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These economies are based on culture rather than a fool-proof system. Labor vouchers, which are inalienable certificates of hours worked. | Wikipedia - Non-monetary economy - Other moneyless systems |
Non-monetary (state) communist currents, ranging from libertarian proposals to the harsh reality of Democratic Kampuchea. Many communists and socialists envisaged a moneyless society. Gift economies: other than the word suggests, the gift in such economies usually comes with an obligation to do something in return. | Wikipedia - Non-monetary economy - Other moneyless systems |
Altruistic society: as proposed by Mark Boyle, a moneyless economy is a model "on the basis of materials and services being shared unconditionally" that is, without explicit or formal exchange. The subsistence economy, which caters only for essentials, often without money. Calculation in kind, which (in a restricted fo... | Wikipedia - Non-monetary economy - Other moneyless systems |
Natural economy, where resources are allocated through direct bartering, entitlement by law, or sharing out according to traditional custom. Non-market ecosocialism as advocated by Anitra Nelson: as for the nonmonetary aspect, each household "guesstimates" its basic needs, which are met in return for "collective produc... | Wikipedia - Non-monetary economy - Other moneyless systems |
In the following, the '1' flag bits indicate the beginning of each segment. 1 2 3 4 5 6 input 1 0 0 1 0 1 flag bits 1 3 6 4 9 6 segmented scan + {\displaystyle {\begin{array}{|rrrrrr|l|}1&2&3&4&5&6&{\text{input}}\\\hline 1&0&0&1&0&1&{\text{flag bits}}\\\hline 1&3&6&4&9&6&{\text{segmented scan +}}\\\end{array}}} Group11... | Wikipedia - Segmented scan - Example |
In the following, the extension L/K is assumed to be a Galois extension. Then the prime avoidance lemma can be used to show the Galois group G = Gal ( L / K ) {\displaystyle G=\operatorname {Gal} (L/K)} acts transitively on the Pj. That is, the prime ideal factors of p in L form a single orbit under the automorphisms... | Wikipedia - Inert prime - The Galois situation |
{\displaystyle =efg.} The relation above shows that /ef equals the number g of prime factors of p in OL. By the orbit-stabilizer formula this number is also equal to |G|/|DPj| for every j, where DPj, the decomposition group of Pj, is the subgroup of elements of G sending a given Pj to itself. | Wikipedia - Inert prime - The Galois situation |
Since the degree of L/K and the order of G are equal by basic Galois theory, it follows that the order of the decomposition group DPj is ef for every j. This decomposition group contains a subgroup IPj, called inertia group of Pj, consisting of automorphisms of L/K that induce the identity automorphism on Fj. In other ... | Wikipedia - Inert prime - The Galois situation |
In the unramified case the order of DPj is f and IPj is trivial, so the Frobenius element is in this case an element of DPj, and thus also an element of G. For varying j, the groups DPj are conjugate subgroups inside G: Recalling that G acts transitively on the Pj, one checks that if σ {\displaystyle \sigma } maps Pj t... | Wikipedia - Inert prime - The Galois situation |
There, given a Galois ramified cover, all but finitely many points have the same number of preimages. The splitting of primes in extensions that are not Galois may be studied by using a splitting field initially, i.e. a Galois extension that is somewhat larger. For example, cubic fields usually are 'regulated' by a deg... | Wikipedia - Inert prime - The Galois situation |
In the following, the ls command is run without any shell functions or aliases that may exist with the same name: | Wikipedia - Command (Unix) - Examples |
In the following, the notation of Mansouri–Sexl is used. They chose the coefficients a, b, d, e of the following transformation between reference frames: t = a T + e x {\displaystyle t=aT+ex\,} x = b ( X − v T ) {\displaystyle x=b(X-vT)\,} y = d Y {\displaystyle y=dY\,} z = d Z {\displaystyle z=dZ\,} where T, X, Y, Z a... | Wikipedia - Test theories of special relativity - Theory |
The purpose of the test theory is to allow a(v) and b(v) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from a ( v ) = b ( v ) = d ( v ) = 1 , and e... | Wikipedia - Test theories of special relativity - Theory |
