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### DefinitionsUpDw('Definitions','-Abz-');

1. 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. (Web site)
2. 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. (Web site)
3. 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. (Web site)
4. This sum is greater than 810.0, its expected value under the null hypothesis of no difference between the two samples Active and Placebo. (Web site)
5. In sum, the low-income population in our sample achieved as well in literacy and language as a normative population through the third grade.

### DimensionUpDw('DIMENSION','-Abz-');

1. Foundations: fields and vector spaces, subspace, linear independence, basis, ordered basis, dimension, direct sum decomposition.

### Simple Lie AlgebrasUpDw('SIMPLE_LIE_ALGEBRAS','-Abz-');

1. 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.
2. In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e.

### ElectronsUpDw('ELECTRONS','-Abz-');

1. The total energy of the ordinary species is the sum of the energies to remove all of the electrons from the ordinary species. (Web site)
2. 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. (Web site)
3. The full scattering amplitude is the sum of all contributions from all possible loops of photons, electrons, positrons, and other available particles.

### Unpaired ElectronsUpDw('UNPAIRED_ELECTRONS','-Abz-');

1. The spin of atoms and molecules is the sum of the spins of unpaired electrons.

### Hilbert SpaceUpDw('HILBERT_SPACE','-Abz-');

1. The bracket is the scalar product on the Hilbert space; the sum on the right hand side converges in the operator norm. (Web site)
2. Two (or more) Hilbert spaces can be combined to produce another Hilbert space by taking either their direct sum or their tensor product.
3. But if there are only finitely many summands, then the Banach space direct sum is isomorphic to the Hilbert space direct sum.

### Orthogonal ComplementUpDw('ORTHOGONAL_COMPLEMENT','-Abz-');

1. In general, the orthogonal complement of a sum of subspaces is the intersection of the orthogonal complements:[ 68]. (Web site)
2. Then, and its orthogonal complement determine a direct sum decomposition of.

### EigenvaluesUpDw('EIGENVALUES','-Abz-');

1. As expected, the sum of the eigenvalues is equal to the number of variables. (Web site)
2. The trace of a square matrix is the sum of its diagonal entries, which equals the sum of its n eigenvalues. (Web site)
3. First, the sum over functions with differences of eigenvalues in the denominator resembles the resolvent in Fredholm theory. (Web site)

### Absolute ValuesUpDw('ABSOLUTE_VALUES','-Abz-');

1. 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.
2. 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. (Web site)
3. The infinity norm (or maximum value of the sum of the absolute values of the rows members of a matrix).

### DifferenceUpDw('DIFFERENCE','-Abz-');

1. 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.
2. The difference between the mean and the predicted value of Y. This is the explained part of the deviation, or (Regression Sum of Squares).
3. The addition (their sum) and subtraction (their difference) of two integers will always result in an integer.

### Algebraic IntegersUpDw('ALGEBRAIC_INTEGERS','-Abz-');

1. The sum of two algebraic integers is an algebraic integer, and so is their difference; their product is too, but not necessarily their ratio.

### DegreesUpDw('DEGREES','-Abz-');

1. The "Chi-square distribution with n degrees of freedom" is therefore the distribution of the sum of n independent squared r.v.
2. 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).
3. The degrees of freedom is equal to the sum of the individual degrees of freedom for each sample. (Web site)

### Mean SquaresUpDw('MEAN_SQUARES','-Abz-');

1. 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. (Web site)

### DimensionsUpDw('DIMENSIONS','-Abz-');

1. 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. (Web site)
2. 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.
3. The dimension of the space is the sum of the dimensions of the two subspaces, minus the dimension of their intersection. (Web site)

### EigenspacesUpDw('EIGENSPACES','-Abz-');

1. For a square matrix A of order n to be diagonalizable, the sum of the dimensions of the eigenspaces must be equal to n.

