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Analytic geometry
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In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.
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Analytic geometry
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In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality. See also
Cross product
Rotation of axes
Translation of axes
Vector space Notes References Books John Casey (1885) Analytic Geometry of the Point, Line, Circle, and Conic Sections, link from Internet Archive. Articles
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Analytic geometry
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External links
Coordinate Geometry topics with interactive animations
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Analysis of algorithms
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In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm.
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Analysis of algorithms
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The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem. These estimates provide an insight into reasonable directions of search for efficient algorithms.
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Analysis of algorithms
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In theoretical analysis of algorithms it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. Big O notation, Big-omega notation and Big-theta notation are used to this end. For instance, binary search is said to run in a number of steps proportional to the logarithm of the size of the sorted list being searched, or in , colloquially "in logarithmic time". Usually asymptotic estimates are used because different implementations of the same algorithm may differ in efficiency. However the efficiencies of any two "reasonable" implementations of a given algorithm are related by a constant multiplicative factor called a hidden constant.
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Analysis of algorithms
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Exact (not asymptotic) measures of efficiency can sometimes be computed but they usually require certain assumptions concerning the particular implementation of the algorithm, called model of computation. A model of computation may be defined in terms of an abstract computer, e.g. Turing machine, and/or by postulating that certain operations are executed in unit time.
For example, if the sorted list to which we apply binary search has elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at most time units are needed to return an answer.
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Analysis of algorithms
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Cost models
Time efficiency estimates depend on what we define to be a step. For the analysis to correspond usefully to the actual run-time, the time required to perform a step must be guaranteed to be bounded above by a constant. One must be careful here; for instance, some analyses count an addition of two numbers as one step. This assumption may not be warranted in certain contexts. For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.
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Analysis of algorithms
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Two cost models are generally used:
the uniform cost model, also called uniform-cost measurement (and similar variations), assigns a constant cost to every machine operation, regardless of the size of the numbers involved
the logarithmic cost model, also called logarithmic-cost measurement (and similar variations), assigns a cost to every machine operation proportional to the number of bits involved The latter is more cumbersome to use, so it's only employed when necessary, for example in the analysis of arbitrary-precision arithmetic algorithms, like those used in cryptography.
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Analysis of algorithms
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A key point which is often overlooked is that published lower bounds for problems are often given for a model of computation that is more restricted than the set of operations that you could use in practice and therefore there are algorithms that are faster than what would naively be thought possible.
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Analysis of algorithms
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Run-time analysis
Run-time analysis is a theoretical classification that estimates and anticipates the increase in running time (or run-time or execution time) of an algorithm as its input size (usually denoted as ) increases. Run-time efficiency is a topic of great interest in computer science: A program can take seconds, hours, or even years to finish executing, depending on which algorithm it implements. While software profiling techniques can be used to measure an algorithm's run-time in practice, they cannot provide timing data for all infinitely many possible inputs; the latter can only be achieved by the theoretical methods of run-time analysis.
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Analysis of algorithms
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Shortcomings of empirical metrics Since algorithms are platform-independent (i.e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system), there are additional significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.
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Analysis of algorithms
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Take as an example a program that looks up a specific entry in a sorted list of size n. Suppose this program were implemented on Computer A, a state-of-the-art machine, using a linear search algorithm, and on Computer B, a much slower machine, using a binary search algorithm. Benchmark testing on the two computers running their respective programs might look something like the following:
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Analysis of algorithms
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Based on these metrics, it would be easy to jump to the conclusion that Computer A is running an algorithm that is far superior in efficiency to that of Computer B. However, if the size of the input-list is increased to a sufficient number, that conclusion is dramatically demonstrated to be in error:
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Analysis of algorithms
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Computer A, running the linear search program, exhibits a linear growth rate. The program's run-time is directly proportional to its input size. Doubling the input size doubles the run-time, quadrupling the input size quadruples the run-time, and so forth. On the other hand, Computer B, running the binary search program, exhibits a logarithmic growth rate. Quadrupling the input size only increases the run-time by a constant amount (in this example, 50,000 ns). Even though Computer A is ostensibly a faster machine, Computer B will inevitably surpass Computer A in run-time because it's running an algorithm with a much slower growth rate.
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Analysis of algorithms
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Orders of growth Informally, an algorithm can be said to exhibit a growth rate on the order of a mathematical function if beyond a certain input size , the function times a positive constant provides an upper bound or limit for the run-time of that algorithm. In other words, for a given input size greater than some 0 and a constant , the run-time of that algorithm will never be larger than . This concept is frequently expressed using Big O notation. For example, since the run-time of insertion sort grows quadratically as its input size increases, insertion sort can be said to be of order .
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Analysis of algorithms
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Big O notation is a convenient way to express the worst-case scenario for a given algorithm, although it can also be used to express the average-case — for example, the worst-case scenario for quicksort is , but the average-case run-time is .
