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The problem of 'applicability' of mathematics to modern physical sciences has been labeled as an 'unreasonably effective' and unexplainable 'miracle' by prominent physicists such as Eugene Wigner and Paul Dirac. Philosophers of science from contending traditions have also contributed to the debates at large. While some have tried to trivialize the problem, others, in particular those with a phenomenological orientation, have attempted to eliminate this riddle, claiming that the two domains are 'identical'. This paper, while challenging some of these interpretations, proposes a solution from a dialectical materialist position. Drawing on Evald Ilyenkov's concept of the 'ideal' as the objectivized form of human activity in social nature, it is suggested that the two realms are necessarily interconnected as schemata of human activity which aim for a highly quantified conceptualization of reality. [ABSTRACT FROM AUTHOR]

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite products, infinite series, elliptic integrals, calculus of variations and the Fourier coefficients. This short article is written to provide a definite impression of Euler's personal and professional life as well as of the range, power and depth of his unique contributions to mathematical and physical sciences. By any standards, his legacy of complete works entitled Opera Omnia of nearly 80 volumes will remain forever as a remarkable example of his scholarly work in the history of mathematics and sciences. [ABSTRACT FROM AUTHOR]

We report static electric (hyper)polarizability values of the three linear isomers of (CN) 2 . Large, flexible basis sets have been especially designed for all three molecules and the electric properties have been obtained from finite-field Møller-Plesset perturbation theory and coupled cluster calculations. All three molecules are characterized by large polarizability anisotropies. Self-consistent field calculations of near-Hartree-Fock quality yield the following mean polarizabilities: for CN-NC, 32.42 for NC-CN and 33.46 for CN-CN. For the second hyperpolarizability we obtain for CN-NC, 3090 for NC-CN and 3748 for CN-CN. Thus, electric (hyper)polarizability increases in the order NC-CN

Thermodynamic perturbation theory is used to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in a good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. Monte Carlo simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer-to-colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces. [ABSTRACT FROM AUTHOR]