) The value of e(v) depends only on the choice of clock synchronization and cannot be determined by experiment. Mansouri–Sexl discussed the following synchronization schemes: Internal clock synchronization like the Poincaré–Einstein synchronization by using light signals, or synchronization by slow clock transport. Tho... | Wikipedia - Test theories of special relativity - Theory |
External clock synchronization by choosing a "preferred" reference frame (like the CMB) and using the clocks of this frame to synchronize the clocks in all other frames ("absolute" synchronization).By giving the effects of time dilation and length contraction the exact relativistic value, this test theory is experiment... | Wikipedia - Test theories of special relativity - Theory |
In the following, the principle channel configuration and operating method of a standard DCMD module as well as a DCMD module with separate permeate gap shall be explained. The design in the adjacent image depicts a flat channel configuration, but can also be understood as a schema for flat-, hollow fibre - or spiral w... | Wikipedia - Membrane distillation - Permeate-gap MD |
For cooling, the condenser channel is flooded with fresh water and the evaporator e.g. with salty feed water. The coolant enters the condenser channel at a temperature of 20 °C (68 °F). After passing through the membrane, the vapour condenses in the cooling water, releasing its latent heat and leading to a temperature ... | Wikipedia - Membrane distillation - Permeate-gap MD |
Sensible heat conduction also heats the cooling water through the surface of the membrane. Due to the mass transport through the membrane the mass flow in the evaporator decreases whilst the condenser channel increases by the same amount. The mass flow of pre-heated coolant leaves the condenser channel at a temperature... | Wikipedia - Membrane distillation - Permeate-gap MD |
This feed water is then delivered to a further heat source and finally enters the evaporator channel of the MD module at a temperature of 80 °C (176 °F). The evaporation process extracts latent heat from the feed flow, which cools down the feed increasingly in flow direction. Additional heat reduction occurs due to sen... | Wikipedia - Membrane distillation - Permeate-gap MD |
The cooled feed water leaves the evaporator channel at approximately 28 °C. Total temperature differences between condenser inlet and evaporator outlet and condenser inlet and evaporator outlet are about equal. In a PGMD module, the permeate channel is separated from the condenser channel by a condensation surface. | Wikipedia - Membrane distillation - Permeate-gap MD |
This enables the direct use of a salt water feed as coolant, since it does not come into contact with the permeate. Considering this, the cooling-or feed water entering the condenser channel at a temperature T1 can now also be used to cool the permeate. Condensation of vapour takes place inside the liquid permeate. | Wikipedia - Membrane distillation - Permeate-gap MD |
Pre-heated feed water that was used to cool the condenser can be conducted directly to a heat source for final heating, after leaving the condenser at a temperature T2. After it has reached temperature T3 it is guided into the evaporator. Permeate is extracted at temperature T5 and the cooled brine is discharged at tem... | Wikipedia - Membrane distillation - Permeate-gap MD |
An advantage of PGMD over DCMD is the direct use of feed water as cooling liquid inside the module and therefore the necessity of only one heat exchanger to heat the feed before entering the evaporator. Hereby heat conduction losses are reduced and expensive components can be cut. A further advantage is the separation ... | Wikipedia - Membrane distillation - Permeate-gap MD |
Therefore, the permeate does not have to be extracted later in the process and the coolant's mass flow in the condenser channel remains constant. The low flow velocity of the permeate in the permeate gap is a disadvantage of this configuration, as it leads to a poor heat conduction from the membrane surface to the cond... | Wikipedia - Membrane distillation - Permeate-gap MD |
However, it is beneficial, that the heat conduction losses through the membrane are also lowered by this effect. This poor gap heat conduction challenge is largely removed with a variant of PGMD called CGMD, or conductive gap membrane distillation, which adds thermally conductive spacers to the gaps. Compared to AGMD, ... | Wikipedia - Membrane distillation - Permeate-gap MD |
