unreferenced date December 2010 pH partition is the tendency for acid s to accumulate in basic fluid compartment s, and chemical base bases to accumulate in acidic compartments. The reason for this phenomenon is that acids become negatively electric charge d in basic fluids, since they donate a proton . On the other hand, bases become positively electric charged in acid fluids, since they receive a proton. Since electric charge decrease the membrane permeability of substances, once an acid enters a basic fluid and becomes electrically charged, then it cannot escape that compartment with ease and therefore accumulates, and vice versa with bases. See also Ion trapping Acid dissociation constant pK sub a sub Henderson Hasselbalch equation DEFAULTSORT Ph Partition Category Acid base chemistry biochemistry stub ... more details
citations missing date December 2009 In mathematics , the notion of partition regularity in combinatorics is one approach to explaining when a set system is quite large. Given a set math X math , a collection of subsets math mathbb S subset mathcal P X math is called partition regular if every set A in the collection has the property that, no matter how A is partitioned into finitely many subsets, at least one of the subsets will also belong to the collection. That is, for any math A in mathbb S math , and any finite partition math A C 1 cup C 2 cup cdots cup C n math , there exists an i &le n , such that math C i math belongs to math mathbb S math . Ramsey theory is sometimes characterized as the study of which collections math mathbb S math are partition regular. Examples the collection of all infinite subsets of an infinite set X is a prototypical example. In this case partition regularity asserts that every finite partition of an infinite set has an infinite cell i.e. the infinite pigeonhole principle . sets with positive upper density in math mathbb N math the upper density math overline d A math of math A subset mathbb N math is defined as math overline d A limsup n rightarrow infty frac 1,2, ldots,n cap A n . math For any ultrafilter math mathbb U math on a set math X math , math mathbb U math is partition regular. If math mathbb U ni A bigcup 1 n C i math , then for exactly ... arbitrarily long arithmetic progressions. Then the collection of a.p. rich subsets is partition ... n, math mathbb S n math is partition regular. Ramsey s theorem Ramsey , 1930 . For each infinite cardinal math kappa math , the collection of stationary set s of math kappa math is partition ... sums. Then the collection of i.p. rich subsets is partition regular Jon Folkman Folkman Richard ..., 1998 References Vitaly Bergelson , N. Hindman http members.aol.com nhfiles2 pdf large.pdf Partition ... cells of a partition of N , J. Combinatorial Theory Series A 17 1974 1 11. Crispin St. J. A. Nash ... more details
books?id 9Tbed6iMNLEC&pg PA60&dq 22Russian partition 22 Google Print, p. 60 ref To Poles ... and adopted by most other historiographies, was the Russian partition . ref name davies History ... of the three partitions in late 18th century . The Russian partition came into existence albeit not under ... partition include formation of the Napoleonic Duchy of Warsaw 1807 and its abolition after ... partition which were not incorporated into Congress Poland were officially known as the Western Krai ... lands of the Commonwealth from the first partition of Poland 1772 Polish Inflants Latgale , the northern ... s, and the southeastern part of the Minsk Voivodeship about 92,000 km from the second partition ... partition of Poland 1795 all the territories east of the Bug River about 120,000. km and after ... partition, Russia gained 92,000 km and 1.3 million people. In the second, 250,000 ... search s Google Print, p.133 ref The Russian partition was thus the largest and most populous of the three partitions the other two being the Austrian partition and the Prussian partition . ref name Wandycz For changes in the administrative division of Russian partition in the 19th century, see administrative ... major political parties of the Second Polish Republic developed around that time in the Russian partition ex. Polish Socialist Party . ref name ag Economy The territories of the Russian partition saw moderate economic growth. Much of the output of the Polish partition was exported to Russia proper, especially ... PPA83,M1 ROSSIYA The Russian Partition 1772 1918 References Reflist coord missing Poland Category History ... more details
