about numbers where permutations of their digits in some base yield related numbers the number theoretic concept cyclicnumber group theory summary in Repeating decimal Merge from 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 ... digits Relation to repeating decimals Cyclic numbers are related to the Repeating decimal recurring digital representations of unit fractions . A cyclicnumber of length L is the digital representation ... represent a cyclicnumber. For example 1 7 0.142857 142857 . Multiples of these fractions exhibit ..., p 7 gives the cyclicnumber 142857. Not all values of p will yield a cyclicnumber using this formula ... the loop. if t p &minus 1 then n is a cyclicnumber. This procedure works by computing the digits ... exceeds p 2, then the number must be cyclic, without the need to compute the remaining digits. Properties ... 19M45FCGNE2KJ8B7 Note that in ternary b 3 , the case p 2 yields 1 as a cyclicnumber. While single ... single digits exist in any numeric base which is a Square number perfect square thus there are no cyclic ... MathWorld urlname CyclicNumber title CyclicNumber Category Number theory Category Permutations de ... 5 repeated digits, e.g. 555 repeated cyclic numbers, e.g. 142857142857 If leading zeros are not permitted on numerals, then 142857 is the only cyclicnumber in decimal Citation needed date May 2011 . Allowing leading zeros, the sequence of cyclic numbers begins 142857 6 digits 0588235294117647 ... 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 group theory 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 graph theory Cycle decomposition group theory 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 ... science.1125248 pmid 16543448 External links http www.cybase.org.au Cybase MeshName Cyclic Peptides ... more details
In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology ..., Michael Puschnigg, and many others. Hints about definition The first definition of the cyclic homology ... 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 ... 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 ..., if the variety V Spec A is smooth, cyclic cohomology of A are expressed in terms of the de ... of a noncommutative algebra A , which was extensively developed by Connes. Variants of cyclic homology One motivation of cyclic homology was the need for an approximation of K theory that be defined, unlike K theory, as the homology of a chain 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 ... 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 ref Ralf Meyer. Analytic cyclic cohomology. PhD thesis, Universit t M nster, 1999 ref or asymptotic and local cyclic homology due to Michael Puschnigg ref Michael Puschnigg. Diffeotopy functors of ind algebras and local cyclic cohomology. Doc. Math., 8 143 245 electronic , 2003. ref ... . Applications One of the applications of cyclic homology is to find new proofs and generalizations ... Homology Homology theory References references Jean Louis Loday, Cyclic Homology , Grundlehren ... mathsci.kaist.ac.kr jinhyun note cyclic cyclic.pdf A personal note on Hochschild and Cyclic homology ... more details
Unreferenced date April 2011 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 ... i else. Definition 2 image 050712 perm 2.png right mapping of permutation A permutation is called a cyclic ... over a set with k elements is a cyclic permutation of definition type 2 if and only if it is a cyclic ... right mapping of permutation 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 ... 4 & 6 & 8 & 3 & 7 & 1 & 2 & 5 end pmatrix 146837 2 5 math See also Cyclic permutation of integer Cycle notation Cycles and fixed points Stirling number Caesar cipher Circular permutation in proteins ... more details
In mathematics , the cyclic category or cycle category or category of cycles is a category theory category of finite cyclically ordered set s and degree 1 maps between them. It was introduced by harvtxt Connes 1983 . Definition The cyclic category has one object sub n sub for each natural number n 0, 1, 2, ... The morphisms from sub m sub to sub n sub are represented by increasing functions f from the integers to the integers, such that f x m n f x , where two functions f and g represent the same morphism when their difference is divisible by n . Informally, the morphisms from sub m sub to sub n sub can be thought of as maps of oriented necklaces with m 1 and n 1 beads. More precisely, the morphisms can be identified with homotopy classes of degree 1 increasing maps from S sup 1 sup to itself that map the subgroup Z m 1 Z to Z n 1 Z . Properties The number of morphisms from sub m sub to sub n sub is m n 1 m n . The cyclic category is self dual. The classifying