unreferenced date September 2009 In mathematics , an exponential sum may be a finite Fourier series i.e. a trigonometric polynomial , or other finite sum formed using the exponential function , usually expressed by means of the function math e x exp 2 pi ix . , math Therefore a typical exponential sum may take the form math sum e x n , math summed over a finite sequence of real number s x sub n sub . Formulation If we allow some real coefficients a sub n sub , to get the form math sum a n e x n math ... . Estimates The main thrust of the subject is that a sum math S sum e x n math is trivially estimated ... proving some cancellation takes place, or in other words that this sum of complex numbers on the unit ... in the big O notation , that the sum resembles a random walk in two dimensions. Such an estimate ... of Weyl differencing investigated by Weyl involving a generating exponential sum math G tau sum e iaf x ia tau n math Was previously studied by Weyl himself, he developed a method to express the sum as the value math G 0 math , where G can be defined via a linear differential equation similar to Dyson equation obtained via summation by parts. History If the sum is of the form math S x e ia ... of the sum. Major advances in the subject were Van der Corput s method c. 1920 , related to the principle ... general application. Types of exponential sum Many types of sums are used in formulating particular ... is between a complete exponential sum , which is typically a sum over all residue class es modular arithmetic modulo some integer N or more general finite ring , and an incomplete exponential sum ... exponential sums are Gauss sum s and Kloosterman sum s these are in some sense finite field ... many structural properties. An example of an incomplete sum is the partial sum of the quadratic Gauss sum indeed, the case investigated by Carl Friedrich Gauss Gauss . Here there are good estimates ... occur in the theory, for example character sum s going back to Harold Davenport s thesis. The Weil ... more details
A sum certain is a specified and set amount of money owed by one person to another. It is a legal term of art , having specialized meaning in the law. Some kinds of legal claims can not be brought at all unless the sum certain can be plead. A document claimed to be a negotiable instrument can not be negotiated unless it is for a sum certain. External links cite web url http law.onecle.com new york uniform commercial code UCC03 106 3 106.html title Section 3 106 Sum Certain date 15 August 2006 work New York Uniform Commercial Code Law accessdate 4 January 2010 Category Legal terms Category Debt Category Negotiable instrument law ... more details
In mathematics the indefinite sum operator also known as the antidifference operator , denoted by math sum x , math or math Delta 1 , math , ref PlanetMath urlname IndefiniteSum title Indefinite Sum ref ... is the function y , then Y is called an indefinite sum of y and denoted sup 1 sup y http books.google.co.uk books?id 5rFOeE0zvY4C&pg PA41&dq 22indefinite sum 22 Introduction to Difference Equations ... integral relates to the derivative . Thus math Delta sum x f x f x , . math More explicitly, if math sum x f x F x , math , then math F x 1 F x f x , . math If F x is a solution of this functional ... sum actually represents a family of functions, differing by an additive constant. Fundamental theorem ..., 1999, ISBN 0849301491 ref math sum k a b f k Delta 1 f b 1 Delta 1 f a math Definitions Laplace summation formula math sum x f x int 0 x f t dt sum k 1 infty frac c k Delta k 1 f x k C math where math ... on Mathworld ref Newton s formula math sum x f x sum k 1 infty frac Delta k 1 f x k x k C math where math x k frac Gamma x 1 Gamma x k 1 math is the falling factorial . Faulhaber s formula math sum x f x sum n 1 infty frac f n 1 0 n B n x C , , math provided that the right hand side of the equation ... sum in his work, i.e. inverse to backwards difference, hence 1 as the lower limit in his formula ref math sum x f x sum n 0 infty left f n f n x right C math Ramanujan s formula math sum x f x int 0 x f t dt frac12 f x sum k 1 infty frac B 2k 2k f 2k 1 x C math Connection to the Ramanujan summation Often the constant C in indefinite sum is fixed from the following equation math int 1 2 sum x f x dx 0 math or math int 0 1 sum x f x dx 0 math In this case, where math F x sum x f x , math then Ramanjuan s sum is defined as math sum x ge 1 Re f x F 0 , math or math sum x ge 1 Re f x F ... by parts main Summation by parts Indefinite summation by parts math sum t f t Delta g t f t g t sum t g t 1 Delta f t , math Definite summation by parts math sum i a b f i Delta g i f b 1 g b 1 ... more details
There are a number of common mathematical meanings of the term digital sum Values The digit sum add the digits of the representation of a number in a given base. For example, considering 84001 in base 10 the digit sum would be 8 4 0 0 1 13. The digital root repeatedly apply the digit sum operation to the representation of a number in a given base until the outcome is a single digit. For example, considering 84001 in base 10 the digital root would be 4 8 4 0 0 1 13, 1 3 4 . Operations The mathematical operation digital sum in base b can also be called the digital sum. This is where each place notation place is summed independently, ignoring digit carry. For example 84001 56734 8 5 1 3 4 6 1 0 0 7 7 0 3 3 1 4 5 30735. disambig Category integers eo Cifereca sumo ... more details