In mathematics , the partition topology is a topological space topology that can be induced on any set X by Partition of a set partitioning X into disjoint subsets P these subsets form the basis topology basis for the topology. There are two important examples which have their own names The odd even topology is the topology where math X mathbb N math and math P left 2k k in mathbb N , 2k 1 k in mathbb N right . math The deleted integer topology is defined by letting math X begin matrix bigcup n in mathbb N n 1,n subset mathbb R end matrix math and math P left 0,1 , 1,2 , 2,3 , dots right math . The trivial partitions yield the discrete topology each point of X is a set in P or indiscrete topology math P X math . Any set X with a partition topology generated by a partition P can be viewed as a pseudometric space with a pseudometric given by math d x,y begin cases 0 & text if x text and y text are in the same partition 1 & text otherwise , end cases math This is not a metric unless P yields the discrete topology. The partition topology provides an important example of the independence of various separation axioms . Unless P is trivial, at least one set in P contains more than one point, and the elements of this set are topologically indistinguishable the topology does not separate points. Hence X is not a Kolmogorov space , nor a T1 space T sub 1 sub space , a Hausdorff space or an Urysohn space . In a partition topology the complement of every open set is also open, and therefore a set is open if and only if it is closed. Therefore, X is a regular space regular , completely regular space completely regular , normal space normal and completely normal space completely normal . We note also that X P is the discrete topology. References Citation last1 Steen first1 Lynn Arthur author1 link Lynn Arthur Steen last2 Seebach first2 J. Arthur Jr. author2 link J. Arthur Seebach, Jr. title Counterexamples in Topology origyear 1978 publisher Springer Verlag location Berlin, New York ... more details
Partition in Politics of Quebec Quebec politics refers to the secession of regions of the province of Quebec , rather than to Partition politics partitions in a strict political sense . It is usually discussed ... for example in the Quebec general election, 2007 2007 provincial election . Partition proposals Broadly speaking, partition proposals have tended to fall into three categories 1. New borders based on a return ... 1992 book Canada Remapped How the Partition of Quebec Will Reshape the Nation , Scott Reid politician Scott Reid argues in favour of partition as determined by local populations and largely dismisses the first two lines of thought on partition listed above. History of the Partition debate The partition ..., I want to introduce a new word into the lexicon of Canadian politics PARTITION. The threat of partition will prevent separation. ref Shaw, William and Lionel Albert, Partition The Price of Quebec ... who believed, along with Shaw, that the threat of a partition in which some parts of Quebec ... Albert, Partition The Price of Quebec s Independence . Montreal Thornhill, 1980, pp. 27 29. ref This faction within the early partition movement bears some resemblance to the movements that have arisen ... is quoted in Charron, Claude G., La partition du Qu bec De Lord Durham a St phane Dion . Montreal vlb ..., Partition The Price of Quebec s Independence . Montreal Thornhill, 1980, p. 16. The Trudeau quote ... Albert had published a book on the subject by the end of the year. Partition The Price of Quebec ... steps, in 1898 and 1912 ref Shaw, William and Lionel Albert, Partition The Price of Quebec s Independence ... had been captured by Britain in 1759 ref Shaw, William and Lionel Albert, Partition The Price of Quebec ... loyalties. ref Shaw, William and Lionel Albert, Partition The Price of Quebec s Independence . Montreal ... separation will not happen. ref Shaw, William and Lionel Albert, Partition The Price of Quebec ..., approached the county councils in several nearby Ontario counties with the following pro partition ... more details
b y but not if it is a x y b or a b x y . In the latter two orders the partition a , b , x , y ... of the partition are disjoint from each other, i.e., they also do not cross each other. The set of all ... order lattice when partially ordered set partially ordered by saying that a finer partition is less than a coarser partition. However, although it is a subset of the lattice of all partitions .... In other words, the finest partition that is coarser than both of two noncrossing partitions is not always the finest noncrossing partition that is coarser than both of them. Unlike the lattice of all ... down . This can be seen by observing that each noncrossing partition has a complement. Indeed, every ... math N j pi math denotes the number of blocks of length math j math in the non crossing partition ... more details
Image Partition3D.svg thumb right A plane partition parts as heights In mathematics , a plane partition see also solid partition for three dimensional array is a two dimensional array of nonnegative integers math n i,j math which are nonincreasing from left to right and top to bottom math n i,j ge n i,j 1 quad mbox and quad n i,j ge n i 1,j , . math Thinking of the stack of math n i,j math unit cubes placed on i,j square, we obtain a solid or 3 dimensional partition. Define the sum of the plane partition by math n sum i,j n i,j , math and let PL n denote the number of plane partitions with sum n . For example, there are six plane partitions with sum 3 math begin matrix 1 & 1 & 1 end matrix qquad begin matrix 1 & 1 1 & end matrix qquad begin matrix 1 1 1 & end matrix qquad begin matrix 2 & 1 & end matrix qquad begin matrix 2 1 & end matrix qquad begin matrix 3 end matrix math so PL 3 6. Generating function By a result of Percy Alexander MacMahon Percy MacMahon , the