"emission energy Δ""E"" = ""hc""/λ, where c is the speed of light). This is useful for calculating the radius of a quantum dot from experimentally determined parameters. The overall equation is ""E"", ""m""*, and ""m""* are unique for each nanocrystal composition. For example, with CdSe nanocrystals: Brus equation The Brus equation can be used to describe the emission energy of quantum dot semiconductor nanocrystals (such as CdSe nanocrystals) in terms of the band gap energy ""E"", Planck's constant ""h"", the radius of the quantum dot ""r"", as well as the effective mass of the excited electron ""m""* and of the"
"space, a bounded, closed convex set ""C"" is the convex hull of its extreme point set ""E"", so that any ""c"" in ""C"" is a (finite) convex combination of points ""e"" of ""E"". Here ""E"" may be a finite or an infinite set. In vector terms, by assigning non-negative weights ""w""(""e"") to the ""e"" in ""E"", almost all 0, we can represent any ""c"" in ""C"" as with In any case the ""w""(""e"") give a probability measure supported on a finite subset of ""E"". For any affine function ""f"" on ""C"", its value at the point ""c"" is In the"
"""c"" are fatigue coefficients and exponents representing material model constants. The generalized Coffin-Manson model accounts for the effects of high cycle fatigue (HCF) primarily due to elastic deformation and low cycle fatigue (LCF) primarily due to plastic deformation. In the 1980s Engelmaier proposed a model, in conjunction with the work of Wild, that accounted for some of the limitations of the Coffin-Manson model such as the effects of the frequency and temperature. His model takes a similar power law form: formula_2 formula_3 Engelmaier relates the total shear strain (∆γ) to cycles to failure (""N""). ""ε'"" and ""c"" are model constants"
"in nuclei to estimate that there was enough energy available to make nuclear fission a favorable process. The implications of this special form of Einstein's formula have thus made it one of the most famous equations in all of science. The equation ""E"" = ""m""""c"" applies only to isolated systems in their center of momentum frame. It has been popularly misunderstood to mean that mass may be ""converted"" to energy, after which the ""mass"" disappears. However, popular explanations of the equation as applied to systems include open (non-isolated) systems for which heat and light are allowed to escape, when they"
"the comultiplication on ""C"" is coassociative. In general, ""C"" is not a bialgebra, and ""C"" is a Hopf *-algebra. Informally, ""C"" can be regarded as the *-algebra of continuous complex-valued functions over the compact matrix quantum group, and ""u"" can be regarded as a finite-dimensional representation of the compact matrix quantum group. A representation of the compact matrix quantum group is given by a corepresentation of the Hopf *-algebra (a corepresentation of a counital coassociative coalgebra ""A"" is a square matrix formula_37 with entries in ""A"" (so ""v"" belongs to M(""n"", ""A"")) such that for all ""i"", ""j"" and ""ε""(""v"")"
"C⋅N⋅m (or equivalent units – in practice ""farads per metre""). In order to establish the numerical value of ""ε"", one makes use of the fact that if one uses the rationalized forms of Coulomb's law and Ampère's force law (and other ideas) to develop Maxwell's equations, then the relationship stated above is found to exist between ""ε"", ""μ"" and ""c"". In principle, one has a choice of deciding whether to make the coulomb or the ampere the fundamental unit of electricity and magnetism. The decision was taken internationally to use the ampere. This means that the value of ""ε"" is"
". The model assigned E and C parameters to many Lewis acids and bases. Each acid is characterized by an E and a C. Each base is likewise characterized by its own E and C. The E and C parameters refer, respectively, to the electrostatic and covalent contributions to the strength of the bonds that the acid and base will form. The equation is The W term represents a constant energy contribution for acid–base reaction such as the cleavage of a dimeric acid or base. The equation predicts reversal of acids and base strengths. The graphical presentations of the equation"
"Δ13C In geochemistry, paleoclimatology and paleoceanography ""δ""C (pronounced ""delta c thirteen"") is an isotopic signature, a measure of the ratio of stable isotopes C : C, reported in parts per thousand (per mil, ‰). The definition is, in per mil: where the standard is an established reference material. ""δ""C varies in time as a function of productivity, the signature of the inorganic source, organic carbon burial and vegetation type. Biological processes preferentially take up the lower mass isotope through kinetic fractionation. However some abiotic processes do the same, methane from hydrothermal vents can be depleted by up to 50%. The"