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Analysis of algorithms
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Empirical orders of growth
Assuming the run-time follows power rule, , the coefficient can be found by taking empirical measurements of run-time } at some problem-size points }, and calculating so that . In other words, this measures the slope of the empirical line on the log–log plot of run-time vs. input size, at some size point. If the order of growth indeed follows the power rule (and so the line on log–log plot is indeed a straight line), the empirical value of will stay constant at different ranges, and if not, it will change (and the line is a curved line)—but still could serve for comparison of any two given algorithms as to their empirical local orders of growth behaviour. Applied to the above table:
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Analysis of algorithms
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It is clearly seen that the first algorithm exhibits a linear order of growth indeed following the power rule. The empirical values for the second one are diminishing rapidly, suggesting it follows another rule of growth and in any case has much lower local orders of growth (and improving further still), empirically, than the first one. Evaluating run-time complexity
The run-time complexity for the worst-case scenario of a given algorithm can sometimes be evaluated by examining the structure of the algorithm and making some simplifying assumptions. Consider the following pseudocode:
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Analysis of algorithms
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1 get a positive integer n from input
2 if n > 10
3 print "This might take a while..."
4 for i = 1 to n
5 for j = 1 to i
6 print i * j
7 print "Done!"
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Analysis of algorithms
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A given computer will take a discrete amount of time to execute each of the instructions involved with carrying out this algorithm. The specific amount of time to carry out a given instruction will vary depending on which instruction is being executed and which computer is executing it, but on a conventional computer, this amount will be deterministic. Say that the actions carried out in step 1 are considered to consume time T1, step 2 uses time T2, and so forth.
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Analysis of algorithms
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In the algorithm above, steps 1, 2 and 7 will only be run once. For a worst-case evaluation, it should be assumed that step 3 will be run as well. Thus the total amount of time to run steps 1-3 and step 7 is:
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Analysis of algorithms
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The loops in steps 4, 5 and 6 are trickier to evaluate. The outer loop test in step 4 will execute ( n + 1 )
times (note that an extra step is required to terminate the for loop, hence n + 1 and not n executions), which will consume T4( n + 1 ) time. The inner loop, on the other hand, is governed by the value of j, which iterates from 1 to i. On the first pass through the outer loop, j iterates from 1 to 1: The inner loop makes one pass, so running the inner loop body (step 6) consumes T6 time, and the inner loop test (step 5) consumes 2T5 time. During the next pass through the outer loop, j iterates from 1 to 2: the inner loop makes two passes, so running the inner loop body (step 6) consumes 2T6 time, and the inner loop test (step 5) consumes 3T5 time.
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Analysis of algorithms
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Altogether, the total time required to run the inner loop body can be expressed as an arithmetic progression: which can be factored as The total time required to run the outer loop test can be evaluated similarly: which can be factored as Therefore, the total run-time for this algorithm is: which reduces to As a rule-of-thumb, one can assume that the highest-order term in any given function dominates its rate of growth and thus defines its run-time order. In this example, n2 is the highest-order term, so one can conclude that . Formally this can be proven as follows:
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Analysis of algorithms
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A more elegant approach to analyzing this algorithm would be to declare that [T1..T7] are all equal to one unit of time, in a system of units chosen so that one unit is greater than or equal to the actual times for these steps. This would mean that the algorithm's run-time breaks down as follows:
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Analysis of algorithms
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Growth rate analysis of other resources
The methodology of run-time analysis can also be utilized for predicting other growth rates, such as consumption of memory space. As an example, consider the following pseudocode which manages and reallocates memory usage by a program based on the size of a file which that program manages: while file is still open:
let n = size of file
for every 100,000 kilobytes of increase in file size
double the amount of memory reserved
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Analysis of algorithms
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In this instance, as the file size n increases, memory will be consumed at an exponential growth rate, which is order . This is an extremely rapid and most likely unmanageable growth rate for consumption of memory resources.
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Analysis of algorithms
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Relevance
Algorithm analysis is important in practice because the accidental or unintentional use of an inefficient algorithm can significantly impact system performance. In time-sensitive applications, an algorithm taking too long to run can render its results outdated or useless. An inefficient algorithm can also end up requiring an uneconomical amount of computing power or storage in order to run, again rendering it practically useless.
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Analysis of algorithms
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Constant factors
Analysis of algorithms typically focuses on the asymptotic performance, particularly at the elementary level, but in practical applications constant factors are important, and real-world data is in practice always limited in size. The limit is typically the size of addressable memory, so on 32-bit machines 232 = 4 GiB (greater if segmented memory is used) and on 64-bit machines 264 = 16 EiB. Thus given a limited size, an order of growth (time or space) can be replaced by a constant factor, and in this sense all practical algorithms are for a large enough constant, or for small enough data.
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Analysis of algorithms
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This interpretation is primarily useful for functions that grow extremely slowly: (binary) iterated logarithm (log*) is less than 5 for all practical data (265536 bits); (binary) log-log (log log n) is less than 6 for virtually all practical data (264 bits); and binary log (log n) is less than 64 for virtually all practical data (264 bits). An algorithm with non-constant complexity may nonetheless be more efficient than an algorithm with constant complexity on practical data if the overhead of the constant time algorithm results in a larger constant factor, e.g., one may have so long as and .
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Analysis of algorithms
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For large data linear or quadratic factors cannot be ignored, but for small data an asymptotically inefficient algorithm may be more efficient. This is particularly used in hybrid algorithms, like Timsort, which use an asymptotically efficient algorithm (here merge sort, with time complexity ), but switch to an asymptotically inefficient algorithm (here insertion sort, with time complexity ) for small data, as the simpler algorithm is faster on small data.
