c1 2 3 1 StdInChIKey XQOAKYYZMDCSIA UHFFFAOYSA N Cyclic ozone is a theoretically predicted form of ozone . Like ordinary ozone O sub 3 sub , it would have three oxygen atoms. It would differ from ordinary ozone how those three oxygen atoms are arranged. In ordinary ozone, the atoms are arranged in a bent line in cyclic ozone they would form an equilateral triangle . Some of properties of cyclic ozone have been predicted theoretically. It should have more energy than ordinary ozone. ref Cite journal last Hoffmann first Roald authorlink Roald Hoffman title The story of O. The Ring journal American Scientist volume 92 issue 1 pages 23 24 publisher location date January February 2004 url http www.americanscientist.org issues pub the story of o 5 issn doi 10.1511 2004.1.23 id accessdate 2010 06 05 ref Evidence has been reported that tiny quantities of cyclic ozone exist at the surface of magnesium oxide crystals in air. ref Cite journal last Plass first Richard coauthors Kenneth Egan, Chris Collazo Davila, Daniel Grozea, Eric Landree, Laurence D. Marks, and Marija Gajdardziska Josifovska title Cyclic Ozone Identified in Magnesium Oxide 111 Surface Reconstructions journal Physical Review Letters volume 81 issue 22 pages 4891 4894 publisher location date November 30, 1998 url http www.numis.northwestern.edu Research Articles 1998 98 PRL Plass.pdf issn doi 10.1103 PhysRevLett.81.4891 id accessdate 2010 06 05 ref Cyclic ozone has not been made in bulk, although at least ... Researcher Attempting To Create Cyclic Ozone journal Science Daily volume issue pages publisher location ... id accessdate 2010 06 05 ref It has been speculated that, if cyclic ozone could be made in bulk, and it proved ... more details
Image Cyclic quadrilateral.svg thumb right Cyclic quadrilaterals. In geometry , a cyclic quadrilateral ... to be concyclic . In a cyclic simple polygon simple non self intersecting quadrilateral, opposite ..., each exterior angle is equal to the opposite interior angle . Area The area of a cyclic ... all quadrilaterals having the same sequence of side lengths. The area of a cyclic quadrilateral with successive ... of the lengths of the two diagonal s p and q of a cyclic quadrilateral as equal to the sum of the products ... partition the quadrilateral into four triangles in a cyclic quadrilateral, opposite pairs of these four triangles are Similarity geometry similar to each other. A cyclic quadrilateral with successive ... , rectangle , or isosceles trapezoid is cyclic. A kite geometry kite is cyclic if and only if it has two right angles. Other properties A cyclic quadrilateral with successive sides a, b, c, d and semiperimeter ... of a cyclic quadrilateral, Mathematical Gazette 84, March 2000, 69 70. ref math frac 1 4 sqrt frac ab cd ac bd ad bc s a s b s c s d . math There are no cyclic quadrilaterals with rational ... ref For a cyclic quadrilateral with successive sides a, b, c, d , semiperimeter s , and angle ... s b s c . math Four lines, each perpendicular to one side of a cyclic quadrilateral and passing through ... Court, College Geometry , Dover Publ., 2007 ref rp p.131 Properties of cyclic quadrilaterals that are also orthodiagonal Brahmagupta s theorem states that for a cyclic quadrilateral that is also ... Altshiller Court rp p.137 If a cyclic quadrilateral is also orthodiagonal, the distance from the circumcenter ... side. ref name Altshiller Court rp p.138 For a cyclic orthodiagonal quadrilateral, suppose the intersection ... cyclic quadrilateral, the sum of the squares of the sides equals eight times the square of the circumradius. See also Circumcircle Cyclic polygon Ptolemy s theorem Brahmagupta s theorem on perpendicular diagonals of cyclic quadrilaterals Orthodiagonal quadrilateral Tangential quadrilateral , a quadrilateral ... more details
