Carathéodory's method for a class of dynamic games

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate feedback Nash equilibria for a class of n-person differential games. Both the finite-horizon and infinite-horizon cases are considered. Examples are given to illustrate the presented results.     

Magnetic-Zenith Effect

We develop a theory of the magnetic-zenith effect (MZE) observed upon the ionosphere modification by powerful radio waves. The dependences of MZE on main parameters, such as the magnetic-field inclination angle, pump-wave frequency and power, and angular width of HF beam are obtained. The optimal elevation angle of pump-wave beam is predicted. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 772–787, September 2005.     

Day-side auroral signatures based on simultaneous, coordinatedobservations at Svalbard and Greenland

The height distribution of the dayside cusp aurora and the relation between optical emissions and net downward electron energy flux are discussed. These two important characteristics of day-side cusp aurora are still unknown. It is instructive to compare particle flux and optical luminosity because these two quantities should be proportional if the cusp aurora is caused by electron impact, as has been found for nighttime aurora in the oval. Furthermore, there should then be a direct relation between auroral altitudes and particle energy. Based on coordinated auroral observations at Svalbard and Greenland, together with simultaneous, overhead F-9 satellite measurements, these quantities have been evaluated     

An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria

In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann (Ref. 1) was further developed in Dockner and Leitmann (Ref. 4) to include the class of open-loop dynamic games. In the present work, we improve the results of Ref. 4 in two directions. First, we enlarge the class of open-loop dynamic games to permit coupling among the dynamic equations via the states of the players; second, we incorporate the modifications given in Refs. 2 and 3. Our results greatly increase the applicability of this method. An example arising from the harvesting of a renewable resource is presented to illustrate the utility of our results.     

Kaon production in\bar pp interactions at c.m. energies from 200 to 900 GeV

A detailed analysis ofK _s ⁰ production in \(\bar pp\) |<2.5 the average transverse momentum is found to be 0.53±0.07 GeV/c at 200 GeV and 0.62±0.08 GeV/c at 900 GeV, which is an increase with respect to data at c.m. energies below 60 GeV. TheK _s ⁰ production cross sections in inelastic collisions are 29±4 mb at 200 GeV and 63±6 mb at 900 GeV, showing an increase compared to lower energy data. The central kaon density is found to increase as a logarithmic function of energy. At 900 GeV, where statistics are sufficient to allow one to draw conclusions, the average transverse momentum is higher in events with large charged multiplicity than in events with low multiplicity.     

Existence of finitely optimal solutions for infinite-horizon optimal control problems

In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.This research forms part of the author's doctoral dissertation written at the University of Delaware, Newark, Delaware under the supervision of Professor Thomas S. Angell.     

Identification of inhibitors for UDP-galactopyranose mutase

The flavoenzyme uridine 5'-diphosphate (UDP)-galactopyranose mutase (UGM) plays a key role in the cell wall biosynthesis of many pathogens, including Mycobacterium tuberculosis. Using a synthetic fluorescent ligand, we screened 16 000 compounds in a fluorescence polarization assay. Effective inhibitors of UGM were identified.     

THE EFFECT OF ACCEPTOR GROUP VARIATION ON THE SOLVATOCHROMISM OF DONOR-ACCEPTOR FLUOROPHORES

Abstract The absorption and emission characteristics of five hydroxytetrahydrochrysenes substituted with acceptor groups (nitro, cyano, methylketone, 1° amide and methyl ester) (THC-NO₂, THC-CN, THC-COCH₃, THC-CONH₂ and THC-CO₂CH₃, respectively) were investigated in an extensive set of solvents. The order of absorption and fluorescence bathochromicity are: THC-NO₂ > THC-COCH₃ > THC-CN ≥ THC-CO₂CH₃ > THC-CONH₂ and THC-NO₂ >> THC-COCH₃ > THC-CO₂CH₃ > THC-CN > THC-CONH₂, respectively. The emission spectra of these compounds are sensitive to the solvent polarity (E_T[30] scale) in the order: THC-NO₂ > THC-COCH₃ > THC-CO₂CH₃ > THC-CONH₂ > THC-CN. The response of the emission maxima of these compounds to the solvent polarity and hydrogen-bond donor/acceptor properties (π*/α/β and acity/basity scales) was also determined. The emission energies of THC-NO₂ were most sensitive to π*, β, acity, and basity of the solvent; those of the amide were least sensitive to the solvent π*, β, and basity. The ground- and excited-state dipole moments were determined by semiempirical molecular orbital calculations and the absorption/fluorescence solvent-shift method, respectively. THC-NO₂ had the largest ground- and excitedstate moments. The ester and amide had the smallest ground- and excited-state moments, respectively. In general, unsatisfactory results were obtained for correlations of the emission and absorption energies, fluorescence solvatochromism and the ground- and excited-state dipole moments with the Hammett substituent constants of the five acceptor groups. Acceptable correlations were obtained for the absorption and emission energies and the fluorescence solvatochromism with the substituent constants if the cyano compound was excluded.