Let A,D, K, k ∈ N with D square free and 2 | /k, B = 1, 2 or 4 and μi ∈ {−1, 1}(i = 1, 2), and let h(−21−eD)(e = 0 or 1) denote the class number of the imaginary quadratic field Q( √−21−eD). In this paper, we give the all-positive integer solutions of the Diophantine equation Ax +μ1B = K ( (Ay +μ2B)/K )n , 2 | / n, n > 1 and we prove that if D > 1, then h(−21−eD) ≡ 0(mod n), where D, and n sati...

We present results for the phase diagram of three flavor QCD for μB<∼500 MeV. Our simulations are performed with imaginary chemical potential μI for which the fermion determinant is positive. Physical observables are then fitted by truncated Taylor series and continued to real chemical potential. We map out the location of the critical line Tc(μB) with an accuracy up to terms of order (μB/T ) 6...

A multi-class M/M/1 system, with service rate μin for class-i customers, is considered with the risk-sensitive cost criterion n−1 logE exp ∑ i ciXi(T ), where ci > 0, T > 0 are constants, Xi(t) denotes the class-i queue-length at time t assuming the system starts empty. It is shown that, as n → ∞, asymptotic optimality is achieved by the service policy that prioritizes the classes in decreasing...

Let us suppose that in a result of some action in a random time X we get a random receipt Y. If actions are repeated one-by-one, then in the time interval [0, t] we are interested in the cumulative process of receipts. Let (X, Y) and (Xn, Yn), with n ! 1, be independent equidistributed random vectors. Let X be a positive random variable and Y be a nonnegative integer random variable. We assume ...

We begin with a long code test, where our goal is that functions which pass this test with high probability are close to a linear function with small support. We do this by examining our old linearity test but add in a bit of noise, in the form a string μ. This little bit of noise will allow us to conclude that the support for the function is small and further is under the control of out and δ ...

A model function f(x1,. . .,xn) defined in the unit hypercube Hn with Lebesque measure dx= dx1. . .dxn is considered. If the unction is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or roups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, unctional...

Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t) h a(t)− n X i=1 ai(t) Z 0 −Ti x(t+θ) dμi(θ)− m X j=1 bj(t) Z 0 −T̂j x′(t+θ) dνj(θ) i , where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The value...

The autonomous mobile robot ARNOLD uses information from a stereo camera system for navigating in an unknown and dynamically changing environment. A method called Inverse Perspective Mapping (IPM) is used for visual obstacle detection. The performance of this algorithm depends on the quality of the internal camera model. In this paper we employ an Evolutionary Algorithm (EA) to improve the para...