If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers...If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers with primes, during the prime factorization, may be viewed as being the outcome of a parallel system which functions properly if and only if Euler’s formula of the product of the reciprocals of the primes is true. An exact formula for the number of primes less than or equal to an arbitrary bound is given. This formula may be implemented using Wolfram’s computer package Mathematica.展开更多
This study analyzes the sample influx (samples per case file) into forensic science laboratory (FSL) and the corresponding analysis costs and uses arbitrary re-sampling plans to establish the minimum cost function. Th...This study analyzes the sample influx (samples per case file) into forensic science laboratory (FSL) and the corresponding analysis costs and uses arbitrary re-sampling plans to establish the minimum cost function. The demand for forensic analysis increased for all disciplines, especially biology/DNA between 2014 and 2015. While the average distribution of case files was about 42.5%, 40.6% and 17% for the three disciplines, the distribution of samples was rather different being 12%, 82.5% and 5.5% for samples requiring forensic biology, chemistry and toxicology analysis, respectively. Results show that most of the analysis workload was on forensic chemistry analysis. The cost of analysis for case files and the corresponding sample influx varied in the ratio of 35:6:1 and 28:12:1 for forensic chemistry, biology/DNA and toxicology for year 2014 for 2015, respectively. In the two consecutive years, the cost for forensic chemistry analysis was comparatively very high, necessitating re-sampling. The time series of sample influx in all disciplines are strongly stochastic, with higher magnitude for chemistry, biology/DNA and toxicology, in this order. The PDFs of sample influx data are highly skewed to the right, especially forensic toxicology and biology/DNA with peaks at 1 and 3 samples per case file. The arbitrary re-sampling plans were best suited to forensic chemistry case files (where re-sampling conditions apply). The locus of arbitrary number of samples to take from the submitted forensic samples was used to establish the minimum and scientifically acceptable samples by applying minimization function developed in this paper. The cost minimization function was also developed based on the average cost per sample and choice of re-sampling plans depending on the range of sample influx, from which the savings were determined and maximized. Thus, the study gives a forensic scientist a business model and scientific decision making tool on minimum number of samples to analyze focusing on savings on analysis cost.展开更多
This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The obj...This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.展开更多
文摘If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers with primes, during the prime factorization, may be viewed as being the outcome of a parallel system which functions properly if and only if Euler’s formula of the product of the reciprocals of the primes is true. An exact formula for the number of primes less than or equal to an arbitrary bound is given. This formula may be implemented using Wolfram’s computer package Mathematica.
文摘This study analyzes the sample influx (samples per case file) into forensic science laboratory (FSL) and the corresponding analysis costs and uses arbitrary re-sampling plans to establish the minimum cost function. The demand for forensic analysis increased for all disciplines, especially biology/DNA between 2014 and 2015. While the average distribution of case files was about 42.5%, 40.6% and 17% for the three disciplines, the distribution of samples was rather different being 12%, 82.5% and 5.5% for samples requiring forensic biology, chemistry and toxicology analysis, respectively. Results show that most of the analysis workload was on forensic chemistry analysis. The cost of analysis for case files and the corresponding sample influx varied in the ratio of 35:6:1 and 28:12:1 for forensic chemistry, biology/DNA and toxicology for year 2014 for 2015, respectively. In the two consecutive years, the cost for forensic chemistry analysis was comparatively very high, necessitating re-sampling. The time series of sample influx in all disciplines are strongly stochastic, with higher magnitude for chemistry, biology/DNA and toxicology, in this order. The PDFs of sample influx data are highly skewed to the right, especially forensic toxicology and biology/DNA with peaks at 1 and 3 samples per case file. The arbitrary re-sampling plans were best suited to forensic chemistry case files (where re-sampling conditions apply). The locus of arbitrary number of samples to take from the submitted forensic samples was used to establish the minimum and scientifically acceptable samples by applying minimization function developed in this paper. The cost minimization function was also developed based on the average cost per sample and choice of re-sampling plans depending on the range of sample influx, from which the savings were determined and maximized. Thus, the study gives a forensic scientist a business model and scientific decision making tool on minimum number of samples to analyze focusing on savings on analysis cost.
基金Sponsored by the National Natural Science Foundation of China Grant No.61004038
文摘This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.