generating function for PL n can be calculated by math sum n 0 infty mbox PL n , x n prod k 1 infty frac 1 1 x k k 1 x 3x 2 6x 3 13x 4 24x 5 cdots. math This is usually referred to as the MacMahon function . This formula is the 2 dimensional analogue of Leonhard Euler Euler s Integer partition Generating function product formula for the number of Partition number theory integer partitions of n . There is no analogous formula for partitions in higher dimensions. Citation needed date March 2011 MacMahon formula Denote by math M a,b,c math the number of solid partitions which fit into math a times b times c math box. In the planar case, we obtain the binomial coefficient s math M a,b,1 binom a b a . math MacMahon formula is the multiplicative formula for general values of math M a,b,c math math M a,b,c prod i 1 a prod j 1 b prod k 1 c frac i j k 1 i j k 2 . math This formula was obtained by Percy Alexander MacMahon ... University Press, 1915 16. External links MathWorld title Plane partition urlname PlanePartition ... more details
In the design of algorithm s, partition refinement is a technique for representing a partition of a set as a data structure that allows the partition to be refined by splitting its sets into a larger number of smaller sets. In that sense it is dual to the Disjoint set data structure union find data structure , which also maintains a partition into disjoint set s but in which the operations merge pairs of sets together. More specifically, a partition refinement algorithm maintains a family of disjoint sets math S sub i sub at the start of the algorithm, this is just a single set containing all the elements in the data structure. At each step of the algorithm, a set mvar X is presented to the algorithm, and each set math S sub i sub that contains members of mvar X is replaced by two sets, the Intersection set theory intersection math S sub i sub &cap X and the Complement set theory difference math S sub i sub X . Partition refinement forms a key component of several efficient algorithms on graph theory graphs and finite automaton finite automata . ref citation last1 Paige first1 Robert ... pages 973 989 title Three partition refinement algorithms volume 16 year 1987 . ref ref citation last1 ... 147 170 title Partition refinement techniques an interesting algorithmic tool kit volume 10 year ... Laurent contribution A synthesis on partition refinement a useful routine for strings, graphs, Boolean ... A partition refinement algorithm may be implemented by maintaining an object for each set that stores ... in the data structure. Applications Possibly the first application of partition refinement was in an algorithm .... The algorithm maintains a partition of the states of the input automaton into subsets, with the property .... Sympos., Technion, Haifa, 1971 year 1971 . ref Partition refinement was applied by harvtxt Sethi ... sets are vertices of the input graph and the sets mvar X used to refine the partition are sets of neighbors ... on Computing pages 73 82 title Scheduling graphs on two processors volume 5 year 1976 . ref Partition ... more details
In mathematics, the graph partition problem is defined on data represented in the form of a graph mathematics graph G V,E , with V vertices and E edges, such that it is possible to partition G into smaller components with specific properties. For instance, a k way partition divides the vertex set into k smaller components. A good partition is defined such that the number of edges running between separated components is small. Uniform graph partition is a type of graph partitioning problem that consists ... 1007912.1007931 isbn 1581138407 ref Recently, the uniform graph partition problem has gained importance ..., graph partition problems fall under the category of NP hard problems. Solutions to these problems ... cutpartition However, uniform graph partitioning or a balanced graph partition problem can be shown ... vertices and E the set of edges. For a k,v balanced partition problem, the objective is to partition ... components. ref name balgraph Also, given G and an integer k 1 , partition V into k parts subsets ... in different parts is minimized. Such partition problems have been discussed in literature ... partition, and cut exactly once otherwise, no matter how many vertices are on each side. This usage is common in electronic design automation . Analysis For a specific k,1 balanced partition problem, we seek to find a minimum cost partition of G into k components with each component containing ... of NP completeness year 1979 isbn 0716710447 publisher W. H. Freeman & Co. ref Next we assess a 3 partition ... assume that we have an finite approximation algorithm for k, 1 balanced partition, then, either the 3 partition instance can be solved using the balanced k,1 partition in G or it cannot be solved. If the 3 Partition instance can be solved, then k, 1 balanced partitioning problem in G can be solved without cutting any edge. Otherwise if the 3 Partition instance cannot be solved, the optimum k, 1 ... factor has to differentiate between these two cases. Hence, it can solve the 3 Partition problem ... more details
