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Mathematically, this means the coefficient for the projection of onto.
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Mathematically and means
Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i. e. the real part of all the poles are less than zero.
Mathematically this means that the Fresnel reflection coefficient becomes a complex rather than a real number.
Mathematically, this means that the size of the phase velocity changes.
Mathematically, this can be expressed by means of the signal to noise ratio ( SNR or S / N ).
r is the coefficient to represent x using D. Mathematically, sparse dictionary learning means the following
Mathematically, the solution to these limitations happens through an alternative calculation of QALYs by means of operations with complex numbers rooted in the well known Pythagorean theorem.
Mathematically, this means that they are asymptotically locally Euclidean ( or perhaps asymptotically locally flat ) hyperkähler 4-manifolds, and in this sense, they are special examples of Einstein manifolds.
Mathematically and coefficient
Mathematically, it is defined using the reflection coefficient.
Mathematically and for
Mathematically, the conjecture states that, for generic initial data, the maximal Cauchy development possesses a complete future null infinity.
Mathematically, this can be represented for n species as:
Mathematically, for rotation about a fixed axis through the center of mass,
Mathematically, the equation may be rearranged to compute torque for a given power output.
Mathematically speaking, however, there seems to be no reason for us to reject the negative-energy solutions.
Mathematically, the D4σ beam width in the x-dimension for the beam profile is expressed as
Mathematically, the LM curve is defined by the equation, where the supply of money is represented as the real amount M / P ( as opposed to the nominal amount M ), with P representing the price level, and L being the real demand for money, which is some function of the interest rate i and the level Y of real income.
Mathematically, this condition is also approached exponentially ; in theory it takes infinite time, but in practice it is over, for all intents and purposes, in a much shorter period.
Mathematically talented, Lamarr also co-invented — with composer George Antheil — an early technique for spread spectrum communications and frequency hopping, necessary for wireless communication from the pre-computer age to the present day.
Mathematically, the criterion for whether spontaneous fission can occur in a time short enough to be observed by present methods, is approximately:
The fundamental requirement for incompressible flow is that the density,, is constant within an infinitesimal volume, dV, which moves at the velocity of the fluid, v. Mathematically, this constraint implies that the material derivative ( discussed below ) of the density must vanish to ensure incompressible flow.
Mathematically, the operator uses two 3 × 3 kernels which are convolved with the original image to calculate approximations of the derivatives-one for horizontal changes, and one for vertical.
If a curve γ represents the path of a particle then the instantaneous velocity of the particle at a given point P is expressed by a vector, called the tangent vector to the curve at P. Mathematically, given a parametrized C < sup > 1 </ sup > curve γ = γ ( t ), for every value t
Mathematically, we can describe the reciprocal lattice as the set of all vectors K that satisfy the above identity for all lattice point position vectors R. This reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice, which reveals the Pontryagin duality of their respective vector spaces.
Mathematically, apart from discretization ( whole euros both for income and for tax ), the tax is a continuous, convex, piecewise linear function of income.
Mathematically speaking, two quantum states and are separated by a selection rule if for any given Hamiltonian, while they are separated by a superselection rule if for all physical observables.
Mathematically, the iterated logarithm is well-defined not only for base 2 and base e, but for any base greater than.
Mathematically, it would be said that the forward / backward algorithm computes for < math > 0 < k < t </ math >.
Mathematically and projection
Mathematically, the parallel projection of the point on the-plane gives.
Mathematically, the difference between artificial perspective projection ( perspective projection onto a flat surface ) and natural perspective projection ( perspective projection onto a spherical surface ) is a distortion resulting from the small-angle approximation which results from projecting onto a flat surface.
Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: left is negative, right is positive.
Mathematically, the first vector is the orthogonal, or least-squares, projection of the data vector onto the subspace spanned by the vector of 1's.
Mathematically and onto
Mathematically, there is an exact one-to-one mapping of impenetrable bosons ( in a one-dimensional system ) onto a system of fermions that do not interact at all.
Mathematically and .
Mathematically, we shall not distinguish the experiment of three dice tossed once from that of one die tossed three times.
Mathematically, the catenary curve is the graph of the hyperbolic cosine function.
Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular Lorentzian manifold.
Mathematically speaking, magnetic fields and electric fields are convertible with relative motion as a 2nd-order tensor or bivector.
In 1827, the German scientist Georg Ohm expressed his law in this famous book " Die galvanische Kette, mathematisch bearbeitet " ( The Galvanic Circuit Investigated Mathematically ) in which he gave his complete theory of electricity.
Mathematically, the unification is accomplished under an SU ( 2 ) × U ( 1 ) gauge group.
Mathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, i. e.,
Mathematically, this is because in reversible processes, the change in entropy of the cold reservoir is the negative of that of the hot reservoir ( i. e., ), keeping the overall change of entropy zero.
Mathematically, this says that the state vector is confined to one of the two eigenspaces of P, and is not allowed to range over the entire Hilbert space.
Mathematically, a sequence of coin flips ( fair or not ) is an example of a Bernoulli process, and its entropy is given by the binary entropy function.
Mathematically, this is expressed by saying that the curl of the flow field is everywhere equal to zero.
Mathematically, the potential of the ion cores can be treated by various models, the simplest being the nearly free electron model.
Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time by the square root of ; or by keeping time a real quantity and embedding the vectors in a Minkowski space.
Mathematically, a neuron's network function is defined as a composition of other functions, which can further be defined as a composition of other functions.
Mathematically, the formula above entails that all incomes are at least the lower bound x < sub > m </ sub >, which is positive.
Mathematically, this correspondendence is supported by the second term, on the r. h. s.
Mathematically, quasicrystals have been shown to be derivable from a general method, which treats them as projections of a higher-dimensional lattice.
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