Infobox disease Name Cyclic neutropenia Image Caption DiseasesDB 30103 ICD10 ICD9 ICD9 288.02 ICDO OMIM 162800 MedlinePlus eMedicineSubj eMedicineTopic MeshID Cyclic neutropenia or cyclical neutropenia is a form of neutropenia which tends to occur every three weeks and lasting three to six days at a time due to changing rates of cell production by the bone marrow. ref name Andrews cite book author James, William D. Berger, Timothy G. et al. title Andrews Diseases of the Skin Clinical Dermatology publisher Saunders Elsevier location year 2006 pages isbn 0 7216 2921 0 oclc doi accessdate ref rp 811 It is often present among several members of the same family. Treatment includes G CSF and usually improves after puberty. Cyclic neutropenia is the result of autosomal dominantly inherited mutations in ELA2 , the gene encoding neutrophil elastase. ref name pmid16079102 cite journal author Sera Y, Kawaguchi H, Nakamura K, et al. title A comparison of the defective granulopoiesis in childhood cyclic neutropenia and in severe congenital neutropenia journal Haematologica volume 90 issue 8 pages 1032 41 year 2005 pmid 16079102 doi url http www.haematologica.org cgi pmidlookup?view long&pmid 16079102 ref See also Acatalasemia List of cutaneous conditions May be associated with oral cankers, canker sores or lesions. http www.aafp.org afp 20000701 149.html External links http www.ncbi.nlm.nih.gov bookshelf br.fcgi?book gene&part cyclic n GeneReview NIH UW entry on ELANE Related Neutropenias including cyclic neutropenia References reflist DEFAULTSORT Cyclic Neutropenia Category Blood disorders Category Conditions of the mucous membranes medicine stub ... more details
In chemistry , a cyclic compound is a, mostly organic, chemical compound compound in which a series of atoms is connected to form a loop or ring. ref JerryMarch ref Cyclic compounds may or may not be Aromaticity aromatic . Benzene is a well known example. The term polycyclic is used when more than one ring is formed in a single molecule for instance in naphthalene , and the term macrocycle is used for a ring containing more than a dozen atoms. gallery Image cycloheptane sticks.png Cycloheptane , a non aromatic cyclic compound. Image Benzene bonds.svg Benzene , a cyclic compound. Image Naphthalene.png Naphthalene , a polycyclic compound. Image Porphyrin.svg Porphyrin , a macrocyclic compound. File Pentazole.png Pentazole , an inorganic cyclic compound. gallery Categorization Cyclic compounds can be categorized Alicyclic compound Cycloalkane Cycloalkene Aromatic hydrocarbon Polycyclic aromatic hydrocarbon Heterocyclic compound Macrocycle Ring closing & opening reactions Image Dieckmann Condensation Scheme.png right thumb Dieckmann ring closing reaction Related concepts in organic chemistry are so called ring closing reactions in which a cyclic compound is formed and ring opening reactions in which rings are opened. Examples of ring closing reactions Ring closing metathesis Nazarov cyclization reaction Ruzicka large ring synthesis Dieckmann condensation Wenker synthesis Radical cyclization Example of ring opening reactions A general type of polymerization reaction Ring opening polymerization Ring opening metathesis polymerisation See also open chain compound Ring expansion and ring contraction Macrocycle Cyclization reaction Effective molarity External links MeshName Polycyclic Compounds MeshName Macrocyclic Compounds References references Category Molecular geometry Category Chemical bond properties ca Compost c clic de Cyclische Verbindungen es Compuesto c clico fr Compos cyclique id Senyawa siklik it Composto ciclico hu Gy r s vegy letek ml nl Cyclische verbinding ... more details
Unreferenced date December 2009 In combinatorics combinatorial mathematics , a cyclic order on a set X with n elements is an arrangement of X as on a clock face, for an n hour clock. That is, rather than an order theory order Relation mathematics relation on X , we define on X just functions element immediately before and element immediately following any given x , in such a way that taking predecessors, or successors, cycles once through the elements as x 1 , x 2 , ..., x n . Another way to put it is to say that we make X into the standard n cycle directed graph on n vertices, by some matching of elements to vertices. A popular example is Rock, Paper, Scissors . Any such cyclic ordering corresponds to n different total order s on X , considered as biting their tails . There are therefore n &minus 1 cyclic orders on X . An infinite set can also be ordered cyclically. The basic idea is the same we arrange elements of the set around a