space B of the cyclic category is a classifying space BS sup 1 sup of the circle group S sup 1 sup . Cyclic sets A cyclic set is a contravariant functor from the cyclic category to sets. More generally a cyclic object in a category C is a contravariant functor from the cyclic category to C . See also Cyclic homology Simplex category References Citation last Connes first Alain authorlink Alain Connes year 1983 title Cohomologie cyclique et foncteurs Ext sup n sup language French journal Comptes Rendus de l Acad mie des Sciences. S rie I. Math matique volume 296 issue 23 pages 953 958 url http www.alainconnes.org docs n83.pdf accessdate 15 May 2011 mr 777584 Citation last Connes first Alain authorlink Alain Connes year 2002 chapter Noncommutative Geometry Year 2000 editor last Fokas editor first A. title Highlights of mathematical physics isbn 0 8218 3223 9 pages 49 110 url http www.alainconnes.org ... isbn 3 540 53373 7 pages 60 61 Citation last1 Loday first1 Jean Louis title Cyclic homology url http ... more details
groups to study and a number of nice properties are known. Given a cyclic group G of order n n may ... property, see cyclicnumber group theory cyclicnumber . The direct product of groups direct product ... the number of coset s that the subgroup has . In other words, any element in a virtually cyclic group ...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 File Cyclic group Z15 cycle graph powers ... commons thumb 5 5a Cyclic group Z15 3B cycle graph 3B powers of wp 2815 2C5 2C11 2C13 29.svg 2048px Cyclic group Z15 3B cycle graph 3B powers of wp 2815 2C5 2C11 2C13 29.svg.png Cycle graph algebra ... 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 that 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 1041 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 Congenital defects of phagocyte number, function, or both Category Conditions of the mucous membranes Cutaneous condition stub ... 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 of succession ... of species, whose cyclic behavior can be characterized by patch dynamics . Based on the current composition ... 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 ..., Inc., pp. 180 186. ISBN 978 0 87893 318 1 ref The three states in the simplest cyclic model ... tolerance models of succession, the key feature of the cyclic model is that A and B are not autosuccession ... 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 ... of interspecific relationships satisfies the conditions described in the model above, a cyclic ... also be indirect drivers for cyclic succession if they differentially modulate plant life history properties ... 656. http www.jstor.org stable 2259156. ref Watt noted that cyclic fluctuations in mortality rate could ... more details
In chemistry , a cyclic compound is a chemical compound compound in which a series of atoms is connected to form a loop or ring. ref JerryMarch ref While the vast majority of cyclic compounds are organic compound organic , a few inorganic substances form cyclic compounds as well, including sulfur, silanes, phosphanes, phosphoric acid, and triboric acid. Cyclic compounds may or may not be Aromaticity aromatic . Benzene is aromatic while cyclohexane is not. 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 Alicyclic compound Alicyclic compounds are named according to the IUPAC system of nomenclature by attaching the prefix cyclo to the name of the corresponding open chain hydrocarbon possessing the same number of carbon atoms. The common names resemble the IUPAC names. For example Cyclo pentane, cyclo butane etc.... 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 Effective molarity External links ... 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 bg 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 ... of the code. An irreducible code is a cyclic code in which the code, as an ideal, is maximal in R , so ... and n 3, the set of codewords contained in the 1,1,0 cyclic code is precisely math 0,0,0 , 1,1,0 , 0,1,1 ... to the codeword 0,1,1 . Trivial examples Trivial examples of cyclic codes are A sup n sup ... x 1 math . Again over 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 ... 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 code . In shortened codes information symbols are deleted to obtain a desired ... and at the receiving end can be reinserted. To convert math n,k math cyclic code to math n b ... more details
