Acids and Bases Unreferenced date April 2009 A weakacid is an acid that dissociates incompletely. It does not release all of its hydrogen s in a solution, donating only a partial amount of its proton s to the solution. These acids have higher pKa than strong acids , which release all of their hydrogen atoms when dissolved in water. Examples of weak acids include acetic acid CH sub 3 sub COOH and oxalic acid H sub 2 sub C sub 2 sub O sub 4 sub . Dissociation Weak acids ionization ionize in water solution to only a moderate extent that is, if the acid was represented by the general formula HA , then in aqueous solution a significant amount of undissociated HA still remains. Weak acids in water dissociate as math mathrm HA aq , leftrightarrow , H , aq , A , aq math The equilibrium concentrations of reactants and products are related by the acid dissociation constant expression, K sub a sub math mathrm K a , , frac H , A , HA math The greater the value of K sub a sub , the more the formation of H sup sup is favored, and the lower the pH of the solution. The K sub a sub of weak acids varies between 1.8× 10 sup 16 sup and 55.5. Acids with a K sub a sub less than 1.8× 10 sup 16 sup are weaker acids than water. For example H sub 2 sub CO sub 3 sub H sub 2 sub O HCO sub 3 sub sup sup H sub 3 sub O sup sup Corrosivity While strong acid s are generally assumed to be the most corrosive , this is not always true why not? . The carborane superacid H CHB sub 11 sub Cl sub 11 sub sub , which is one million times stronger than sulfuric acid , is entirely non corrosive, whereas the weakacid hydrofluoric acid HF is extremely corrosive and can dissolve, among other things, glass and all metals citation needed date August 2010 except iridium . See also Strong acidWeak base Category Acids ar da Svag syre es cido d bil fr Acide faible hr Slabe kiseline id Asam lemah it Acido debole ms Asid lemah nl Zwak zuur no Svak syre pt cido fraco simple Weakacid sl ibka kislina ... more details
wiktionary TOC right Weak is a generic adjective pertaining to a general state of feebleness, a lack of strength, wikt durability durability , or wikt vigor vigor . Weakness Computing In concurrent programming refers to weaker consistency models. A weak entity is a database entity that cannot be uniquely identified by its own attributes alone. A weak reference is a reference that does not protect the referent object from collection by the garbage collector. A weak symbol is a symbol definition in an object file or dynamic library that may be overridden by other symbol definitions. A vulnerability computing weak software system a software system that can be exploited to do something unforeseen by its designers against the system security Music Weak SWV song Weak SWV song , a song by SWV Weak Skunk Anansie song Weak Skunk Anansie song , a song by Skunk Anansie Weak , a song by Westlife from Gravity Westlife album Gravity Science WeakacidWeak convergence Hilbert space of a sequence in a Hilbert space Weak derivative defined on Sobolev spaces Weak key in cryptography Weak nuclear force , one of the four fundamental forces of nature Weak topology of functional analysis Weak topology polar topology Weak operator topology Other Weak inflection Weak Law & Order Special Victims Unit Weak Law & Order Special Victims Unit , an episode of Law & Order Special Victims Unit Strict weak ordering Weak In Call of Duty See also lookfrom intitle Strong disambiguation opposite Week disambiguation possible misspelling Debile , Latin equivalent of the word disambig fr Faible it Debole ... more details
Unreferenced date May 2007 Weak salts or weak electrolyte salts are, as the name suggests, composed of weak electrolyte s. They are generally more volatility chemistry volatile than strong salt s. They may be similar in odor to the acid or base chemistry base they are derived from. For example, sodium acetate , NaCH sub 3 sub COO, smells similar to acetic acid CH sub 3 sub COOH. Category Electrochemistry physical chemistry stub ... more details
In mathematics , weak convergence may refer to The weak convergence of random variables of a probability distribution . The Weak convergence of measures weak convergence of a sequence of probability measures. The weak convergence Hilbert space weak convergence of a sequence in a Hilbert space , or, more generally, convergence in weak topology in a Banach space or a topological vector space . mathdab ... more details