In the following, the terms host, client and peer are used almost interchangeably. local endpoint, internal endpoint the local IP:port as seen locally by the host and the internal part of the NAT. public endpoint, external endpoint the external IP:port mapped by the NAT, as seen by the network and the external part of ... | Wikipedia - TCP hole punching - Terminology |
In the following, there are several tables of statistical data illustrating the distributions of Chinese characters among all stroke numbers of some representative character sets. | Wikipedia - Stroke number - Distribution of characters |
In the following, three important theta function values are to be derived as examples: This is how the Euler beta function is defined in its reduced form: β ( x ) = Γ ( x ) 2 Γ ( 2 x ) {\displaystyle \beta (x)={\frac {\Gamma (x)^{2}}{\Gamma (2x)}}} In general, for all natural numbers n ∈ N {\displaystyle n\in \mathbb {... | Wikipedia - Jacobi theta functions - Identity of the Euler beta function |
In the following, we assume that the N×M matrix is stored in row-major order with zero-based indices. This means that the (n,m) element, for n = 0,...,N−1 and m = 0,...,M−1, is stored at an address a = Mn + m (plus some offset in memory, which we ignore). In the transposed M×N matrix, the corresponding (m,n) element is... | Wikipedia - In-place matrix transposition - Properties of the permutation |
{\displaystyle (n,m)\in \times \,.} This defines a permutation on the numbers a = 0 , … , M N − 1 {\displaystyle a=0,\ldots ,MN-1} . | Wikipedia - In-place matrix transposition - Properties of the permutation |
It turns out that one can define simple formulas for P and its inverse (Cate & Twigg, 1977). First: P ( a ) = { M N − 1 if a = M N − 1 , N a mod ( M N − 1 ) otherwise , {\displaystyle P(a)={\begin{cases}MN-1&{\text{if }}a=MN-1,\\Na{\bmod {(}}MN-1)&{\text{otherwise}},\end{cases}}} where "mod" is the modulo operation. Se... | Wikipedia - In-place matrix transposition - Properties of the permutation |
{\displaystyle P^{-1}(a')={\begin{cases}MN-1&{\text{if }}a'=MN-1,\\Ma'{\bmod {(}}MN-1)&{\text{otherwise}}.\end{cases}}} (This is just a consequence of the fact that the inverse of an N×M transpose is an M×N transpose, although it is also easy to show explicitly that P−1 composed with P gives the identity.) As proved by... | Wikipedia - In-place matrix transposition - Properties of the permutation |
If N − 1 and M − 1 are coprime, on the other hand, the only two fixed points are the upper-left and lower-right corners of the matrix. The number of cycles of any length k>1 is given by (Cate & Twigg, 1977): 1 k ∑ d | k μ ( k / d ) gcd ( N d − 1 , M N − 1 ) , {\displaystyle {\frac {1}{k}}\sum _{d|k}\mu (k/d)\gcd(N^{d}-... | Wikipedia - In-place matrix transposition - Properties of the permutation |
This theorem is useful in searching for cycles of the permutation, since an efficient search can look only at multiples of divisors of MN−1 (Brenner, 1973). Laflin & Brebner (1970) pointed out that the cycles often come in pairs, which is exploited by several algorithms that permute pairs of cycles at a time. In partic... | Wikipedia - In-place matrix transposition - Properties of the permutation |
In the following, we consider a (monotone) Galois connection f = ( f ∗, f∗), where f ∗: A → B is the lower adjoint as introduced above. Some helpful and instructive basic properties can be obtained immediately. By the defining property of Galois connections, f ∗(x) ≤ f ∗(x) is equivalent to x ≤ f∗( f ∗(x)), for all x i... | Wikipedia - Galois correspondence - Properties |
Applying the basic property of Galois connections, one can now conclude that f ∗(x) ≤ f ∗(y). But this just shows that f ∗ preserves the order of any two elements, i.e. it is monotone. Again, a similar reasoning yields monotonicity of f∗. | Wikipedia - Galois correspondence - Properties |
Thus monotonicity does not have to be included in the definition explicitly. However, mentioning monotonicity helps to avoid confusion about the two alternative notions of Galois connections. Another basic property of Galois connections is the fact that f∗( f ∗( f∗(x))) = f∗(x), for all x in B. Clearly we find that f∗(... | Wikipedia - Galois correspondence - Properties |
On the other hand, since f ∗∘ f∗ is deflationary, while f∗ is monotonic, one finds that f∗( f ∗( f∗(x))) ≤ f∗(x).This shows the desired equality. Furthermore, we can use this property to conclude that f ∗( f∗( f ∗( f∗(x)))) = f ∗( f∗(x))and f∗( f ∗( f∗( f ∗(x)))) = f∗( f ∗(x))i.e., f ∗∘ f∗ and f∗∘ f ∗ are idempotent. | Wikipedia - Galois correspondence - Properties |