### FigUpDw('FIG','-Abz-');

1. 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.
2. Thus the sum of z 1 and z 2 corresponds to the diagonal OB of the parallelogram shown in Fig.

### FacesUpDw('FACES','-Abz-');

1. The following formulae can be used to find the probability of rolling a sum S using N dice of M faces. (Web site)
2. The surface area of any prism equals the sum of the areas of its faces, which include the floor, roof and walls.

### CategoryUpDw('CATEGORY','-Abz-');

1. In an abelian category, for example the category of abelian groups or a category of modules, the direct sum is the categorical coproduct.
2. 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.
3. Semisimple means that each object in the category is (isomorphic to) the direct sum of (finitely many) simple objects.

### Free ProductUpDw('FREE_PRODUCT','-Abz-');

1. 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.
2. 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. (Web site)

### VerticesUpDw('VERTICES','-Abz-');

1. Given such a polyhedron, the sum of the vertices and the faces is always the number of edges plus two. (Web site)
2. 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. (Web site)
3. 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.

### Tensor BundleUpDw('TENSOR_BUNDLE','-Abz-');

1. 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.
2. The tensor bundle is the direct sum of all tensor product s of the tangent bundle and the cotangent bundle. (Web site)

### AtomUpDw('ATOM','-Abz-');

1. 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.
2. An atom or molecule has less mass (by a negligible but real amount) than the sum of the masses of its components taken separately. (Web site)
3. The formal charge of the atom, the sum of the charge of the proton and the charge of the electron, is zero. (Web site)

### Nuclear MassUpDw('NUCLEAR_MASS','-Abz-');

1. 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.

### SubmoduleUpDw('SUBMODULE','-Abz-');

1. Properties The direct sum is a submodule of the direct product of the modules M i.

### SummandUpDw('SUMMAND','-Abz-');

1. 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′.
2. 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. (Web site)

### Human KnowledgeUpDw('HUMAN_KNOWLEDGE','-Abz-');

1. 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.

### NucleusUpDw('NUCLEUS','-Abz-');

1. Nuclear - Binding energy The sum of the individual masses of various particle in the nucleus must be equal to the nuclear mass.
2. 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. (Web site)
3. 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. (Web site)

### Constituent ParticlesUpDw('CONSTITUENT_PARTICLES','-Abz-');

1. Mass Defect The difference in the mass of a nucleus and the sum of the masses of its constituent particles.
2. Composite particles, such as nuclei and atoms, are classified as bosons or fermions based on the sum of the spins of their constituent particles. (Web site)

### CosinesUpDw('COSINES','-Abz-');

1. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods.
2. Average the cosines: Find the cosines of the sum and difference angles using a cosine table and average them. (Web site)

### Absolute DeviationsUpDw('ABSOLUTE_DEVIATIONS','-Abz-');

1. 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.
2. Any point in the 4 to 7 region will have the same value of 22 for the sum of the absolute deviations.

### Arithmetic MeanUpDw('ARITHMETIC_MEAN','-Abz-');

1. Mean(arithmetic mean or average) is the sum of the data in a frequency distribution divided by the number of data elements. (Web site)
2. 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.
3. Mean: More accurately called the arithmetic mean, it is defined as the sum of scores divided by the number of scores.

### ReciprocalsUpDw('RECIPROCALS','-Abz-');

1. Different examples include maximising the distance to the nearest point, or using electrons to maximise the sum of all reciprocals of squares of distances.
2. 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. (Web site)
3. 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 → ∞.

### Periodic FunctionUpDw('PERIODIC_FUNCTION','-Abz-');

1. A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. (Web site)
2. 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. (Web site)

### Fourier SeriesUpDw('FOURIER_SERIES','-Abz-');

1. In mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions, namely sines and cosines.
2. In the study of Fourier series, complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines.
3. The spectral method, which represents functions as a sum of particular basis functions, for example using a Fourier series.

### VertexUpDw('VERTEX','-Abz-');

1. 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. (Web site)
2. 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. (Web site)
3. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees.