circle. However, in the infinite case we cannot use the immediate successor relation instead we use a ternary relation denoting that elements x , y , z occur after each other not necessarily immediately as we go around the circle. The general definition is as follows a cyclic order on a set X is a relation math R subseteq X 3 math such that R x , y , z implies R y , z , x not R x , y , y if x y z x , then R x , y , z or R x , z , y if R x , y , z and R x , z , w , then R x , y , w for all x , y , z , w in X . It can be instinctive to use cyclic orders for symmetric function s, for example as in math xy yz zx , math where writing the final monomial as math xz math would distract from the pattern. A substantial use of cyclic orders is in the determination of the conjugacy class es of free group s. Two elements g and h of the free group F on a set ... in Y, and then those products are put in cyclic order, the cyclic orders are equivalent under ... Cyclic Order Category Mathematical relations Category Combinatorics ... more details
Unreferenced date December 2009 Cyclic history is a theory which dictates that the major forces that motivate human actions return in a cycle. Among these forces are religion spirituality , politics , science , philosophy , curiosity , and creativity . Religion recurs whenever a new sect reaches a large population. Christianity peaked three times around the 2nd century AD, when the core of believers gained political power in the Middle Ages , when the Church controlled almost all knowledge in Europe during the Protestant Reformation reformation , where the religion split and the many branches modernized themselves. The theory of cyclic history was considered in A. E. van Vogt s 1950 science fiction novel, The Voyage of the Space Beagle . Recursion of historical cycles For more articles about the concept of recursion of historical cycles see The ricorso of Giambattista Vico Major works and their reception Giambattista Vico . The Decline of the West by Oswald Spengler . DEFAULTSORT Cyclic History Category Historiography Category Theories of history ... more details
Cyclic stress in engineering refers to an internal distribution of forces a stress that changes over time in a repetitive fashion. As an example, consider one of the large wheels used to drive an aerial lift such as a ski lift . The Wire rope wire cable wrapped around the wheel exerts a downward force on the wheel and the drive shaft supporting the wheel. Although the shaft, wheel, and cable move the force remains nearly vertical relative to the ground. Thus a point on the surface of the drive shaft will undergo tension when it is pointing towards the ground and compression when it is pointing to the sky. Because the wheel rotates many times during the use of the machine, this cycle of Tensile stress tension and Compressive stress compression is repeated many times &mdash hence the name cyclic stress. Types of cyclic stress Cyclic stress is frequently encountered in rotating machinery where a bending moment is applied to a rotating part. This is called a cyclic bending stress and the aerial lift above is a good example. However, cyclic axial stress es and cyclic torsional stress es also exist. An example of cyclic axial stress would be a bungee cord see bungee jumping , which must support the mass of people as they jump off structures such as bridges. When a person reaches the end of a cord, the cord deflects Elastic deformation elastical ly and stops the person s descent. This creates a large axial stress in the cord. A fraction of the elastic potential energy stored in the cord is typically transferred back to the person, throwing the person upwards some fraction of the distance ..., but have a torque that varies significantly over time. Cyclic stress and material failure When cyclic stresses are applied to a material, even though the stresses do not cause plastic deformation ... cyclic stresses into mean and alternating components. Mean stress is the time average of the principal ... are subjected to a single type bending, axial, or torsional of cyclic stress because this more ... more details
