Katz's Theory Research Articles

Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of W3 Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one n-th level semi-degenerate field and a fully-degenerate one in the fundamental sl3 representation are associated to Fuchsian rigid systems. We show how to apply Katz theory to determine the explicit form of the differential equations, the integral expression of solutions and the monodromy group representation. The theory of twisted homology is also used in the analysis of the integral expression. This approach allows to construct the corresponding fusion matrices and to perform the whole bootstrap program: new explicit factorization of W3 correlation functions as well shift relations between structure constants are also provided.

Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution

AbstractWe collect evidence in support of a conjecture of Griffiths, Green, and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a result of Iritani implies this conjecture for a collection of hypergeometric Calabi–Yau threefold examples studied by Doran and Morgan, the authors investigate a sequence of (non-hypergeometric) examples in dimensions 1 ≤d≤ 6 arising from Katz's theory of the middle convolution. A crucial role is played by the Mumford-Tate group (which isG2) of the family of 6-folds, and the theory of boundary components of Mumford–Tate domains.

Comparison study of the charge density distribution induced by heavy ions and pulsed lasers in silicon

Heavy ions and pulsed lasers are important means to simulate the ionization damage effects on semiconductor materials. The analytic solution of high-energy heavy ion energy loss in silicon has been obtained using the Bethe–Bloch formula and the Kobetich–Katz theory, and some ionization damage parameters of Fe ions in silicon, such as the track structure and ionized charge density distribution, have been calculated and analyzed according to the theoretical calculation results. Using the Gaussian function and Beer's law, the parameters of the track structure and charge density distribution induced by a pulsed laser in silicon have also been calculated and compared with those of Fe ions in silicon, which provides a theoretical basis for ionization damage effect modeling.

A new approach to the rest potential of biological membranes

In a series of recent papers, Bonciocat et al., have shown that the faradaic current density of an electrode redox reactions occurring with combined limitations, of charge transfer and nonstationary linear, semi-infinite diffusion, is the solution of an integral equation of Volterra type. This integral equation has been transformed to describe the transport of ions through the interface between two immiscible electrolytic solutions. According to Goldman, Hodkin, Katz theory, the rest potential of a biological membrane is determined by the maintenance of different concentrations of the ions Na +, K + and Cl −, in the two aqueous solutions separated by the membrane. Using the integral equations (of Volterra type) for the ionic current densities i Na, i K, i Cl, and applying the open circuit condition (i.e., i Na + i K + i Cl = 0), the potential differences at the junctions: aqueous solution (I)/membrane, respective membrane/aqueous solution (II), have been obtained. To get the diffusion potential across the membrane, the Planck's theory has been used. The sum of these three contributions gives the expression of the rest potential (and a comparison with the Goldman–Hodkin–Katz formula is made, showing in what conditions they become identical formulae).

How Can We Ignore the Why?

Katz's (1960) theory of the Functional Approach to Attitude Change is applied to the largely atheoretical world of health care professionals' attitudes toward older adults. A brief summary of the research on health care professionals' attitudes toward older adults is presented and the application of Katz's theory to these attitudes is explored in depth. Empirical studies which test even trace elements of this theory are examined. Directions for future research are suggested, and social workers, possessing so many relevant skills and holding positions in the health care arena, are encouraged to become actively involved.

Playing for Celebrity

If we are to understand series such as the first U.K. version of Big Brother as events, rather than just as texts or production processes, we need to draw on anthropological theory, for example, Dayan and Katz's theory of media events. This article develops an anthropologically informed argument about the status of Big Brother as event, its ambiguous claims to present social “reality,” and the connection of those claims with its other claim to offer “liveness” in a new web-enhanced form. These ambiguities can be traced not only in the discourse of the program but also in the discourses by producers and others that surrounded it, ambiguities that are ideological in the same way that “myth” was for Roland Barthes.

Filmwise condensation of a pure fluid and a binary mixture in a bundle of enhanced surface tubes

An experimental study has been carried out to investigate the characteristics of condensation in a bundle of horizontal tubes. These tubes have different types of external surfaces: smooth surface (1D), low trapezoidal fins with several fin pitches (2D) and specific fins (3D, C+ tube). The used fluids are either pure refrigerant (HFC 134a) or binary mixture of refrigerants (HFC 134a/HFC23). For the pure fluid and a single tube, the influence of fin spacing has been studied (11, 19, 26, 32 and 40 fins/inch) and a comparison has been made with the Gewa C+ tube. The results were analysed with the Beatty and Katz theory and compared to a specific model, taking into account both gravity and surface tension effects, developed for the Gewa C+ tube. For the bundle and for a pure fluid, the inundation of the lowest tubes has a strong effect on the Gewa C+ tubes performances contrary to the finned tubes. For the mixture the heat transfer coefficient decreases dramatically especially for Gewa C+ tube.

