According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor $\hat \Theta _{ik}$ satisfying the relation $\hat \Theta _{i;k}^k = 0$ . The tensor $\hat \Theta _{ik}$ is formed from the Einstein-Cartan torsion field given by the anholonomy objects, (...) FAik=2hA[i,k], and appears together with Hilbert’s energy-momentum tensor T* ik and Poincaré’s pressure λgik on the right-hand side of Einstein’s equations so that one has $$R_{ik} - (1/2)g_{ik} R = - \kappa T*_{ik} - \lambda g_{ik} - \hat \Theta _{ik}$$ According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincaré and Einstein-Cartan terms to exist. The torsion field FAik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics. (shrink)

In recent papers the authors have discussed the dynamical properties of “large Poincaré systems” (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. We show that this Poincaré “catastrophe” can be eliminated by a natural time ordering of the dynamical states. We obtain then a (...) dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that this time ordering can be performed in an “extended” Hilbert space. In general, we need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space. (shrink)

This anthology collects readings from important nineteenth and early twentieth century figures who contributed to the philosophy of science before that discipline emerged in the last 40 years as an area of study in its own right. It begins with a seldom-read selection by Kant ) and ends with a selection from Bridgman's The Logic of Modern Physics. Each selection is preceded by a three-page biography of the author together with a bibliography of his major writings and some writings on (...) his work. Many familiar names appear, e.g., Mill, Mach, Pearson, Hertz, Poincare, Peirce, Duhem, Russell, Whitehead, and Campbell. But there are others represented whose actual writings are not so familiar to many students of the philosophy of science, e.g., J. F. W. Herschel, William Whewell, Hermann Von Helmholtz, J. B. Stallo, Emile Boutroux and William Ostwald. With the exception of Stallo, the writings of these figures have been long out of print. In one case, a selection from Ludwig Boltzmann on the nature of mechanics, the editor has translated the selected passage into English expressly for this volume. A wide range of topics are considered in the readings: physical laws, theories, induction, observation, space, time, and others; but, as the nature of the case requires, the focus of attention is on classical science. For this reason most existing courses in the philosophy of science could use this collection only as a supplementary text. But it would function well in such a role. Moreover, specialized courses in the history of philosophical thinking about science will find it very useful.--R. H. K. (shrink)

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear (...) may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB. (shrink)