Image DC8.png right In mathematics , a cyclic order is a way to arrange a set of objects in a circle . ref cyclic order nb Unlike most structures in order theory , a cyclic order cannot be modeled as a binary relation math a b . One does not say that east is more clockwise than west. Instead, a cyclic ... before mvar c . For example, June, October, February . A ternary relation is called a cyclic order if it is The cyclic order relation cyclic, asymmetric, transitive, and total . Dropping the total requirement results in a partial cyclic order . A set mathematics set with a cyclic order is called a cyclically ... a Finite set finite number of element mathematics element s there are seven days of the week , four .... Cyclic orders are closely related to the more familiar linear order s, which arrange objects in a line geometry line . Any linear order can be bent into a circle, and any cyclic order can be cut at a point ... maps, mean that questions about cyclic orders can often be transformed into questions about ... of linear structures, as in the finite cyclic group s or the real projective line . Finite cycles Image Orientovan kru nice.svg thumb A 5 element cycle A cyclic order on a set mvar X with mvar ... cycles exactly once through the elements as math x 1 , x 2 , ..., x n . In other words, a cyclic ... n sub torsor a set with a free transitive group action action by a finite cyclic group . sfn Brown ... on mvar n vertices, by some matching of elements to vertices. It can be instinctive to use cyclic ... xz would distract from the pattern. A substantial use of cyclic orders is in the determination ... y sup 1 sup with mvar y in mvar Y , and then those products are put in cyclic order, the cyclic ... and math y sup &minus 1 sup . A cyclic order on a set mvar X can be determined by a linear order on mvar ..., so there are exactly mvar n linear orders that induce a given cyclic order. Since there are math n possible linear orders, there are math n &minus 1 possible cyclic orders. Definitions An infinite set ... 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 of 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 Category Module theory Abstract algebra stub sv Cyklisk modul fr Module monog ne ... 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 The moment curve in math mathbb R d math is defined by math mathbf x mathbb R rightarrow mathbb R d, mathbf x t begin bmatrix t ,t 2 , ldots ,t d end bmatrix T math . The math d math dimensional cyclic polytope with math n math vertices is the convex hull math C n,d mathbf conv mathbf x t 1 , mathbf x t 2 , ldots, mathbf x t n math of math n d ge 2 math distinct points math mathbf x t i math with math t 1 t 2 ldots t n math on the moment curve. 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 . Gale evenness condition The Gale evenness condition ref cite book title Lectures on Polytopes last Ziegler first G nter authorlink year 1994 publisher Springer location isbn 0 387 94365 X pages 14 ref provides a necessary and sufficient condition to determine a facet on a cyclic polytope . Let math T t 1,t 2, ldots,t n math . Then, a math d math subset math T d subseteq T math forms a facet of math C n,d math iff any two elements in math T setminus T d math are separated by an even number of elements from math T d math in the sequence math t 1,t 2, ldots,t n math . The upper bound conjecture The number of i dimensional faces of &Delta n , d is given by the formula ... 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 DEFAULTSORT Cyclic Symmetries Category ... more details
Unreferenced date December 2009 A Cyclic pump is an Equipment 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 File Ram Pump Vogn 2011 ubt.ogv thumb A cyclic hydraulic ram ram pump in Vogn , Denmark 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
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
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
for the mathematical cyclic sets cyclic category In music , a cyclic set is a set music set , whose alternate elements unfold Complement music Rule of twelve complementary interval cycle cycles of a single interval music interval . ref name Perle Perle, George 1996 . Twelve Tone Tonality , p.21. ISBN 0 520 20142 6. ref Those cycles are ascending and descending, being related by inversion since complementary Image Berg s Lyric Suite cyclic set.png thumb center 400px Cyclic set sum 9 from Alban Berg Berg s Lyric Suite , and complementary interval cycle s P7 and I5 producing the cyclic set ref name Perle In the above example, as explained, one interval 7 and its compliment 7 5 , creates two series of pitches starting from the same note 8 P7 8 7 3 7 10 7 5 ... 1 7 8 I5 8 5 1 5 6 5 11 ... 