For two independent L\'{e}vy processes $\xi$ and $\eta$ an exponentially distributed random variable $\tau$ with parameter $q>0$ that is of $\eta$, the killed exponential functional given by $V_{q,\xi,\eta} := \int_0^\tau \mathrm{e}^{-\xi_{s-}} \, \mathrm{d} \eta_s$. With arising as stationary distribution a Markov process, we calculate infinitesimal generator process use it to derive different...

We analysed short-period seismograms from about 250 very local events recorded by a network of high dynamic range short-period seismic stations deployed on Mt Vesuvius to estimate the site-corrected short-period seismic attenuation. We calculated Q{1 C , the inverse of the quality factor for coda waves, for short lapse times (12 s), and Q{1 P and Q{1 S , the inverse of the direct body wave qual...

Let (X t , t ≥ 0) be a continuous time simple random walk on Z d , and let l T (x) be the time spent by (X t , t ≥ 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I T = x∈Z d l T (x) q in the critical dimension d = 2q q−1. When q is integer, we obtain similar results for the intersection local times of q independent simple random ...

We prove the following main theorem of the theory of (r, q)-polycycles. Suppose a nonseparable plane graph satisfies the following two conditions: (1) each internal face is an r-gon, where r ≥ 3 ; (2) the degree of each internal vertex is q , where q ≥ 3 , and the degree of each boundary vertex is at most q and at least 2 . Then it also possesses the following third property: (3) the vertices, ...

By a theorem of Johansson, every triangle-free graph G maximum degree Δ has chromatic number at most (C+o(1))Δ/log⁡Δ for some universal constant C>0. Using the entropy compression method, Molloy proved that one can in fact take C=1. Here we show q⩾(1+o(1))Δ/log⁡Δ, c(G,q) proper q-colorings satisfiesc(G,q)⩾(1−1q)m((1−o(1))q)n, where n=|V(G)| and m=|E(G)|. Except o(1) term, this lower bound is be...

Field-theoretic models for fields taking values in quantum groups are investigated. First we consider SU q (2) σ model (q real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in which the σ models fields are represented as products of conventional σ fields and of the coordinate-independent algebra. An explicit example is provided by the U q (2) ...

This article investigates the performance of independent reinforcement learners in multiagent games. Convergence to Nash equilibria and parameter settings for desired learning behavior are discussed for Q-learning, Frequency Maximum Q value (FMQ) learning and lenient Q-learning. FMQ and lenient Q-learning are shown to outperform regular Q-learning significantly in the context of coordination ga...

Biexciton photoluminescence (PL) quantum yields (Q(2X)) of individual CdSe/CdS core-shell nanocrystal quantum dots with various shell thicknesses are derived from independent PL saturation and two-photon correlation measurements. We observe a near-unity Q(2X) for some nanocrystals with an ultrathick 19-monolayer shell. High Q(2X)'s are, however, not universal and vary widely among nominally ide...

Let C be an elliptic curve defined over Q by the equation y2 = x3+Ax+B where A,B ∈ Q. A sequence of rational points (xi, yi) ∈ C(Q), i = 1, 2, . . . , is said to form a sequence of consecutive squares on C if the sequence of x-coordinates, xi, i = 1, 2, . . ., consists of consecutive squares. We produce an infinite family of elliptic curves C with a 5-term sequence of consecutive squares. Furth...

In this article we propose new methods for computing the asymptotic value for the logarithm of the partition function (free energy) for certain statistical physics models on certain type of finite graphs, as the size of the underlying graph goes to infinity. The two models considered are the hard-core (independent set) model when the activity parameter λ is small, and also the Potts (q-coloring...