Abstract: The main sources of error in chromatographic analysis are described, particular attention being drawn to variable bias. This is one of the major potential sources as it is not easily detected. A comparison is made between the charateristics of the three basic methods of calculating results, normalization, constant volume injection, and internal standard. Despite its popularity normalization has many disadvantages and the presentation of results as ratios of compounds to one another is suggested in preference to normalization.

Abstract: The problem of normalization of Bethe-Salpeter wave functions has been discussed by several authors. Mandelstam put forward a theory of normalization which is valid only for charged bound states.1 Allcock removed this restriction and proved that the normalization of Bethe-Salpeter wave function by Mandelstam holds even for neutral bound states.2 Recently the interest in the problem of bound states revived since experimentally observed particles are unlikely to be all elementary. A theory of normalization of Bethe-Salpeter wave functions was proposed recently by several authors, for instance, Cutkosky and Leon,3 Nakanishi4 and others. However, Allcock’s work is rather complicated, whereas the Cutkosky and Leon paper is too short and compact to be understood.

Abstract: A technique is described for removing certain errors in two-port parameters obtained from transmission measurements. The calibration procedures and necessary transformations for error removal are presented. Included is a general transformation for changing S-parameter impedance normalization.

Abstract: Curves giving (S/N)R, the required input (S/N), for a specified detection probability versus probability of noise marking are commonly used for describing processor performance. These curves are commonly produced by assuming stationary background noise. However, backgrounds are generally nonstationary, so that normalization techniques are utilized to produce a more stationary processor‐output waveform. In order to predict the effects of various normalization techniques on sonar performance, a model has been developed that defines ideal normalization and gives a method for describing the effects of normalization in terms of (S/N)R for fixed clutter probability. This method involves measurement of degradation in (S/N)R due to nonideal normalization. The results are given in the form of two curves and an average degradation over the display. One curve gives a plot of Δ(S/N)R as a function of time where Δ(S/N)R is the increase in (S/N)R due to nonideal normalization relative to (S/N)R required with ideal norm...

Abstract: A technique is used which “normalizes” the standard deviation of student test scores so that the explicit weights assigned to different questions and tests by the instructor are in fact reflected in the students9 total scores. It is then shown, using actual classroom data, that this normalization can be important in determining a student’s final grade: 10 to 20 percent of the students received grade changes as a result of normalization. Using a randomization test it is further found that these changes are not related to attributes of the students. A multiple regression analysis on selected student attributes-GPA, class, and major-also supports the same conclusion. Finally, evidence is presented which suggests that the grade changes due to normalization are systematically related to the method of grading a question. It is concluded that lack of normalization results in a significant distortion of student grades.

Abstract: : This is a complete documentation (program description) of a computer package for analyzing finite time stability properties of equilibrium points of time-independent Hamiltonian systems. Using this package, approximate analytic solutions which contain nonlinear effects can be constructed near these equilibrium points. Three main programs constitute the complete package. The first program normalizes and computes the generating functions for a time-independent Hamiltonian in the neighborhood of an equilibrium point, the second expresses coordinate transformations as truncated power series, and the third program computes point-by-point coordinate transformations. To demonstrate the procedure, the report describes in detail the application of the computer package to the construction of solutions of the planar restricted three-body problem near the L4 equilibrium point. Numerical results compare very favorably in precision with values obtained by numerical integration. The computer time required for the entire normalization process is only a small fraction of the integration time, however. (Author)

Abstract: A simple inequality, expressed in terms of two arbitrary distribution functions of the same normalization, is shown to be useful. By choosing various different forms for the distribution functions one can derive important results, such as the upper and lower bounds of the configurational free energy.

Abstract: ƒ = k[xi9 • • • , #» , %n+i, • • • » #iv] = £[-X\"i, • • • , XivJ/O, where Q = (gi, • • • , q8) is a, finitely generated ideal. The classical solution is nonconstructive in a typical way. One exhibits J a s a submodule of a finite .R-module and then invokes the Hubert Basis Theorem, first to assert that 7 is a finite i?-module, and again to assert that O is finitely generated. But the Basis Theorem is, at best, a guarantee that no particular J or O will ever require infinitely many generators. It does not help us to decide whether generators for I and O can actually be constructed or, if they can, how to construct them, how many are needed, and how they depend on the initial data $ = (£i, • • , pr)* In this note we will describe a method that treats these questions —in the case that k(xi, • • • , xn) is separably generated over k. This restriction and also the requirement that k be a field reflect the limitations of our technique. Also, k must be defined in such a way that the polynomial ring k[T] is constructively a unique factorization domain (or else the class of prime ideals $ = (pi, • • • , pr) would have to be restricted). A fairly general description of such fields is given in [2], following Kronecker's method of interpolation. Any finitely generated extension of a prime field, or even the algebraic closure of such a field, is allowed. But not the reals nor the complexes nor any £-adic field. The same methods apply in the projective case, yielding a constructive version of projectively normal normalization and the completeness of the linear system of hypersurface sections of a fixed high degree on a normal projective variety.