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54-566: (Redirected from C01 ) For the Misplaced Pages C1 criterion for speedy deletion, see Misplaced Pages:Criteria for speedy deletion § C1 . [REDACTED] Look up c1 in Wiktionary, the free dictionary. C1 , C01 , C.I or C-1 may refer to: Arts and media [ edit ] C1, a note-octave in music C1 Television , a Mongolian television channel Schecter C-1 Hellraiser FR ,

108-392: A {\textstyle x=a} when Although this definition looks similar to the differentiability of single-variable real functions, it is however a more restrictive condition. A function f : C → C {\textstyle f:\mathbb {C} \to \mathbb {C} } , that is complex-differentiable at a point x = a {\textstyle x=a}

162-892: A NRS social grade in the United Kingdom for the lower middle class a 2001 1.3 megapixels Olympus digital camera model a class of FM radio broadcasting in North America C1 pylon , a type of high voltage pylon Caldwell 1 ( NGC 188 ), an open cluster in Cepheus C-1 visa , a type of visa for individuals transiting through the United States C1 Espresso , café in Christchurch, New Zealand See also [ edit ] Cl (disambiguation) CI (disambiguation) 1C (disambiguation) [REDACTED] Topics referred to by

216-478: A jump discontinuity , it is possible for the derivative to have an essential discontinuity . For example, the function f ( x ) = { x 2 sin ⁡ ( 1 / x )  if  x ≠ 0 0  if  x = 0 {\displaystyle f(x)\;=\;{\begin{cases}x^{2}\sin(1/x)&{\text{ if }}x\neq 0\\0&{\text{ if }}x=0\end{cases}}}

270-702: A pro forma bill normally introduced at the start of a parliamentary session in the Canadian House of Commons C1, also known as Vlakplaas , a unit of the South African Police responsible for assassinating opponents of Apartheid during the 1980s C1, a level in the Common European Framework of Reference for Languages C1, the use class for hotels, in town and country planning in the United Kingdom C1,

324-552: A road in Metro Manila , Philippines Massachusetts State Route C1 Land vehicles [ edit ] BMW C1 , a cabin scooter Chevrolet Corvette C1 , first generation sold from 1953 to 1962, denoted a solid-axle rear-end Citroën C1 , a small car Ford C1 platform , the Ford Motor Company's global compact car automobile platform Leapmotor C01 , a battery electric executive sedan Lit C-1 ,

378-501: A 1915 German reconnaissance biplane Rumpler C.I , a 1915 German two-seater single-engine reconnaissance biplane Southern Cross Airport (New Jersey) (FAA LID: C01) Land [ edit ] Routes [ edit ] Circumferential Road 1 or C-1, an arterial road of Manila, Philippines London Buses route C1 Route C1 (Shuto Expressway) , the Inner Loop of Tokyo's Shuto Expressway system Claro M. Recto Avenue,

432-487: A British 4-4-2 steam locomotive class (classified C2 during LNER ownership) GNR Class C1 (large boiler) , a British 4-4-2 steam locomotive class LB&SCR C1 class , an 1882 British freight steam locomotive Long Island Rail Road C1 , a bilevel railcar built by Tokyu Car Corporation NER Class C1 , a British 0-6-0 steam locomotive class PRR C1 , an American PRR steam locomotive Finnish Steam Locomotive Class C1 Sea [ edit ] HMS  C1 ,

486-823: A C-class submarine of the Royal Navy USS ; C-1  (SS-9) , a C-class submarine of the United States Navy USS ; Newark  (C-1) , a protected cruiser of the United States Navy Type C1 ship , a small cargo vessel built by the United States in large numbers before and during World War II Isaac Peral (C-1), a Spanish submarine Space [ edit ] Cluster 1 , also known as Rumba, an ESA satellite Sports [ edit ] For racing cars, see § Land vehicles . C1,

540-576: A cargo-version of the S-2 Tracker anti-submarine warfare aircraft of the United States Navy AEG C.I , a German World War I reconnaissance aircraft AGO C.I , a 1915 German reconnaissance biplane Albatros C.I , a 1915 German two-seat general-purpose biplane Aviatik C.I , a 1915 German observation plane Cierva C.1 , a 1920 Spanish experimental autogyro DFW C.I , a WWI German reconnaissance aircraft Douglas C-1 ,

