This research addresses the design of intensity-curvature functional(ICF)based digital high pass filter(HPF).ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF.In ord...This research addresses the design of intensity-curvature functional(ICF)based digital high pass filter(HPF).ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF.In order to calculate ICF,the model function needs to be second order differentiable and to have non-null classic-curvature calculated at the origin(0,0)of the pixel coordinate system.The theoretical basis of this research is called intensitycurvature concept.The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function.Extrapolation of the concept in two-dimensions(2D)makes it possible to calculate the ICF of an image.Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal.Empirical evidence then validates the assumption and also extends the comparison between ICF-based HPF and ten different HPFs among which is traditional HPF and particle swarm optimization(PSO)based HPF.Through comparison of image space and k-space magnitude,results indicate that HPFs behave differently.Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering.Images filtered with traditional HPF are sharper than images filtered with ICF-based filter.The contribution of this research can be summarized as follows:(1)Math description of the constraints that ICF need to obey to in order to function as HPF;(2)Math of ICF-based HPF of bivariate cubic B-spline;(3)Image space comparisons between HPFs;(4)K-space magnitude comparisons between HPFs.This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function.展开更多
In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma fu...In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].展开更多
General linear non-autonomous functional differential equations are considered. Explicit criteria for exponential stability are given. Furthermore, the authors present an explicit robust stability bound for systems su...General linear non-autonomous functional differential equations are considered. Explicit criteria for exponential stability are given. Furthermore, the authors present an explicit robust stability bound for systems subject to time-varying perturbations. Two examples are given to illustrate the obtained results.展开更多
文摘This research addresses the design of intensity-curvature functional(ICF)based digital high pass filter(HPF).ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF.In order to calculate ICF,the model function needs to be second order differentiable and to have non-null classic-curvature calculated at the origin(0,0)of the pixel coordinate system.The theoretical basis of this research is called intensitycurvature concept.The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function.Extrapolation of the concept in two-dimensions(2D)makes it possible to calculate the ICF of an image.Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal.Empirical evidence then validates the assumption and also extends the comparison between ICF-based HPF and ten different HPFs among which is traditional HPF and particle swarm optimization(PSO)based HPF.Through comparison of image space and k-space magnitude,results indicate that HPFs behave differently.Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering.Images filtered with traditional HPF are sharper than images filtered with ICF-based filter.The contribution of this research can be summarized as follows:(1)Math description of the constraints that ICF need to obey to in order to function as HPF;(2)Math of ICF-based HPF of bivariate cubic B-spline;(3)Image space comparisons between HPFs;(4)K-space magnitude comparisons between HPFs.This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function.
文摘In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].
基金supported by Vietnam National University Ho Chi Minh City(VNU-HCM)under Grant No.C2017-26-02
文摘General linear non-autonomous functional differential equations are considered. Explicit criteria for exponential stability are given. Furthermore, the authors present an explicit robust stability bound for systems subject to time-varying perturbations. Two examples are given to illustrate the obtained results.