the geographical perspective, much of the Austrian partition corresponded to the Galicia Central ... 20th century, out of the three partitioned regions, the Austrian partition had the most ... frontcover&source gbs summary r&cad 0 PPA102,M1 GALICIA The Austrian Partition 1773 1918 References ... more details
In computer science , the partition problem is an NP complete problem. The problem is to decide whether a given multiset of integers can be partition of a set partitioned into two halves that have the same sum. More precisely, given a multiset S of integers, is there a way to partition S into two subsets S sub 1 sub and S sub 2 sub such that the sum of the numbers in S sub 1 sub equals the sum of the numbers in S sub 2 sub ? The subsets S sub 1 sub and S sub 2 sub must form a Partition of a set partition in the sense that they are Disjoint sets disjoint and they Cover topology cover S . The optimization problem optimization version asks for the best partition, and can be stated as Find a partition into two subsets math S 1, S 2 math such that math max operatorname sum S 1 , operatorname sum ... with the additional constraint that the sizes of the two sets in the partition must be equal, or differ by at most 1 . The partition problem is equivalent to the following special case of the subset ... time dynamic programming solution to subset sum applies to the partition problem as well. A variation of the partition problem is the 3 partition problem , in which the set S must be partitioned into S 3 triples each with the same sum. In contrast to partition, 3 partition has no pseudo polynomial time algorithm unless P NP 3 partition remains NP complete even when using unary coding . Methods Although the partition problem is NP complete, there are heuristics that solve the problem in many instances ... time dynamic programming solution for the subset sum problem applies to the partition problem as well ..., and for each partition of them, extends the partition by adding the remaining elements successively ... a polynomial time approximation scheme PTAS for the number partition problem, though this is not an FPTAS ..., and hence for the partition problem as well. ref name knapsack ref name MartelloToth cite book chapter ... of a perfect partition goes to 1 or 0 respectively. This was originally argued using methods ... more details
context date December 2010 A Markov partition is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic system s. By using a Markov partition, the system can be made to resemble a discrete time Markov process , with the long term dynamical characteristics of the system represented as a Markov shift . The appellation Markov is appropriate because the resulting dynamics of the system obeys the Markov property . The Markov partition thus allows standard techniques from symbolic dynamics to be applied, including the computation of expectation value s, correlation s, topological entropy , topological zeta function s, Fredholm determinant s and the like. Motivation Let M , be a discrete dynamical system. A basic method of studying its dynamics is to find a symbolic representation a faithful encoding of the points of M by sequences of symbols such that the map becomes the shift map . Suppose that M has been divided into a number of pieces E sub 1 sub , E sub 2 sub , , E sub r sub , which are thought to be as small and localized, with virtually no overlaps. The behavior of a point x under the iterates of can be tracked by recording, for each n , the part E sub i sub which contains sup n sup x . This results in an infinite sequence on the alphabet 1,2, r which encodes the point. In general, this encoding may be imprecise the same sequence may represent many different points and the set of sequences which arise in this way may be difficult to describe. Under certain conditions, which are made explicit in the rigorous definition of a Markov partition, the assignment of the sequence to a point of M becomes an almost one to one map whose image is a symbolic dynamical system of a special kind called a shift of finite ... of the dynamical system M , &phi . Formal definition A Markov partition ref Pierre Gaspard ... DEFAULTSORT Markov Partition Category Dynamical systems Category Symbolic dynamics Category Diffeomorphisms ... more details
of Posen from 1848 1919 Society Poles in the Prussian partition were subject to extensive Germanization ... gbs summary r&cad 0 PPA83,M1 PREUSSEN The Prussian Partition 1772 1918 References See http en.wikipedia.org ... more details
