Necessary optimality condition for the singular controls in an optimal control problem with nonlocal conditions

In this paper, we continue investigation of the problem considered in our earlier works. The paper deals with an optimal control problem for an ordinary differential equation with integral boundary conditions that generalizes the Cauchy problem. The problem is investigated the case when Pontryagin?s maximum principle is degenerate. Moreover, the second order optimality conditions are derived for the considered problem.

G˚arding Cones and Bellman Equations in the Theory of Hessian Operators and Equations

In this work, we continue investigation of algebraic properties of G˚arding cones in the space of symmetric matrices. Based on this theory, we propose a new approach to study of fully nonlinear differential operators and second-order partial differential equations. We prove new-type comparison theorems for evolution Hessian operators and establish a relation between Hessian and Bellman equations.

Training Aspiring Entrepreneurs to Pitch Experienced Investors: Evidence from a Field Experiment in the United States

Accredited investors finance more than 75,000 U.S. start-ups annually. We explain how training aspiring entrepreneurs to pitch their new business ideas to these investors affects their odds of continued funding discussions. We model accredited investors’ decision to continue investigation as a real option whose value is a function of their experience and the information contained in the entrepreneurs’ pitches. We derive four hypotheses from the model, which we test through a field experiment that randomly assigns pitch training at four elevator pitch competitions. The data support all four hypotheses, and are inconsistent with alternative explanations.

NUMBER OF RETRIALS IN A FINITE SOURCE RETRIAL QUEUE WITH UNRELIABLE SERVER

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

SOFT BREAKING OF BRST SYMMETRY AND GAUGE DEPENDENCE

We continue investigation of soft breaking of BRST symmetry in the Batalin–Vilkovisky (BV) formalism beyond regularizations like dimensional ones used in our previous paper [JHEP 1110, 043 (2011)]. We generalize a definition of soft breaking of BRST symmetry valid for general gauge theories and arbitrary gauge fixing. The gauge dependence of generating functionals of Green's functions is investigated. It is proved that such introduction of a soft breaking of BRST symmetry into gauge theories leads to inconsistency of the conventional BV formalism.

Effect of Vibration on Forward Split Flexibility and Pain Perception in Young Male Gymnasts

Serious stretching in many sports involves discomfort and is often an early ceiling on improvements.Purpose:To continue investigation of the use of vibration to enhance acute range of motion while assessing the influence of vibration and stretching on pressure-to-pain threshold perception.Methods:Ten young male gymnasts were assessed for split range of motion. One side split was randomly assigned as the experimental condition, and the other side split was assigned as the control. Both side splits were performed on a vibration device; the experimental condition had the device turned on and the control condition was performed with the device turned off. In addition, the athletes were assessed for pressure-to-pain transition using an algometer on the biceps femoris (stretched muscle) and vastus lateralis (nonstretched muscle) bilaterally.Results:Pre-post difference scores between the vibrated split (most improved) and the nonvibrated split were statistically different (P = .001, 95% confidence interval of the difference 2.3 to 5.8 cm). Following the stretching protocol, the force values for the pressure-to-pain threshold comparing the vibrated and nonvibrated biceps femoris muscle were not statistically different. The nonstretched vastus lateralis muscle also showed no statistical difference in pressure-to-pain threshold between the vibration and nonvibration conditions.Conclusion:This study showed that vibration improved split range of motion over stretching alone, but did not show a difference in pressure-to-pain perception in either the stretched or nonstretched muscles.

ON STATIONARITY IN THE ARCH(∞) MODEL

We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of Econometrics 52, 115–127) to the ARCH(∞) model.

The supposed Egyptian earthquakes of 184 and 95 B.C. Critical review and some lines of research in historical seismology using Greek papyri from Egypt

In the context of a project to update the data collected in the catalogue of Guidoboni et al.(1994), we noticed that two Egyptian earthquakes of 184 and 95 B.C. mentioned in the catalogue of Ambraseys et al. (1994, p. 20) were not included. A search to verify whether these two events should be added to the list of seismic events in the ancient Mediterranean area led to the conclusion that the two Egyptian earthquakes of 184 and 95 B.C. never occurred. The texts cited by the authors (a papyrus and an inscription) seem to deal with other events; in fact the word seismós, which has among others the meaning of 'earthquake', in these sources means 'blackmail' or 'extortion'. This conclusion leads to further discussion of relationships between ancient history and historical seismology and in particular of the use of Greek papyri from Egypt to study ancient earthquakes. A research project on Greek papyri, which will also consider other kinds of evidence such as Coptic literary and documentary texts, has been initiated by a group of researchers belonging to the SGA, in order to continue investigation of ancient earthquakes in the Mediterranean area.