The standard NF T 65-001 gives a classification for bitumen as a function of their hardness. This is measured using a needle penetrability test, which measures the penetration depth of a weighted needle into the bitumen. Five grades have been defined. [Pg.287]

The linear integral equation (5) is solved by a standard technique, including expansion of the unknown An z) by some basis functions and transformation of (5) into a matrix equation to [Pg.128]

At first, in order to use some standard results from the theory of the Radon transform, we restrict the analysis to 2-D tensor fields whose elements belong to either the space of rapidly decreasing C° functions or the space of compactly supported C°° functions. Thus, some of the detailed issues associated with the boundary conditions are avoided. [Pg.132]

Finally, each coefficient were standardized by the division of the sum of all coefficients(2). This definition allows also to regard as the co-occurrence matrix as a function of probability distribution, it can be represented by an image of KxK dimensions. [Pg.232]

The program uses all the standard controls in Windows programs. In addition, the use of an extensive number of shortcuts and function keys makes it possible to control the system without the use of a mouse, which is convenient for operating the system in the field. [Pg.786]

Helgaker T, Gauss J, J0rgensen P and Olsen J 1997 The prediction of molecular equilibrium structures by the standard electronic wave functions J. Chem. Phys. 106 6430-40 [Pg.2201]

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. [Pg.251]

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