It can be shown (see Blyth or Erné for proofs) that a function f is a lower (resp. upper) adjoint if and only if f is a residuated mapping (resp. residual mapping). Therefore, the notion of residuated mapping and monotone Galois connection are essentially the same. | Wikipedia - Galois correspondence - Properties |
In the following, we have n kinds of items, a 1 {\displaystyle a_{1}} through a n {\displaystyle a_{n}} and m kinds of bins b 1 {\displaystyle b_{1}} through b m {\displaystyle b_{m}} . Each bin b i {\displaystyle b_{i}} is associated with a budget t i {\displaystyle t_{i}} . For a bin b i {\displaystyle b_{i}} , each ... | Wikipedia - Generalized Assignment Problem - Explanation of definition |
A feasible solution is a solution in which for each bin b i {\displaystyle b_{i}} the total weight of assigned items is at most t i {\displaystyle t_{i}} . The solution's profit is the sum of profits for each item-bin assignment. | Wikipedia - Generalized Assignment Problem - Explanation of definition |
The goal is to find a maximum profit feasible solution. Mathematically the generalized assignment problem can be formulated as an integer program: maximize ∑ i = 1 m ∑ j = 1 n p i j x i j . subject to ∑ j = 1 n w i j x i j ≤ t i i = 1 , … , m ; ∑ i = 1 m x i j ≤ 1 j = 1 , … , n ; x i j ∈ { 0 , 1 } i = 1 , … , m , j = 1... | Wikipedia - Generalized Assignment Problem - Explanation of definition |
In the following, we have to remind ourselves that every one of Turing's “computing machines” is a binary-number generator/creator that begins work on “blank tape”. Properly constructed, it always cranks away ad infinitum, but its instructions are always finite. In Turing's proofs, Turing's tape had a “left end” but ex... | Wikipedia - Turing's proof - An example to illustrate the third proof |
Our example is based on a modified Post–Turing machine model of a Turing Machine. This model prints only the symbols 0 and 1. The blank tape is considered to be all b's. | Wikipedia - Turing's proof - An example to illustrate the third proof |
Our modified model requires us to add two more instructions to the 7 Post–Turing instructions. The abbreviations that we will use are: In the cases of R, L, E, P0, and P1 after doing its task the machine continues on to the next instruction in numerical sequence; ditto for the jumps if their tests fail. But, for brevit... | Wikipedia - Turing's proof - An example to illustrate the third proof |
And these will always start as there blanks with the scanned square on the left: i.e. bbb. With two symbols 1, 0 and blank we can have 27 distinct configurations: bbb, bb0, bb1, b0b, b00, b01, b1b, b10, b11, 0bb, 0b0, 0b1, 00b, 000, 001, 01b, 010, 011, 1bb, 1b0, 1b1, 10b, 100, 101, 11b, 110, 111 We must be careful here... | Wikipedia - Turing's proof - An example to illustrate the third proof |
In fact, Turing's machine does this—it prints on alternate squares, leaving blanks between figures so it can print locator symbols. Turing always left alternate squares blank so his machine could place a symbol to the left of a figure (or a letter if the machine is the universal machine and the scanned square is actual... | Wikipedia - Turing's proof - An example to illustrate the third proof |
The complete configuration prints the symbols on the tape followed by the next instruction: Let us add “jump” into the formula. When we do this we discover why the complete configuration must include the tape symbols. (Actually, we see this better, below.) | Wikipedia - Turing's proof - An example to illustrate the third proof |
This little program prints three “1”s to the right, reverses direction and moves left printing 0’s until it hits a blank. We will print all the symbols that our machine uses: Here at the end we find that a blank on the left has “come into play” so we leave it as part of the total configuration. Given that we have done ... | Wikipedia - Turing's proof - An example to illustrate the third proof |
The resulting configuration—the number 110—is the PROOF. Turing's first task had to write a generalized expression using logic symbols to express exactly what his Un(M) would do. Turing's second task is to "Gödelize" this hugely long string-of-string-of-symbols using Gödel's technique of assigning primes to the symbols... | Wikipedia - Turing's proof - An example to illustrate the third proof |