14.00. Weak bases exist in chemical equilibrium much in the same way as weakacid s do, with a Base ... , C sub 5 sub H sub 5 sub N Other weak bases are essentially any bases not on the list of strong base strong bases . See also Strong base Weakacid References reflist Atkins, Peter, and Loretta ...Acids and Bases Onesource date April 2009 In chemistry, a weak base is a chemical base chemistry base that does not ionize fully in an aqueous solution . As Bronsted Lowry bases are proton acceptors, a weak base may also be defined as a chemical base in which protonation is incomplete. This results in a relatively low pH level compared to Base chemistry Strong bases strong bases . Bases range from a pH of greater than 7 7 is neutral, like pure water to 14 though some bases are greater than 14 . The pH level has the formula math mbox pH log 10 left mbox H right math Since bases are proton acceptors, the base receives a hydrogen ion from water, H sub 2 sub O, and the remaining H sup sup concentration in the solution determines the pH level. Weak bases will have a higher H sup sup concentration because they are less completely protonated than stronger bases and, therefore, more hydrogen ions remain in the solution. If you plug in a higher H sup sup concentration into the formula, a low pH level results. However, the pH level of bases is usually calculated using the OH sup sup concentration ... a conjugate acid such as NH sub 4 sub sup sup and a conjugate base such as NH sub 3 sub the following ... describe the strengths of weak bases, it is helpful to know the percentage protonated the percentage ... because both numbers result from the amount of protonation. A weak base is less protonated, leading ... http www.chemguide.co.uk physical acidbaseeqia bases.html Explanation of strong and weak bases from ChemGuide http bouman.chem.georgetown.edu S02 lect16 lect16.htm Guide to Weak Bases from Georgetown ... of Solutions of Weak Bases from Intute Category Bases ar it Base debole nl Zwakke base pt ... more details
Weak verb may refer to light verb , or semantically weak verb , verb participating in complex predication that has little semantic content of its own, but provides through inflection some details on the event semantics, such as aspect, mood, or tense weak inflection , conjugation class opposed to strong inflection Germanic weak verb , weak inflection class in Germanic languages disambig br Verb gwan ... more details
Unreferenced auto yes date December 2009 Orphan date December 2009 In computing , a weak symbol is a symbol definition in an object file or dynamic library that may be overridden by other symbol definitions, its value will be zero if no definition found by loader. Weak symbols are not mentioned by C or C language standards as such, inserting them into code is not portable. Some compilers can create a weak symbol with a special pragma pragma , code pragma weak code . However, the GNU Compiler Collection also supports a code attribute weak code syntax as in the example below. Example Example written for the GNU Compiler Collection Source of libfoo.so source lang c extern void foo void attribute weak void fun void if foo foo source weak test.c source lang c include < stdio.h> void fun void void foo void printf Hello n int main fun return 0 source Compile with gcc weak test.c o weak test lfoo External References http gcc.gnu.org ml gcc 1999 02n msg01219.html See also Link editor Program loader Dynamic linking Weak reference DEFAULTSORT Weak Symbol Compsci stub Category Data types Category Debugging ... more details
Weak emergence is a type of emergence in which the emergent property is reducible to its individual constituents. This is opposed to strong emergence , in which the emergent property is irreducible to its individual constituents. See also Emergence Strong and weak emergence External links http consc.net papers granada.html Emergence Category Emergence philo stub ... more details
Weak mindedness is the state of being easily impressionable or possessing a weak sense of self will, judgement or conviction. A weak minded individual s opinion may be easily swayed by propaganda or psychological manipulation emotional manipulation tactics, as they do not possess an adequate ability to judge or discern the quality of an assertion, or they may exhibit a lack of discipline . Weak mindedness can result from several factors, including but not limited to lack of education , lack of critical thinking skills, lack of interpersonal experience or understanding, or developmental disability. Category Figures of speech Category Cognition Category Critical thinking psych stub ... more details
