Asymptotic nonnegative rank of matrices

The nonnegative rank of nonnegative matrices is an important quantity that appears in many fields, such as combinatorial optimization, communication complexity, and information theory. In this paper, we study the asymptotic growth of the nonnegative rank of a fixed nonnegative matrix under Kronecker product. This quantity is called the asymptotic nonnegative rank, which is already studied in information theory. By applying the theory of asymptotic spectra of V. Strassen (J. Reine Angew. Math. 1988), we introduce the asymptotic spectrum of nonnegative matrices and give a dual characterization of the asymptotic nonnegative rank. As the opposite of nonnegative rank, we introduce the notion of the subrank of a nonnegative matrix and show that it is exactly equal to the size of the maximum induced matching of the bipartite graph defined on the support of the matrix (therefore, independent of the value of entries). Finally, we show that two matrix parameters, namely rank and fractional cover number, belong to the asymptotic spectrum of nonnegative matrices

BOUNDS FOR VOLUMES OF SUB-LEVEL SETS OF POLYNOMIALS AND APPLICATIONS

In this paper, we present some explicit exponents in the estimates for the volumes of sub-level sets of polynomials on bounded sets and applications to the decay of oscillatory integrals and the convergence of singular integrals

Investigation of chemical heat storage processes for recovering exhaust gas energy in internal combustion engines

© 2018 Australasian Fluid Mechanics Society. All rights reserved. Improving the energy efficiency of the IC engine and hybrid vehicles has become more and more important. Chemical heat storage system is one of the approaches to address it by utilising the wasted energy. This study was aimed to develop a chemical heat storage (CHS) system using magnesium hydroxide (Mg(OH)2) to recover the thermal energy wasted by the exhaust gas in internal combustion (IC) engines. The stored heat can be used to heat the intake air, catalysts, lubricants in IC engines and batteries in hybrid vehicles. Experiments were conducted on a diesel engine (D1146TI) to estimate the efficiency of CHS technology in the heat storage process. Experimental results showed that at engine load 60% to 80%, 33.68% to 61% of the chemical material reacted with 3.69% to 5.05 % heat energy of exhaust gas stored in one hour time. The percentages of the reacted chemical material and the stored exhaust gas heat energy decreased with the decreased engine load

Noise and vibration from building-mounted micro wind turbines Part 2: Results of measurements and analysis

Description To research the quantification of vibration from a micro turbine, and to develop a method of prediction of vibration and structure borne noise in a wide variety of installations in the UK. Objective The objectives of the study are as follows: 1) Develop a methodology to quantify the amount of source vibration from a building mounted micro wind turbine installation, and to predict the level of vibration and structure-borne noise impact within such buildings in the UK. 2) Test and validate the hypothesis on a statically robust sample size 3) Report the developed methodology in a form suitable for widespread adoption by industry and regulators, and report back on the suitability of the method on which to base policy decisions for a future inclusion for building mounted turbines in the GPDO