Orphan date February 2009 Infobox comics character Wikipedia WikiProject Comics character name David Sum image Agent Sum.jpg converted y caption David Sum br Art by Adriana Melo and Chris Sotomayor . comic color background ff8080 real name Hui Lin species Human publisher Marvel Comics debut Ms. Marvel vol. 2 13 creators Brian Reed br Aaron Lopresti alliance color background c0c0ff status alliances S.H.I.E.L.D. br Operation Lightning Storm previous alliances aliases David Sum relatives powers List of superpowers Accelerated healing Healing Factor Agent David Sum is a fictional character in the Marvel Universe . Fictional character biography Agent Sum is a S.H.I.E.L.D. officer with unexplained and very effective healing powers that allow him to regenerate even from being burned down to the bones. However he has some facial marks that suggest his powers were not present at his birth. He was born as Hui Lin in the year 1320. References reflist S.H.I.E.L.D. DEFAULTSORT Sum, David Category Fictional secret agents and spies Category Marvel Comics martial artists Category Marvel Comics superheroes Marvel hero stub ... more details
File Dedekind Macneille completion.svg thumb 240px The Hasse diagram of a partially ordered set left and its Dedekind MacNeille completion right . In order theory order theoretic mathematics , the Dedekind ... Holbrook Mann MacNeille whose 1937 paper first defined and constructed it, and after Richard Dedekind because its construction generalizes the Dedekind cut s used by Dedekind to construct the real number ... 2004 isbn 9780470850558 page 10 . ref Among all possible lattice completions, the Dedekind MacNeille ... element in mvar A . Then the Dedekind MacNeille completion of mvar S consists of all subsets mvar A for which ... sub is an order embedding. An alternative definition of the Dedekind MacNeille completion that more closely resembles the definition of a Dedekind cut is sometimes used. ref This is the definition originally ... set , gives an equivalent definition of the Dedekind MacNeille completion. With the alternative ... s, viewed as a totally ordered set with the usual numerical order, then each element of the Dedekind MacNeille completion of Q may be viewed as a Dedekind cut , and the Dedekind MacNeille completion ... numbers is an example of the Dedekind completion of a totally ordered set , and the Dedekind MacNeille ... a set of elements no two of which are comparable then the Dedekind MacNeille completion of mvar ... in this way, the Dedekind MacNeille completion of mvar S is known as a concept lattice , and it plays a central role in the field of formal concept analysis . Properties The Dedekind MacNeille completion ... lattice completion of mvar S , then the Dedekind MacNeille completion is a sublattice of mvar L . ref ... dense and meet dense in the Dedekind MacNeille completion that is, every element of the completion ... S . ref harvtxt Siegfried Schr der 2003 , Proposition 5.3.7, p. 121. ref The Dedekind MacNeille completion is characterized among completions of mvar S by this property. The Dedekind MacNeille ... harvtxt Birkhoff 1995 , Theorem 27, p. 130. ref Similarly, the Dedekind MacNeille completion of a residuated ... more details
Jum sum is the Chinese mythology Chinese god of sleep or pillow, also of dreams. Originating sometime in the 1st century BC and almost a forgotten deity. References Lo Zu, Jill 1992 . Chinese history comprehensive guide , Hongo Book Company. p. 197. Category Chinese gods Category Dreaming Category Sleep China myth stub pt Jum Sum ... more details
Sum is a core Unix utility available on all Unix and Linux distributions . There is a GNU utility written by Kayvan Aghaiepour and David MacKenzie programmer David MacKenzie and distributed with the UNIX and Linux based operating systems. This utility outputs the checksum of each argument computer file file , as well as the number of Block data storage blocks they take on disk. ref Sum manual page available with most NIX distributions invoked via code man sum code ref According to the http www.gnu.org software coreutils manual html node sum invocation.html manual page , code sum code uses two different algorithm s for calculating the checksum and blocks, the SYSV checksum algorithm and the BSD checksum Default computer science default algorithm. Switching between the two algorithms is done via command line options. The algorithms implemented in this program are less sensitive than more modern checksum methods simple sums do not depend on the order of the data. The GNU manual page states sum is provided for compatibility the cksum program is preferable in new applications. The code sum code utility is invoked from the command line interface command line according to the following syntax code sum OPTION ... FILE ... code with the possible option parameters being code r code use BSD checksum algorithm, use 1K blocks defeats s code s code , code sysv code use SYSV checksum algorithm, use 512 bytes blocks code help code display the help screen and exit code version code output version information and exit When no file parameter is given, or when FILE is code code , the standard input is used as input file. References div class references small See http en.wikipedia.org wiki Wikipedia Footnotes for an explanation of how to generate footnotes using the ref erences tags references div See also GNU Core Utilities UnxUtils port to native Win32 Category Linux package management related software Category Unix package management related software Category Linux security software Category ... more details