About regular verbs regular verb weak verbs in Germanic languages Germanic weak verb semantically weak verbs light verb Unreferenced date December 2009 In grammar , the term weak originally coined in German ... feature in all the grammatical usages of the word weak is that it forms a polarity with strong there is not necessarily ... weak verb , Germanic strong verb This terminology seems to have been used first in relation to Germanic ... European ablaut ablaut the vocalic conjugations , weak those that need the addition of a dental suffix ... English. By extension, the terminology was also applied to Germanic nouns. Here too, the weak noun ... noun der Mann, des Mannes man . weak noun or n declension der Junge, des Jungen boy . Although the term weak noun is very useful in German grammar to describe this very small and distinctive group ... die M nner , but most do not. There are also strong and weak declensions of German adjectives . This differs ... the strong or the weak declension. As with the nouns, weak in this case means the declension in n . In this context, the terms strong and weak seem particularly appropriate, since the strong declension carries more information about case and gender, while the weak declension is used in situations ... Wein acc gut em Wein dat adjectives signal case with unambiguous inflections. weak der gut e Wein ... specificity. Other languages In other languages the strong weak polarity is used to express distinctions ... known as radicals. These can be strong able to carry a full syllable or weak likely to collapse under the weight of a prefix or suffix . Verbs with a weak radical are termed weak verbs, and form partially ... waw , and Nun letter nun are among those likely to make a verb weak. Regularity The terms weak and strong ... weak with irregular , but this is misleading. It is true that most English or German weak verbs ... as irregular verbs but there are also irregular weak verbs in English and German, and in Hebrew the weak ..., while the weak noun is usually taught as the anomalous form, though in fact it has its own regularity ... more details
In cryptography , a weak key is a key cryptography key , which, used with a specific cipher , makes the cipher behave in some undesirable way. Weak keys usually represent a very small fraction of the overall keyspace, which usually means that, if one generates a random key to encrypt a message, weak ... for a cipher to have no weak keys. A cipher with no weak keys is said to have a flat , or linear , key ... flaws that lead to a substantial number of weak keys being created. Some machines have more problems with weak keys than others, as modern block and stream ciphers do. The German Enigma machine ... Enigma cipher machine, in its 3 and 4 rotor implementations had the equivalent of weak keys. Certain ... also rotor machines had some of the same problems of weak keys as the more traditional rotor machines. The T52 was one such stream cipher machine that had weak key problems. The British first detected .... While the T52a b and T52c were cryptologically weak, the last two were more advanced devices the movement ... the keystream to a fixed point, which led to key reuse by undisciplined machine operators. Weak keys in DES The block cipher Data Encryption Standard DES has a few specific keys termed weak keys and semi weak keys . These are keys that cause the encryption mode of DES to act identically to the decryption ... DES rounds. DES weak keys produce sixteen identical subkeys. This occurs when the key bits are ref ... bits, the corresponding keys with the inverted parity bits may also work as weak keys all zeros 0x0000000000000000 all ones 0xFFFFFFFFFFFFFFFF 0xE1E1E1E1F0F0F0F0 0x1E1E1E1E0F0F0F0F Using weak ... the original plaintext. DES also has semi weak keys , which only produce two different subkeys, each ... and 0xFEE0FEE0FEF1FEF1 There are also 48 possibly weak keys that produce only four distinct ... Publication 800 67 , page 14 ref These weak and semiweak keys are not considered fatal flaws of DES ... four are weak and twelve are semiweak. This is such a tiny fraction of the possible keyspace ... more details
dablink This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology . For the weak topology generated by a cover of a space see coherent topology . In mathematics , weak topology is an alternative term for initial topology ... respectively, compact, etc. with respect to the weak topology. Likewise, functions are sometimes called ..., derivative differentiable , analytic function analytic , etc. with respect to the weak topology. The strong and weak topologies Let X be a topological vector space , then in particular X is a topological ... the strong topology on X . The weak topology on X is defined using the continuous dual space X ... R or C which are continuous function topology continuous with respect to the strong topology. The weak ... of X sup sup remain continuous. Explicitly, a subbase for the weak topology is the collection ... field R or C . In other words, a subset of X is open in the weak topology if and only if it can be written ... F , denoted by &sigma X , F , is sometimes also called the weak topology with respect to F . If F X is the continuous dual space of X , then the weak topology with respect to F coincides with the weak topology defined above. The weak topology &sigma X , F is induced by the family of seminorm s, math x f overset text def f x math for all f &isin F and x &isin X . In particular, weak topologies are locally convex space locally convex . In this formulation, the weak topology is the coarsest polar topology see weak topology polar topology for details. Specifically, if F is a vector space ... to the topology &sigma X , F is precisely equal to F harv Rudin 1991 loc Theorem 3.10 . Weak convergence selfref For further information, see Weak convergence Hilbert space The weak topology is characterized by the following condition a net mathematics net x sub &lambda sub in X converges in the weak ..., math x n rightharpoonup x. math Other properties If X is equipped with the weak topology, then addition ... more details