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Analysis of algorithms
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See also
Amortized analysis
Analysis of parallel algorithms
Asymptotic computational complexity
Best, worst and average case
Big O notation
Computational complexity theory
Master theorem (analysis of algorithms)
NP-Complete
Numerical analysis
Polynomial time
Program optimization
Profiling (computer programming)
Scalability
Smoothed analysis
Termination analysis — the subproblem of checking whether a program will terminate at all
Time complexity — includes table of orders of growth for common algorithms
Information-based complexity Notes References External links Computational complexity theory
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Chemistry of ascorbic acid
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Ascorbic acid is an organic compound with formula , originally called hexuronic acid. It is a white solid, but impure samples can appear yellowish. It dissolves well in water to give mildly acidic solutions. It is a mild reducing agent.
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Chemistry of ascorbic acid
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Ascorbic acid exists as two enantiomers (mirror-image isomers), commonly denoted "" (for "levo") and "" (for "dextro"). The isomer is the one most often encountered: it occurs naturally in many foods, and is one form ("vitamer") of vitamin C, an essential nutrient for humans and many animals. Deficiency of vitamin C causes scurvy, formerly a major disease of sailors in long sea voyages. It is used as a food additive and a dietary supplement for its antioxidant properties. The "" form can be made via chemical synthesis but has no significant biological role.
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Chemistry of ascorbic acid
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History The antiscorbutic properties of certain foods were demonstrated in the 18th century by James Lind. In 1907, Axel Holst and Theodor Frølich discovered that the antiscorbutic factor was a water-soluble chemical substance, distinct from the one that prevented beriberi. Between 1928 and 1932, Albert Szent-Györgyi isolated a candidate for this substance, which he called it "hexuronic acid", first from plants and later from animal adrenal glands. In 1932 Charles Glen King confirmed that it was indeed the antiscorbutic factor.
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Chemistry of ascorbic acid
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In 1933, sugar chemist Walter Norman Haworth, working with samples of "hexuronic acid" that Szent-Györgyi had isolated from paprika and sent him in the previous year, deduced the correct structure and optical-isomeric nature of the compound, and in 1934 reported its first synthesis. In reference to the compound's antiscorbutic properties, Haworth and Szent-Györgyi proposed to rename it "a-scorbic acid" for the compound, and later specifically -ascorbic acid. Because of their work, in 1937 the Nobel Prizes for chemistry and medicine were awarded to Haworth and Szent-Györgyi, respectively.
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Chemistry of ascorbic acid
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Chemical properties Acidity
Ascorbic acid is a vinylogous acid and forms the ascorbate anion when deprotonated on one of the hydroxyls. This property is characteristic of reductones: enediols with a carbonyl group adjacent to the enediol group, namely with the group –C(OH)=C(OH)–C(=O)–. The ascorbate anion is stabilized by electron delocalization that results from resonance between two forms:
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Chemistry of ascorbic acid
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For this reason, ascorbic acid is much more acidic than would be expected if the compound contained only isolated hydroxyl groups. Salts
The ascorbate anion forms salts, such as sodium ascorbate, calcium ascorbate, and potassium ascorbate. Esters
Ascorbic acid can also react with organic acids as an alcohol forming esters such as ascorbyl palmitate and ascorbyl stearate. Nucleophilic attack
Nucleophilic attack of ascorbic acid on a proton results in a 1,3-diketone: Oxidation
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Chemistry of ascorbic acid
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The ascorbate ion is the predominant species at typical biological pH values. It is a mild reducing agent and antioxidant. It is oxidized with loss of one electron to form a radical cation and then with loss of a second electron to form dehydroascorbic acid. It typically reacts with oxidants of the reactive oxygen species, such as the hydroxyl radical. Ascorbic acid is special because it can transfer a single electron, owing to the resonance-stabilized nature of its own radical ion, called semidehydroascorbate. The net reaction is:
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Chemistry of ascorbic acid
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RO• + → RO− + C6H7O → ROH + C6H6O6 On exposure to oxygen, ascorbic acid will undergo further oxidative decomposition to various products including diketogulonic acid, xylonic acid, threonic acid and oxalic acid.
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Reactive oxygen species are damaging to animals and plants at the molecular level due to their possible interaction with nucleic acids, proteins, and lipids. Sometimes these radicals initiate chain reactions. Ascorbate can terminate these chain radical reactions by electron transfer. The oxidized forms of ascorbate are relatively unreactive and do not cause cellular damage. However, being a good electron donor, excess ascorbate in the presence of free metal ions can not only promote but also initiate free radical reactions, thus making it a potentially dangerous pro-oxidative compound in certain metabolic contexts.
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Chemistry of ascorbic acid
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Ascorbic acid and its sodium, potassium, and calcium salts are commonly used as antioxidant food additives. These compounds are water-soluble and, thus, cannot protect fats from oxidation: For this purpose, the fat-soluble esters of ascorbic acid with long-chain fatty acids (ascorbyl palmitate or ascorbyl stearate) can be used as food antioxidants. Other reactions
It creates volatile compounds when mixed with glucose and amino acids in 90 °C. It is a cofactor in tyrosine oxidation. Uses
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Food additive
The main use of -ascorbic acid and its salts is as food additives, mostly to combat oxidation. It is approved for this purpose in the EU with E number E300, USA, Australia, and New Zealand) Dietary supplement
Another major use of -ascorbic acid is as dietary supplement. Niche, non-food uses
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Ascorbic acid is easily oxidized and so is used as a reductant in photographic developer solutions (among others) and as a preservative.
