Mathematical Morphological concepts outline techniques for analysing and processing geometric structures based on set theory. In this paper, we present proofs of our theorems on morphological distributive properties o...Mathematical Morphological concepts outline techniques for analysing and processing geometric structures based on set theory. In this paper, we present proofs of our theorems on morphological distributive properties over Unions and Intersections with respect to Dilation and Erosion. These results provide new realizations of Dilation, Erosion and conclude that they are distributive over Unions but non-distributive over Intersections.展开更多
Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute th...Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list ∧ and dependency parameters. Explicit computations are performed for n≤5 and r≤4 to illustrate the result.展开更多
The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation ...The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data. We indicate that, the price process is driven by a semi-martingale and the data are evenly spaced. The results of Malliavin and Mancino [1] are extended by adding a compensated poisson jump that uses a quadratic variation to calculate volatility. The volatility is computed from a daily data without assuming its functional form. Our result is well suited for financial market applications and in particular the analysis of high frequency data for the computation of volatility.展开更多
We revise some mathematical morphological operators such as Dilation, Erosion, Opening and Closing. We show proofs of our theorems for the above operators when the structural elements are partitioned. Our results show...We revise some mathematical morphological operators such as Dilation, Erosion, Opening and Closing. We show proofs of our theorems for the above operators when the structural elements are partitioned. Our results show that structural elements can be partitioned before carrying out morphological operations.展开更多
文摘Mathematical Morphological concepts outline techniques for analysing and processing geometric structures based on set theory. In this paper, we present proofs of our theorems on morphological distributive properties over Unions and Intersections with respect to Dilation and Erosion. These results provide new realizations of Dilation, Erosion and conclude that they are distributive over Unions but non-distributive over Intersections.
文摘Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list ∧ and dependency parameters. Explicit computations are performed for n≤5 and r≤4 to illustrate the result.
文摘The degree of variation of trading prices with respect to time is volatility-measured by the standard deviation of returns. We present the estimation of stochastic volatility from the stochastic differential equation for evenly spaced data. We indicate that, the price process is driven by a semi-martingale and the data are evenly spaced. The results of Malliavin and Mancino [1] are extended by adding a compensated poisson jump that uses a quadratic variation to calculate volatility. The volatility is computed from a daily data without assuming its functional form. Our result is well suited for financial market applications and in particular the analysis of high frequency data for the computation of volatility.
文摘We revise some mathematical morphological operators such as Dilation, Erosion, Opening and Closing. We show proofs of our theorems for the above operators when the structural elements are partitioned. Our results show that structural elements can be partitioned before carrying out morphological operations.