594-541: A cargo/transport airplane produced by Douglas Aircraft for the U.S. Army Air Service starting in 1925 Fokker C.I , a 1918 German reconnaissance biplane Friedrichshafen C.I , a 1914 German single-engined amphibious reconnaissance biplane Hansa-Brandenburg C.I , a 1916 German 2-seater armed single-engine reconnaissance biplane Kawasaki C-1 , an indigenous transport aircraft of the Japanese Air Self-Defense Forces Otto C.I ,

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648-791: A form of prostaglandins Other uses in biology and medicine [ edit ] C1 and P1 (neuroscience) , a component of the visual evoked potential ATC code C01 , a subgroup of the Anatomical Therapeutic Chemical Classification System C01, the ICD-10 code for "malignant neoplasm of base of tongue", a form of oral cancer C1, the short name for a microfluidic single-cell analysis system sold by Fluidigm Chemistry [ edit ] C1 Chemistry , study of methane, methanol, carbon monoxide, carbon dioxide Computing [ edit ] Hardware [ edit ] C-One ,

702-415: A function is necessarily infinitely differentiable, and in fact analytic . If M is a differentiable manifold , a real or complex-valued function f on M is said to be differentiable at a point p if it is differentiable with respect to some (or any) coordinate chart defined around p . If M and N are differentiable manifolds, a function f :  M  →  N is said to be differentiable at

756-478: A function that is continuous everywhere but differentiable nowhere is the Weierstrass function . A function f {\textstyle f} is said to be continuously differentiable if the derivative f ′ ( x ) {\textstyle f^{\prime }(x)} exists and is itself a continuous function. Although the derivative of a differentiable function never has

810-414: A guitar model A Yamaha grand piano model "C1", a slang expression in the video game Counter-Strike , used to express agreement Biology and medicine [ edit ] Anatomy [ edit ] Cervical vertebra 1 , the first cervical vertebrae of the vertebral column Cervical spinal nerve 1 , a spinal nerve of the cervical segment Biochemistry [ edit ] C1 complex ,

864-403: A multi-variable function, while not being complex-differentiable. For example, f ( z ) = z + z ¯ 2 {\displaystyle f(z)={\frac {z+{\overline {z}}}{2}}} is differentiable at every point, viewed as the 2-variable real function f ( x , y ) = x {\displaystyle f(x,y)=x} , but it

918-476: A note in terms of textual notation rather than frequency, while at the same time avoiding the transposition conventions that are used in writing the music for instruments such as the clarinet and guitar . It is also easily translated into staff notation, as needed. In describing musical pitches, nominally enharmonic spellings can give rise to anomalies where, for example in Pythagorean intonation C 4

972-630: A prototype cabin motorcycle Nimrod NRA/C1 , a 1981 test design racing car Sauber C1, a Sauber sport car Other uses in land transport [ edit ] C-1, the numberplate of the Prime Minister of Australia 's official VIP transportation A type of heavy goods vehicle licence A one-way traffic sign in the Vienna Convention on Road Signs and Signals Rail [ edit ] Bavarian C I , an 1847 German steam locomotives class GNR Class C1 (small boiler) ,

1026-506: A single-board microcomputer C1 NES TV , a family of Nintendo-television-set hybrids manufactured by Sharp Corporation in 1983 ATI C1, codename of the Xbox 360 GPU Xenos Other uses in computing [ edit ] C0 and C1 control codes defined in ISO 6429 C1 (protocol) , a 1984 protocol for file transfer, also known as "Punter" TCSEC C1 security class A CPU power state in

1080-856: A solo canoe discipline including sprint canoe and canoe slalom C1 (classification) , a para-cycling classification C1, an abbreviation for Class One offshore powerboat racing 'C1', the top category in Group C sportscar racing, used between 1985 and 1990 C1, the UEFA Champions League (formerly known as the European Cup) in football Serie C1 , the third highest football league in Italy until 2008 Other uses [ edit ] C1, an international standard paper size defined in ISO 216 (648×917 mm) Bills C-1 and S-1 ,