In fluorescence microscopy and related fluorescence-based techniques, ascorbic acid can be used as an antioxidant to increase fluorescent signal and chemically retard dye photobleaching.
It is also commonly used to remove dissolved metal stains, such as iron, from fiberglass swimming pool surfaces.
In plastic manufacturing, ascorbic acid can be used to assemble molecular chains more quickly and with less waste than traditional synthesis methods.
Heroin users are known to use ascorbic acid as a means to convert heroin base to a water-soluble salt so that it can be injected.
As justified by its reaction with iodine, it is used to negate the effects of iodine tablets in water purification. It reacts with the sterilized water, removing the taste, color, and smell of the iodine. This is why it is often sold as a second set of tablets in most sporting goods stores as Potable Aqua-Neutralizing Tablets, along with the potassium iodide tablets.
Intravenous high-dose ascorbate is being used as a chemotherapeutic and biological response modifying agent. Currently it is still under clinical trials.
It is sometimes used as a urinary acidifier to enhance the antiseptic effect of methenamine.
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Chemistry of ascorbic acid
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Synthesis
Natural biosynthesis of vitamin C occurs in many plants, and animals, by a variety of processes. Industrial preparation
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Chemistry of ascorbic acid
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Eighty percent of the world's supply of ascorbic acid is produced in China.
Ascorbic acid is prepared in industry from glucose in a method based on the historical Reichstein process. In the first of a five-step process, glucose is catalytically hydrogenated to sorbitol, which is then oxidized by the microorganism Acetobacter suboxydans to sorbose. Only one of the six hydroxy groups is oxidized by this enzymatic reaction. From this point, two routes are available. Treatment of the product with acetone in the presence of an acid catalyst converts four of the remaining hydroxyl groups to acetals. The unprotected hydroxyl group is oxidized to the carboxylic acid by reaction with the catalytic oxidant TEMPO (regenerated by sodium hypochlorite — bleaching solution). Historically, industrial preparation via the Reichstein process used potassium permanganate as the bleaching solution. Acid-catalyzed hydrolysis of this product performs the dual function of removing the two acetal groups and ring-closing lactonization. This step yields ascorbic acid. Each of the five steps has a yield larger than 90%.
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Chemistry of ascorbic acid
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A more biotechnological process, first developed in China in the 1960s, but further developed in the 1990s, bypasses the use of acetone-protecting groups. A second genetically modified microbe species, such as mutant Erwinia, among others, oxidises sorbose into 2-ketogluconic acid (2-KGA), which can then undergo ring-closing lactonization via dehydration. This method is used in the predominant process used by the ascorbic acid industry in China, which supplies 80% of world's ascorbic acid. American and Chinese researchers are competing to engineer a mutant that can carry out a one-pot fermentation directly from glucose to 2-KGA, bypassing both the need for a second fermentation and the need to reduce glucose to sorbitol.
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Chemistry of ascorbic acid
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There exists a -ascorbic acid, which does not occur in nature but can be synthesized artificially. To be specific, -ascorbate is known to participate in many specific enzyme reactions that require the correct enantiomer (-ascorbate and not -ascorbate). -Ascorbic acid has a specific rotation of [α] = +23°. Determination
The traditional way to analyze the ascorbic acid content is the process of titration with an oxidizing agent, and several procedures have been developed.
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Chemistry of ascorbic acid
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The popular iodometry approach uses iodine in the presence of a starch indicator. Iodine is reduced by ascorbic acid, and, when all the ascorbic acid has reacted, the iodine is then in excess, forming a blue-black complex with the starch indicator. This indicates the end-point of the titration. As an alternative, ascorbic acid can be treated with iodine in excess, followed by back titration with sodium thiosulfate using starch as an indicator.
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Chemistry of ascorbic acid
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This iodometric method has been revised to exploit reaction of ascorbic acid with iodate and iodide in acid solution. Electrolyzing the solution of potassium iodide produces iodine, which reacts with ascorbic acid. The end of process is determined by potentiometric titration in a manner similar to Karl Fischer titration. The amount of ascorbic acid can be calculated by Faraday's law.
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Chemistry of ascorbic acid
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Another alternative uses N-bromosuccinimide (NBS) as the oxidizing agent, in the presence of potassium iodide and starch. The NBS first oxidizes the ascorbic acid; when the latter is exhausted, the NBS liberates the iodine from the potassium iodide, which then forms the blue-black complex with starch. See also
Colour retention agent
Erythorbic acid: a diastereomer of ascorbic acid.
Mineral ascorbates: salts of ascorbic acid
Acids in wine Notes and references Further reading External links
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Chemistry of ascorbic acid
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IPCS Poisons Information Monograph (PIM) 046
Interactive 3D-structure of vitamin C with details on the x-ray structure Organic acids
Antioxidants
Dietary antioxidants
Coenzymes
Corrosion inhibitors
Furanones
Vitamers
Vitamin C
Biomolecules
3-Hydroxypropenals
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Audio signal processing
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Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals. Audio signals are electronic representations of sound waves—longitudinal waves which travel through air, consisting of compressions and rarefactions. The energy contained in audio signals is typically measured in decibels. As audio signals may be represented in either digital or analog format, processing may occur in either domain. Analog processors operate directly on the electrical signal, while digital processors operate mathematically on its digital representation.