In computer programming , a weak reference is a Reference computer science reference that does not protect ... . An object referenced only by weak references is considered Unreachable memory unreachable or weakly reachable and so may be collected at any time. Weak references are used to avoid keeping memory ... feature or support various levels of weak references, such as Java programming language Java , C Sharp ... of a memory leak . Weak references may be used to solve the problem of circular references if the reference cycles are avoided by using weak references for some of the references within the group. Weak references are also used to minimize the number of unnecessary objects in memory by allowing ... Some languages have multiple levels of weak reference strength. For example, Java programming language Java has &mdash in order of decreasing strength &mdash soft reference soft , weak, and phantom ... weak references Understanding Weak References . http www.java.net about javanet java.net . published ... weak strong reference functionality as part of supporting garbage collection libraries. In the case of C , normal pointers are weak and smart pointer s are strong although pointers are not true weak references, as weak references are supposed to know when the object becomes unreachable . Examples Weak .... This list must have weak links to the objects. Otherwise, once objects are added to the list ... create a weak reference and then elsewhere in the code you can use code http java.sun.com j2se 1.4.2 docs api java lang ref Reference.html get get code to get the actual object, the weak reference ... blog 2006 05 04 understanding weak references Java Examples ref source lang java import ... Another use of weak references is in writing a cache . Using, for example, a weak hash map , one can store in the cache the various referred objects via a weak reference. When the garbage collector ... Example source lang lua weak table setmetatable , mode v weak table.item print weak table.item collectgarbage ... more details
or deities nor atheism rejecting belief in all deities . Weak agnostics who also consider themselves ... a crisis of faith . Weak agnosticism is compatible with weak atheism , as weak atheists also do not assert that it is false that any deities exist. Weak agnosticism is also referred to as empirical agnosticism and as negative agnosticism . According to Graham Oppy , weak agnosticism is the view which ... of God s existence. ref cite journal last Oppy first Graham title Weak Agnosticism Defended ... ref Justification of weak agnosticism main Existence of God Image T.H.Huxley Woodburytype .jpg left .... One reason why weak agnostics may hold such beliefs is their belief that no irrefutable or sufficiently strong evidence exists proving or disproving the existence of god s . Weak agnostics ... be proven by science or philosophy . Weak agnostics simply feel that humanity is not there yet, weak ... if it can be proved, either way, then the weak agnostic will acknowledge it. In a western monotheistic ... . A weak agnostic would say, I don t know whether any deities exist or not, but maybe one day, when ... Weak agnostics have often been accused of being fence sitters , that is, indecisive. This arises ... do not believe in a deity. Richard Dawkins refers to weak agnostics as Temporary Agnostics in Practice .... Dawkins, however, argues that weak agnostics are really de facto atheists . ref The God Delusion , Richard Dawkins ref References references irreligion Belief systems DEFAULTSORT Weak Agnosticism ... more details
Weak AI is used to refer to An artificial intelligence system which is not intended to match or exceed the capabilities of human beings, as opposed to strong AI , which is. Also known as applied AI or narrow AI . See strong AI The philosophy of artificial intelligence weak AI hypothesis the Proposition philosophical position that machines can demonstrate intelligence, but do not necessarily have a mind , mental states or consciousness . See philosophy of artificial intelligence or John Searle s definition of Chinese Room Strong AI Strong AI in Chinese Room disambig ... more details
