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Given a differential equation of the form ( for example, when F has zero slope in the x and y direction at F ( x, y ) ):
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Given and differential
Given the particular differential operators involved, this is a linear partial differential equation.
Given a linear differential operator T
Given a collection of differential 1-forms α < sub > i </ sub >, i = 1, 2, ..., k on an n-dimensional manifold M, an integral manifold is a submanifold whose tangent space at every point p ∈ M is annihilated by each α < sub > i </ sub >.
Given an ordinary non-homogeneous linear differential equation of order n
Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere holomorphic ; on an algebraic variety V that is non-singular it would be a global section of the coherent sheaf Ω < sup > 1 </ sup > of Kähler differentials.
Given some x ∈ M, the differential of φ at x is a linear map
Given the significant terracing of the building's Sparks Street façade above the fourth floor and the grade differential between Queen Street and Sparks Street, the building is 12 storeys on Queen Street, but appears to be only four storeys in height from ground level on Sparks Street.
Given a system of differential equations,
Given a simply connected and open subset D of R < sup > 2 </ sup > and two functions I and J which are continuous on D then an implicit first-order ordinary differential equation of the form
Given an exact differential equation defined on some simply connected and open subset D of R < sup > 2 </ sup > with potential function F then a differentiable function f with ( x, f ( x )) in D is a solution if and only if there exists real number c so that
Given and equation
Given r, the rate of rotation is easy to infer from the constant angular momentum L, so a 2D solution can be easily reconstructed from a 1D solution of this equation.
Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.
Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age ( i. e. BA ), leads to the equation 19B-8A
Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education.
Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.
The functional equation was established by Riemann in his 1859 paper On the Number of Primes Less Than a Given Magnitude and used to construct the analytic continuation in the first place.
Given samples from a population, the equation for the sample skewness above is a biased estimator of the population skewness.
Given the factorization in terms of these matrices, one can now write down immediately an equation
Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.
Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.
Given the equation
Given the quartic equation
Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.
Given the initial velocity of a particle launched from the ground, the downward ( i. e. gravitational ) acceleration, and the projectile's angle of projection θ ( measured relative to the horizontal ), then a simple rearrangement of the SUVAT equation
Given the integral representation of a principal branch of γ, the following equation holds for all positive real s, x:
Given a polynomial equation with rational coefficients, if it has rational solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics: a global solution yields local solutions at each prime.
Given the complex macro-rheological behavior of blood, it is not surprising that a single equation fails to completely describe the effects of various rheological variables ( e. g., hematocrit, shear rate ).
Given four circles with curvatures k < sub > i </ sub > and centers z < sub > i </ sub > ( for i = 1 ... 4 ), the following equality holds in addition to equation ( 1 ):
Given a Hi of 0. 40, if the H_m is assumed to be 0. 25. then from the equation above RCM count is still high and ANH is not necessary, if BLs does not exceed 2303mL, since the hemotocrit will not fall below H_m.
Given this equation of state, Navier – Stokes and the continuity equation are invariant under the transformations
Given the equation A x = 0 attempt to solve it using
Given and form
* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.
* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.
Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).
Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.
Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.
Given a finite dimensional real quadratic space with quadratic form, the geometric algebra for this quadratic space is the Clifford algebra Cℓ ( V, Q ).
Given a set of training examples of the form, a learning algorithm seeks a function, where is the input space and
Given a vector space V and a quadratic form g an explicit matrix representation of the Clifford algebra can be defined as follows.
Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement.
Given " mappings " of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of " rules ", each of the form:
Given that any proposition containing conjunction, disjunction, and negation can be equivalently rephrased using conjunction and negation alone ( the conjunctive normal form ), we can now handle any compound proposition.
Given any topological space X, the zero sets form the base for the closed sets of some topology on X.
Given the distance from the main body, our problem is to determine the form of the surface that satisfies the equipotential condition.
Given a ring R and a unit u in R, the map ƒ ( x ) = u < sup >− 1 </ sup > xu is a ring automorphism of R. The ring automorphisms of this form are called inner automorphisms of R. They form a normal subgroup of the automorphism group of R.
Given some training data, a set of n points of the form
Given these considerations, graphologists proceed to evaluate the pattern, form, movement, rhythm, quality, and consistency of the graphic stroke in terms of psychological interpretations.
Given that male authors had limited knowledge of her rites and attributes, ancient speculations about her identity abound, among them that she was an aspect of Terra, Ops, the Magna Mater, or Ceres, or a Latin form of Damia.
The word Datta means " Given ", Datta is called so because the divine trinity have " given " themselves in the form of a son to the sage couple Atri and Anasuya.
Given ω = ( xθ, yθ, zθ ), with v = ( x, y, z ) a unit vector, the correct skew-symmetric matrix form of ω is
Given the theoretical ' fog ' around this issue, in practice most industry practitioners rely on some form of proxy for the risk free rate, or use other forms of benchmark rate which are presupposed to incorporate the risk free rate plus some risk of default.
Given that power is not innate and can be granted to others, to acquire power you must possess or control a form of power currency.
Given a transfer function in the form
Given a transfer function in the same form as above:
Given a Hermitian form Ψ on a complex vector space V, the unitary group U ( Ψ ) is the group of transforms that preserve the form: the transform M such that Ψ ( Mv, Mw ) = Ψ ( v, w ) for all v, w ∈ V. In terms of matrices, representing the form by a matrix denoted, this says that.
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