Katz on Names Without Bearers

Since the name 'Santa Claus' does not refer, Millian theories seem to imply that (1) is not meaningful. But (1) is not only meaningful-it is true. This problem, and other problems with Millian theories, have led some philosophers to accept description theories of proper names. These theories say (roughly) that proper names are synonymous with definite descriptions; thus they can allow proper names to be meaningful even when they fail to refer. But Donnellan, Kripke, and others have shown that the classical description theories of Frege and Russell are fraught with difficulties, to say the least. In his paper Names Without Bearers, Jerrold J. Katz claims to have found a solution to the problems raised by names without bearers.' He presents a new metalinguistic description theory of proper names that he says can explain why (1) and other sentences containing names without bearers are meaningful. He moreover claims that this new description theory is invulnerable to the (by now) standard objections to classical description theories. I disagree with Katz on two major points. First, I believe that Millian theories can account for the meaningfulness of (1) and other sentences containing names without bearers. I have argued for this point elsewhere (Braun 1993). Second, I believe that Katz's theory is not a viable alternative to Millian theories and that his

Management development programs: The effects of management level and corporate strategy

AbstractIn this study of 155 organizations, the relationship between management development programs, managerial level, and organizational strategy was examined. Limited support was established for Katz's theory about skill requirements for managers (1974). Greater emphasis was placed on technical skills at lower management levels and on entrepreneurial skills at senior management levels. A relationship between corporate strategy and the focus of management development programs also was found. Although organizations with growth strategies focused on many management development areas to a greater extent than did organizations with stability or retrenchment strategies, there were no differences in the focus on ethical decision making or technical‐skills training between the three strategies. Implications for management and for future research are also discussed.

Effect of using an auditory trainer on the attentional, language, and social behaviors of autistic children

Two groups of seven autistic children wore an auditory trainer for an average of 24 minutes per day over two 5-week periods interspersed with 5-week control periods in a time series design. Videotapes were coded for three attentional states (normal, withdrawn, attacking), for verbalization and signing, and for appropriate and acceptable behaviors. Results demonstrated a decrease in time spent withdrawn and increases in signing and in school-appropriate behavior. Results are interpreted as congruent with Katz's theory of reduced attention due to deficits in auditory conductance.

Dependence of track width on charge and velocity of slow heavy ions in nuclear emulsion

Track widths of stopping heavy ions ( 12C to ∼ 40A) accelerated by the Berkeley Hilac, with energy of 10 MeV/nucleon in Ilford G-5 emulsion have been measured by a new photometric method. The experimental data are compared with the theoretical values deduced by Bizzeti and Della Corte, which do not agree with our experimental values over the whole range. Two track-formation models based on simple assumptions are studied. The experimental track widhts of slow heavy ions with velocities β < 0.13 are found to be proportional to Z eff 2/3. β 5/3 rather than to Z/β given by Katz's theory.

Track width of slow heavy ions in nuclear emulsion by photometric measurements

Track width of slow Ne and Ar ions recorded in nuclear emulsions was photometrically studied. For β≦0.08, photometrical measurements are influenced by the grain noise, the inaccuracy of charge determination increasing with the decreasing residual range. It was found that Katz's theory of track-formation mechanism does not explain track structure at small residual ranges.

Analytic/synthetic and semantic theory

A somewhat simplified version of Jerrold J. Katz's theory of the analytic/synthetic distinction for natural languages is presented. Katz's account is criticized on the following grounds. (1) the ‘antonymy operator’ is not well defined; it leaves certain sentences without readings. (2) The account of negation is defective; it has the consequence that certain nonsynonymous sentences are marked as synonymous. (3) The account of entailment is defective; it has the consequence that analytic sentences entail synthetic ones. (4) Katz's account of “indeterminable sentences” is criticized; it has the consequence that certain logical truths are not marked as analytic. (5) Katz's semantics provides no account of truth, so that he is unable to show that analytic sentences are true and that ‘indeterminable’ sentences are not.