We investigate collective synchronous behaviors in random complex networks of limit-cycle oscillators with the non-identical asymmetric coupling scheme, and find a uniform coupling criticality of collective synchronization which is independent of complexity of network topologies. Numerically simulations on categories of random complex networks have verified this conclusion.

We describe the design and operation principle of a new displacement sensor with a substantial improvement in resolution over what is currently possible. The potential for significant improvement in the measurement of displacement has profound implications for several high-impact gravitational physics and particle physics projects: the detection of gravitational waves, the test of the equivalen...

We analyze limit order markets and floor exchanges, assuming an informed trader and discretionary liquidity traders use market orders and can either submit block orders or work their demands as a series of small orders. By working their demands, large market order traders pool with small traders. We show that every equilibrium on a floor exchange must involve at least partial pooling. Moreover,...

We consider semilinear parabolic equations ut = uxx+f(u) on R. We give an overview of results on the large time behavior of bounded solutions, focusing in particular on their limit profiles as t→ ∞ with respect to the locally uniform convergence. The collection of such limit profiles, or, the ω-limit set of the solution, always contains a steady state. Questions of interest then are whether—or ...

We construct the uniform infinite planar map (UIPM), obtained as the n → ∞ local limit of planar maps with n edges, chosen uniformly at random. We then describe how the UIPM can be sampled using a “peeling” process, in a similar way as for uniform triangulations. This process allows us to prove that for bond and site percolation on the UIPM, the percolation thresholds are p c = 1/2 and p site c...

In this work, an integrated model of economic production quantity, economic design of an -control chart, and preventive maintenance are investigated under non-uniform quality control parameters. The effect on the expected total cost and quality control cost is investigated with three different assumptions of the quality control parameters. Using a tabu seach algorithm, the optimal values of qua...

We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and momentum eigenstates with the diamagnetism of a free electron gas as an example. When the field is non-uniform but weakly varying, we discuss both perturbative an...

For the uniform approximation of xα on [0, 1] by rational functions the following strong error estimate is proved: Let Enn(x, [0, 1]) denote the minimal approximation error in the uniform norm on [0, 1] of rational approximants to xα with numerator and denominator degree at most n, then the the limit lim n→∞ e √ Enn(x , [0, 1]) = 4| sinπα| holds for all α > 0.

We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the boundary of the diagrams. The grandcanonical ensembles, which were introduced by Vershik [17], are uniform measures under conditioning on their size (or equivalently, area). We then show that, as the...

The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane and the disc. These analytical solutions are shown to be in excellent agreement with the numerical results obtained from the Schrödinger equations even for the...