record Partition types on IBM PC compatible computers ref name Brouwer 2002 Partition IDs Partition ID Introduction Support Description tt 0x00 tt IBM All anchor PID 00h Empty partition entry tt 0x01 tt Microsoft DOS 2.0 anchor PID 01h FAT12 as primary partition of up to 16 MB in size in first ... MegaByte 1024 KB or 1,048,576 bytes MB abbr . As primary partition it must reside in first ... partition with Cylinder head sector CHS addressing tt 0x06 tt Compaq DOS 3.31 anchor PID ... used for logical drives in an tt PID 0Fh 0x0F tt extended partition else use tt PID 0Eh 0x0E tt ... 1.x 2.x QNX qny ref name QNX4 ref group nb name QNX SplitDrive Dell partition spanning multiple drives ... NB HiddenBootManager Mark Williams Company Coherent Coherent swap partition Unisys OPUS Open Parallel ... partition with Logical block addressing LBA rowspan 2 tt 0x11 tt Leading Edge company Leading ... tt Compaq anchor PID 12h configuration partition bootable File Allocation Table FAT ref name obscure MS DOS Compaq Compaq Contura hibernation partition ref name obscure NCR diagnostics and firmware partition bootable File Allocation Table FAT ref name obscure MS DOS or ROM DOS Intel service partition ... partition ref name obscure rowspan 2 tt 0x14 tt AST Research AST anchor PID 14h AST MS ... Extended Boot Record extended partition with Cylinder head sector CHS addressing corresponds with tt ... Zero Volt Suspend or SmartSleep partition AST Windows swapfile? tt 0x19 tt Willow Schlanger Willowtech ... extended partition with Logical block addressing LBA addressing corresponds with tt PID 0Fh 0x0F tt ... tt tt 0x22 tt Dave Poirier Oxygen anchor PID 22h Oxygen Extended Partition Table see tt PID 21h 0x21 ... rowspan 4 tt 0x27 tt Microsoft Windows anchor PID 27h Windows recovery environment RE partition hidden NTFS partition type tt PID 07h 0x07 tt ref name Microsoft 2009 Recovery Acer PQservice FAT32 or NTFS rescue partition press ALT F10 to start MirOS BSD MirOS partition RooterBOOT RooterBOOT ... more details
borders by the Ambassadors and Boundary Commission. The Partition of Albania lang sq Cop timi i Shqip ris is a term used for the partition of the Albanian state, which proclaimed its independence ... viewed this as partition of claimed Albanian inhabited territories, also territories contained ... pages 230 url http books.google.ee books?id iQ3qG1s0LSgC&pg PA230&dq partition of Albania 1913&hl en&sa X&ei T3cpT6j8Dav24QTXk7HUAw&redir esc y v onepage&q partition 20of 20Albania 201913&f false ... books?id dbUuX0mnvQMC&pg PA180&dq partition of Albania 1913&hl en&sa X&ei nHkpT6uqJ8iK4gSt pWoAw&redir esc y v onepage&q partition 20of 20Albania 201913&f false author Multicultural History Society ... 2, 9780253341891 pages 44 url http books.google.ee books?id oRASDq3rc YC&pg PA44&dq partition of Albania 1913&hl en&sa X&ei nHkpT6uqJ8iK4gSt pWoAw&redir esc y v onepage&q partition 20of 20Albania ... of the Albanian state, there were plans to partition Albania during World War I , ref cite book ... plans of partition were negotiated during and after World War II . ref cite book last Fischer first ... villages of Gusinje and Plav , which Albanian leaders considered Albanian territory,and viewed this as a partition ... Albanians view the Congress of Berlin as the partition of some of the Albanian inhabited territories ... at the plans of Montenegro, Serbia and Greece to partition between them the territories of the western ...?id IzI0uOZ2j6gC&pg PA87&dq partition of Albania&hl en&sa X&ei OjcoT96ALPP14QSCqtCxAw&redir esc y v onepage&q partition 20of 20Albania&f false ref Delination of the Albanian border A number of boundary ... Albanian state. Plans of Partition of Albania After the establishment of the Albanian state, in 1912, there were plans to partition Albania during World War I . In 1915 a secret Treaty signed in London ... with Italy, there were plans of partition between Yugoslavia and Italy. ref cite book last Fischer ... Any plans of partition of the Albanian state were unsuccessful and Albania retained its 1913 territories ... more details
File Diadochi satraps babylon.png thumb 300px right Allocation of key positions and satrapies at the Partition of Babylon, following Arrian and Diodorus The Partition of Babylon designates the attribution of the territories of Alexander the Great between his generals after his death in 323 BC . Background The partition was a result of a compromise, essentially brokered by Eumenes , following a conflict of opinion between the party of Meleager general Meleager , who wished to give full power to Philip III of Macedon , and the party of Perdiccas , who wished to wait for the birth of the heir of Alexander the future Alexander IV of Macedon to give him the throne under the control of a regent. Under the agreement, Philip III became king, but Perdiccas, as a regent, ruled. Perdiccas , as regent, managed the repartition of the territories between the former generals and satraps of Alexander. Meleager and about 300 of his partisans were eliminated by Perdiccas soon after. The Partition Europe ... satrap of Caria after the Partition of Triparadisus, it is possible that both Arrian and Justin ... only became satrap of Babylonia at the second partition the Partition of Triparadisus , so ... was definitely satrap of Carmania after the second partition, and Diodorus places him as satrap at the first partition, so this was probably the case. Hyrcania and Parthia Diodorus allots these regions ... confused on this point. Since Peithon was definitely satrap of Greater Media after the second partition ... Susiana at the first partition, but both mention it at the second partition it was therefore a real satrapy. Only Justin gives a name, Scynus , for this satrapy at the first partition, but this person ... resolved. Sources There are four ancient sources which describe the Partition of Babylon. The only .... References reflist DEFAULTSORT Partition Of Babylon Category Hellenistic dynasties Category Partition politics Category Treaties of the Diadochi Babylon Category 4th century BC treaties bg ... more details
