Search results
Results From The WOW.Com Content Network
Furthermore, if the Jacobian determinant at p is positive, then f preserves orientation near p; if it is negative, f reverses orientation. The absolute value of the Jacobian determinant at p gives us the factor by which the function f expands or shrinks volumes near p; this is why it occurs in the general substitution rule.
If the discriminant is positive, the number of non-real roots is a multiple of 4. That is, there is a nonnegative integer k ≤ n /4 such that there are 2 k pairs of complex conjugate roots and n − 4 k real roots.
A meaning can be given to the Leibniz formula provided that the order for the product is specified, and similarly for other definitions of the determinant, but non-commutativity then leads to the loss of many fundamental properties of the determinant, such as the multiplicative property or that the determinant is unchanged under transposition ...
This implies that at a local minimum the Hessian is positive-semidefinite, and at a local maximum the Hessian is negative-semidefinite. For positive-semidefinite and negative-semidefinite Hessians the test is inconclusive (a critical point where the Hessian is semidefinite but not definite may be a local extremum or a saddle point).
In inorganic chemistry, Fajans' rules, formulated by Kazimierz Fajans in 1923, [1] [2] [3] are used to predict whether a chemical bond will be covalent or ionic, and depend on the charge on the cation and the relative sizes of the cation and anion. They can be summarized in the following table:
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...
Definition of the D-value The P-value only correctly refers to the concentration ratio of a single substance distributed between the octanol and water phases. In the case of a substance that occurs as multiple species, it can therefore be calculated by summing the concentrations of all n species in the octanol phase and the concentrations of ...
Evaluation of discriminant (divergent) validity – The construct being measured by a test should not correlate highly with different constructs. Trait-method unit - Each task or test used in measuring a construct is considered a trait-method unit; in that the variance contained in the measure is part trait, and part method.