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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.
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Mathematically and sequence
Mathematically, a sequence of estimators
Mathematically, a sequence in NRZ code can be described as a sequence of unit pulses or shifted rect functions, each pulse being weighted by + 1 if the bit is " 1 " and by 0 if the bit is " 0 ".
Mathematically, the Mandelbrot set consists of the set of points c in the complex plane for which the iteratively defined sequence
Mathematically and is
Mathematically it is defined as follows:
Mathematically, the motion of a continuum using the Eulerian description is expressed by the mapping function
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, density is defined as mass divided by volume:
Mathematically this is described as the convolution of a time-varying input signal x ( t ) with the filter's impulse response h, defined as:
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, this is expressed by saying that the curl of the flow field is everywhere equal to zero.
Mathematically, the logistic map is written
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 total electromagnetic energy density ( radiation energy density ) in thermodynamic equilibrium from Planck's law is
Mathematically, the light received from stars as a function of star distance in a hypothetical fractal cosmos is:
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, QED is an abelian gauge theory with the symmetry group U ( 1 ).
Mathematically, this tunneling current is given by
Mathematically, QCD is a non-Abelian gauge theory based on a local ( gauge ) symmetry group called SU ( 3 ).
Mathematically and example
Mathematically, two Luenberger observers can be used, if is properly selected, using, for example, positive systems properties: one for the upper bound ( that ensures that converges to zero from above when, in the absence of noise and uncertainty ), and a lower bound ( that ensures that converges to zero from below ).
Mathematically, homogeneity has the connotation of invariance, as all components of the equation have the same degree of value whether or not each of these components are scaled to different values, for example, by multiplication or addition.
Mathematically and process
Mathematically, the process is the same as that of quantum tunneling, except with electromagnetic waves instead of quantum-mechanical wavefunctions.
Mathematically speaking it is an Iteration | Iterative process.
Mathematically, the process of constructing a flownet consists of contouring the two harmonic or analytic functions of potential and stream function.
Mathematically and its
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, the wavelet will resonate if the unknown signal contains information of similar frequency – just as a tuning fork physically resonates with sound waves of its specific tuning frequency.
Mathematically, the rate of change of X ( its derivative with respect to time ) vanishes,
Mathematically, an object approaches its terminal velocity asymptotically.
Mathematically, the extremely wideband excitation provided by the spark gap was bandpass filtered by the self-oscillating antenna side circuit, which because of its simple construction, also had a relatively broad and badly controlled filter characteristic.
Mathematically, the carbonate anion concentration is counted twice due to its ability to neutralize two protons, while bicarbonate is counted once as it can neutralize one proton.
Mathematically, the Ricci decomposition is the decomposition of the space of all tensors having the symmetries of the Riemann tensor into its irreducible representations for the action of the orthogonal group.
Mathematically, each cell can be modeled as a dissipative, nonlinear dynamical system where information is encoded via its initial state, inputs, and variables used to define its behavior.
Mathematically, the relationship between a cell and its neighbors, located within an area of influence, can be defined by a coupling law, and this is what primarily determines the behavior of the processor.
Mathematically and entropy
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmann's constant k < sub > B </ sub >.
Mathematically and given
Mathematically, the restoring force F is given by
Mathematically, the equation may be rearranged to compute torque for a given power output.
Mathematically, Bayes ' theorem gives the relationship between the probabilities of and, and, and the conditional probabilities of given and given, and.
Mathematically, terminal velocity — without considering buoyancy effects — is given by
Mathematically, the Levenshtein distance between two strings is given by where
Mathematically, the gradient of a two-variable function ( here the image intensity function ) is at each image point, a 2D vector with the components given by the derivatives in the horizontal and vertical directions.
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, the axiom states that the probability of selecting item i from a pool of j items is given by:
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 stated, given two different prefixes p1, p2, the attack finds two appendages m1 and m2 such that hash ( p1 ∥ m1 ) = hash ( p2 ∥ m2 ) ( where ∥ is the concatenation operation ).
Mathematically, each physical law can be expressed with respect to the coordinates given by an inertial frame of reference by a mathematical equation ( for instance, a differential equation ) which relates the various coordinates of the various objects in the spacetime.
Mathematically, the gradient of a two-variable function ( here the image intensity function ) is at each image point a 2D vector with the components given by the derivatives in the horizontal and vertical directions.
Mathematically, spacetime is represented by a 4-dimensional differentiable manifold M and the metric is given as a covariant, second-rank, symmetric tensor on M, conventionally denoted by g. Moreover the metric is required to be nondegenerate with signature (< tt >-+++</ tt >).
Mathematically, the URR is closely related to Kt / V, and the two quantities can be derived from another with more or less precision, depending on the amount of additional information available about a given dialysis session.
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