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Audio signal processing
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History
The motivation for audio signal processing began at the beginning of the 20th century with inventions like the telephone, phonograph, and radio that allowed for the transmission and storage of audio signals. Audio processing was necessary for early radio broadcasting, as there were many problems with studio-to-transmitter links. The theory of signal processing and its application to audio was largely developed at Bell Labs in the mid 20th century. Claude Shannon and Harry Nyquist's early work on communication theory, sampling theory and pulse-code modulation (PCM) laid the foundations for the field. In 1957, Max Mathews became the first person to synthesize audio from a computer, giving birth to computer music.
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Audio signal processing
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Major developments in digital audio coding and audio data compression include differential pulse-code modulation (DPCM) by C. Chapin Cutler at Bell Labs in 1950, linear predictive coding (LPC) by Fumitada Itakura (Nagoya University) and Shuzo Saito (Nippon Telegraph and Telephone) in 1966, adaptive DPCM (ADPCM) by P. Cummiskey, Nikil S. Jayant and James L. Flanagan at Bell Labs in 1973, discrete cosine transform (DCT) coding by Nasir Ahmed, T. Natarajan and K. R. Rao in 1974, and modified discrete cosine transform (MDCT) coding by J. P. Princen, A. W. Johnson and A. B. Bradley at the University of Surrey in 1987. LPC is the basis for perceptual coding and is widely used in speech coding, while MDCT coding is widely used in modern audio coding formats such as MP3 and Advanced Audio Coding (AAC).
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Audio signal processing
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Analog signals An analog audio signal is a continuous signal represented by an electrical voltage or current that is analogous to the sound waves in the air. Analog signal processing then involves physically altering the continuous signal by changing the voltage or current or charge via electrical circuits. Historically, before the advent of widespread digital technology, analog was the only method by which to manipulate a signal. Since that time, as computers and software have become more capable and affordable, digital signal processing has become the method of choice. However, in music applications, analog technology is often still desirable as it often produces nonlinear responses that are difficult to replicate with digital filters. Digital signals
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Audio signal processing
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A digital representation expresses the audio waveform as a sequence of symbols, usually binary numbers. This permits signal processing using digital circuits such as digital signal processors, microprocessors and general-purpose computers. Most modern audio systems use a digital approach as the techniques of digital signal processing are much more powerful and efficient than analog domain signal processing. Applications
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Audio signal processing
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Processing methods and application areas include storage, data compression, music information retrieval, speech processing, localization, acoustic detection, transmission, noise cancellation, acoustic fingerprinting, sound recognition, synthesis, and enhancement (e.g. equalization, filtering, level compression, echo and reverb removal or addition, etc.). Audio broadcasting
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Audio signal processing
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Audio signal processing is used when broadcasting audio signals in order to enhance their fidelity or optimize for bandwidth or latency. In this domain, the most important audio processing takes place just before the transmitter. The audio processor here must prevent or minimize overmodulation, compensate for non-linear transmitters (a potential issue with medium wave and shortwave broadcasting), and adjust overall loudness to desired level. Active noise control Active noise control is a technique designed to reduce unwanted sound. By creating a signal that is identical to the unwanted noise but with the opposite polarity, the two signals cancel out due to destructive interference. Audio synthesis
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Audio signal processing
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Audio synthesis is the electronic generation of audio signals. A musical instrument that accomplishes this is called a synthesizer. Synthesizers can either imitate sounds or generate new ones. Audio synthesis is also used to generate human speech using speech synthesis. Audio effects
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Audio signal processing
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Audio effects alter the sound of a musical instrument or other audio source. Common effects include distortion, often used with electric guitar in electric blues and rock music; dynamic effects such as volume pedals and compressors, which affect loudness; filters such as wah-wah pedals and graphic equalizers, which modify frequency ranges; modulation effects, such as chorus, flangers and phasers; pitch effects such as pitch shifters; and time effects, such as reverb and delay, which create echoing sounds and emulate the sound of different spaces.
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Audio signal processing
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Musicians, audio engineers and record producers use effects units during live performances or in the studio, typically with electric guitar, bass guitar, electronic keyboard or electric piano. While effects are most frequently used with electric or electronic instruments, they can be used with any audio source, such as acoustic instruments, drums, and vocals. See also
Sound card
Sound effect References Further reading Audio electronics
Signal processing
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Analytical chemistry
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Analytical chemistry studies and uses instruments and methods used to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separation isolates analytes. Qualitative analysis identifies analytes, while quantitative analysis determines the numerical amount or concentration. Analytical chemistry is the science of obtaining, processing, and communicating information about the composition and structure of matter. In other words, it is the art and science of determining what matter is and how much of it exists. ... It is one of the most popular fields of work for ACS chemists.
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Analytical chemistry
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Analytical chemistry consists of classical, wet chemical methods and modern, instrumental methods. Classical qualitative methods use separations such as precipitation, extraction, and distillation. Identification may be based on differences in color, odor, melting point, boiling point, solubility, radioactivity or reactivity. Classical quantitative analysis uses mass or volume changes to quantify amount. Instrumental methods may be used to separate samples using chromatography, electrophoresis or field flow fractionation. Then qualitative and quantitative analysis can be performed, often with the same instrument and may use light interaction, heat interaction, electric fields or magnetic fields. Often the same instrument can separate, identify and quantify an analyte.