1134-505: Is always C 4 , and C 4 is never any note but middle C. This notation system also avoids the "fussiness" of having to visually distinguish between four and five primes, as well as the typographic issues involved in producing acceptable subscripts or substitutes for them. C 7 is much easier to quickly distinguish visually from C 8 , than is, for example, c′′′′ from c′′′′′ , and the use of simple integers (e.g. C7 and C8) makes subscripts unnecessary altogether. Although pitch notation

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1188-567: Is a lower frequency than B 3 ; but such paradoxes usually do not arise in a scientific context. Scientific pitch notation avoids possible confusion between various derivatives of Helmholtz notation which use similar symbols to refer to different notes. For example, "C" in Helmholtz's original notation refers to the C two octaves below middle C, whereas "C" in ABC Notation refers to middle C itself. With scientific pitch notation, middle C

1242-528: Is an absolute pitch standard , first proposed in 1713 by French physicist Joseph Sauveur . It was defined so that all Cs are integer powers of 2, with middle C (C 4 ) at 256  hertz . As already noted, it is not dependent upon, nor a part of scientific pitch notation described here. To avoid the confusion in names, scientific pitch is sometimes also called "Verdi tuning" or "philosophical pitch". The current international pitch standard, using A 4 as exactly 440  Hz , had been informally adopted by

1296-432: Is automatically differentiable at that point, when viewed as a function f : R 2 → R 2 {\displaystyle f:\mathbb {R} ^{2}\to \mathbb {R} ^{2}} . This is because the complex-differentiability implies that However, a function f : C → C {\textstyle f:\mathbb {C} \to \mathbb {C} } can be differentiable as

1350-571: Is different from Wikidata All article disambiguation pages All disambiguation pages Note-octave Although scientific pitch notation was originally designed as a companion to scientific pitch (see below), the two are not synonymous. Scientific pitch is a pitch standard —a system that defines the specific frequencies of particular pitches (see below). Scientific pitch notation concerns only how pitch names are notated, that is, how they are designated in printed and written text, and does not inherently specify actual frequencies. Thus,

1404-896: Is differentiable at 0, since f ′ ( 0 ) = lim ε → 0 ( ε 2 sin ⁡ ( 1 / ε ) − 0 ε ) = 0 {\displaystyle f'(0)=\lim _{\varepsilon \to 0}\left({\frac {\varepsilon ^{2}\sin(1/\varepsilon )-0}{\varepsilon }}\right)=0} exists. However, for x ≠ 0 , {\displaystyle x\neq 0,} differentiation rules imply f ′ ( x ) = 2 x sin ⁡ ( 1 / x ) − cos ⁡ ( 1 / x ) , {\displaystyle f'(x)=2x\sin(1/x)-\cos(1/x)\;,} which has no limit as x → 0. {\displaystyle x\to 0.} Thus, this example shows

1458-450: Is given in the section Differentiability classes ). If f is differentiable at a point x 0 , then f must also be continuous at x 0 . In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold : a continuous function need not be differentiable. For example, a function with a bend, cusp , or vertical tangent may be continuous, but fails to be differentiable at

1512-440: Is intended to describe sounds audibly perceptible as pitches, it can also be used to specify the frequency of non-pitch phenomena. Notes below E 0 or higher than E 10 are outside most humans' hearing range , although notes slightly outside the hearing range on the low end may still be indirectly perceptible as pitches due to their overtones falling within the hearing range. For an example of truly inaudible frequencies, when

1566-421: Is not complex-differentiable at any point because the limit lim h → 0 h + h ¯ 2 h {\textstyle \lim _{h\to 0}{\frac {h+{\bar {h}}}{2h}}} does not exist (the limit depends on the angle of approach). Any function that is complex-differentiable in a neighborhood of a point is called holomorphic at that point. Such

1620-408: Is not necessarily differentiable, but a differentiable function is necessarily continuous (at every point where it is differentiable) as being shown below (in the section Differentiability and continuity ). A function is said to be continuously differentiable if its derivative is also a continuous function; there exist functions that are differentiable but not continuously differentiable (an example