2006 10 13 ref Early attempts at Partition The earliest recorded attempt to divide Midnapore ... not implemented it, due to the volatile situation in the province following the Partition of Bengal 1905 Partition of Bengal . ref name Local cite book last Chakrabarty first Bidyut year 1997 title ... 72 76 ref The announcement of the partition on 26 January 1915 was greeted with protests from zamindar ... 76 ref Birendranath Sasmal , a prominent barrister and politician, initially supported the partition ... pages 72 76 ref A number of members of the Indian National Congress also opposed the partition citing ... of the undivided district. Agitation against the partition continued until 1921, when the whole ... New Delhi pages 72 76 ref Partition on 1 January 2002 In independent India, successive governments ... Minister Buddhadev Bhattacharya finalized the details of the partition and set a date. ref name ... national.htm head3 title Tamluk readies for giant s partition format HTML accessdate 2006 10 13 location ... 1011231 national.htm head3 title Tamluk readies for giant s partition format HTML ... buildings began to come up immediately in Tamluk after the partition came into effect. ref name ... national.htm head3 title Tamluk readies for giant s partition format HTML accessdate 2006 10 13 location ... more details
plate The Partition Sejm lang pl Sejm Rozbiorowy was a General sejm Sejm lasting from 1773 to 1775 ... the Russian Empire , Prussia and Austria in order to legalize their First Partition of Poland ... seen as the most proud and constructive achievement of the otherwise often deplored Partition ... by Jean Michel Moreau Jean Michel Moreau le Jeune for the First Partition of Poland Ref label .... ref name Luk ref name Scott The Partition Sejm and the First Partition occurred after the balance ... land, such as Ermland. After Henry informed him of the proposal, Frederick suggested a partition of the Polish ... 978 0 19 828007 1, http books.google.com books?id ueDO1dJyjrUC&pg PA75&dq first partition of Poland anarchy Google Print, p.75 ref File Rzeczpospolita Rozbiory 1.png thumb left 300px The First Partition ... of Royal Prussia , the three powers agreed on the First Partition of Poland . This was proposed .... ref name Brit2 On February 19, 1772, the agreement of partition was signed in Vienna .... ref name Brit The partition treaty was ratified by its signatories on September 22, 1772. ref ... of the Sejm. ref name Corwin The European powers reacted to the partition with utmost ... parliament to ratify the partition. ref name Smole ski1919 In another sign of their influence, the next ... by Karl Reviczky . ref name Horne1916 Partition Treaty main First Partition of Poland File Rejtan Upadek Polski Matejko.jpg thumb right 300px Tadeusz Rejtan protesting against the partition .... ref name Smole ski1919 The Sejm on 30 September 1773 accepted the partition treaty. ref name J druch1982 162 163 By the first partition the Polish Lithuanian Commonwealth lost about 211,000 ... of Prussia Prussian partition Prussia s share might have been the smallest, but it was also significantly ... partition Russia received the largest, but economically least important area, in the northeast. ref name Brit2 Notable supporters of the partition, in addition to Poni ski, included Micha Hieronim ... more details
In number theory , a multiplicative partition or unordered factorization of an integer n that is greater than 1 is a way of writing n as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. The number n is itself considered one of these products. Multiplicative partitions closely parallel the study of multipartite partitions , discussed in harvtxt Andrews 1976 , which are additive Partition number theory partitions of finite sequences of positive integers, with the addition made pointwise . Although the study of multiplicative partitions has been ongoing since at least 1923, the name multiplicative partition appears to have been introduced by harvtxt Hughes Shallit 1983 . The Latin name factorisatio numerorum had been used previously. MathWorld uses the term unordered factorization . Examples The number 20 has four multiplicative partitions 2 × 2 × 5, 2 × 10, 4 × 5, and 20. 3 × 3 × 3 × 3, 3 × 3 × 9, 3 × 27, 9 × 9, and 81 are the five multiplicative partitions of 81 3 sup 4 sup . Because it is the fourth power of a prime number prime , 81 has the same number five of multiplicative partitions as 4 does of partition number theory additive partitions . The number 30 has five multiplicative partitions 2 × 3 × 5 2 × 15 6 × 5 3 × 10 30. In general, the number of multiplicative partitions of a Square free integer squarefree number with i prime factors is the ith Bell number , B sub i sub . Application harvtxt Hughes Shallit 1983 describe an application of multiplicative ...× 3 respectively. More generally, for each multiplicative partition math k prod t i math of the integer ... N . See also partition number theory divisor References citation first G. last Andrews authorlink ... more details