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Analytical chemistry
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Analytical chemistry is also focused on improvements in experimental design, chemometrics, and the creation of new measurement tools. Analytical chemistry has broad applications to medicine, science, and engineering. History Analytical chemistry has been important since the early days of chemistry, providing methods for determining which elements and chemicals are present in the object in question. During this period, significant contributions to analytical chemistry included the development of systematic elemental analysis by Justus von Liebig and systematized organic analysis based on the specific reactions of functional groups.
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Analytical chemistry
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The first instrumental analysis was flame emissive spectrometry developed by Robert Bunsen and Gustav Kirchhoff who discovered rubidium (Rb) and caesium (Cs) in 1860. Most of the major developments in analytical chemistry take place after 1900. During this period instrumental analysis becomes progressively dominant in the field. In particular many of the basic spectroscopic and spectrometric techniques were discovered in the early 20th century and refined in the late 20th century.
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Analytical chemistry
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The separation sciences follow a similar time line of development and also become increasingly transformed into high performance instruments. In the 1970s many of these techniques began to be used together as hybrid techniques to achieve a complete characterization of samples.
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Analytical chemistry
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Starting in approximately the 1970s into the present day analytical chemistry has progressively become more inclusive of biological questions (bioanalytical chemistry), whereas it had previously been largely focused on inorganic or small organic molecules. Lasers have been increasingly used in chemistry as probes and even to initiate and influence a wide variety of reactions. The late 20th century also saw an expansion of the application of analytical chemistry from somewhat academic chemical questions to forensic, environmental, industrial and medical questions, such as in histology.
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Analytical chemistry
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Modern analytical chemistry is dominated by instrumental analysis. Many analytical chemists focus on a single type of instrument. Academics tend to either focus on new applications and discoveries or on new methods of analysis. The discovery of a chemical present in blood that increases the risk of cancer would be a discovery that an analytical chemist might be involved in. An effort to develop a new method might involve the use of a tunable laser to increase the specificity and sensitivity of a spectrometric method. Many methods, once developed, are kept purposely static so that data can be compared over long periods of time. This is particularly true in industrial quality assurance (QA), forensic and environmental applications. Analytical chemistry plays an increasingly important role in the pharmaceutical industry where, aside from QA, it is used in discovery of new drug candidates and in clinical applications where understanding the interactions between the drug and the patient are critical.
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Analytical chemistry
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Classical methods Although modern analytical chemistry is dominated by sophisticated instrumentation, the roots of analytical chemistry and some of the principles used in modern instruments are from traditional techniques, many of which are still used today. These techniques also tend to form the backbone of most undergraduate analytical chemistry educational labs. Qualitative analysis
Qualitative analysis determines the presence or absence of a particular compound, but not the mass or concentration. By definition, qualitative analyses do not measure quantity. Chemical tests There are numerous qualitative chemical tests, for example, the acid test for gold and the Kastle-Meyer test for the presence of blood. Flame test
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Analytical chemistry
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Inorganic qualitative analysis generally refers to a systematic scheme to confirm the presence of certain aqueous ions or elements by performing a series of reactions that eliminate ranges of possibilities and then confirms suspected ions with a confirming test. Sometimes small carbon-containing ions are included in such schemes. With modern instrumentation, these tests are rarely used but can be useful for educational purposes and in fieldwork or other situations where access to state-of-the-art instruments is not available or expedient. Quantitative analysis
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Analytical chemistry
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Quantitative analysis is the measurement of the quantities of particular chemical constituents present in a substance. Quantities can be measured by mass (gravimetric analysis) or volume (volumetric analysis). Gravimetric analysis Gravimetric analysis involves determining the amount of material present by weighing the sample before and/or after some transformation. A common example used in undergraduate education is the determination of the amount of water in a hydrate by heating the sample to remove the water such that the difference in weight is due to the loss of water. Volumetric analysis
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Analytical chemistry
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Titration involves the addition of a reactant to a solution being analyzed until some equivalence point is reached. Often the amount of material in the solution being analyzed may be determined. Most familiar to those who have taken chemistry during secondary education is the acid-base titration involving a color-changing indicator. There are many other types of titrations, for example, potentiometric titrations.
These titrations may use different types of indicators to reach some equivalence point. Instrumental methods Spectroscopy
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Analytical chemistry
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Spectroscopy measures the interaction of the molecules with electromagnetic radiation. Spectroscopy consists of many different applications such as atomic absorption spectroscopy, atomic emission spectroscopy, ultraviolet-visible spectroscopy, x-ray spectroscopy, fluorescence spectroscopy, infrared spectroscopy, Raman spectroscopy, dual polarization interferometry, nuclear magnetic resonance spectroscopy, photoemission spectroscopy, Mössbauer spectroscopy and so on. Mass spectrometry
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Analytical chemistry
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Mass spectrometry measures mass-to-charge ratio of molecules using electric and magnetic fields. There are several ionization methods: electron ionization, chemical ionization, electrospray ionization, fast atom bombardment, matrix assisted laser desorption/ionization, and others. Also, mass spectrometry is categorized by approaches of mass analyzers: magnetic-sector, quadrupole mass analyzer, quadrupole ion trap, time-of-flight, Fourier transform ion cyclotron resonance, and so on. Electrochemical analysis
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Analytical chemistry
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Electroanalytical methods measure the potential (volts) and/or current (amps) in an electrochemical cell containing the analyte. These methods can be categorized according to which aspects of the cell are controlled and which are measured. The four main categories are potentiometry (the difference in electrode potentials is measured), coulometry (the transferred charge is measured over time), amperometry (the cell's current is measured over time), and voltammetry (the cell's current is measured while actively altering the cell's potential). Thermal analysis
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Analytical chemistry
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Calorimetry and thermogravimetric analysis measure the interaction of a material and heat. Separation Separation processes are used to decrease the complexity of material mixtures. Chromatography, electrophoresis and field flow fractionation are representative of this field.