Choy sum or choi sum zh c literally means vegetable heart in Cantonese . While frequently used to describe edible stem of either of the two varieties of Chinese cabbage , usually the soft inner core of bok choy with the tougher outer leaf leaves removed, the term can be applied to the heart the soft core or flower ing stem of almost any vegetable such as kai lan , including non traditionally East Asian greens such as broccoli . Outside of China , the Cantonese spelling of choy sum is more common than the standard Mandarin Chinese Mandarin pinyin spelling c ix n due to the greater influence of Cantonese cuisine in the Western world West . Gallery ChineseText gallery Image Bokchoyflower.jpg Bok choy s yellow flowers gallery Category Vegetables China cuisine stub vegetable stub zh ... more details
A lump sum is a single payment of money , as opposed to a series of payments made over time such as an Annuity ... PA455&dq 22lump sum is a single payment 22&hl en&ei 8HsfTqeDDsbv0gHlh jaAw&sa X&oi book result&ct result&resnum ... books?id 3DcheXOZIU0C&pg PA99&dq 22lump sum 22 22is a single payment 22&hl en&ei RHsfTr bKoy00AHXvYnbAw ... http books.google.com books?id nEt4kWB7vJ4C&pg PA102&dq 22lump sum 22 22is a single payment 22&hl en&ei ... ref cite book url http books.google.com books?id iThSAAAAMAAJ&q 22lump sum is a single payment 22&dq 22lump sum is a single payment 22&hl en&ei 8HsfTqeDDsbv0gHlh jaAw&sa X&oi book result&ct result&resnum ... maker compares lump sum amounts, or subjects contract prices to an itemized cost breakdown. ref ... sum proposal before negotiating the change in contract price. ref In 1911, American union ... lump sum&hl en title Lump Sum Payment is Strongly Opposed Labor Leaders Favor Periodical Payments in Workmen ..., 2011 ref USA Today reported in 2003 that experts said that retirees tend to handle lump sum payments to them by either being overly frugal, or alternatively by using a lot of the lump sum payment quickly ... money perfi retirement 2003 08 08 mym x.htm title Many retirees select lump sum work USA Today ... pension that year took a lump sum at their retirement, as compared to 76 in 2008. ref name ftadviser1 ... 11e0 ab6f 00144f2af8e8 Pensioners regret taking lump sum.jsp title Pensioners regret taking lump sum ... was of the view that for many retirees, a lump sum at the time of retirement was the most tax efficient ... also Lump sum tax Lottery payouts Structured settlement Distortions economics Annuity financial contracts Annuity References Notes Reflist External links http www.sec.gov investor pubs lump sum payouts.htm SEC guidelines for lump sum payouts http books.google.com books?id 4l7dMj1QTQ4C&dq 22lump sum 22&source gbs navlinks s Red Book Form of Contract, Lump Sum Contracts , Contracts Working Party, IChemE, 2001, ISBN 0852954433 http books.google.com books?id 6ItPZuAZQ1sC&q 22lump sum 22&dq 22lump sum ... more details
In mathematics , specifically in topology , the operation of connected sum is a geometric modification ... is often called the fiber sum . There is also a closely related notion of a connected sum on knot mathematics knot s, called the knot sum or composition of knots. Image Connected sum.svg right thumb 220px Illustration of connected sum. Connected sum at a point A connected sum of two ... , there is a unique connected sum defined by having the gluing map reverse orientation. Although ... sum. This uniqueness depends crucially on the disc theorem , which is not at all obvious. The operation of connected sum is denoted by math math for example math A B math denotes the connected sum of math A math and math B math . The operation of connected sum has the sphere math S m math as an identity ..., states that any closed surface can be expressed as the connected sum of a sphere with some number math g math of torus tori and some number math k math of real projective plane s. Connected sum ... involution math v mapsto v v 2 math on normal vector s. The connected sum of math M 1 math ... preserving diffeomorphism. The sum is often denoted math M 1, V M 2, V . math Its diffeomorphism ... V math , and the connected sum along math V math is simply the connected sum as described in the preceding section, performed along each fiber. For this reason, the connected sum along math V math is often called the fiber sum . The special case of math V math a point recovers the connected sum of the preceding section. Connected sum along a codimension two submanifold Another important special ... integral cohomology group math H 1 V math . So the diffeomorphism type of the sum depends on the choice of math psi math and a choice of element from math H 1 V math . A connected sum along a codimension ... is called the symplectic sum . Local operation The connected sum is a local operation on manifolds ... V math . This implies, for example, that the sum can be carried out on a single manifold math M math ... more details