The partition of Ireland lang ga cr ochdheighilt na h ireann was the division of the island of Ireland into two distinct territories, now Northern Ireland a part of the United Kingdom and the Republic of Ireland an independent state . Partition occurred when the British Parliament passed the Government ... two separate self governing territories within the UK, but partition was reinforced in 1922 when the greater part of Ireland was separated from the United Kingdom. Since partition began, a key ... will not change without the consent of the majority there. Process of partition Overview Beginning ... the Act provided for partition as between the six counties of Northern Ireland and the rest of Ireland ... conventions in Dublin and Belfast to oppose the Bill and the proposed partition. ref Patrick Maume ... met for the last time before partition. The Ulster Unionists preferred to remain within the United ... Unionists argued against partition. The nascent Sinn F in party refused to attend. Soon after ... Ireland , rather than as an independent all Ireland republic , but continuing partition was a significant matter for Ulstermen like Sean MacEntee , who spoke strongly against partition or re partition ... partition for the time being, and of the rest of Treaty text as signed in regard to Northern ... at the National Archives of Ireland in file DE 4 5 13. ref Details of the partition Debate on Ulster ... in dispute 3 June 2009 publisher Londonderrysentinel.co.uk date accessdate 2011 04 04 ref Partition and sport Main Sport in Ireland Following partition some social and sporting bodies divided but others ... affiliated to the British Olympic Association UK s Olympic association . Partition and rail transport history of rail transport in Ireland Rail transport in Ireland was seriously affected by partition .... After partition Constitution of Ireland 1937 De Valera came to power in Dublin in 1932 and drafted ... . To unionists in Northern Ireland, the 1937 constitution made the ending of partition even less ... more details
flatcars . Mechanically, a partition or panel through which connectors pass, or a connector designed to pass through a partition. Architecture The term is frequently used to denote any boxed in beam ... more details
The Partition of Triparadisus was a power sharing agreement passed at Triparadisus in 321 BCE between the generals diadochi of Alexander the Great , in which they named a new regent and established the repartition of their satrapies. It followed and modified the Partition of Babylon made in 323 BCE upon the death of Alexander the Great . Following the death of Alexander the Great in 323 BCE, the rule of his empire was given to his half brother Philip III of Macedon Philip Arrhidaeus and Alexander s son Alexander IV of Macedon Alexander IV . However, since Philip was mentally ill and Alexander IV born only after the death of his father, a regent was named in Perdiccas . In the meantime, the former generals of Alexander were named satrap s of the various regions of his Empire. Several satrap s were eager to gain more power, and when Ptolemy I Soter Ptolemy , satrap of Egypt , rebelled with other generals, Perdiccas moved against the former, but was killed by a mutiny in his camp. Ptolemy declined the regency, and instead brought to the office Peithon and Arrhidaeus . This designation met the strong opposition of Eurydice III of Macedon Eurydice , wife of king Philip III, bringing, in the meeting called in 321 BCE at Triparadisus of all the diadochi, to their replacement with Antipater . The meeting also proceeded to divide again the satrapies between the various generals. The treaty Arrian described the result of the meeting in Events after Alexander , which were transmitted to us by the Byzantine Empire Byzantine Patriarchs of Constantinople patriach Photius I of Constantinople Photius 820 897 Then and there Antipater made a new division of Asia, wherein he partly confirmed the former and partly annulled it, according as the exigency of affairs required. For, in the first place, Egypt with Libya , and all the vast waste beyond it, and whatever else had been acquired to the westward, he assigned to Ptolemy I Soter Ptolemy Syria to Laomedon of Mytilene Cilicia to Philoxenus ... more details
Politics of Belgium The partition of Belgium , or the dissolution of the Belgium Belgian state through the separation of the Dutch language Dutch speaking people of the Flanders Flanders region and Brussels from the French language French speaking people of the Wallonia Walloon region and Brussels , granting them either independence or respective accession to the Netherlands and France , is currently being discussed in the Belgian and international media. ref name nytGermany cite news url http query.nytimes.com mem archive free pdf?res 9E06EFD91E3CE433A25751C2A9629C946197D6CF title Belgium faces a crisis work New York Times date May 22, 1900 accessdate July 12, 2008 format PDF ref ref name nytJulesDestree ref name forbes cite web url http www.forbes.com afxnewslimited feeds afx 2007 12 04 afx4401225.html title Belgium s AA rating, stable