Infobox Album See Wikipedia WikiProject Albums Name Decimate the Weak Type studio Artist Winds of Plague Cover Decimate The Weak.jpg Released February 5, 2008 Recorded Genre Deathcore , Symphonic Black Metal Length Label Century Media Records Century Media Producer Daniel Castleman Reviews About.com rating 3 5 ref name about cite web url http heavymetal.about.com od cdreviews fr wofplaguedecima.htm title Review Decimate the Weak last Bowar first Chad publisher About.com accessdate 11 August, 2009 ref Allmusic rating 3 5 ref name amg cite web url Allmusic class album id r1311508 pure url yes title Review Decimate the Weak last Henderson first Alex publisher Allmusic accessdate 11 August, 2009 ref Lambgoat Rating 4 10 ref name lambgoat cite web url http www.lambgoat.com albums view.aspx?id 2579&band Winds 20Of 20Plague&record Decimate 20the 20Weak title Review Decimate the Weak last Parker first Rob date 3 9 2008 publisher Lambgoat.com accessdate 11 August, 2009 ref Last album A Cold Day in Hell br 2005 This album Decimate the Weak br 2008 Next album The Great Stone War br 2009 Decimate the Weak is the second album by American deathcore band Winds of Plague , released February 5, 2008 ... yes title Review Decimate the Weak last Henderson first Alex publisher Allmusic accessdate 11 August ..., and is the last to include drummer Jeff Tenney. Overview Decimate the Weak peaked at 9 on the Billboard ... awards pure url yes title Decimate the Weak Chart & Awards publisher Allmusic accessdate 11 August ... recorded for Decimate the Weak . Track listing tracklist all writing Winds of Plague title1 A Cold ... Decimate the Weak note4 featuring Sal Lococo of Sworn Enemy length4 3 38 title5 Origins and Endings ... and mastered By Tue Madsen References reflist Winds of Plague DEFAULTSORT Decimate the Weak Category 2008 albums Category Winds of Plague albums Category Century Media Records albums fr Decimate the Weak pl Decimate the Weak ... more details
Infobox Single Name Flavor of the Weak Cover AHFflavoroftheweak.jpg Artist American Hi Fi from Album American Hi Fi album American Hi Fi Released January 29, 2001 Format Compact Disc Recorded 2001 Genre Pop punk Length 3 10 Label Island Records Island Writer Stacy Jones musician Stacy Jones Producer Bob Rock Last single This single Flavor of the Weak br 2001 Next single Another Perfect Day song Another Perfect Day br 2001 Flavor of the Weak is a song by American rock music rock band American Hi Fi . The song is released as the first single from their American Hi Fi album self titled debut album . It peaked at number five on the Alternative Songs Modern Rock Tracks chart in the U.S. and number 41 on the Billboard Hot 100 Billboard Hot 100 . It reached number 31 on the UK Singles Chart . Track listing US single Flavor of the Weak Mainstream version Flavor of the Weak Album version Call Out Research Hook Japan single Flavor of the Weak Vertigo Demo Flavor of the Weak Acoustic UK single Flavor of the Weak Blue Day Vertigo Demo Flavor of the Weak Acoustic Personnel American Hi Fi Stacy Jones lead vocals, rhythm guitar Jamie Arentzen lead guitar, backing vocals Drew Parsons musician Drew Parsons bass guitar, backing vocals Brian Nolan drums Production Written by Stacy Jones Produced by Bob Rock Music video The music video for the song is a parody of the Heavy metal music heavy metal documentary Heavy Metal Parking Lot . It begins with a teenage boy and his friends cussing about how the heavy metal genre and its artists should be praised. The video then begins, flashforwarding between a storyline about a girl who acts subservient to her boyfriend , not knowing about his cheating escapades, and the band performing. External links youtube uAmINmjpQxw Flavor of the Weak Official music video American Hi Fi band Category 2001 singles Category American Hi Fi songs Category Music videos directed by Chris Applebaum ... more details
Flavour quantum numbers In particle physics , weak isospin is a quantum number relating to the weak interaction , and parallels the idea of isospin under the strong interaction . Weak isospin is usually given the symbol T or I with the third component written as T sub z sub , T sub 3 sub , I sub z sub or I sub 3 sub . ref Ambiguities I is also used as sign for the normal isospin , same for the third component I sub 3 sub aka I sub z sub . T is also used as the sign for Topness . This article uses T and T sub 3 sub . ref Weak isospin is a component of the weak hypercharge , which unifies weak interactions with Electromagnetic force electromagnetic interactions. The weak isospin conservation law relates the conservation of T sub 3 sub all weak interactions must preserve T sub 3 sub . It is also conserved by the other fundamental interaction interactions and is therefore a conserved quantity in general. For this reason T sub 3 sub is more important than T and often the term weak isospin refers to the 3rd component of weak isospin . Relation with chirality Fermion