showflag pj s t p di n xin j dim2 sam1 y d m s m poj ti m sim piccap small Typical dim sum ... and vegetable congee , steamed dumpling , rice noodle roll on plate , cha siu baau small Dim sum refers ... of food traditionally served in small steamer baskets or on small plates. Dim sum is also well known for the unique way it is served in some restaurants, wherein fully cooked and ready to serve dim sum .... Eating dim sum at a restaurant is usually known in Cantonese as going to drink tea yum cha , , as tea is typically served with dim sum. History Dim sum is usually linked with the older tradition ... various snacks. Citation needed date February 2007 The unique culinary art of dim sum originated ... province, many restaurants start serving dim sum as early as five in the morning. It is a tradition for the elderly to gather to eat dim sum after morning exercises. For many in southern China, yum cha is treated as a weekend family day. More traditional dim sum restaurants typically serve dim sum until ... it has become common place for restaurants to serve dim sum at dinner time, various dim sum items are even sold as take out for students and office workers on the go. While dim sum literally meaning ... have recently criticized the high amount of saturated fat and sodium in some dim sum dishes, warning that steamed dim sum should not automatically be assumed to be healthy. ref http www.phillyburbs.com ... dim sum tobkes ref Cuisine File Dim sum HK.JPG thumb right 200px Serving dim sum in a restaurant in Hong Kong Traditional dim sum includes various types of steamed buns such as cha siu baau , dumpling ... beef , chicken, pork, prawn s and vegetarianism vegetarian options. Many dim sum restaurants ... dim sum is also available and many places offer the customary egg tart . Dim sum can be cooked .... Dishes File Dumplings AH.jpg thumb right 200px Dim sum dumpling in Chicago File Char siew sou.JPG thumb right 200px Sou pastry Cha siu sou as served in a dim sum restaurant in Singapore File Lo mai ... more details
In topology , the wedge sum is a one point union of a family of topological space s. Specifically, if X and Y are pointed space s i.e. topological spaces with distinguished basepoints x sub 0 sub and y sub 0 sub the wedge sum of X and Y is the quotient space quotient of the disjoint union topology disjoint union of X and Y by the identification x sub 0 sub y sub 0 sub math X vee Y X amalg Y sim, , math where is the equivalence closure of the relation x sub 0 sub , y sub 0 sub . More generally, suppose X sub i sub pad 0.1em sub i I sub is a indexed family family of pointed spaces with basepoints p sub i sub pad 0.1em . The wedge sum of the family is given by math bigvee i X i coprod i X i sim, , math where is the equivalence relation p sub i sub pad 0.1em , p sub j sub pad 0.1em i,j I pad 0.1em . In other words, the wedge sum is the joining of several spaces at a single point. This definition is sensitive to the choice of the basepoints p sub i sub , unless the spaces X sub i sub pad 0.1em are homogeneous space homogeneous . The wedge sum is again a pointed space, and the binary operation is associative and commutative up to isomorphism . Sometimes the wedge sum is called the wedge product ... product. Examples The wedge sum of two circles is homeomorphic to a figure eight space . The wedge sum of n circles is often called a bouquet of circles , while a wedge product of arbitrary spheres ... defined the wedge sum of two functions, which was possible because math f s 0 g s 0 x 0 math , which was the point that is equivalenced in the wedge sum of the underlying spaces. Categorical description The wedge sum can be understood as the coproduct in the category of pointed spaces . Alternatively, the wedge sum can be seen as the pushout category theory pushout of the diagram X Y in the category ... which the fundamental group of the wedge sum of two spaces X and Y is the free product of the fundamental ... Topology , Springer, 2004, p. 153. ISBN 0 387 96678 1 DEFAULTSORT Wedge Sum Category ... more details
confused Zero sum In mathematics , an empty sum , or nullary sum , is a summation involving no terms at all. The value of any empty sum of numbers is conventionally taken to be 0 number zero . For summations ... of an empty summation is taken to be the zero element of that group. An empty sum can arise in particular for expressions of the form math sum i a bt i, math when a b in such case ... exactly once as operand, has the same value this defines the sum of the collection. For infinite collections ... addition operations the notion of a series mathematics series can be used to attach a definite sum ... decide to leave the sum of such collections undefined, on the grounds that there are too few values ... the sum of any finite collection of values. Doing so should be done without invalidating the usual ... x to the sum of the collection. This property then implies that the sum of a collection containing a single value v is v , and that the sum of a collection of no values at all is 0, the neutral element for addition. An alternative approach is to define the sum of a finite sequence of values by induction on its length, with as starting case the empty sequence whose sum is 0. Both approaches define the same notion of sum, and the latter does so without making any separate definition for an empty sum. Relevance of defining empty sums The necessity to define a value for empty summations ... integer s whose sum is n . It is important that there is exactly one partition of the number ... of a given class by virtue of an empty sum, for instance 0 is a triangular number because of math sum ... vector is a linear combination of no vectors at all, which is an empty sum of vectors. Also every ... can be expressed as a linear combination of no elements, which again is an empty sum. Significance of terms of an empty sum Since an empty sum by definition has no terms, it seems contradictory to talk ... is never instantiated in an empty sum, its value is irrelevant for instance the harmonic ... more details
