Review of Short Phrases and Links|
This Review contains major "Sum"- related terms, short phrases and links grouped together in the form of Encyclopedia article.
- A sum is the second level administrative subdivision below the Aimags (provinces), roughly comparable to a County in the USA. There are 331 sums in Mongolia.
- Sum (Siao, Fong Sai-Yuk) is a well known Cantonese opera star, a woman who has played only male roles for the last twenty years.
- The sum is finite since p i can only be less than or equal to n for finitely many values of i, and the floor function results in 0 when applied for p i n.
- This sum is greater than 810.0, its expected value under the null hypothesis of no difference between the two samples Active and Placebo.
- In sum, the low-income population in our sample achieved as well in literacy and language as a normative population through the third grade.
- Foundations: fields and vector spaces, subspace, linear independence, basis, ordered basis, dimension, direct sum decomposition.
- Conversely, it can be proven that any semisimple Lie algebra is the direct sum of its minimal ideals, which are canonically determined simple Lie algebras.
- In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e.
- The total energy of the ordinary species is the sum of the energies to remove all of the electrons from the ordinary species.
- The total number of electrons represented in a Lewis structure is equal to the sum of the numbers of valence electrons on each individual atom.
- The full scattering amplitude is the sum of all contributions from all possible loops of photons, electrons, positrons, and other available particles.
- The spin of atoms and molecules is the sum of the spins of unpaired electrons.
- The bracket is the scalar product on the Hilbert space; the sum on the right hand side converges in the operator norm.
- Two (or more) Hilbert spaces can be combined to produce another Hilbert space by taking either their direct sum or their tensor product.
- But if there are only finitely many summands, then the Banach space direct sum is isomorphic to the Hilbert space direct sum.
- In general, the orthogonal complement of a sum of subspaces is the intersection of the orthogonal complements:[ 68].
- Then, and its orthogonal complement determine a direct sum decomposition of.
- As expected, the sum of the eigenvalues is equal to the number of variables.
- The trace of a square matrix is the sum of its diagonal entries, which equals the sum of its n eigenvalues.
- First, the sum over functions with differences of eigenvalues in the denominator resembles the resolvent in Fredholm theory.
- But that is very easy indeed: given a polynomial we define to be the degree of plus the sum of the absolute values of the coefficients of.
- Of the robust estimators considered in the paper, the one based on minimizing the sum of the absolute values of the residuals performed the best.
- The infinity norm (or maximum value of the sum of the absolute values of the rows members of a matrix).
- Binding energy - The difference between the total energy of a molecular system and the sum of the energies of its isolated p - and s -bonds.
- The difference between the mean and the predicted value of Y. This is the explained part of the deviation, or (Regression Sum of Squares).
- The addition (their sum) and subtraction (their difference) of two integers will always result in an integer.
- The sum of two algebraic integers is an algebraic integer, and so is their difference; their product is too, but not necessarily their ratio.
- The "Chi-square distribution with n degrees of freedom" is therefore the distribution of the sum of n independent squared r.v.
- A graph with n vertices (n ≥ 3) is Hamiltonian if, for each pair of non-adjacent vertices, the sum of their degrees is n or greater (see Ore's theorem).
- The degrees of freedom is equal to the sum of the individual degrees of freedom for each sample.
- Notice that each Mean Square is just the Sum of Squares divided by its degrees of freedom, and the F value is the ratio of the mean squares.
- Thus, the sum of all the eigenvalues is equal to the sum squared distance of the points with their mean divided by the number of dimensions.
- If the M i are actually vector spaces, then the dimension of the direct sum is equal to the sum of the dimensions of the M i.
- The dimension of the space is the sum of the dimensions of the two subspaces, minus the dimension of their intersection.
- For a square matrix A of order n to be diagonalizable, the sum of the dimensions of the eigenspaces must be equal to n.
- FIG. 14A is a graph showing the sum of hydrophilic peaks as detected by HPLC when a variety of synthetic adsorbents were added to the beer.