In the following, we state two equivalent forms of the theorem, and show their equivalence. Later, we prove the theorem. This is done in the following steps: Reducing the theorem to sentences (formulas with no free variables) in prenex form, i.e. with all quantifiers (∀ and ∃) at the beginning. | Wikipedia - Original proof of Gödel's completeness theorem - Statement of the theorem and its proof |
Furthermore, we reduce it to formulas whose first quantifier is ∀. This is possible because for every sentence, there is an equivalent one in prenex form whose first quantifier is ∀. Reducing the theorem to sentences of the form ∀x1 ∀x2 ... ∀xk ∃y1 ∃y2 ... ∃ym φ(x1 ... xk, y1 ... ym). | Wikipedia - Original proof of Gödel's completeness theorem - Statement of the theorem and its proof |
While we cannot do this by simply rearranging the quantifiers, we show that it is yet enough to prove the theorem for sentences of that form. Finally we prove the theorem for sentences of that form. This is done by first noting that a sentence such as B = ∀x1∀x2...∀xk ∃y1∃y2...∃ym φ(x1...xk, y1...ym) is either refutabl... | Wikipedia - Original proof of Gödel's completeness theorem - Statement of the theorem and its proof |
The reason for that is the completeness of propositional logic, with the existential quantifiers playing no role. We extend this result to more and more complex and lengthy sentences, Dn (n = 1,2...), built out from B, so that either any of them is refutable and therefore so is φ, or all of them are not refutable and t... | Wikipedia - Original proof of Gödel's completeness theorem - Statement of the theorem and its proof |
In the following, we will describe properties of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases. These properties hold for wide-sense stationary processes. A fundamental property of the autocorrelation is symmetry, R f f (... | Wikipedia - Serial correlation - Properties |
The continuous autocorrelation function reaches its peak at the origin, where it takes a real value, i.e. for any delay τ {\displaystyle \tau } , | R f f ( τ ) | ≤ R f f ( 0 ) {\displaystyle |R_{ff}(\tau )|\leq R_{ff}(0)} . : p.410 This is a consequence of the rearrangement inequality. | Wikipedia - Serial correlation - Properties |
The same result holds in the discrete case. The autocorrelation of a periodic function is, itself, periodic with the same period. The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all τ {\displaystyle \tau } ) is the sum of the autocorrelations of each function s... | Wikipedia - Serial correlation - Properties |
In the following, { xi } denotes a sample of n observations, g1 and g2 are the sample skewness and kurtosis, mj’s are the j-th sample central moments, and x ¯ {\displaystyle {\bar {x}}} is the sample mean. Frequently in the literature related to normality testing, the skewness and kurtosis are denoted as √β1 and β2 res... | Wikipedia - D'Agostino's K-squared test - Skewness and kurtosis |
In the following, ω is a non-principal ultrafilter on N {\displaystyle \mathbb {N} } . If ( x n ) n ∈ N {\displaystyle (x_{n})_{n\in \mathbb {N} }} is a sequence of points in a metric space (X,d) and x∈ X, then the point x is called the ω-limit of xn, denoted as x = lim ω x n {\displaystyle x=\lim _{\omega }x_{n}} . If... | Wikipedia - Asymptotic cone - Limit of a sequence of points with respect to an ultrafilter |
It is observed that, If an ω-limit of a sequence of points exists, it is unique. If x = lim n → ∞ x n {\displaystyle x=\lim _{n\to \infty }x_{n}} in the standard sense, x = lim ω x n {\displaystyle x=\lim _{\omega }x_{n}} . (For this property to hold, it is crucial that the ultrafilter should be non-principal. )A funda... | Wikipedia - Asymptotic cone - Limit of a sequence of points with respect to an ultrafilter |
In the food industry and biochemistry, interesterification (IE) is a process that rearranges the fatty acids of a fat product, typically a mixture of triglyceride. The process implies breaking and reforming the ester bonds C–O–C that connect the fatty acid chains to the glycerol hubs of the fat molecules. These reactio... | Wikipedia - Fat interesterification - Summary |
It can be used, for instance, to turn oils into solid or semisolid products by combining them with other solid fats. It can also be used to prevent separation of solid fractions in palm oil and lauric fats, slow rancidification, or create oils more suitable for deep frying. In contrast to hydrogenation, interesterifica... | Wikipedia - Fat interesterification - Summary |