In mathematics , the digit sum of a given integer is the Addition sum of all its numerical digit digit s, e.g. the digit sum of 84001 is calculated as 8 4 0 0 1 13 . Digit sums are most often computed using the decimal representation of the given number, but they may be calculated in any other base exponentiation base different bases give different digit sums, with the digit sums for binary being on average smaller than those for any other base. ref name lebush citation doi 10.2307 2304217 first L. E. last Bush title An asymptotic formula for the average sum of the digits of integers ... Association of America jstor 2304217 . ref Let S r , N be the digit sum for radix r of all non negative ... large N , S r sub 1 sub , N < S r sub 2 sub , N . ref name lebush The sum ... personal pborwein PAPERS P56.pdf jstor 2324993 . ref The concept of a decimal digit sum is closely ... sum operation until the remaining value is only a single digit. The digital root of any non zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value. Digit sums ... by 3 or 9 if and only if its digit sum or digital root is divisible by 3 or 9, respectively ... The digit sum of the Binary numeral system binary representation of a number is known as its Hamming .... harvtxt Perry 2005 studies the question of how many integers are mapped to the same value by the sum ... Perry journal Scientia Magna year 2005 title On the number of numbers with a given digit sum pages 191 196 . ref 6 of the numbers below 100000 have a digit sum of 23, which is along with 22 the most common digit sum within this limit. ref http johannes.jakeapp.com blog category science 200909 distribution of digit sums Analysis of the digit sum distribution ref References reflist External links mathworld urlname DigitSum title Digit Sum http www.applet magic.com Digitsum.htm Simple applications of digit sum Category Number theory cs Cifern sou et da Tv rsum de Quersumme et Ristsumma is versumma ... more details
In computational complexity theory there is an open problem whether some information about the sum of radicals may be computed in polynomial time depending on the input size, i.e., in the number of bits necessary to represent this sum. It is of importance for many problems in computational geometry , since the computation of the Euclidean distance between two points in general case involves the computation of a square root , and therefore the perimeter of a polygon or the length of a polygonal chain takes the form of a sum of radicals. ref name mulzer Wolfgang Mulzer, G nter Rote, Minimum Weight Triangulation Is NP Hard , In Proceedings of the 22nd Annual Symposium on Computational Geometry , Sedona, June 5&ndash 7, 2006, Journal of the ACM , Vol. 55, No. 2, 2008. ref The sum of radicals is defined as a finite linear combination of radicals math Sigma i 1 n k i sqrt r i x i , math where math n, r i math are natural number s and math k i, x i math are real number s. Most theoretical research in computational geometry of combinatorial character assumes the computational model of infinite precision real RAM, i.e., an abstract computer in which real numbers and operations with them are performed with infinite precision and the input size of a real number and the cost of an elementary operation are constants. ref cite book author Franco P. Preparata and Michael Ian Shamos title Computational Geometry An Introduction publisher Springer Verlag year 1985 id 1st edition 2nd printing, corrected ... is the problem of determining the sign function sign of the sum of radicals . For instance, the length ... theorem as a sum of integer square roots, so in order to determine whether one path is longer ... is a sum of radicals. In a similar way, the sum of radicals problem is inherent in the problem of minimum ... Carlo algorithm for determining whether a sum of radicals is zero , or more generally whether it represents ... While Bl mer s result does not resolve the computational complexity of finding the sign of the sum ... more details