- Thus the sum of z 1 and z 2 corresponds to the diagonal OB of the parallelogram shown in Fig.
- The following formulae can be used to find the probability of rolling a sum S using N dice of M faces.
- The surface area of any prism equals the sum of the areas of its faces, which include the floor, roof and walls.
- In an abelian category, for example the category of abelian groups or a category of modules, the direct sum is the categorical coproduct.
- There is sort of a semi-ring structure on that category in that vector bundles can be added, using the direct sum, and multiplied, using the direct product.
- Semisimple means that each object in the category is (isomorphic to) the direct sum of (finitely many) simple objects.
- Analogous examples are given by the direct sum of vector spaces and modules, by the free product of groups and by the disjoint union of sets.
- Analogous examples are given by the direct sum of vector space s and modules, by the free product of groups and by the disjoint union of sets.
- Given such a polyhedron, the sum of the vertices and the faces is always the number of edges plus two.
- The sum of two points A and B of the complex plane is the point X = A + B such that the triangles with vertices 0, A, B, and X, B, A, are congruent.
- X A + B: The sum of two points A and B of the complex plane is the point X A + B such that the triangle s with vertices 0, A, B, and X, B, A, are congruent.
- In mathematics, the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold.
- The tensor bundle is the direct sum of all tensor product s of the tangent bundle and the cotangent bundle.
- Mass Defect and Binding Energy Summary Mass defect is the difference between the mass of the atom and the sum of the masses of its constituent parts.
- An atom or molecule has less mass (by a negligible but real amount) than the sum of the masses of its components taken separately.
- The formal charge of the atom, the sum of the charge of the proton and the charge of the electron, is zero.
- So this difference in the actual nuclear mass and the expected nuclear mass (sum of the individual masses of nuclear particles) is called mass defect.
- Properties The direct sum is a submodule of the direct product of the modules M i.
- A direct summand of M is a submodule N such that there is some other submodule N′ of M such that M is the internal direct sum of N and N′.
- A finite direct sum of modules is Noetherian if and only if each summand is Noetherian; it is Artinian if and only if each summand is Artinian.
- But centuries and centuries elapsed before the sum of human knowledge was equal to what it had been at the fall of the Roman empire.
- Nuclear - Binding energy The sum of the individual masses of various particle in the nucleus must be equal to the nuclear mass.
- To calculate the binding energy of a nucleus, all you have to do is sum the mass of the individual nucleons, and then subtract the mass of the atom itself.
- The net magnetic moment of an atom is equal to the vector sum of orbital and spin magnetic moments of all electrons and the nucleus.
- Mass Defect The difference in the mass of a nucleus and the sum of the masses of its constituent particles.
- Composite particles, such as nuclei and atoms, are classified as bosons or fermions based on the sum of the spins of their constituent particles.
- For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods.
- Average the cosines: Find the cosines of the sum and difference angles using a cosine table and average them.
- For example, instead of the usual least squares you could request a minimum of the sum of the absolute deviations or possibly the minimum maximum error.
- Any point in the 4 to 7 region will have the same value of 22 for the sum of the absolute deviations.
- Mean(arithmetic mean or average) is the sum of the data in a frequency distribution divided by the number of data elements.
- In mathematics and statistics, the arithmetic mean of a set of numbers is the sum of all the members of the set divided by the number of items in the set.
- Mean: More accurately called the arithmetic mean, it is defined as the sum of scores divided by the number of scores.
- Different examples include maximising the distance to the nearest point, or using electrons to maximise the sum of all reciprocals of squares of distances.
- If the inputs are error forms, the error is the square root of the reciprocal of the sum of the reciprocals of the squares of the input errors.
- More precisely, if S(x) denotes the sum of the reciprocals of all prime numbers p with p ≤ x, then S(x) = ln ln x + O(1) for x → ∞.
- A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines.
