Abstract We investigate Maker–Breaker games on graphs of size $\aleph _1$ in which Maker’s goal is to build a copy the host graph. establish firm dependence outcome game axiomatic framework. Relating this, we prove that there winning strategy for Maker $K_{\omega ,\omega _1}$ -game under ZFC+MA+ $\neg $ CH and Breaker ZFC+CH. similar result -game. Here, has ZF+DC+AD, while one ZFC+CH again.

BACKGROUND LV diastolic vortex formation has been suggested to critically contribute to efficient blood pumping function, while altered vortex formation has been associated with LV pathologies. Therefore, quantitative characterization of vortex flow might provide a novel objective tool for evaluating LV function. The objectives of this study were 1) assess feasibility of vortex flow analysis du...

The motion of two-dimensional inviscid, incompressible fluid with regions of constant vorticity is studied for three classes of geophysically motivated problem. First, equilibria consisting of point vortices located near a vorticity interface generated by a shear flow are found analytically in the linear (small-amplitude) limit and then numerically for the fully nonlinear problem. The equilibri...

A Lagrangian describing a gas of ideal pointlike vortices interacting with a quantum gas of spin-0 particles confined in an infinite or finite subset of R2 is derived. Singleand two-vortex dynamics is studied in the special case of a homogeneous gas in infinite and finite systems. Special attention is given to the case of the annulus (ring) for which new analytic and numerical solutions are fou...

To one double-breaker model, experimental investigation on blow open force was carried out. It demonstrates that the ratio between the emerging blow open force and arc power FB/ui decreases with the arcing time, the contact gap has less effect on FB/ui, and the characteristics of the blow open force are similar when the peak value of the short circuit current is beyond 4 kA. Then, according to ...

The aim of this paper was to present a new two-source extractor for min-entropy nα for some α < 1 having exponentially-small error. Say we are given two independent sources X and Y . The technique was to condense Y using a somewhere-random condenser to a somewhere-random source with t rows, where one of the rows has a high min-entropy rate. Then, in order to break correlations between the rows,...

We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being “clever”. The reverse scenario is treated in a separate paper. We determine the sharp threshold bias of classical games played on the edge set of the complete graph Kn, such...

This paper investigates technical and organizational tools to improve performances of a multi-state degraded system subject to multiple competing failure processes. The competing failure processes treated in this paper are oil insulating aging and electrical contacts wear out of high voltage oil circuit breaker. To degradation processes, is associated random shocks process highlighted by the st...

Frequent Switching of arc furnace in steel company causes a great effect on the insulation of arc furnace transformer winding which in turn may causes a shutdown of production for long periods of time. Therefore, it is necessary to study and analyze the causes of these outages and design an adequate protective device. In this paper the transient overvoltage resulted from vacuum circuit breaker ...

A design scheme of the intelligent SSB (Solid State Breaker) based on the IGCT (Integrated Gate Commutated Thyristor) is presented. The topology of switch module and the structure of the SSB are proposed. Firstly, to the IGCT’s over-voltage sensitivity problem, a new technique of reducing the over-voltage is introduced, which releases the elect romantics energy of faulty line by a capacitive cu...