s with negative chirality physics chirality also called left handed fermions have T frac 1 2 and can be grouped into doublets with T sub 3 sub frac 1 2 that behave the same way under the weak interaction . For example, up type quarks up quark u , charm quark c , top quark t have T sub 3 sub frac 1 2 and always transform into down type quarks down quark d , strange quark s , bottom quark ... that do not undergo weak interactions. Electric charge, Q , is related to weak isospin, T sub 3 sub , and weak hypercharge, Y sub W sub , by math Q T 3 frac Y mathrm W 2 . math Weak isospin and the W ... weak isospin charges bosons SubatomicParticle W boson , SubatomicParticle W boson and SubatomicParticle ... electroweak unification, the SubatomicParticle W boson0 boson mixes with the weak hypercharge gauge ... details Field theoretical formulation of standard model Weak hypercharge Category Theoretical physics ... more details
Image Weak focusing w2.gif right thumb A particle accelerator is able to contain particles in a relatively large channel by applying a magnetic field along the rotation axis of the accelerator In particle accelerators Weak focusing occurs when particles are kept in reasonably strong, uniform magnetic fields that causes them to move in circles under the influence of the Lorentz force . Weak focusing is a name for the fact that the trajectories of non mutually interacting particles moving on these circles intersect. ref http www.bnl.gov bnlweb history focusing.asp Brookhaven history The Alternating Gradient Concept ref The effect is reminiscent of the way that similar orbits in space intersect twice per revolution due to gravity. See also Strong focusing focusing due to asymmetric magnetic fields can achieve much narrower focusing Particle accelerator References references Category Particle accelerators particle stub ... more details
Infobox Album See Wikipedia WikiProject Albums Name Slaughter the Weak Type studio Artist Jungle Rot Released June 23, 1998 Genre Death metal Length 33 31 Label Pavement Records Last album Skin the Living br 1996 This album Slaughter the Weak br 1998 Next album Dead and Buried album Dead and Buried br 2001 Slaughter the Weak is the second studio album by the American death metal band Jungle Rot , released through Pavement Records in 1998. Track listing Left for Dead 3 54 Gore Bag 3 51 Infectious 2 47 Demigorgon 2 08 Consumed in Darkness 3 33 Murder One 2 13 Butchering Death 3 21 World of Hate 3 33 Deadly Force 1 36 Darkness Foretold 6 35 Category 1998 albums 1990s death metal album stub ... more details
Image Weak 2 coloring.svg frame right Weak 2 coloring. In graph theory , a weak coloring is a special case of a graph labeling . A weak k coloring of a graph G V , E assigns a color c v 1, 2, ..., k to each vertex v V , such that each non isolated vertex is adjacent to at least one vertex with different color. In notation, for each non isolated v V , there is a vertex u U with u , v E and c u c v . The figure on the right shows a weak 2 coloring of a graph. Each dark vertex color 1 is adjacent to at least one light vertex color 2 and vice versa. clear Image Weak 2 coloring construct.svg frame right Constructing a weak 2 coloring. Properties A graph vertex coloring is a weak coloring, but not necessarily vice versa. Every graph has a weak 2 coloring. The figure on the right illustrates a simple algorithm for constructing a weak 2 coloring in an arbitrary graph. Part a shows the original graph. Part b shows a breadth first search tree of the same graph. Part c shows how to color the tree starting from the root, the layers of the tree are colored alternatingly with colors 1 dark and 2 light . If there is no isolated vertex in the graph G , then a weak 2 coloring determines a domatic partition the set of the nodes with c v 1 is a dominating set , and the set of the nodes with c v 2 is another dominating set. Applications Historically, weak coloring served as the first non trivial example of a graph problem that can be solved with a local algorithm a distributed algorithm that runs in a constant number of synchronous communication rounds . More precisely, if the degree graph theory degree of each node is odd and bounded by a constant, then there is a constant time distributed algorithm for weak 2 coloring. ref name naor stockmeyer 1995 Moni Naor ... Journal on Computing 24 6 1995 , p. 1259 1277. ref This is different from non weak vertex coloring ... more details