In the food industry, especially in agriculture, there has been a rise in problems toward the production of some food products. For instance, growing vegetables and fruits has become more expensive. It is difficult to grow some agricultural crops because some have a preferable climate condition for developing. | Wikipedia - Sustainable food - Production decision-making |
There has also been an incline on food shortages as production has decreased. Though the world still produces enough food for the population, not everyone receives good quality food because it is not accessible to them, since it depends on their location and/or income. In addition, the amount of overweight people has i... | Wikipedia - Sustainable food - Production decision-making |
In the food industry, food-grade castor oil is used in food additives, flavorings, candy (e.g., polyglycerol polyricinoleate in chocolate), as a mold inhibitor, and in packaging. Polyoxyethylated castor oil (e.g., Kolliphor EL) is also used in the food industries.In India, Pakistan, and Nepal, food grains are preserved... | Wikipedia - Caster oil - Food and preservative |
In the food industry, it is important to reduce the number of microbes in products to ensure proper food safety. This is usually done by thermal processing and finding ways to reduce the number of bacteria in the product. Time-temperature measurements of bacterial reduction is determined by a D-value, meaning how long ... | Wikipedia - Thermal death time - Applications |
z or z-value is used to determine the time values with different D-values at different temperatures with its equation shown below: z = T 2 − T 1 log D 1 − log D 2 {\displaystyle z={\frac {T_{2}-T_{1}}{\log D_{1}-\log D_{2}}}} where T is temperature in °F or °C. This D-value is affected by pH of the product where lo... | Wikipedia - Thermal death time - Applications |
The target of reduction in canning is the 12-D reduction of C. botulinum, which means that processing time will reduce the amount of this bacteria by a factor of 1012. The DR for C. botulinum is 0.21 minute (12.6 seconds). A 12-D reduction will take 2.52 minutes (151 seconds). This is taught in university courses in fo... | Wikipedia - Thermal death time - Applications |
In the food industry, levan is incorporated due to its prebiotic effects, cholesterol lowering ability, and adhesive properties. It also occurs naturally in low amounts in food for human consumption. Levan is also included in many dairy products as fiber or sweetener. Commercial, non-alcoholic beverages use levan as we... | Wikipedia - Levan polysaccharide - Food |
In the food industry, low-intensity ultrasonics has already been used since the 1980s to provide information about the concentration, structure, and physical state of components in foods such as vegetables, meats, and dairy products and also for quality control, for example to evaluate the rheological qualities of chee... | Wikipedia - Tactile imaging - Transient elastography |
An important advantage of transient elastography compared to harmonic elastography techniques is the separation of shear waves and compression waves. The technique can be implemented in 1D and 2D which required the development of an ultrafast ultrasound scanner.Transient elastography gives a quantitative one-dimensiona... | Wikipedia - Tactile imaging - Transient elastography |
It then displays a quantitative line of tissue stiffness data (the Young's modulus). This technique is used mainly by the Fibroscan system, which is used for liver assessment, for example, to diagnose cirrhosis.A specific implementation of 1D transient elastography called VCTE has been developed to assess average liver... | Wikipedia - Tactile imaging - Transient elastography |
In the food industry, pullulanase works well as an ingredient. Pullulan can be applied directly to foods as a protective glaze or edible film due to its ability to form films. It can be used as a spice and flavoring agent for micro-encapsulation. It is used in mayonnaise to maintain consistency and quality. It is addit... | Wikipedia - Pullulanase - Pullulanase Enzyme in the Food Industry |
In the food industry, refrigeration contributes to reducing post-harvest losses while supplying foods to consumers, enabling perishable foods to be preserved at all stages from production to consumption. In the medical sector, refrigeration is used for transport of vaccines, organs, and stem cells, while cryotechnology... | Wikipedia - Ice maker - Health applications |