"EC50 Half maximal effective concentration (EC) refers to the concentration of a drug, antibody or toxicant which induces a response halfway between the baseline and maximum after a specified exposure time. It is commonly used as a measure of a drug's potency. EC is expressed in molar units (M), where 1 M is equivalent to 1 mol/L. The EC of a ""graded"" dose response curve therefore represents the concentration of a compound where 50% of its maximal effect is observed. The EC of a ""quantal"" dose response curve represents the concentration of a compound where 50% of the population exhibit"
"determined by the values of ""c"" and ""μ"", as stated above. For a brief explanation of how the value of ""μ"" is decided, see the article about ""μ"". By convention, the electric constant ""ε"" appears in the relationship that defines the electric displacement field D in terms of the electric field E and classical electrical polarization density P of the medium. In general, this relationship has the form: For a linear dielectric, P is assumed to be proportional to E, but a delayed response is permitted and a spatially non-local response, so one has: In the event that nonlocality and"
"C and B, formula_2 would in turn represent the current from C to E. In this case, C would again denote the collector end of a transistor, and E would denote the emitter end of the transistor. This is the same as saying ""the current in the direction going from C to E"". Power supply pins on integrated circuits utilize the same letters for denoting what kind of voltage the pin would receive. For example, a power input labeled V would be a positive input that would presumably connect to the collector pin of a BJT transistor in the circuit,"
"and C numbers is found in this article and the complete set is available in the literature. In the ECW model, a new term W was added to the equation. The W term represents a constant energy for cleavage of a dimeric acid or base. For example the enthalpy of cleavage the [Rh(CO)Cl] by base B involves two steps. The first step is cleavage of the dimer, which is ""W"": The second step is the binding of B to RhCl(CO) monomer. In this case, ""W"" = -10.39 kcal/mol. In other cases, W is the enthalpy needed to cleave the internal"
"chain, ""Q"", is by first finding its embedded Markov chain (EMC). Strictly speaking, the EMC is a regular discrete-time Markov chain, sometimes referred to as a jump process. Each element of the one-step transition probability matrix of the EMC, ""S"", is denoted by ""s"", and represents the conditional probability of transitioning from state ""i"" into state ""j"". These conditional probabilities may be found by From this, ""S"" may be written as where ""I"" is the identity matrix and diag(""Q"") is the diagonal matrix formed by selecting the main diagonal from the matrix ""Q"" and setting all other elements to zero."
"chemistry. The ECW model is quantitative model that describes and predicts the strength of Lewis acid base interactions, −Δ""H"". The model assigned ""E"" and ""C"" parameters to many Lewis acids and bases. Each acid is characterized by an ""E"" and a ""C"". Each base is likewise characterized by its own ""E"" and ""C"". The ""E"" and ""C"" parameters refer, respectively, to the electrostatic and covalent contributions to the strength of the bonds that the acid and base will form. The equation is The ""W"" term represents a constant energy contribution for acid–base reaction such as the cleavage of a dimeric"
"radiation or heat) of amount ""E"", its mass decreased by the amount ""E"" /""c"". This led to the famous mass–energy equivalence formula: ""E"" = ""mc"". Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the ""rest energy"", distinct from its classical kinetic and potential energies. As it was shown above, many authors before Einstein arrived at similar formulas (including a 4/3-factor) for the relation of mass to energy. However, their work was focused on electromagnetic energy which (as we know today) only represents a small part of the entire"
"the mean flow. The mean energy ""E"" of the fluctuating motion (the sum of the kinetic and potential energies satisfies: where "":"" denotes the double-dot product, and ""ε"" denotes the dissipation of mean mechanical energy (for instance by wave breaking). The term formula_22 is the exchange of energy with the mean motion, due to wave–current interaction. The mean horizontal wave-energy transport ( + c) ""E"" consists of two contributions: In a Cartesian coordinate system, the above equation for the mean energy ""E"" of the flow fluctuations becomes: So the radiation stress changes the wave energy ""E"" only in case of"