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Analytical chemistry
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Hybrid techniques
Combinations of the above techniques produce a "hybrid" or "hyphenated" technique. Several examples are in popular use today and new hybrid techniques are under development. For example, gas chromatography-mass spectrometry, gas chromatography-infrared spectroscopy, liquid chromatography-mass spectrometry, liquid chromatography-NMR spectroscopy. liquid chromagraphy-infrared spectroscopy and capillary electrophoresis-mass spectrometry.
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Analytical chemistry
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Hyphenated separation techniques refer to a combination of two (or more) techniques to detect and separate chemicals from solutions. Most often the other technique is some form of chromatography. Hyphenated techniques are widely used in chemistry and biochemistry. A slash is sometimes used instead of hyphen, especially if the name of one of the methods contains a hyphen itself. Microscopy
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Analytical chemistry
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The visualization of single molecules, single cells, biological tissues, and nanomaterials is an important and attractive approach in analytical science. Also, hybridization with other traditional analytical tools is revolutionizing analytical science. Microscopy can be categorized into three different fields: optical microscopy, electron microscopy, and scanning probe microscopy. Recently, this field is rapidly progressing because of the rapid development of the computer and camera industries. Lab-on-a-chip
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Analytical chemistry
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Devices that integrate (multiple) laboratory functions on a single chip of only millimeters to a few square centimeters in size and that are capable of handling extremely small fluid volumes down to less than picoliters. Errors Error can be defined as numerical difference between observed value and true value. The experimental error can be divided into two types, systematic error and random error. Systematic error results from a flaw in equipment or the design of an experiment while random error results from uncontrolled or uncontrollable variables in the experiment. In error the true value and observed value in chemical analysis can be related with each other by the equation
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Analytical chemistry
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where
is the absolute error.
is the true value.
is the observed value.
Error of a measurement is an inverse measure of accurate measurement i.e. smaller the error greater the accuracy of the measurement. Errors can be expressed relatively. Given the relative error(): The percent error can also be calculated: If we want to use these values in a function, we may also want to calculate the error of the function. Let be a function with variables. Therefore, the propagation of uncertainty must be calculated in order to know the error in : Standards Standard curve
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Analytical chemistry
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A general method for analysis of concentration involves the creation of a calibration curve. This allows for determination of the amount of a chemical in a material by comparing the results of an unknown sample to those of a series of known standards. If the concentration of element or compound in a sample is too high for the detection range of the technique, it can simply be diluted in a pure solvent. If the amount in the sample is below an instrument's range of measurement, the method of addition can be used. In this method, a known quantity of the element or compound under study is added, and the difference between the concentration added, and the concentration observed is the amount actually in the sample.
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Analytical chemistry
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Internal standards
Sometimes an internal standard is added at a known concentration directly to an analytical sample to aid in quantitation. The amount of analyte present is then determined relative to the internal standard as a calibrant. An ideal internal standard is an isotopically-enriched analyte which gives rise to the method of isotope dilution.
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Analytical chemistry
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Standard addition
The method of standard addition is used in instrumental analysis to determine the concentration of a substance (analyte) in an unknown sample by comparison to a set of samples of known concentration, similar to using a calibration curve. Standard addition can be applied to most analytical techniques and is used instead of a calibration curve to solve the matrix effect problem. Signals and noise
One of the most important components of analytical chemistry is maximizing the desired signal while minimizing the associated noise. The analytical figure of merit is known as the signal-to-noise ratio (S/N or SNR).