unreferenced date March 2010 In mathematics , a weak derivative is a generalization of the concept of the derivative of a function mathematics function strong derivative for functions not assumed differentiable , but only Integrable function integrable , i.e. to lie in the Lebesgue space math L 1 a,b math . See distribution mathematics distribution s for an even more general definition. Definition Let math u math be a function in the Lebesgue space math L 1 a,b math . We say that math v math in math L 1 a,b math is a weak derivative of math u math if, math int a b u t varphi t dt int a b v t varphi t dt math for all infinitely differentiable function s math varphi math with math varphi a varphi ... alpha math is a multiindex , we say that math v math is the math alpha th math weak derivative of math ... in math U math . If math u math has a weak derivative, it is often written math D alpha u math since weak derivatives are unique at least, up to a set of measure zero , see below . Examples The absolute ... is not differentiable at t 0, has a weak derivative v known as the sign function given ... if t 0. end cases math This is not the only weak derivative for u any w that is equal to v almost everywhere is also a weak derivative for u . Usually, this is not a problem, since in the theory of Lp ... yet has a weak derivative everywhere. Since the Lebesgue measure of the rational numbers is zero, math int 1 mathbb Q t varphi t dt 0 math Thus math v t 0 math is the weak derivative of math 1 ... space, math 1 mathbb Q math is identified with the zero function. Properties If two functions are weak ... functions are equivalent if they are equal almost everywhere, then the weak derivative is unique. Also, if u is differentiable in the conventional sense then its weak derivative is identical in the sense given above to its conventional strong derivative. Thus the weak derivative is a generalization ... also hold for the weak derivative. Extensions This concept gives rise to the definition weak solution ... more details
Unreferenced stub auto yes date December 2009 Infobox Album See Wikipedia WikiProject Albums Name Butcher the Weak Type studio Artist Devourment Cover Butcher the Weak.jpg thumb right Background darkseagreen Released 2005 2006 Recorded Genre Death metal Length 30 34 Label Self released Brutal Bands Producer Reviews Last album This album Next album Butcher the Weak is an album by death metal band Devourment and was originally released in 2005 by the band. It was re recorded in May 2006 and released with a slightly different cover in August 2006 by Brutal Bands Records. Track listing Butcher the Weak 3 50 Masturbating at the Slab 3 43 Serial Cocksucker 3 31 Tomb of Scabs 3 35 Autoerotic Asphyxiation 3 13 Anal Electrocution 4 09 Fuck Her Head Off 4 00 Babykiller 4 28 Credits Mike Majewski Vocals Ruben Rosas Guitars Chris Andrews Bass Eric Park Drums Devourment DEFAULTSORT Butcher The Weak Category 2005 albums Category Devourment albums 2000s death metal album stub ... more details
In mathematics , the term weak inverse is used with several meanings. Theory of semigroups In the theory of semigroup s, a weak inverse of an element x in a semigroup nowrap S , is an element y such that nowrap 1 y x y y . An element x of S for which there is an element y of S such that nowrap 1 x y x x is called regular. A regular semigroup is a semigroup in which every element is regular. If every element x in S has a unique inverse y in S in the sense that nowrap 1 x y x x and nowrap 1 y x y y then S is called an inverse semigroup . Category theory In category theory , a weak inverse of an object category theory object A in a monoidal category C with monoidal product and unit object I is an object B such that both A B and B A are isomorphism isomorphic to the unit object I of C . A monoidal category in which every morphism is invertible and every object has a weak inverse is called a 2 group . See also Generalized inverse Von Neumann regular ring algebra stub cattheory stub Category Monoidal categories Category Semigroup theory ... more details
Infobox film name The Flesh Is Weak image image size caption director Don Chaffey writer producer Raymond Stross starring John Derek br Milly Vitale music Tristram Cary cinematography Gerry Massy Collier editing studio distributor released May 27, 1958 runtime 88 min. country FilmUK language English budget gross preceded by followed by The Flesh Is Weak is a 1957 in film 1957 British film directed by Don Chaffey . It stars John Derek and Milly Vitale . ref http allmovie.com work the flesh is weak 91719 ref Cast John Derek as Tony Giani Milly Vitale as Marissa Cooper William Franklyn as Lloyd Buxton Martin Benson actor Martin Benson as Angelo Giani Freda Jackson as Trixie Norman Wooland as Inspector Kingcombe Harold Lang as Henry Patricia Jessel as Millie John Paul actor John Paul as Sergeant Franks Denis Shaw as Saradine Joe Robinson actor Joe Robinson as Lofty Roger Snowden as Benny Patricia Plunkett as Doris Newman Shirley Anne Field as Susan References reflist External links imdb title id 0050399 title The Flesh Is Weak Don Chaffey DEFAULTSORT Flesh is Weak, The Category 1957 films Category Films directed by Don Chaffey ... more details
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