1674-801: Is of class C 2 {\displaystyle C^{2}} if the first and second derivative of the function both exist and are continuous. More generally, a function is said to be of class C k {\displaystyle C^{k}} if the first k {\displaystyle k} derivatives f ′ ( x ) , f ′ ′ ( x ) , … , f ( k ) ( x ) {\textstyle f^{\prime }(x),f^{\prime \prime }(x),\ldots ,f^{(k)}(x)} all exist and are continuous. If derivatives f ( n ) {\displaystyle f^{(n)}} exist for all positive integers n , {\textstyle n,}

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1728-498: Is said to be differentiable at a ∈ U {\displaystyle a\in U} if the derivative exists. This implies that the function is continuous at a . This function f is said to be differentiable on U if it is differentiable at every point of U . In this case, the derivative of f is thus a function from U into R . {\displaystyle \mathbb {R} .} A continuous function

1782-475: Is traditionally called the sub-contra octave , and the tone marked C 0 in SPN is written as ,,C or C,, or CCC in traditional systems, such as Helmholtz notation . Octave 0 of SPN marks the low end of what humans can actually perceive, with the average person being able to hear frequencies no lower than 20 Hz as pitches. The octave number increases by 1 upon an ascension from B to C. Thus, A 0 refers to

1836-581: Is understandably easier to simply refer to notes by their closest modern equivalent, as opposed to specifying the difference using cents every time. The table below gives notation for pitches based on standard piano key frequencies : standard concert pitch and twelve-tone equal temperament . When a piano is tuned to just intonation , C 4 refers to the same key on the keyboard, but a slightly different frequency. Notes not produced by any piano are highlighted in medium gray, and those produced only by an extended 108-key piano, light gray. Mathematically, given

1890-613: The Acoustical Society of America in 1939, and adopted by the International Organization for Standardization in 1955. C 0 , which was exactly 16 Hz under the scientific pitch standard, is now 16.35160 Hz under the current international standard system. Continuously differentiable In mathematics , a differentiable function of one real variable is a function whose derivative exists at each point in its domain . In other words,

1944-561: The Advanced Configuration and Power Interface Mathematics [ edit ] C 1 {\displaystyle C^{1}} , the set of all continuously differentiable functions C1 field , a quasi-algebraically closed field C1, the first of four pure modules taken in the Advanced Level (UK) Maths syllabus Transportation [ edit ] Air [ edit ] C-1 Trader ,

1998-495: The Chandra X-ray Observatory observed the waves of pressure fronts propagating away from a black hole, their one oscillation every 10 million years was described by NASA as corresponding to the B ♭ fifty-seven octaves below middle C (B −53 or 3.235  fHz ). The notation is sometimes used in the context of meantone temperament , and does not always assume equal temperament nor

2052-419: The graph of a differentiable function has a non- vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp . If x 0 is an interior point in the domain of a function f , then f is said to be differentiable at x 0 if

2106-415: The derivative f ′ ( x 0 ) {\displaystyle f'(x_{0})} exists. In other words, the graph of f has a non-vertical tangent line at the point ( x 0 , f ( x 0 )) . f is said to be differentiable on U if it is differentiable at every point of U . f is said to be continuously differentiable if its derivative is also a continuous function over

2160-445: The domain of the function f {\textstyle f} . For a multivariable function, as shown here , the differentiability of it is something more complex than the existence of the partial derivatives of it. A function f : U → R {\displaystyle f:U\to \mathbb {R} } , defined on an open set U ⊂ R {\textstyle U\subset \mathbb {R} } ,

2214-542: The domain of the function f {\textstyle f} . Generally speaking, f is said to be of class C k {\displaystyle C^{k}} if its first k {\displaystyle k} derivatives f ′ ( x ) , f ′ ′ ( x ) , … , f ( k ) ( x ) {\textstyle f^{\prime }(x),f^{\prime \prime }(x),\ldots ,f^{(k)}(x)} exist and are continuous over

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2268-569: The existence of a function that is differentiable but not continuously differentiable (i.e., the derivative is not a continuous function). Nevertheless, Darboux's theorem implies that the derivative of any function satisfies the conclusion of the intermediate value theorem . Similarly to how continuous functions are said to be of class C 0 , {\displaystyle C^{0},} continuously differentiable functions are sometimes said to be of class C 1 {\displaystyle C^{1}} . A function

