Retardation in rigid motion and degree of rigidity

Retardation features of rigid motion, in flat two-dimensional space-time, are interpreted in terms of a consistent picture of signals. A similar analysis is adopted to effect a natural transition from rigid to nonrigid frames for which a degree of rigidity, having a simple physical meaning, can be defined.     

On the statistical origins of the learning curve

This paper presents a statistical rationale for the existence of the learning curve phenomenon. We consider a firm which allocates a fixed amount of input into several activities under uncertainty concerning the values of the parameters of the production function. It is shown, under fairly reasonable assumptions, that if the firm learns about the parameters of the production function from previous observations of allocations and outputs, then a learning curve phenomenon will emerge. This result occurs since the estimates of the parameters become more precise over time, and thus the allocation of the production factor into the various activities becomes more efficient (i.e. closer to the optimum allocation that would have been determined if the parameters were known with certainty). Output, therefore, increases and inputs per unit of output decrease as a function of time (and cumulative output), and a learning curve emerges.‘Plateauing’ of the learning curve is discussed, as are the conditions sufficient for the existence of this phenomenon, for which the model presented herein is offered as a possible explanation.     

The Effect of Increased Risk on the Expected Proceeds and Sale Strategy of a Machine

In this paper, a machine is considered that at any moment of time can be in one of a finite number of states. Transitions of the machine between states are governed by a stationary Markov chain. The sale value of the machine is a random variable depending on the state of the machine and on its age. In this case the optimal sale strategy is to sell the machine when its sale value exceeds some critical limit (which is a function of the state and age of the machine).It is shown that when uncertainty rises (or equivalently, when the dispersion of the sale value rises), the critical limits which determine the optimal sale policy also rise. It is also shown that the expected discounted proceeds from operating the machine rise when uncertainty increases. In the formulation, the sale date of the machine is a random variable which depends on the random sale value of the machine. Increased uncertainty can either increase or decrease the expected value of the sale date depending on the values of the parameters of the problem.     

Chemical and photochemical electron transfer of new helianthrone derivatives: aspects of their photodynamic activity

Helianthrones 2-4 are a new class of synthetic photosensitizers, which have a molecular skeleton related to that of hypericin. We established that irradiation of heliantrones with visible light leads to the formation of semiquinone radicals and reactive oxygen species. The structures of the paramagnetic anion species produced by electron transfer were calculated on the density functional level and investigated by cyclovoltammetry, UV/vis, and EPR/ENDOR spectroscopy. As with hypericin, the pi system of the helianthrones was found to be considerably deviated from planarity, and, upon electron transfer, deprotonation in the bay region occurs. The structure of the semiquinone radicals was found to be identical in THF, DMF, and aqueous buffered solutions regardless of the means by which reduction was achieved. Semiquinone radicals can be formed via self-electron transfer between the excited state and the ground state or via electron transfer from an electron donor to the excited state of helianthrone. Therefore, the presence of an electron donor significantly enhanced the photogeneration of semiquinone and superoxide radical. The kinetic studies showed that no significant photochemical destruction of helianthrones occurred upon irradiation. Generation of superoxide and singlet oxygen upon irradiation of helianthrones was established by spin trapping techniques. This shows that both type I and type II mechanisms are of importance for the photodynamic action of these compounds.     

Large number hypothesis and the matter-dominated universe

Dirac’s large number hypothesis (LNH), in the formG/G ₀=HH ₀ ⁻¹ , is applied to the matter-dominated cosmological era, using the framework of the scale covariant theory (Canuto et al., 1977). We obtain explicit expressions forR andβ _a as functions ofR _E , whereR andR _E are the scale factors of the cosmological Robertson-Walker metric, expressed in atomic and gravitational units, respectively, andβ _a is the ratio between the rates of gravitational and atomic clocks. The parameters in these expressions are , the deceleration parameter in gravitational units, and (t ₀)H ₀ ⁻¹ where (t ₀) is the present epoch value of the derivative ofβ _a with respect to atomic time. We find that a necessary condition for the LNH to be compatible with a Robertson-Walker model is that (t ₀)H ₀ ⁻¹ ≥ ₂ ¹ . The only experimental values for (t ₀) available at present are those based on the lengthening of the Moon’s period of revolution around the Earth, suggesting 0.86≥ (t ₀)H ₀ ⁻¹ ≥0.21; the more promising technique of radar ranging to the inner planets has not yet produced a value for (t ₀). Using the lunar data, it follows that 0≤ ≲0.42 corresponding to an open universe (k=−1). Closed models (k=1, >1/2) are not compatible with the LNH since the required values of (t ₀)H ₀ ⁻¹ are more than an order of magnitude above the observational upper limit. Presented at the Dirac Symposium, Loyola University, New Orleans, 1981.     

The optimal frequency of information purchases

This paper considers the problem of determining the optimal intervals between consecutive purchases of perfect information. It is shown that these intervals, which determine the frequency of information purchases, can be obtained by solving a dynamic programming problem, and a method for solving the problem is suggested. An example is provided, showing a possible application of our model to the determination of the optimal intervals between two consecutive market researches.     

Inertial and gravitational masses in the bimetric theory of gravitation

The inertial mass of a static spherically symmetric body is evaluated in the framework of Rosen's bimetric theory of gravitation. It is shown that the inertial mass equals the gravitational mass independently of the specific equation of state chosen, and hence that the theory satisfies the equivalence principle.     

STM detection of imprints left on graphite by nuclear reaction products

We present STM imaging of HOPG surfaces which have been in contact with an aluminum foil and have been irradiated with thermal neutrons. We have detected imprints of aluminum nuclei recoil following neutron capture. These include local amorphous structures, piles of few tens of atoms and craters.