On the semicircular law of large dimensional random quaternion matrices

It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a natural idea we want to get more universal results by removing the Gaussian condition. For the first step, in this paper we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.Comment: 20 page

On the limit of extreme eigenvalues of large dimensional random quaternion matrices

Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin (1988) obtained the necessary and sufficient conditions for the strong convergence of the extreme eigenvalues of a Wigner matrix. In this paper, we consider the case of quaternion self-dual Hermitian matrices. We prove the necessary and sufficient conditions for the strong convergence of extreme eigenvalues of quaternion self-dual Hermitian matrices corresponding to the Wigner case.Comment: 16 pages, 5 figure

A note on a Mar\v{c}enko-Pastur type theorem for time series

In this note we develop an extension of the Mar\v{c}enko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for its Stieltjes transform depending on the spectral density of the time series. A numerical algorithm is then given to compute the density functions of these LSD's

A temperature control strategy to achieve low-temperature district heating in North China

The data includes historical actual operating data of a District Heating System (DHS) in Tianjin and weather forecast data. The DHS operating data, which includes supply and return temperature from February 16, 2018, to March 12, 2018, is collected from a heat exchange station in Tianjin, China. The exchange station supplies heat for nearly 40 residential buildings in winter. The weather forecast data consists of outdoor temperatures, relative humidity, wind speed and air quality index (AQI)

Controlling Aflatoxicosis in Poultry Using Plant-Derived Antimicrobials

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Sharp Bounds for Sums Associated to Graphs of Matrices

We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form S_pi(N) := sum_{j_1, ..., j_2m = 1}^N t^1_{j_1 j_2} t^2_{j_3 j_4} ... t^m_{j_2m-1 j_2m} where some of the summation indices are constrained to be equal. The upper bound is easily obtained from a graph G associated to the constraints in the sum.Comment: 20 page

Material tests of 316L austenitic stainless-clad steel at elevated temperatures

[EN] Mechanical properties of stainless-clad (SC) steel plates at elevated temperatures are key parameters for fire resistant design and numerical simulation analysis of SC steel structures. Compared with pure stainless steel and pure ordinary steel, SC steel not only combines advantages of the two component metals, but may also balance the performance and cost; however, it behaves quite differently in terms of material properties. In order to quantify this performance, tension coupon tests at room as well as elevated temperatures are conducted on the SC steel plate. Based on the test results, failure modes of the tension coupons are analysed, and full-range stress-strain curves are obtained; material properties are accordingly determined and described herein, and analyses are performed on several properties including yield strength, ultimate tensile stress, elastic modulus and elongation after fracture. It is found that with an increase of the temperature, both the elastic modulus and strengths are reduced remarkably. For determining these material properties quantitatively and developing robust constitutive models of the SC steel at elevated temperatures, more test data are needed, and the incorporation of the effects of the clad ratio on the material properties at both room and elevated temperatures is also necessary. The present research outcomes may provide valuable reference for fire design and calculations of the SC steel.This work was financially supported by the National Natural Science Foundation of China (Nos. 51608300, 51778329), which are gratefully acknowledged.Bai, R.; Ban, H.; Chung, K.; Bai, Y. (2018). Material tests of 316L austenitic stainless-clad steel at elevated temperatures. En Proceedings of the 12th International Conference on Advances in Steel-Concrete Composite Structures. ASCCS 2018. Editorial Universitat Politècnica de València. 851-855. https://doi.org/10.4995/ASCCS2018.2018.7011OCS85185

Limiting behavior of the eigenvalues of a multivariate F matrix

AbstractThe spectral distribution of a central multivariate F matrix is shown to tend to a limit distribution in probability under certain conditions as the number of variables and the degrees of freedom tend to infinity