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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.
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Mathematically and each
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, if each question is structured to eliminate half the objects, 20 questions will allow the questioner to distinguish between 2 < sup > 20 </ sup > or 1, 048, 576 objects.
Mathematically, the state of each two-electron composite system can be described by the state vector
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, nominal numbering is a one-to-one function from a set of objects being named to the set of numerals: it is a function because each object is assigned a numeral, and it is one-to-one because different objects are assigned different numerals.
Mathematically, there are exactly q < sup > m </ sup > possible messages of length m, and each such message can be regarded as a vector of length m. The encoding scheme converts an m-dimensional vector into an n-dimensional vector.
Mathematically, a STRIPS instance is a quadruple, in which each component has the following meaning:
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, 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, 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 physical
Mathematically, the factor of two relating physical angles to their counterparts in Stokes space derives from the use of second-order moments and correlations, and incorporates the loss of information due to absolute phase invariance.
Mathematically, a Yang – Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.
Mathematically speaking, the simplification reduces the state space of the system to a finite number, and the partial differential equations ( PDEs ) of the continuous ( infinite-dimensional ) time and space model of the physical system into ordinary differential equations ( ODEs ) with a finite number of parameters.
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, this is represented as a ' hopping integral ' or ' transfer integral ' between neighboring atoms, which can be viewed as the physical principle that creates electron bands in crystalline materials, due to overlapping between atomic orbitals.
Mathematically and law
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 total electromagnetic energy density ( radiation energy density ) in thermodynamic equilibrium from Planck's law is
Mathematically this law is now written:
Mathematically, Hooke's law states that
Mathematically, Gauss's law takes the form of an integral equation:
Mathematically, the probability of finding a particle at depth x into the material is calculated by Beer-Lambert law:
Mathematically, the law is stated:
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 can
Mathematically, this can be represented for n species as:
Mathematically the 0-1-knapsack problem can be formulated as:
Mathematically the bounded knapsack problem can be formulated as:
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 modulated wave can be written in the form:
Mathematically ( using the Laplace transform ) the impedance of this network can be written as:
Mathematically, the E field can be thought of as a function that associates a vector with every point in space.
Mathematically, convection can be described by the convection – diffusion equation or the generic scalar transport equation.
Mathematically, the pressure of a mixture of gases can be defined as the summation
Mathematically corrected punch motions can be programmed to simulate any type and model of production tablet press.
Mathematically, this can be expressed by means of the signal to noise ratio ( SNR or S / N ).
Mathematically speaking, there are seventeen basic patterns, described as wallpaper groups, that can be used to tile an infinite plane.
Mathematically, evanescent waves can be characterized by a wave vector where one or more of the vector's components has an imaginary value.
Mathematically, the maximum lift-to-drag ratio can be estimated as:
Mathematically, this can be written as:
Mathematically the problem can be stated like this:
Mathematically, the criterion for whether spontaneous fission can occur in a time short enough to be observed by present methods, is approximately:
Mathematically, we can represent this constraint in terms of a surface integral:
Mathematically, a vector x in an n-dimensional Euclidean space can be defined as an ordered list of n real numbers ( the Cartesian coordinates of P ): x = x < sub > 2 </ sub >, ..., x < sub > n </ sub >.
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, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus.
Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.
Mathematically, a basic parametric mixture model can be described as follows:
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