3 5 8 According to George Perle , a Klumpenhouwer network is a chord music chord musical analysis analyzed in terms of its Dyad music dyadic Inversion music Musical set theory sums and interval music differences , and, this kind of analysis of triad music triadic combinations was implicit in, his, concept of the cyclic set from the beginning ref name Perle Perle, George 1993 . Letter from George Perle , Music Theory Spectrum , Vol. 15, No. 2 Autumn , pp. 300 303. ref . File Berg s Lyric Suite cyclic set overlapping three note segments.png thumb center 400px Overlapping three note segments, ref name Perle of the sum 9 cyclic set A cognate set is a set created from joining two sets related through inversion music inversion such that they share a single series of dyads ref name Perle 22 Perle 1996 , p.22. ref . Image Cognate set on C.png thumb center 400px Cognate set created from paired interval 7 cycles of sum 0 ref name Perle 22 0 7 2 9 4 11 6 1 8 3 10 5 0 0 5 10 3 8 1 6 11 4 9 2 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The two cycles may also be aligned as pairs of sum 7 or sum 5 dyads ref name Perle 22 . All together these pairs of cycles form a set complex , any cyclic set of the set complex may ... more details
Chembox Verifiedfields changed Watchedfields changed verifiedrevid 433035864 ImageFile Cyclic ozone 3D balls.png ImageFile Ref chemboximage correct ?? ImageSize 100 ImageName Ball and stick model of cyclic ozone PIN 1,2,3 Trioxacyclopropane Citation needed date April 2012 SystematicName Trioxirane ref Cite web title CID 16206854 Compound Summary url http pubchem.ncbi.nlm.nih.gov summary summary.cgi?cid 16206854 work PubChem Compound publisher National Center for Biotechnology Information accessdate 21 October 2011 location USA date 11 July 2007 at Identification and Related Records ref Section1 Chembox Identifiers CASNo 153851 84 4 CASNo Ref cascite changed ?? PubChem 16206854 PubChem Ref Pubchemcite correct Pubchem ChemSpiderID 13375217 ChemSpiderID Ref chemspidercite correct chemspider SMILES O1OO1 StdInChI 1S O3 c1 2 3 1 StdInChI Ref stdinchicite correct chemspider StdInChIKey XQOAKYYZMDCSIA UHFFFAOYSA N StdInChIKey Ref stdinchicite correct chemspider Section2 Chembox Properties O 3 ExactMass 47.984743866 g mol sup 1 sup 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 in 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 ... that tiny quantities of cyclic ozone exist at the surface of magnesium oxide crystals ... Grozea, Eric Landree, Laurence D. Marks, and Marija Gajdardziska Josifovska title Cyclic Ozone Identified ... 1998PhRvL..81.4891P ref Cyclic ozone has not been made in bulk, although at least one researcher ... Attempting To Create Cyclic Ozone journal Science Daily volume issue pages publisher location date February ... 06 05 ref It has been speculated that, if cyclic ozone could be made in bulk, and it proved to have ... more details
Expert subject Technology date March 2010 In telecommunications , the term cyclic prefix refers to the prefixing of a symbol data symbol with a repetition of the end. Although the receiver is typically configured to discard the cyclic prefix samples, the cyclic prefix serves two purposes. As a guard interval , it eliminates the intersymbol interference from the previous symbol. As a repetition of the end of the symbol, it allows the linear convolution of a frequency selective multipath channel to be modelled as circular convolution, which in turn may be transformed to the frequency domain using a discrete Fourier transform . This approach allows for simple frequency domain processing, such as channel estimation and equalization. In order for the cyclic prefix to be effective i.e. to serve its aforementioned objectives , the length of the cyclic prefix must be at least equal to the length of the multipath channel. Although the concept of cyclic prefix has been traditionally associated with OFDM systems, the cyclic prefix is now also used in single carrier systems to improve the robustness to multipath. Principle Cyclic prefix is often used in conjunction with modulation in order to retain sinusoid sinusoids properties in multipath propagation multipath channels. It is well known that sinusoidal signals are eigenfunctions of linear , and time invariant systems. Therefore, if the channel is assumed to be linear and time invariant , then a sinusoid of infinite duration would be an eigenfunction . However, in practice, this cannot be achieved, as real signals are always time limited ... this property in the part of the symbol after the cyclic prefix. Use in OFDM Cyclic Prefixes are used ... symbol, followed by a cyclic prefixing. Let the symbol obtained by the IDFT be denoted by math mathbf x 0 x 0 , x 1 , ldots x N 1 T math . Prefixing it with a cyclic prefix of length math L ... Tutorial Nisar.pdf the significance of cyclic prefix in OFDM systems . Category Quantized radio modulation ... 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
Encyclopedia
top