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Analytical chemistry
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Noise can arise from environmental factors as well as from fundamental physical processes. Thermal noise Thermal noise results from the motion of charge carriers (usually electrons) in an electrical circuit generated by their thermal motion. Thermal noise is white noise meaning that the power spectral density is constant throughout the frequency spectrum. The root mean square value of the thermal noise in a resistor is given by where kB is Boltzmann's constant, T is the temperature, R is the resistance, and is the bandwidth of the frequency . Shot noise
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Analytical chemistry
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Shot noise is a type of electronic noise that occurs when the finite number of particles (such as electrons in an electronic circuit or photons in an optical device) is small enough to give rise to statistical fluctuations in a signal. Shot noise is a Poisson process and the charge carriers that make up the current follow a Poisson distribution. The root mean square current fluctuation is given by where e is the elementary charge and I is the average current. Shot noise is white noise. Flicker noise
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Analytical chemistry
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Flicker noise is electronic noise with a 1/ƒ frequency spectrum; as f increases, the noise decreases. Flicker noise arises from a variety of sources, such as impurities in a conductive channel, generation, and recombination noise in a transistor due to base current, and so on. This noise can be avoided by modulation of the signal at a higher frequency, for example through the use of a lock-in amplifier. Environmental noise
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Analytical chemistry
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Environmental noise arises from the surroundings of the analytical instrument. Sources of electromagnetic noise are power lines, radio and television stations, wireless devices, compact fluorescent lamps and electric motors. Many of these noise sources are narrow bandwidth and therefore can be avoided. Temperature and vibration isolation may be required for some instruments. Noise reduction
Noise reduction can be accomplished either in computer hardware or software. Examples of hardware noise reduction are the use of shielded cable, analog filtering, and signal modulation. Examples of software noise reduction are digital filtering, ensemble average, boxcar average, and correlation methods. Applications
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Analytical chemistry
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Analytical chemistry has applications including in forensic science, bioanalysis, clinical analysis, environmental analysis, and materials analysis. Analytical chemistry research is largely driven by performance (sensitivity, detection limit, selectivity, robustness, dynamic range, linear range, accuracy, precision, and speed), and cost (purchase, operation, training, time, and space). Among the main branches of contemporary analytical atomic spectrometry, the most widespread and universal are optical and mass spectrometry. In the direct elemental analysis of solid samples, the new leaders are laser-induced breakdown and laser ablation mass spectrometry, and the related techniques with transfer of the laser ablation products into inductively coupled plasma. Advances in design of diode lasers and optical parametric oscillators promote developments in fluorescence and ionization spectrometry and also in absorption techniques where uses of optical cavities for increased effective absorption pathlength are expected to expand. The use of plasma- and laser-based methods is increasing. An interest towards absolute (standardless) analysis has revived, particularly in emission spectrometry.
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Analytical chemistry
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Great effort is being put in shrinking the analysis techniques to chip size. Although there are few examples of such systems competitive with traditional analysis techniques, potential advantages include size/portability, speed, and cost. (micro total analysis system (µTAS) or lab-on-a-chip). Microscale chemistry reduces the amounts of chemicals used.
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Analytical chemistry
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Many developments improve the analysis of biological systems. Examples of rapidly expanding fields in this area are genomics, DNA sequencing and related research in genetic fingerprinting and DNA microarray; proteomics, the analysis of protein concentrations and modifications, especially in response to various stressors, at various developmental stages, or in various parts of the body, metabolomics, which deals with metabolites; transcriptomics, including mRNA and associated fields; lipidomics - lipids and its associated fields; peptidomics - peptides and its associated fields; and metalomics, dealing with metal concentrations and especially with their binding to proteins and other molecules.
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Analytical chemistry
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Analytical chemistry has played critical roles in the understanding of basic science to a variety of practical applications, such as biomedical applications, environmental monitoring, quality control of industrial manufacturing, forensic science, and so on.
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The recent developments of computer automation and information technologies have extended analytical chemistry into a number of new biological fields. For example, automated DNA sequencing machines were the basis to complete human genome projects leading to the birth of genomics. Protein identification and peptide sequencing by mass spectrometry opened a new field of proteomics. In addition to automating specific processes, there is effort to automate larger sections of lab testing, such as in companies like Emerald Cloud Lab and Transcriptic.
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Analytical chemistry
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Analytical chemistry has been an indispensable area in the development of nanotechnology. Surface characterization instruments, electron microscopes and scanning probe microscopes enable scientists to visualize atomic structures with chemical characterizations. See also Important publications in analytical chemistry
List of chemical analysis methods
List of materials analysis methods
Measurement uncertainty
Metrology
Sensory analysis - in the field of Food science
Virtual instrumentation
Microanalysis
Quality of analytical results
Working range References Further reading
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Analytical chemistry
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Gurdeep, Chatwal Anand (2008). Instrumental Methods of Chemical Analysis Himalaya Publishing House (India)
Ralph L. Shriner, Reynold C. Fuson, David Y. Curtin, Terence C. Morill: The systematic identification of organic compounds - a laboratory manual, Verlag Wiley, New York 1980, 6. edition, .
Bettencourt da Silva, R; Bulska, E; Godlewska-Zylkiewicz, B; Hedrich, M; Majcen, N; Magnusson, B; Marincic, S; Papadakis, I; Patriarca, M; Vassileva, E; Taylor, P; Analytical measurement: measurement uncertainty and statistics, 2012, .
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External links Infografik and animation showing the progress of analytical chemistry
aas Atomic Absorption Spectrophotometer Materials science
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Analog computer
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An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (analog signals) to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude (digital signals). Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Systems for process control and protective relays used analog computation to perform control and protective functions.
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Analog computer
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Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they remained in use in some specific applications, such as aircraft flight simulators, the flight computer in aircraft, and for teaching control systems in universities. Perhaps the most relatable example of analog computers are mechanical watches where the continuous and periodic rotation of interlinked gears drives the seconds, minutes and hours needles in the clock. More complex applications, such as aircraft flight simulators and synthetic-aperture radar, remained the domain of analog computing (and hybrid computing) well into the 1980s, since digital computers were insufficient for the task.
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Analog computer
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Timeline of analog computers Precursors This is a list of examples of early computation devices considered precursors of the modern computers. Some of them may even have been dubbed 'computers' by the press, though they may fail to fit modern definitions.
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