Unreferenced date December 2009 The disjunctive sum of two combinatorial game theory games is a game in which the two games are played in parallel, with each player being allowed to move in just one of the games per turn. This is extended to disjunctive sums of any number of games by associativity , which results in allowing each player to move in just one of the games per turn. This is the fundamental operation that is used in the Sprague Grundy theorem for impartial game s and which led to the field of combinatorial game theory for partisan game s. The importance of disjunctive sums arises in games that naturally break up into components or regions that do not interact except in that each player in turn must choose just one component to play in. Examples of such games are Go board game Go , Nim , Sprouts game Sprouts , Domineering , and the map coloring games . By analyzing each component, it is possible to find simplifications of the component that do not affect its outcome or the outcome of its disjunctive sum with other games. In addition, the components can be combined by taking the disjunctive sum of two games at a time, combining them into a single game. The disjunctive sum is a fairly well studied tool for analysis of mis re game normal play games, in which a player who is unable to play loses. Some progress has been made in analyzing impartial game s in mis re game mis re play, where a player unable to play wins. Mathematically, the disjunctive sum imposes an Abelian group structure on games, that can be extended to a field mathematics field for an important subclass of games called the surreal numbers . Impartial mis re game mis re play games form an commutativity commutative monoid with only one nontrivial invertible element, called star game theory star star game theory , of order two. DEFAULTSORT Disjunctive Sum Category Combinatorial game theory ... more details
Unreferenced date February 2009 In geometric topology , a band sum of two n dimensional knots K sub 1 sub and K sub 2 sub along an n 1 dimensional 1 handle h called a band is an n dimensional knot K such that There is an n 1 dimensional 1 handle h connected to K sub 1 sub , K sub 2 sub embedded in S sup n 2 sub . There are points math p 1 in K 1 math and math p 2 in K 2 math such that math h math is attached to math K 1 sqcup K 2 math along math p 1 sqcup p 2 math . K is the n dimensional knot obtained by this surgery. A band sum is thus a generalization of the usual connected sum of knots. See also Manifold decomposition Category Topology Category Differential topology Category Knot theory Category Binary operations knottheory stub eo Banda sumo ... more details
primarysource date February 2011 Infobox Album See Wikipedia WikiProject Albums Name The Sum of No Evil Type Studio album Artist The Flower Kings Cover The Sum of No Evil Album Cover.jpg Released September 25, 2007 Recorded Spring, 2007 Genre Progressive rock Length 74 52 Label InsideOut Music Producer Roine Stolt , Petrus K nigson Last album The Road Back Home br 2007 This album The Sum of No Evil br 2007 Next album Carpe Diem The Flower Kings Live in USA br 2008 Album ratings rev1 DPRP rev1Score Rating 5.0 5 ref cite web url http www.dprp.net reviews 200747.php tfk title DPRP CD & DVD REVIEWS first last work dprp.net year 2011 last update accessdate 3 August 2011 ref rev2 rev2Score The Sum of No Evil is the tenth studio album by progressive rock artists The Flower Kings . It features the return of drummer Zoltan Cs rsz . ref http www.flowerkings.se ?s news The Flower Kings Official Website ref The limited Edition comes in a digipak and a bonus disc. Track listing tracklist all writing Roine Stolt , except where noted title1 One More Time length1 13 04 title2 Love Is The Only Answer length2 24 28 title3 Trading My Soul length3 6 25 title4 The Sum Of No Reason length4 13 25 title5 Flight 999 Brimstone Air note5 Tomas Bodin length5 5 00 title6 Life In Motion length6 12 34 Bonus disc tracklist title1 The River length1 5 40 title2 Turn The Stone length2 5 05 title3 Regal Divers note3 demo length3 6 02 Videofilms from the studio tracklist title1 Love Is The Only Answer length1 10 47 title2 Bonusviews length2 10 12 Personnel Roine Stolt Vocals, guitars, additional keyboards Tomas Bodin Piano, organ, synthesizers, mellotron Hasse Fr berg Vocals, guitars Jonas Reingold Bass Zoltan ... 2 Ed Unitsky Album artwork References reflist The Flower Kings DEFAULTSORT Sum of No Evil, The Category The Flower Kings albums Category 2007 albums Category Inside Out Music albums hu The Sum of No Evil nl The Sum of No Evil pt The Sum of No Evil ... more details
Infobox musical artist name Sum 41 image Sum 41 at the West Palm Beach Warped Tour 2010.jpg caption Sum ... D Angelo coauthors title Sum 41 Testing Their Metal date publisher Viacom work MTV.com url http www.mtv.com bands s sum 41 news feature 080202 index.jhtml pages accessdate 2008 10 20 language ref DO ... Sum 41 is a Canadians Canadian Punk Rock band from Ajax, Ontario Ajax , Ontario . ref name Juno ... and in the UK. ref cite news first Gavin last Edwards title People of the Year 2001 Sum 41 date ... 2001 sum 41 work Rolling Stone publisher Wenner Media accessdate 2008 08 19 ref The band has since .... ref name official website cite news title Sum 41 Past Tour Dates publisher Island Records url http ... in 2002 and Juno Award for Rock Album of the Year Rock Album of the Year for Chuck in 2005 . Sum 41 ... date 2011 11 30 accessdate 2012 02 28 ref History Formative years 1996 2000 Sum 41 was formed by singer ... februari 2010 url http www.youtube.com watch?v zd4zA1P C1E title SUM 41 STUDIO UPDATE 18 publisher ... of summer. ref name answers cite news title Answers.com Topic Sum 41 publisher Answers.com url http www.answers.com topic sum 41 accessdate 2008 08 17 ref ref cite news title Artists Sum 41 publisher 100xr.com url http www.100xr.com 100 XR Artists S Sum 41.htm accessdate 2008 08 17 ref In 1998, the band ... known that are with the original bassist, Richard Roy. ref cite news title Sum 41 B sides ... of a theater. Sum 41 released the Extended play EP , Half Hour of Power on June 27, 2000. The first ... showed the band performing at a house party. ref cite news title Sum 41 Bio year 2007 publisher Viacom work VH1 .com url http www.vh1.com artists az sum 41 bio.jhtml accessdate 2008 08 17 ref The EP ... Ogg Sum 41 s first full length album, All Killer, No Filler , was released on May 8, 2001. Fat ... cite news title Billboard.com Artist Chart History Sum 41 publisher Nielsen Company url http www.billboard.com bbcom retrieve chart history.do?model.chartFormatGroupName Singles&model. Sum 41 ... more details