2322-421: The existence of the partial derivatives (or even of all the directional derivatives ) does not guarantee that a function is differentiable at a point. For example, the function f : R → R defined by is not differentiable at (0, 0) , but all of the partial derivatives and directional derivatives exist at this point. For a continuous example, the function is not differentiable at (0, 0) , but again all of

2376-473: The first A above C 0 and middle C (the one-line octave 's C or simply c′ ) is denoted as C 4 in SPN. For example, C 4 is one note above B 3 , and A 5 is one note above G 5 . The octave number is tied to the alphabetic character used to describe the pitch, with the division between note letters ‘B’ and ‘C’, thus: Scientific pitch notation is often used to specify the range of an instrument. It provides an unambiguous means of identifying

2430-606: The first component of the classical complement pathway C1 domain , an important secondary messenger protein domain C1-inhibitor , a human serine protease inhibitor C1 regulatory sequence for the insulin gene Apolipoprotein C1 , a human lipoprotein Chlorophyll c1 , a form of chlorophyll Cytochrome C1 , a precursor protein to Cytochrome C Proanthocyanidin C1 , a type of polyphenolic compound Prostaglandin C1 ,

2484-422: The function is smooth or equivalently, of class C ∞ . {\displaystyle C^{\infty }.} A function of several real variables f : R → R is said to be differentiable at a point x 0 if there exists a linear map J : R → R such that If a function is differentiable at x 0 , then all of the partial derivatives exist at x 0 , and

2538-499: The linear map J is given by the Jacobian matrix , an n × m matrix in this case. A similar formulation of the higher-dimensional derivative is provided by the fundamental increment lemma found in single-variable calculus. If all the partial derivatives of a function exist in a neighborhood of a point x 0 and are continuous at the point x 0 , then the function is differentiable at that point x 0 . However,

2592-421: The location of the anomaly. Most functions that occur in practice have derivatives at all points or at almost every point. However, a result of Stefan Banach states that the set of functions that have a derivative at some point is a meagre set in the space of all continuous functions. Informally, this means that differentiable functions are very atypical among continuous functions. The first known example of

2646-439: The music industry as far back as 1926, and A440 became the official international pitch standard in 1955. SPN is routinely used to designate pitch in this system. A 4 may be tuned to other frequencies under different tuning standards, and SPN octave designations still apply (ISO 16). With changes in concert pitch and the widespread adoption of A440 as a musical standard, new scientific frequency tables were published by

2700-584: The number n of semitones above middle C, the fundamental frequency in hertz is given by 440 ⋅ 2 ( n − 9 ) / 12 {\displaystyle 440\cdot 2^{(n-9)/12}} (see twelfth root of two ). Given the MIDI NoteOn number m , the frequency of the note is normally 440 ⋅ 2 ( m − 69 ) / 12 {\displaystyle 440\cdot 2^{(m-69)/12}} Hz, using standard tuning. Scientific pitch

2754-420: The partial derivatives and directional derivatives exist. In complex analysis , complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers . So, a function f : C → C {\textstyle f:\mathbb {C} \to \mathbb {C} } is said to be differentiable at x =

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2808-447: The same term This disambiguation page lists articles associated with the same title formed as a letter–number combination. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=C1&oldid=1218868198 " Category : Letter–number combination disambiguation pages Hidden categories: Short description

2862-490: The standard concert A 4 of 440  Hz ; this is particularly the case in connection with earlier music. The standard proposed to the Acoustical Society of America explicitly states a logarithmic scale for frequency, which excludes meantone temperament, and the base frequency it uses gives A 4 a frequency of exactly 440 Hz. However, when dealing with earlier music that did not use equal temperament, it

2916-425: The use of scientific pitch notation to distinguish octaves does not depend on the pitch standard used. The notation makes use of the traditional tone names (A to G) which are followed by numbers showing which octave they are part of. For standard A440 pitch equal temperament , the system begins at a frequency of 16.35160 Hz , which is assigned the value C 0 . The octave 0 of the scientific pitch notation

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