Physics, mind, society: Back and forth

The life course of the physicist and biologist George Feher may be seen as an epitome of science of the second half of the 20th century and the beginning of the 21st century. Feher, a native of Slovakia, barely escaped Nazism and communism and became a scientist in the USA. The Nazi concentration camps and the communist gulags have become a symbol of the 20th century. This symbol stands here to pose a question: How the two totalitarian systems, fraught with irrationality, may have arisen and thrived in parallel with an unprecedented expansion of science, the paragon of rationalism? The question has become even more urgent in the 21st century. The Ground Zero, an empty spot left after the collapse of the twin towers of the World Trade Center on 11 September 2001, has become the symbol of the entrance of humankind into the new millennium. We can do much, but we understand too little about who we are and what we are doing — this is a message that the two symbols convey about the precarious stage of our evolution. The second message concerns the role of artifacts, specifically scientific instruments, in the advancement of science. Human cultural evolution has been steadily progressing, in a form of a ratchet, only because artifacts have been continually evolving. Contrary to the common Popperian wisdom, the demarcation in science may not consist in the amenability to theoretical falsification, but rather in the amenability to instrumental grasping. Scientific instruments have empowered humans for impressive feats of manipulation with Nature and themselves. Knowledge arising in the course of autonomous evolution of artifacts may surpass the horizon of human understanding and grasping. New knowledge may still be power, but no longer the power of humans. We may need a revision of some fundamental ideas of European thought. Our understanding of the human mind may entirely reshape our comprehension of the nature of physical knowledge, and vice versa.     

Causality, Poincaré Invariance, and Goldstone Theorem in DLCQ

We study three problems of the light-front field theory quantized in a finite volume with fields (anti-)periodic in x⁻: (a) microcausality by deriving an integral representation for the discrete Pauli-Jordan function; (b) surface terms violating Poincaré algebra; (c) a LF version of the Goldstone theorem. The first two problems are resolved by careful mathematical treatment. The third one illustrates the usefulness of DLCQ as an analytical scheme.     

On zeta-functions associated to certain cusp forms. I

In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained. Partially supported by Lithuanian Foundation of Studies and Science     

Generalized Relative Entropies as Contrast Functionals on Density Matrices

We use a class of generalized relative entropies on density matrices to obtain one-parameter families of torsion-free affine connections.     

Students' Verification Strategies for Combinatorial Problems

We focus on a major difficulty in solving combinatorial problems, namely, on the verification of a solution. Our study aimed at identifying undergraduate students' tendencies to verify their solutions, and the verification strategies that they employ when solving these problems. In addition, an attempt was made to evaluate the level of efficiency of the students' various verification strategies in terms of their contribution to reaching a correct solution. 14 undergraduate students, who had taken at least 1 course in combinatorics, participated in the study. None of the students had prior direct learning experience with combinatorial verification strategies. Data were collected through interviews with individual or pairs of participants as they solved, 1 by 1, 10 combinatorial problems. 5 types of verification strategies were identified, 2 of which were more frequent and more helpful than others. Students' verifications proved most efficient in terms of reaching a correct solution when they were informed that their solution was incorrect. Implications for teaching and learning combinatorics are discussed.     

Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Confidence regions in a multivariate regression model with constraints II

The multivariate model, where not only parameters of the mean value of the observation matrix, but also some other parameters occur in constraints, is considered in the paper. Some basic inference is presented under the condition that the covariance matrix is either unknown, or partially unknown, or known. Supported by the grant of the Council of Czech Republic MSM 6 198 959 214.     

Compact coaxial driver for small-size Z-pinch

The presented one-capacitor pinch driver, designed as a compact coaxial structure (including spark-gap and discharge section) consistent with the capacitor output, generates a current of 200 kA with 700 ns quarter-period, suitable for studying the optimization of Z-pinch radiative characteristics. The driver is described, measurements of its parameters summarized, and relations to our previous and future activities briefly reviewed.This work was supported in part by the Grant Agency of the Czech Republic under contract No. 202/93/1023.     

1H and13C nuclear magnetic relaxation and local dynamics of lysozyme and synthetic polypeptides

The combined analysis of¹H and¹³C NMR relaxation data in solid lysozyme and some typical homopolypeptides was carried out by using “model-free” approach. Three types of relaxation transitions (γ’, γ and β) were revealed in the temperature range investigated. The microdynamical parameters of these motions were determined. From the comparison of these parameters with those of selected synthetic polymers it follows that the molecular motions in proteins and synthetic polymers are of the same nature. All these motions show pronounced anisotropic character. In the investigated temperature range no molecular motions corresponding to α-relaxation (liquid-like) transition were revealed. The hydration effects on parameters of the motions in proteins were considered. The most pronounced effect takes place for β-transition. The effect of Brownian rotation of protein molecule in solution on measured correlation function of local motions was also discussed.