Hamiltonian graphs of given order and minimum algebraic connectivity

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs on n vertices.     

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown.     

再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

A note on a priori error estimates for augmented mixed methods

In this note we describe a strategy that improves the a priori error bounds for augmented mixed methods under appropriate hypotheses. This means that we can derive a priori error estimates for each one of the involved unknowns. Usually, the standard a priori error estimate is for the total error. Finally, a numerical example is included, that illustrates the theoretical results proven in this paper.     

Comparison of scale factor estimators for ultrasonic temperature monitoring: Application to structural health monitoring

In Structural Health Monitoring (SHM) of materials, estimating the effects of environmental and operational conditions such as temperature is important. Indeed, temperature changes induce modifications of the mechanical properties of the material and therefore cause a dilation of the acoustic signals characterized by a scale factor. This paper described four scale factor estimators able to monitor changes in temperature: The short-time cross-correlation (STXC) method, the stretching method (STRE), the Minimum Variance Based Estimator method (MVBE) and the Scale Transform Based Estimator method (STBE). The first two methods have already been assessed in the literature while the latter two have been specifically developed for this study. First, closed-form for the Cramer-Rao bound on the estimates of the scale factor, from a simplified deterministic signal, are derived and simplified expressions are given. Then, a statistical evaluation of the quality of estimates is conducted through Monte-Carlo simulations using synthetic signals, based on a model taking into account the influence of temperature. A raw estimate of the computational complexity of signal processing methods also completes this evaluation phase. Finally, the experimental validation of estimation methods is conducted on an aluminum plate subjected to temperatures variations in a controlled thermal environment. The temperature estimates are then faced with an analytical model describing the material behavior.     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.