outlook unaffected by political stalemate Fitch work Thomson Financial News work forbes .com date 2007 04 12 accessdate 2008 06 20 quote Fitch Ratings Fitch believes while the eventual partition of Belgium has always been a possibility, it is unlikely ... title Divisions could lead to a partition in Belgium author Elizabeth Bryant work San Francisco Chronicle ... opinion polls showing sizable support for a partition. However, support for a unified state remains ... partition. Some political observers have suggested that a possible partition of Belgium ... year 1922 accessdate June 11, 2008 ref Image Partition plan Talleyrand en.svg thumb left 200px Belgium, French partition plan, 1830 Major European powers which included France, Prussia and the United ... ambassador to the United Kingdom, proposed a Talleyrand partition plan for Belgium partition ... commune of the Belgian people. ref name FL Supporters of a partition of Belgium argue ... explicitly for a partition of Belgium along linguistic lines. However, Destr e was using the word ... of complete partition. The New York Times explained that Destr e was afraid of the domination ... more details
The Partition of Jin zh t linktext s linktext p S n Ji F n J n , the watershed between the Spring and Autumn Period Spring and Autumn and Warring States Period Warring States periods, refers to the division of the Jin Chinese state State of Jin between rival families into the three states of Han state Han , Zhao state Zhao and Wei state Wei . Because the process took several decades, there is some debate between scholars as to the year that best marks the true partition of Jin. Harvcoltxt Kiser Cai 2003 state that the four most common dates picked by historians are 481, 475, 468, and 403 BCE. The last date, according to Sima Guang marks the conferring of Marquessates by King Weilie of Zhou on Marquess Wen of Wei Wei Si , ruler of the Wei state State of Wei Marquess Lie of Zhao Zhao Ji , ruler of the Zhao state State of Zhao , and Marquess Jing of Han Han Qian , ruler of the Han state State of Han . ref Sima Guang , Zizhi Tongjian Comprehensive Mirror to Aid in Government ref In 376 BCE, the states of Han, Wei and Zhao deposed Duke Jing of Jin zh t linktext s linktext p J n J ng G ng and divided the Jin territory between themselves. As a result the three states were often referred to as the Three Jins zh t linktext s linktext p S n J n . Background Succession issues were constant in Jin as far back as seventh century. Even when, for example, King Xi of Zhou used his royal clout to give legitimacy to Duke Wu of Jin Wu of Quwo as the rightful duke of Jin in 678 BCE, succession issues continued to arise. ref Harvcoltxt Blakeley 1979 pp 91 92 ref At the same time that the Jin duke was conquering new lands territory, a process of secondary feudalization occurred in the early and middle parts of the Spring and Autumn Period, wherein aristocratic title and territory were awarded to vassals loyal to Jin, rather than to the Zhou royalty. ref Harvcoltxt Hsu 1999 p 570 ref Over time, while other powerful states like Chu state Chu were centralizing ... more details
Multiple issues advert April 2010 cleanup rewrite April 2010 Database virtualization it is the decoupling of the database layer, which lies between the storage and application layers within the application stack. Virtualization at the database layer allows hardware resources to be extended to allow for better sharing resources between applications and users, masking of the physical location and configuration of a database from querying programs, as well as enable more scalable computing. Virtual Data Partitioning The act of partitioning data stores as a database grows has been in use for several decades. There are two primary ways that data has been partitioned inside legacy data management solutions I. Shared All Databases an architecture that assumes all database cluster nodes share a single partition. Inter node communications is used to synchronize update activities performed by different nodes on the cluster. Shared all data management systems are limited to single digit node clusters. II. Shared Nothing Databases an architecture in which all data is segregated to internally managed ... partition management. In virtual partitioning, logical data is abstracted from physical data by autonomously ... partitions and cross partition querying and transaction processing without full partition scanning. Horizontal Data Partitioning Partitioning database sources from consumers is a fundamental concept. With greater number of database sources, inserting a horizontal data virtualization layer between the sources ... Clearly Defining Data Virtualization, Data Federation, and Data Integration ref Database Virtualization Advantages Added flexibility and agility for existing computing infrastructure Enhanced database ... is Database Virtualization http www.havemacwillblog.com 2008 09 what is database virtualization Databases The Next Big Virtualization Thing http www.eweek.com c a Database Databases The Next Big Virtualization Thing 197097 Database Category Databases ... more details
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