- Suppose that ƒ(x) is periodic function with period 2 π, in this case one can attempt to decompose ƒ(x) as a sum of complex exponentials functions.
- In mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions, namely sines and cosines.
- In the study of Fourier series, complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines.
- The spectral method, which represents functions as a sum of particular basis functions, for example using a Fourier series.
- The angle defect at a vertex of a polygon is defined to be minus the sum of the angles at the corners of the faces at that vertex.
- The conservation of momentum is obtained by adding to the vertices a delta function on the sum of the 4-momenta coming into the vertex.
- The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees.
- A quadratic identity is used by Louis de Lagrange (1706–1783) to show that every positive integer is the sum of four squares of integers.
- In 1770, Lagrange showed that every positive integer could be written as the sum of at most four squares.
- For instance, it was proven by Lagrange that every positive integer is the sum of four squares.
- In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition.
- A double sum is often the product of two sums, which may be Fourier series.
- Direct sums are also commutative and associative (up to isomorphism), meaning that it doesn't matter in which order one forms the direct sum.
- It is remarkable that two random variables, the sum of squares of the residuals and the sample mean, can be shown to be independent of each other.
- Linear regression fits a line to a scatterplot in such a way as to minimize the sum of the squares of the residuals.
- In statistics, the residual sum of squares (RSS) is the sum of squares of residuals.
- A square matrix is diagonalizable if the sum of the dimensions of the eigenspaces is the number of rows or columns of the matrix.
- The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix.
- As the trace of a matrix is equal to the sum of its eigenvalues, this implies that the estimated eigenvalues are biased.
- The tr is the trace operator and represents the sum of the diagonal elements of the matrix.
- Dimension. Sum of diagonal elements.
- Note that the sum of the diagonal elements is conserved; this is the signature of the metric [ +2 ].
- Principal: The original amount of a debt; a sum of money agreed to by the borrower and the lender to be repaid on a schedule.
- The borrower may redeem by paying the lender the sum for which the property was sold at foreclosure, plus interest at the same rate as the mortgage.
- When the interest rate is reduced for a specified period of time by depositing a sum of money with the lender.
- Mortgage Note: A written promise to pay a sum of money at a stated interest rate during a specified term.
- Energy of an Orbit The Total energy of an object in orbit is the sum of kinetic energy (KE) and gravitational potential energy (PE).
- The energy of a volume V at any point is the sum of its kinetic energy and its potential energy (pV). Effects of gravitation and viscosity are neglected.
- One term not listed among manifestations of energy is mechanical energy, which is something different altogether: the sum of potential and kinetic energy.
- The energy released is equal to the sum of the rest energies of the particles and their kinetic energies.
- For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles.
- In this model the atomic Hamiltonian is a sum of kinetic energies of the electrons and the spherical symmetric electron-nucleus interactions.
- Related subjects: Mathematics On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry).
- Then an elementary calculation of angles shows that the sum of the exterior angles of the polygon is equal to the sum of the face angles at the vertex.
- Legendre proved that Euclid 's fifth postulate is equivalent to:- The sum of the angles of a triangle is equal to two right angles.
- The sum of interior angles of a geodesic triangle is equal to π plus the total curvature enclosed by the triangle.
- One way in which elliptic geometry differs from Euclidean geometry is that the sum of the interior angles of a triangle is greater than 180 degrees.
- The sum of the interior angles must be 180 degrees, as with all triangles.
- Each coordinate in the sum of squares is inverse weighted by the sample variance of that coordinate.
- Information > Science > Mathematics > Zero
- Mathematics > Algebra > Linear Algebra > Vectors
* Finite Sum
* Graph Showing
* Independent Random Variables
* Internal Angles
* Ion-Exchange Resins
* Low-Malt Beer
* Lump Sum
* Mean Curvature
* Partial Pressures
* Positive Integer
* Squared Deviations
* Squared Residuals
* Unique Line
* Vector Sum
* Wedge Sum
* Weighted Sum
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