In the food industry, tyrosinase inhibition is desired as tyrosinase catalyzes the oxidation of phenolic compounds found in fruits and vegetables into quinones, which gives an undesirable taste and color and also decreases the availability of certain essential amino acids as well as the digestibility of the products. A... | Wikipedia - TYR gene - In the food industry |
In the food processing industry, hyperspectral imaging, combined with intelligent software, enables digital sorters (also called optical sorters) to identify and remove defects and foreign material (FM) that are invisible to traditional camera and laser sorters. By improving the accuracy of defect and FM removal, the f... | Wikipedia - Hyperspectral imaging - Food processing |
The sorter’s software compares the hyperspectral images collected to user-defined accept/reject thresholds, and the ejection system automatically removes defects and foreign material. The recent commercial adoption of hyperspectral sensor-based food sorters is most advanced in the nut industry where installed systems m... | Wikipedia - Hyperspectral imaging - Food processing |
In the foot, the nerve terminates by dividing into medial and lateral plantar branches. Medial plantar nerve - It is the larger terminal branch of the tibial nerve. It passes between the abductor hallucis and flexor digitorum brevis to divide further into branches. Its distribution resembles to that of the distribution... | Wikipedia - Tibial nerve - Foot |
Its muscular branches supply the abductor hallucis, the flexor digitorum brevis, the flexor hallucis brevis and the first lumbrical. Cutaneous distribution of the medial plantar nerve supplies the medial sole and medial three and one half toes through four digital branches. Each digital branch give off a dorsal branch ... | Wikipedia - Tibial nerve - Foot |
This nerve also gives off articular branches to supply the bones of the tarsus and metatarsus. Lateral plantar nerve - It is the smaller terminal branch of the tibial nerve. | Wikipedia - Tibial nerve - Foot |
It courses laterally and forward until the base of fifth metatarsal bone, where it divides into superficial and deep branches. Its distribution resembles to the distribution of ulnar nerve in the hand. | Wikipedia - Tibial nerve - Foot |
The main trunk of the nerve supplies two muscles: flexor digitorum accessorius and abductor digiti minimi. This nerve also supplies the skin of the sole. The superficial branch is divided into medial and lateral branches. | Wikipedia - Tibial nerve - Foot |
The lateral branch supplies three muscles: flexor digiti minimi, 3rd and 4th interossei, and the skin over the lateral side of the toe. The medial branch communicates with the medial plantar nerve and supplies the skin over the fourth interdigital cleft. The deep branch supplies the 2nd, 3rd, and 4th lumbricals, first ... | Wikipedia - Tibial nerve - Foot |
In the forearm, it is divided into a superficial branch (primarily sensory) and a deep branch (primarily motor). The superficial branch of the radial nerve is widely separated from the radial artery in the upper one third of the forearm, closely related to radial artery in the middle third of the forearm, and in the lo... | Wikipedia - Radial nerve - Forearm and hand |
The deep branch of the radial nerve (also known as posterior interosseous nerve by some authors)) pierces the supinator muscle, winds around the radius under the cover of supinator to reach posterior of forearm where it again pierces supinator and after which it is known as the posterior interosseous nerve. It pierces ... | Wikipedia - Radial nerve - Forearm and hand |
In the foregoing part of this chapter I have endeavoured to show, even upon the principles of the commercial system, how unnecessary it is to lay extraordinary restraints upon the importation of goods from those countries with which the balance of trade is supposed to be disadvantageous. Nothing, however, can be more a... | Wikipedia - Balance of trade - Adam Smith on the balance of trade |
In the forest. This follows the first scene at once. Bradford enters, followed by two Puritans who drag Marigold between them. One carries a dark lantern; the minister bids him open it and leave the couple together. | Wikipedia - Merry Mount (opera) - Scene 2 |
He wishes, he says, to wrestle with her soul. The two men leave, and Bradford declares his love to Marigold, who responds with dismay and loathing. He threatens to kill her rather than see her with Lackland; he seizes her, and she strikes him. | Wikipedia - Merry Mount (opera) - Scene 2 |
