Quasi-definiteness

D. Kazhdan, Arithmetic varieties and their fields of quasi-definition, (Actes du Cong. Int., Nice, Vol. 2). 

Theorem 6. Suppose the strategy space of the game is convex and all equilibria are interior. Then if the determinant H is negative quasi-definite (i.e., if the matrix H + is negative definite) on the players strategy set, there is a unique NE. 

An experimental teclmique that is usefiil for structure studies of biological macromolecules and other crystals with large unit cells uses neither the broad, white , spectrum characteristic of Lane methods nor a sharp, monocliromatic spectrum, but rather a spectral band with AX/X 20%. Because of its relation to the Lane method, this teclmique is called quasi-Laue. It was believed for many years diat the Lane method was not usefiil for structure studies because reflections of different orders would be superposed on the same point of a film or an image plate. It was realized recently, however, that, if there is a definite minimum wavelengdi in the spectral band, more than 80% of all reflections would contain only a single order. Quasi-Laue methods are now used with both neutrons and x-rays, particularly x-rays from synclirotron sources, which give an intense, white spectrum. 

The term quasi-isotropic iaminate is used to describe laminates that have isotropic extensionai stiffnesses (the same in all directions in the plane of the laminate). As background to the definition, recall that the term isotropy is a material property whereas laminate stiffnesses are a function of both material properties and geometry. Note also that the prefix quasi means in a sense or manner. Thus, a quasi-isotropic laminate must mean a laminate that, in some sense, appears isotropic, but is not actually isotropic in all senses. In this case, a quasi-isotropic... 

The respiratory quotient (RQ) is often used to estimate metabolic stoichiometry. Using quasi-steady-state and by definition of RQ, develop a system of two linear equations with two unknowns by solving a matrix under the following conditions the coefficient of the matrix with yeast growth (y = 4.14), ammonia (yN = 0) and glucose (ys = 4.0), where the evolution of C02 and biosynthesis are very small (o- = 0.095). Calculate the stoichiometric coefficient for RQ =1.0 for the above biological processes ... 

According to Vitanov et a/.,61,151 C,- varies in the order Ag(100) < Ag(lll), i.e., in the reverse order with respect to that of Valette and Hamelin.24 63 67 150 383-390 The order of electrolytically grown planes clashes with the results of quantum-chemical calculations,436 439 as well as with the results of the jellium/hard sphere model for the metal/electro-lyte interface.428 429 435 A comparison of C, values for quasi-perfect Ag planes with the data of real Ag planes shows that for quasi-perfect Ag planes, the values of Cf 0 are remarkably higher than those for real Ag planes. A definite difference between real and quasi-perfect Ag electrodes may be the higher number of defects expected for a real Ag crystal. 15 32 i25 401407 10-416-422 since the defects seem to be the sites of stronger adsorption, one would expect that quasi-perfect surfaces would have a smaller surface activity toward H20 molecules and so lower Cf"0 values. The influence of the surface defects on H20 adsorption at Ag from a gas phase has been demonstrated by Klaua and Madey.445... 

The importance of Equation (2.294) is that it establishes a relationship between the height anomaly, N, and the disturbing potential T at the same point of the earth. By definition, we have for the normal height h of the point A over a quasi-geoid... 

Time is a fundamental property of the physical world. Because time encompasses the antinomic qualities of transience and duration, the definition of time poses a dilemma for the formulation of a comprehensive physical theory. The partial elimination of time is a common solution to this dilemma. In his mechanical philosophy, Newton appears to resort to the elimination of the transient quality of time by identifying time with duration. It is suggested, however, that the transient quality of time may be identified as the active component of the Newtonian concept of inertia, a quasi occult quality of matter that is correlated with change, and that is essential to defining duration. The assignment of the transient quality of time to matter is a necessary consequence of Newton s attempt to render a world system of divine mathematical order. Newton s interest in alchemy reflects this view that matter is active and mutable in nature... 

The statistical fundamentals of the definition of CV and LD are illustrated by Fig. 7.8 showing a quasi-three-dimensional representation of the relationship between measured values and analytical values which is characterized by a calibration straight line y = a + bx and their two-sided confidence limits and, in addition (in z-direction) the probability density function the measured values. 

Procedures that compute a search direction using only first derivatives of/provide an attractive alternative to Newton s method. The most popular of these are the quasi-Newton methods that replace H(x ) in Equation (6.11) by a positive-definite approximation W ... 

Both difficulties are eliminated by replacing V L by a positive-definite quasi-Newton (QN) approximation B, which is updated using only values of L and V L (See Section 6.4 for a discussion of QN updates.) Most SQP algorithms use Powell s modification (see Nash and Sofer, 1996) of the BFGS update. Hence the QP subproblem becomes... 

Finally, we attack the problem of the transport coefficients, which, by definition, are calculated in the stationary or quasi-stationary state. The variation of the distribution functions during the time rc is consequently rigorously nil, which allows us to calculate these coefficients from more simple quantities than the generalized Boltzmann operators which we call asymptotic cross-sections or transport operators. 

Liquid chromatography (LC) and, in particular, high performance liquid chromatography (HPLC), is at present the most popular and widely used separation procedure based on a quasi-equilibrium -type of molecular distribution between two phases. Officially, LC is defined as a physical method... in which the components to be separated are distributed between two phases, one of which is stationary (stationary phase) while the other (the mobile phase) moves in a definite direction [ 1 ]. In other words, all chromatographic methods have one thing in common and that is the dynamic separation of a substance mixture in a flow system. Since the interphase molecular distribution of the respective substances is the main condition of the separation layer functionality in this method, chromatography can be considered as an excellent model of other methods based on similar distributions and carried out at dynamic conditions. 

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