Abstract. Additional of fiber in concrete creates fiber reinforced concrete (FRC) with an improvement of the mechanical properties of the concrete. However, fiber incorporation in FRC is limited to 2% to allow normal mixing procedure. To address this issue, high performance fiber reinforced concrete (HPFRC) is introduced and it is relatively new in

In this talk, we first review some basic results of square stochastic matrices concerning the convergence of power of square stochastic matrix. We also discuss a linear operator associated with a square stochastic matrix. This gives an advantage to interpret all results by means of the language of dynamical system. In the second part of this talk,

We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic matrix does not hold true. We know that a cubic st

Based on some numerical calculations, S.M. Ulam has conjectured that the ergodic theorem holds true for any quadratic stochastic operator acting on the finite dimensional simplex. However, M.I. Zakharevich showed that Ulam's conjecture is false in general. Later, N.N. Ganikhodjaev and D.V. Zanin have generalized Zakharevich's example in the

In this paper, we provide a sufficient condition in which the ergodic theorem will fail for V

In this keynote address, we shall present a time-invariant (varying) nonlinear model (rule or protocol) of discrete-time MAS. Our model is a generalization of the classical time invariant DeGroot model. Based on our proposed time-invariant model, we show a consensus in the discrete-time MAS. It seems that, unlike a linear case, a consensus can be e

The p-adic models of statistical mechanics require the investigation of the roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is that whether a root of a polynomial equation belongs to the classic domains not. This question was open even for a quadratic equation. In this

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On the basis of some numerical calculations,Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich’s example to the class of quadratic stochasti

Unlike the real number field, a set of p−adic Gibbs measures of p−adic lattice models of statistical mechanics has a complex structure in a sense that it is strongly tied up with a Diophantine problem over p−adic fields. Recently, all translation-invariant p−adic Gibbs measures of the p−adic Potts model on the Cayley tree of order two wer