Generic vector

Given a generic vector of values = [Xf,...,x, ...,Xi Yei, what are reasonable estimates for the conditional probabilities (7b)... 

A vector is defined by length and direction. The length F of a generic vector V is given by its modulus ... 

A homogenous document type, stored in a standard graphical file format. Includes scanned paper documents. Many file formats exist, from raw bit-mapped pictures to highly complex vectored drawings in a CAD environment. Simplest file formats are bit-mapped formats (e.g., TIFF, PCX, GIF, JPEG) or generic vectored formats (e.g., WMF, CGM, DXF). Many proprietary formats exist. Some CAD formats include product database information. 

The algorithm can be implemented as described in Buzzi-Ferraris and Manenti (2010a) and requires only an efficient product of the matrix A and a generic vector to be performed. 

Xpp a generic pointwise decision policy, i.e., a vector whose components are values of decision variables,... 

Xqp a generic interval vector decision policy, whose components are ranges of decision variables... 

Table II shows the dimensions of the block-diagonal matrices of Y p= Ap[y]p — C, the dimension m of the variable vector y, and the number of equality constraints s in Eq. (4) relative to the number r of spin orbitals of a generic reference basis [15].

The value of the drift coefficients required by each type of SDE may be obtained by comparing the value of the drift velocity generated by the SDE to that required by statistical mechanics. The desired drift velocity vector for a system of coordinates X, ..., X may be expressed in generic form as a sum... 

Derivatives of the determinants S and f of the generic projected tensors Sah and Tij defined in Eqs. (2.20) and (2.24) may be expressed compactly in terms of the reciprocal vectors that are generated by applying Eqs. (2.207) and (2.208) to the corresponding Cartesian tensors S v and respectively. Using Eq. (A.14) to differentiate In 5 with respect to a soft variable gives... 

Spectrum or Spectra To simplify the discussions, the term spectrum or spectra is used in this book as a generic term to refer to a collection of measurements on a sample (i.e., a measurement vector). The reader should not infer from the use of this term that the methods can only be applied to spectroscopic data. (5ee also Measurement Vector.)... 

Generically, a G-invariant ansatz has the form (11), where v = h. However, provided the infinitesimal operators of the group G are of the form (17), G-invariant ansatz for the vector held u can be represented in the linear form [33]... 

By contrast, any n-dimensional vector space has a generic way, by means of a basis set, to be mapped onto 72 , such that the basic operations becomes simply the corresponding element-by-element scalar operations on the arrays. Furthermore, the basis set can always be choosen such that the scalar product assumes the standard form... 

A useful tool for stability calculations is the tangent plane distance [20], Let us first define this generically for a system with (a vector of) densities p, free energy density/(p) and chemical potentials p(p) = V/(p) this... 

Fig. 1.5. Two magnetic bars, and anchored at generic points A and B at distance r in a magnetic field Bo. y is the angle between the magnetic field and the AB vector.

Fig. 2.6. A molecule possessing magnetic anisotropy, with the z axis oriented along a generic y direction, a is the angle of the z axis with the external field direction k d is the angle between the metal-nucleus vector r and the z-axis y is the angle between the metal-nucleus vector and the external field 2 defines the position of r on the surface of the cone about X.

It is also possible to consider the holonomy of the generic A in the vacuum. This is a round trip or closed loop in Minkowski spacetime. The general vector A is transported from point A, where it is denoted Aa 0 around a closed loop with covariant derivatives back to the point Aa () in the vacuum. The result [46] is the field tensor for any gauge group... 

The total Lagrangian X = JS G + JS D + JS , then involves the interaction between fermions and the gauge field. The Dirac field will be generically considered to be the electron and the gauge theory will be considered to be the non-Abelian electromagnetic field. The theory then describes the interaction between electrons and photons. A gauge theory involves the conveyance of momentum form one particle (electron) to another by the virtual creation and destruction of a vector boson (photon) that couples to the two electrons. The process can be diagrammatically represented as... 

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