Searching for a Solution to Program Verification=Equation Solving in CCS

International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides “agent-specific” results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model

Directivity of low frequency solar type 3 radio bursts

The occurrence rate of type 3 solar bursts in the frequency range 4.9 MHz to 30 kHz was analyzed as a function of burst intensity and burst arrival direction. Results show that: (1) the occurrence rate of bursts falls off with increasing flux and (2) the distribution of burst arrival directions at each frequency shows a significantly larger number of bursts observed west of the earth-sun line than east of it. This western excess in occurrence rate appears to be correlated with the direction of the average interplanetary magnetic field, and is interpreted as beaming of the observed burst radiation along the magnetic field direction

The Hilbert-Huang Transform: A Theoretical Framework and Applications to Leak Identification in Pressurized Space Modules

Any manned space mission must provide breathable air to its crew. For this reason, air leaks in spacecraft pose a danger to the mission and any astronauts on board. The purpose of this work is twofold: the first is to address the issue of air pressure loss from leaks in spacecraft. Air leaks present a danger to spacecraft crew, and so a method of finding air leaks when they occur is needed. Most leak detection systems localize the leak in some way. Instead, we address the identification of air leaks in a pressurized space module, we aim to determine the material in which the leak occurs. This is done with methods centered on statistics and machine learning. In addition to these findings, we investigate one of the methods used in the leak identification section, the Hilbert-Huang Transform. This method has seen many demonstrations of its effectiveness, however this method lacks a solid theoretical framework. We make some contributions to the background of the Hilbert-Huang Transform

The Theory Behind TheoryMine

Abstract. We describe the technology behind the TheoryMine novelty gift company, which sells the rights to name novel mathematical theorems. A tower of four computer systems is used to generate recursive theories, then to speculate conjectures in those theories and then to prove these conjectures. All stages of the process are entirely automatic. The process guarantees large numbers of sound, novel theorems of some intrinsic merit.

BURNOUT HEAT FLUXES FOR LOW-PRESSURE WATER IN NATURAL CIRCULATION

Twenty-nine experimental determinations of burn-out heat flux were made with water flowing by natural circulaion through electrically heated vertical tubes with and without internal twisted tapes and through rectangular cross sections of three aspect ratios. Heated lengths varied from 10 to 33 in., system pressure at the testsection flow exit from 14.7 to 26.3 psia, inlet subcooling from 36 to 170 deg F, and burn-out heat flux from 13,000 to 218,500 Btu/hr/sq ft. Tests were made with both unrestricted and restricted return flow paths. Three correlations were developed for predicting natural-circulation burn-out heat fluxes for such conditions. Two are useful for rapid estimation but the third involves a more fundamental assessment of the coolant mass velocity at burn-out by a graphical matching of the heat flux that a given flow rate can sustain to the heat flux that will produce that flow rate. For all the data, this approach gave average and maximum deviations of 15 and 38%, respectively. It was found that use of a slip ratio of unity is adequate for burnout prediction, and the reasons for this are discussed in detail. The small burn-out penalty incurred by a substantial restriction of return flow path, experimentally observed, is in complete accord with the theoretical model. (auth