In mathematics , a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity , typically math G chi G chi, psi sum chi r cdot psi r math where the sum is over elements r of some finite commutative ring R , &psi r is a group homomorphism of the additive group R sup sup into the unit circle , and &chi r is a group homomorphism of the unit group R sup × sup into the unit circle, extended to non unit r where it takes the value 0. Gauss sums are the analogues for finite fields of the Gamma function . Such sums are ubiquitous in number theory. They occur, for example, in the functional equations of Dirichlet L function s, where for a Dirichlet character the equation relating L s , &chi and L 1 &minus s , overline involves a factor math G chi G chi , math where overline is the complex conjugate of . The case originally considered by C. F. Gauss was the quadratic Gauss sum , for R the field of residues modulo a prime number p , and &chi the Legendre symbol . In this case Gauss proved that G &chi p sup 1 2 sup or ip sup 1 2 sup according as p is congruent to 1 or 3 modulo 4. An alternate form for this Gauss sum is math sum e frac 2 pi i r 2 p math Quadratic Gauss sums are closely connected with the theory of theta function s. The general theory of Gauss sums was developed in the early nineteenth century, with the use of Jacobi sum s and their prime decomposition in cyclotomic field s. Gauss sums over a residue ring of integers mod N are linear ... standing issue. For some cases see Kummer sum . Properties of Gauss sums of Dirichlet characters The Gauss sum of a Dirichlet character modulo N is math G chi sum a 1 N chi a e 2 pi ia N . math ... sum of is related to that of sub 0 sub by math G chi mu N N 0 chi 0 N N 0 G chi 0 ... by the Jacobi sum J , . Specifically, math G chi chi prime frac G chi G chi prime J chi, chi ... 0 471 12807 4 DEFAULTSORT Gauss Sum Category Cyclotomic fields ca Sumatori de Gauss de Gau sche Summe ... more details
The prescribed sum is the maximum fine that may be imposed on summary conviction of certain offences in the United Kingdom . In England and Wales and Northern Ireland, it is now equivalent to level 5 on the standard scale , which it predates. In Scotland , it is now equal to twice level 5 on the standard scale. England and Wales The prescribed sum is defined by http www.legislation.gov.uk ukpga 1980 43 section 32 section 32 9 of the Magistrates Courts Act 1980 . It can be altered under section 143 1 of that Act. It was previously defined by section 28 7 of the Criminal Law Act 1977 . It could be altered under section 61 1 of that Act. The prescribed sum, within the meaning of the said section 32, may be referred to in legislation as the statutory maximum . ref The Interpretation Act 1978 , section 5 and http www.legislation.gov.uk ukpga 1978 30 schedule 1 Schedule 1 as amended by the Criminal Justice Act 1988 , section 170 1 and Schedule 15, http www.legislation.gov.uk ukpga 1988 33 schedule 15 paragraph 58 paragraph 58 b ref Scotland The prescribed sum is defined by http www.legislation.gov.uk ukpga 1995 46 section 225 section 225 8 of the Criminal Procedure Scotland Act 1995 . The prescribed sum was defined by http www.legislation.gov.uk ukpga 1975 21 section 289B section 289B 6 of the Criminal Procedure Scotland Act 1975 . The prescribed sum, within the meaning of the said section 225 8 , may be referred to in legislation as the statutory maximum . ref The Interpretation Act 1978 , section 5 and Schedule 1 as amended by the Criminal Justice Act 1988 , section 170 1 and Schedule 15, http www.legislation.gov.uk ukpga 1988 33 schedule 15 paragraph 58 paragraph 58 b and the Criminal Procedure Consequential Provisions Scotland Act 1995 , section 5 and Schedule 4, http www.legislation.gov.uk ... sum is defined by http www.legislation.gov.uk nisi 1984 703 article 4 article 4 8 of the Fines ... 17 of that Order. The prescribed sum, within the meaning of the said article 4, may be referred to in legislation ... more details
