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The theorem extends to unbounded intervals by defining the sign at +∞ of a polynomial as the sign of its leading coefficient (that is, the coefficient of the term of highest degree). At –∞ the sign of a polynomial is the sign of its leading coefficient for a polynomial of even degree, and the opposite sign for a polynomial of odd degree.
The leading entry (sometimes leading coefficient [citation needed]) of a row in a matrix is the first nonzero entry in that row. So, for example, in the matrix ( 1 2 0 6 0 2 9 4 0 0 0 4 0 0 0 0 ) , {\displaystyle {\begin{pmatrix}1&2&0&6\\0&2&9&4\\0&0&0&4\\0&0&0&0\end{pmatrix}},} the leading coefficient of the first row is 1; that of the second ...
In theoretical chemistry, Specific ion Interaction Theory (SIT theory) is a theory used to estimate single-ion activity coefficients in electrolyte solutions at relatively high concentrations. [ 1 ] [ 2 ] It does so by taking into consideration interaction coefficients between the various ions present in solution.
A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas.The reactant entities are given on the left-hand side and the product entities are on the right-hand side with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the products to show the direction of the reaction. [1]
The horizontal axis is the concentration of the ligand. As the Hill coefficient is increased, the saturation curve becomes steeper. In biochemistry and pharmacology, the Hill equation refers to two closely related equations that reflect the binding of ligands to macromolecules, as a function of the ligand concentration.
Exact wave functions, however, cannot generally be expressed as single determinants. The single-determinant approximation does not take into account Coulomb correlation, leading to a total electronic energy different from the exact solution of the non-relativistic Schrödinger equation within the Born–Oppenheimer approximation .
If the degree of p is greater than the degree of q, then the limit is positive or negative infinity depending on the signs of the leading coefficients; If the degree of p and q are equal, the limit is the leading coefficient of p divided by the leading coefficient of q; If the degree of p is less than the degree of q, the limit is 0.
The Hilbert function, the Hilbert series and the Hilbert polynomial of a filtered algebra are those of the associated graded algebra. The Hilbert polynomial of a projective variety V in P n is defined as the Hilbert polynomial of the homogeneous coordinate ring of V .