Unreferenced stub auto yes date December 2009 A Cyclic pump is an apparatus which moves a fluid in a periodic uni directional direction from one containment system to another while overcoming static conditions that would, without intervention, not move. The intervention predicated by the pump alters pressures, volumes and sometimes temperatures of fluids gasseous, liquid, colloidal, plasmic, etc. in such a way that the fluids are transported to other chambers or enclosures including pipes , thus flowing in a consistent direction, usually having characteristics of pulsation as is the case with the Human heart or of uniform motion as is the case with an Automobile motor oil pump . Cyclic pumps are generally incorporated into machine s to deal with all sorts of fluids associated with that machine s functionality. See also Water hammer Hydraulic ram Fluid dynamics Switched mode power supply Boost converter Buck converter Buck&ndash boost converter DEFAULTSORT Cyclic Pump Category Pumps Tech stub ... more details
Orphan date January 2011 IPstack CUDP stands for Cyclic User Datagram Protocol UDP . It is used for streaming media and resides in the Transport layer of the ISO OSI protocol stack. External links http www.cs.cornell.edu zeno papers cyclicudp.pdf Paper on CUDP Compu network stub Category Transport layer protocols ... more details
Unreferenced date January 2007 In logic , cyclic negation is assuming that the truth value s are linear order linearly ordered a unary truth function that takes a truth value n and returns n 1 as value if n isn t the lowest value otherwise it returns the highest value. For example, let i be the set of truth values be 0,1,2 , ii denote negation, and iii p be a variable over truth values i.e. whose range is truth values . Thus if p 0 then p 2 and if p 1 then p 0. It was originally introduced by the logician and mathematician Emil Leon Post Emil Post . DEFAULTSORT Cyclic Negation Category Logic Category Mathematical logic Mathlogic stub ... more details
nd sub , it contains a number of improper rotations without containing the corresponding rotations ... pyramid Image Pentagonal pyramid.png 100px BR Pentagonal pyramid hi,sophia DEFAULTSORT Cyclic Symmetries ... more details
Infobox Magazine title Cyclic Defrost image file Cyclic Defrost 16.png image size 225px image caption Cyclic Defrost Issue 16 editor Sebastian Chan, Shaun Prescott & Alexandra Savvides editor title Editors frequency Three times a year circulation 5000 category Music magazine company publisher Cyclic Defrost firstdate 2002 country flagcountry Australia language English Language English website http www.cyclicdefrost.com www.cyclicdefrost.com issn 1832 4835 Cyclic Defrost is Australia s only specialist electronic music magazine. It is edited by Sebastian Chan, Shaun Prescott and Alexandra Savvides, and covers independent electronic music, avant rock, experimental sound art and left field hip hop. The magazine started as a photocopied zine in 1998 ref http www.abc.net.au triplej review print s1216124.htm Cyclic Defrost triple j print reviews Bot generated title ref , as an offshoot of the weekly Sydney club night Frigid, run by Chan and co editor designer Dale Harrison. Harrison resigned and was replaced by Levinson and designer Bim Ricketson. Each issue features local and international feature articles, and until Issue 16, comprehensive reviews covering CDs, DVDs, vinyl these are now found on the Cyclic Defrost website as well as record sleeve designs and artwork. Each issue features a guest cover designer and a section dedicated to sleeve design reviews. Past cover designers include Rinzen, Bim Ricketson and Build. The magazine is published three times a year and the print run of 5000 is available free in selected record stores and other outlets across Australia distributed by Inertia Distribution. Cyclic Defrost contributors Col begin Col 1 of 3 Sebastian Chan Matthew Levinson Chris Downton Peter Hollo Shaun Prescott Emmy Hennings Oliver Laing Renae Mason Bob Baker Fish ... below.glenn brandon nowiki reflist External links http www.cyclicdefrost.com Cyclic Defrost http ... Music review Cyclic Defrost issue 15 launch 22 11 2006 http www.amo.org.au interview.asp?id 1063 Australian ... more details
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