"""C"" is a modification factor used in the equation for nominal flexural strength when determining lateral-torsional buckling. The reason for this factor is to allow for non-uniform moment diagrams when the ends of a beam segment are braced. The conservative value for ""C"" can be taken as 1, regardless of beam configuration or loading, but in some cases it may be excessively conservative. ""C"" is always equal to or greater than 1, never less. For cantilevers or overhangs where the free end is unbraced, C is equal to 1. Tables of values of ""C"" for simply supported beams exist. If"
"of MEE is the mediation that ""Dose"" and ""Effect"" or ""Mass"" and ""Function"" are interchangeable. The ""Mass"" vs ""Energy"" was defined E=MC for subatomic fission and fusion; Now ""Mass"" vs ""Action"" is defined by MEE for supramolecular dynamics. The combination index (CI) concept was introduced by Chou T.C. and Talalay P. during 1983-84[3] The derived combination index equation for two drugs is: Where (Dx) is for (D) “alone” that inhibits a system x%, and (Dx) is for (D) “alone” that inhibits a system x% whereas in the numerator, (D) + (D), “in combination” also inhibit x%. Note that the denominators"
"to replace ""1 F"" with ""(10 ""c"") cm"" within an equation or formula. (This warning is a special aspect of electromagnetism units in CGS. By contrast, for example, it is ""always"" correct to replace ""1 m"" with ""100 cm"" within an equation or formula.) One can think of the SI value of the Coulomb constant ""k"" as: This explains why SI to ESU conversions involving factors of ""c"" lead to significant simplifications of the ESU units, such as 1 statF = 1 cm and 1 statΩ = 1 s/cm: this is the consequence of the fact that in ESU system"
"""C"" of genus ""g"" over a prime field formula_1 where ""q"" = ""p"" (""p"" prime) of odd characteristic is defined as where ""f"" monic, deg(""f"") = 2""g"" + 1 and deg(""h"") ≤ g. The curve has at least one formula_1-rational Weierstraßpoint. The Jacobian variety formula_4 of ""C"" is for all finite extension formula_5 isomorphic to the ideal class group formula_6. With the ""Mumford's representation"" it is possible to represent the elements of formula_4 with a pair of polynomials ""[u, v]"", where ""u"", ""v"" ∈ formula_8. The ""Frobenius endomorphism"" σ is used on an element ""[u, v]"" of formula_4 to raise"
"Coulomb The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: ""Q"" or ""q"") transported by a constant current of one ampere in one second: Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt: The coulomb is equivalent to the charge of approximately ( mol) protons, and −1 C is equivalent to the charge of approximately electrons. A new definition, in terms of the elementary charge, will take effect on 20 May 2019. The new definition,"
"This equation reproduces and predicts the enthalpy, Δ""H"", of a reaction between many acids and a bases. Δ""H"" is a measure of strength of the bond between the acid and the base, both in the gas phase and in weakly solvating media. Entropy effects are ignored. A matrix presentation of the equation enhances its utility. Four values, two E and two C were assigned as references. E and C of I were chosen as standards. Since I has little tendency to undergo electrostatic bonding, the E parameter was assigned a small value, 0.5, while the value of C for the"
"on ""S"" via Here invariance means that for all ""ξ"" in so(""n"",C) and ""φ"", ""ψ"" in ""S"" — in other words the action of ""ξ"" is skew with respect to ""β"". In fact, more is true: ""S"" is a representation of the opposite Clifford algebra, and therefore, since ClC only has two nontrivial simple modules ""S"" and ""S""′, related by the parity involution ""α"", there is an antiautomorphism ""τ"" of ClC such that for any ""A"" in ClC. In fact ""τ"" is reversion (the antiautomorphism induced by the identity on ""V"") for ""m"" even, and conjugation (the antiautomorphism induced by"
"curve ""C"", i.e. the complement of ""n"" points in a projective algebraic curve of genus ""g"", taken to be smooth and irreducible, defined over a field ""K"" that is finitely generated (over its prime field), such that Grothendieck conjectured that the algebraic fundamental group ""G"" of ""C"", a profinite group, determines ""C"" itself (i.e. the isomorphism class of ""G"" determines that of ""C""). This was proved by Mochizuki. An example is for the case of ""g"" = 0 (the projective line) and ""n"" = 4, when the isomorphism class of ""C"" is determined by the cross-ratio in ""K"" of the"
"(C) is an isotope of carbon. The mole is currently defined as ""the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon12"". Thus, the current definition of the mole requires that moles ( mol) of C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is experimentally determined, and the current best estimate of its value is This new definition of the kilogram proposed to fix the Avogadro constant at precisely with the kilogram being defined as"