Lackland staggers in during their struggle. His costume is dishevelled and torn. | Wikipedia - Merry Mount (opera) - Scene 2 |
He fights the minister, but breaks off when Tewke enters with other Puritans, who are armed and carry axes and lanterns. Lackland seizes an axe, but is immediately run through, to Tewke's dismay, by a pike carried by one of the Puritans. He dies in Marigold's arms; she kisses his brow, then stands and calls for vengean... | Wikipedia - Merry Mount (opera) - Scene 2 |
Tewke orders her taken to the village as a prisoner, and his men exit, dragging her away and removing Lackland's body. Left alone with him, Tewke rebukes the minister, and urges his repentance. He leaves, and Bradford prays for divine aid. Exhausted by his anguish and his fight, he falls asleep to the sound of mystic v... | Wikipedia - Merry Mount (opera) - Scene 2 |
In the foreword to his Chronologica, Gerard Mercator stated the intention to publish an atlas which would cover everything of the then-known cosmos, geography and history of the earth. During his life, Mercator published five volumes of his atlas, the last one being published by his son Rumold. After Mercator's death, ... | Wikipedia - Harmonia Macrocosmica - History |
He and fellow-cartographer Hendricus Hondius published their Novus Atlas in 1636, which featured over 320 maps in four languages. In 1660, Andreas Cellarius' Harmonia Macrocosmica was published as the seventh volume of the project. With the final addition of a volume describing the cities of the world from 1657, the pr... | Wikipedia - Harmonia Macrocosmica - History |
In the foreword to the paperback edition, written by Tim Berners-Lee shortly after Michael Dertouzos's death, he succinctly summarizes the objectives of the book by stating the three areas he believes computers still need improvement in: "helping us to communicate better with each other, by helping with the actual proc... | Wikipedia - The Unfinished Revolution - Summary |
In the foreword, the author explains that instead of the “futile and impossible task” of improving on Hecke’s classical treatment of algebraic number theory, he “rather tried to draw the conclusions from the developments of the last thirty years, whereby locally compact groups, measure and integration have been seen to... | Wikipedia - Basic Number Theory - Mathematical context and purpose |
In a striking choice of wording for a foreword written in the United States in 1967, the author chooses to drive this particular viewpoint home by explaining that the two classes of global fields “must be granted a fully simultaneous treatment instead of the segregated status, and at best the separate but equal facili... | Wikipedia - Basic Number Theory - Mathematical context and purpose |
Alongside the desire to consider algebraic number fields alongside function fields over finite fields, the work of Chevalley is particularly emphasised. In order to derive the theorems of global class field theory from those of local class field theory, Chevalley introduced what he called the élément idéal, later calle... | Wikipedia - Basic Number Theory - Mathematical context and purpose |
In the form 4 x y z = n ( x y + x z + y z ) {\displaystyle 4xyz=n(xy+xz+yz)} , a polynomial equation with integer variables, the Erdős–Straus conjecture is an example of a Diophantine equation. The Hasse principle for Diophantine equations suggests that these equations should be studied using modular arithmetic. If an ... | Wikipedia - Erdős–Straus conjecture - Theoretical results |
The power of the Hasse principle to solve some problems is limited by the Manin obstruction, but for the Erdős–Straus conjecture this obstruction does not exist.On the face of it this principle makes little sense for the Erdős–Straus conjecture. For every n {\displaystyle n} , the equation 4 x y z = n ( x y + x z + y z... | Wikipedia - Erdős–Straus conjecture - Theoretical results |
In the form mentioned above, including in particular the fundamental theorem of Galois theory, the theory only considers Galois extensions, which are in particular separable. General field extensions can be split into a separable, followed by a purely inseparable field extension. For a purely inseparable extension F / ... | Wikipedia - Galois group of a polynomial - Inseparable extensions |
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