### Four SquaresUpDw('FOUR_SQUARES','-Abz-');

1. 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.
2. In 1770, Lagrange showed that every positive integer could be written as the sum of at most four squares. (Web site)
3. For instance, it was proven by Lagrange that every positive integer is the sum of four squares.

### SumsUpDw('SUMS','-Abz-');

1. 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.
2. A double sum is often the product of two sums, which may be Fourier series. (Web site)
3. Direct sums are also commutative and associative (up to isomorphism), meaning that it doesn't matter in which order one forms the direct sum. (Web site)

### ResidualsUpDw('RESIDUALS','-Abz-');

1. 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.
2. Linear regression fits a line to a scatterplot in such a way as to minimize the sum of the squares of the residuals. (Web site)
3. In statistics, the residual sum of squares (RSS) is the sum of squares of residuals. (Web site)

### MatrixUpDw('MATRIX','-Abz-');

1. A square matrix is diagonalizable if the sum of the dimensions of the eigenspaces is the number of rows or columns of the matrix. (Web site)
2. The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix. (Web site)
3. As the trace of a matrix is equal to the sum of its eigenvalues, this implies that the estimated eigenvalues are biased.

### Diagonal ElementsUpDw('DIAGONAL_ELEMENTS','-Abz-');

1. The tr is the trace operator and represents the sum of the diagonal elements of the matrix. (Web site)
2. Dimension. Sum of diagonal elements.
3. Note that the sum of the diagonal elements is conserved; this is the signature of the metric [ +2 ]. (Web site)

### LenderUpDw('LENDER','-Abz-');

1. 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. (Web site)
2. 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.
3. When the interest rate is reduced for a specified period of time by depositing a sum of money with the lender.

### Written PromiseUpDw('WRITTEN_PROMISE','-Abz-');

1. Mortgage Note: A written promise to pay a sum of money at a stated interest rate during a specified term. (Web site)

### Kinetic EnergyUpDw('KINETIC_ENERGY','-Abz-');

1. Energy of an Orbit The Total energy of an object in orbit is the sum of kinetic energy (KE) and gravitational potential energy (PE).
2. 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.
3. One term not listed among manifestations of energy is mechanical energy, which is something different altogether: the sum of potential and kinetic energy. (Web site)

### Kinetic EnergiesUpDw('KINETIC_ENERGIES','-Abz-');

1. The energy released is equal to the sum of the rest energies of the particles and their kinetic energies. (Web site)
2. For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles. (Web site)
3. In this model the atomic Hamiltonian is a sum of kinetic energies of the electrons and the spherical symmetric electron-nucleus interactions. (Web site)

### AnglesUpDw('ANGLES','-Abz-');

1. Related subjects: Mathematics On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). (Web site)
2. 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. (Web site)
3. Legendre proved that Euclid 's fifth postulate is equivalent to:- The sum of the angles of a triangle is equal to two right angles. (Web site)

### Interior AnglesUpDw('INTERIOR_ANGLES','-Abz-');

1. The sum of interior angles of a geodesic triangle is equal to π plus the total curvature enclosed by the triangle.
2. 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. (Web site)
3. The sum of the interior angles must be 180 degrees, as with all triangles. (Web site)

### Sample VarianceUpDw('SAMPLE_VARIANCE','-Abz-');

1. Each coordinate in the sum of squares is inverse weighted by the sample variance of that coordinate. (Web site)

### CategoriesUpDw('Categories','-Abz-');

1. Equal
2. Information > Science > Mathematics > Zero
3. Mathematics > Algebra > Linear Algebra > Vectors
4. Masses
5. Condorcet

### Related Keywords

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1. Books about "Sum" in Amazon.com  Short phrases about "Sum"   Originally created: April 04, 2011.   Links checked: June 04, 2013.   Please send us comments and questions by this Online Form   Please click on to move good phrases up.
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