"magnitude but opposite sign: The proportionality constant ""κ"" reads: where ""q"", ""m"", r are the electron charge, mass, and radius, respectively; ""c"" is the vacuum speed of light and ""ϵ"" is the vacuum permittivity. The value of the constant is approximately ""κ"" ≈ 40.308193 m·s; the units can be expressed equivalently as m·m·Hz to highlight the cancellation involved in yielding delays τ in meters, given ""f"" in Hz and TEC in m. Total electron content Total electron content (or TEC) is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons integrated between"
"an irreducible representation of so(""n"",C) of dimension 2: the Clifford action of a unit vector ""u"" ∈ ""U"" is given by and so elements of so(""n"",C) of the form ""u""∧""w"" or ""u""∧""w"" do not preserve the even and odd parts of the exterior algebra of ""W"". The highest weight of ""S"" is The Clifford action is not faithful on ""S"": ClC can be identified with End(""S"") ⊕ End(""S""′), where ""u"" acts with the opposite sign on ""S""′. More precisely, the two representations are related by the parity involution ""α"" of ClC (also known as the principal automorphism), which is the"
"names are denoted by a corresponding SI name with an attached prefix ""ab"" or with a separate abbreviation ""emu"". The ESU and EMU subsystems of CGS are connected by the fundamental relationship formula_17 (see above), where ""c"" = 29,979,245,800 ≈ 3⋅10 is the speed of light in vacuum in centimetres per second. Therefore, the ratio of the corresponding ""primary"" electrical and magnetic units (e.g. current, charge, voltage, etc. – quantities proportional to those that enter directly into Coulomb's law or Ampère's force law) is equal either to ""c"" or ""c"": and Units derived from these may have ratios equal to"
"""λ"" is the wavelength and ""c"" is the phase speed of the wave. Further, ""K""(""m"") and ""E""(""m"") are complete elliptic integrals of the first and second kind, respectively. Searching for the elliptic parameter ""m"" can be done by trial and error, or by use of a numerical root-finding algorithm. In this case, starting from an initial guess ""m"" = 0.99, by trial and error the answer is found. Within the process, the wavelength ""λ"" and phase speed ""c"" have been computed: The phase speed ""c"" can be compared with its value formula_66 according to the shallow water equations: showing a"
"be represented by its Taylor series about 0: where (by Cauchy's integral formula) and ""C"" is the circle about 0 of radius ""r"" > 0. Suppose ""f"" is bounded: i.e. there exists a constant ""M"" such that |""f""(""z"")| ≤ ""M"" for all ""z"". We can estimate directly where in the second inequality we have used the fact that |""z""|=""r"" on the circle ""C"". But the choice of ""r"" in the above is an arbitrary positive number. Therefore, letting ""r"" tend to infinity (we let ""r"" tend to infinity since f is analytic on the entire plane) gives ""a"" = 0"
"the spherical aberration ""C"" that limits spatial coherency and defines ""E(u)"" and the chromatic aberration ""C"", together with current and voltage instabilities that define the temporal coherency in ""E(u)"". These two envelopes determine the information limit by damping the signal transfer in Fourier space with increasing spatial frequency ""u"" where α is the semiangle of the pencil of rays illuminating the sample. Clearly, if the wave aberration ('here represented by ""C"" and Δ""f"") vanished, this envelope function would be a constant one. In case of an uncorrected TEM with fixed ""C"", the damping due to this envelope function can be"
"slightly changed since the definition of these canonical illuminants, whose SPDs are based on the original values in Planck's law. In order to match all significant digits of the published data of the canonical illuminants the values of M and M have to be rounded to three decimal places before calculation of ""S."" Illuminant E is an equal-energy radiator; it has a constant SPD inside the visible spectrum. It is useful as a theoretical reference; an illuminant that gives equal weight to all wavelengths, presenting an even color. It also has equal CIE XYZ tristimulus values, thus its chromaticity coordinates"
"follows: The symbol ∧ denotes the lattice operation on the projections in ""Z""(M): ""F"" ∧ ""F"" is the projection onto the closed subspace Ran(""F"") ∩ Ran(""F""). The abelian algebra ""Z""(M), being the intersection of two von Neumann algebras, is also a von Neumann algebra. Therefore, ""C""(""E"") lies in ""Z""(M). If one thinks of M as a direct sum (or more accurately, a direct integral) of its factors, then the central projections are the projections that are direct sums (direct integrals) of identity operators of (measurable sets of) the factors. If ""E"" is confined to a single factor, then ""C""(""E"") is"