In mathematics , specifically in symplectic geometry , the symplectic sum is a geometric modification ... version of connected sum mation along a submanifold, often called a fiber sum. The symplectic sum is the inverse ... sum and cut may be viewed as a deformation of symplectic manifolds, analogous for example to blowing up deformation to the normal cone in algebraic geometry . The symplectic sum has been ... . math In the 1995 paper that defined the symplectic sum, Robert Gompf proved that for any orientation ... isotopy class of symplectic structures on the connected sum math M 1, V M 2, V math meeting several ... a symplectic sum operation whose result is a symplectic manifold, unique up to isotopy. To produce a well defined symplectic structure, the connected sum must be performed with special attention paid ... generality, the symplectic sum can be performed on a single symplectic manifold math M math containing ... description of the sum of two manifolds then corresponds to the special case where math X math consists of two connected components, each containing a copy of math V math . Additionally, the sum ... M i math , as the following argument shows. A symplectic sum along a submanifold of codimension math ... R . math But this second cohomology group is zero unless math 2k 2 math . So the symplectic sum is possible ... V infty math , which has opposite normal bundle. Therefore one may symplectically sum math M, V math ... an identity mathematics identity element math P math for the symplectic sum. Such identity elements have been used both in establishing theory and in computations see below. Symplectic sum and cut as deformation It is sometimes profitable to view the symplectic sum as a family of manifolds ... V math , and the generic fiber math Z epsilon math is a symplectic sum of the math M i math . That is, the generic fibers are all members of the unique isotopy class of the symplectic sum. Loosely speaking ... sum math N M 1 V oplus N M 2 V, math with math v i math representing a normal vector to math V math ... more details
merge Riemann Integral date February 2012 File Riemann sum convergence.png right thumb 300px Four of the Riemann ... from top left to bottom right. calculus In mathematics , a Riemann sum is a method for approximating ... sum of f over I with partition P is defined as math S sum i 1 n f x i x i x i 1 math where x sub .... If x big big sub i sub x sub i 1 sub for all i , then S is called a left Riemann sum . If x big big sub i sub x sub i sub , then S is called a right Riemann sum . If x big big sub i sub frac 1 2 x sub i sub x sub i 1 sub , then S is called a middle Riemann sum . The average of the left and right Riemann sum is the trapezoidal sum . If it is given that math S sum i 1 n v i x i x i 1 math ... Riemann sum . Similarly, if v sub i sub is the infimum of f over x sub i &minus 1 sub , x sub i sub , then S is a lower Riemann sum . Any Riemann sum on a given partition that is, for any choice ... sum methods of x sup 3 sup over 0,2 using 4 subdivisions width 200 image1 LeftRiemann2.svg caption1 ... Delta x, a n 1 Delta x, b. math Left sum For the left Riemann sum, approximating the function by its ... f a f a Delta x f a 2 Delta x cdots f b Delta x right . , math The left Riemann sum amounts to an overestimation ... increasing . Right sum f is here approximated by the value at the right endpoint. This gives ... f a Delta x f a 2 Delta x cdots f b right . , math The right Riemann sum amounts to an overestimation ... . Middle sum Approximating f at the midpoint of intervals gives f a Q 2 for the first interval ... Riemann sum is to be used, the sequence of x coordinates for the boxes will be math scriptstyle x 1 ... frac 2 n , times , x i 2 math and therefore the n th right Riemann sum will be math scriptstyle ... 3 math Animations gallery Image Riemann sum leftbox .gif Left sum Image Riemann sum rightbox .gif Right sum Image Riemann sum middlebox .gif Middle sum Image Riemann sum y x 2 .gif With math y x 2 math ... Riemann sum sv Riemannsumma tr Riemann toplam ... more details
Infobox book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name Sum Forty Tales from ... Sum forty tales from the afterlives work Catalog Record publisher Library of Congress ref Hardback ... S86 2009 ref name loccr oclc 228676738 ref name loccr Sum Forty Tales from the Afterlives IPAc en icon s m respell suum , also simply called Sum , is a work of speculative fiction by the neuroscientist ... la ca discoveries1 2009feb01,0,6815929.story David Eagleman s Sum book review , Los Angeles Times, February ... Chronicle. Feb 16, 2009. ref The title word Sum refers to the Latin for I am, as in Cogito ergo sum . Like Italo Calvino s Invisible Cities , Sum does not fall cleanly under the traditional category ... bookreviews.php David Eagleman s Sum Forty Tales from the Afterlives book review , Texas Monthly, February ... arts stories DN bk sum 0208gd.ART.State.Edition1.4c0ace5.html Sum by David Eagleman Engaging stories ... Journal, February 13, 2009. ref The New York Times Book Review called Sum a delightful, thought provoking ... 2009 06 14 books review Smith t.html Eternal Whimsy Review of David Eagleman s Sum , New York Times Book Review, June 12, 2009. Retrieved on 2009 06 14. ref Sum was chosen by Time Magazine for their 2009 Summer Reading list, with the acclaim Eagleman is a true original. Read Sum and be amazed. Reread Sum and be reamazed. . ref http www.time.com time specials packages article 0,28804,1908352 1908227,00.html TIME Magazine s 2009 Summer Reading list , July 13, 2009. ref Sum was selected as Book of the Week by both The Guardian ref Nick Lezard , http www.guardian.co.uk books 2009 jun 13 sum ... and The Week , ref http www.theweek.com article index 93761 Book of the week Sum Forty Tales From the Afterlives by David Eagleman Book of the week Sum Forty Tales From the Afterlives by David Eagleman ..., The Big Issue and Humanitie . On September 10, 2009, Sum was ranked by Amazon as the 2 bestselling ... of Stephen Fry , Philip Pullman , Brian Greene , Brian Eno , and others appear on the cover, and Sum ... more details
Encyclopedia
top
