In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient c...In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.展开更多
In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find seve...In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.展开更多
The current study provides a quantum calculus-based medical image enhancement technique that dynamically chooses the spatial distribution of image pixel intensity values.The technique focuses on boosting the edges and...The current study provides a quantum calculus-based medical image enhancement technique that dynamically chooses the spatial distribution of image pixel intensity values.The technique focuses on boosting the edges and texture of an image while leaving the smooth areas alone.The brain Magnetic Resonance Imaging(MRI)scans are used to visualize the tumors that have spread throughout the brain in order to gain a better understanding of the stage of brain cancer.Accurately detecting brain cancer is a complex challenge that the medical system faces when diagnosing the disease.To solve this issue,this research offers a quantum calculus-based MRI image enhancement as a pre-processing step for brain cancer diagnosis.The proposed image enhancement approach improves images with low gray level changes by estimating the pixel’s quantum probability.The suggested image enhancement technique is demonstrated to be robust and resistant to major quality changes on a variety ofMRIscan datasets of variable quality.ForMRI scans,the BRISQUE“blind/referenceless image spatial quality evaluator”and the NIQE“natural image quality evaluator”measures were 39.38 and 3.58,respectively.The proposed image enhancement model,according to the data,produces the best image quality ratings,and it may be able to aid medical experts in the diagnosis process.The experimental results were achieved using a publicly available collection of MRI scans.展开更多
This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we esta...This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.展开更多
On Seidel representation in quantum K-theory of Grassmannians.Changzheng Li,Zhaoyang Liu,Jiayu Song&Mingzhi Yang.Abstract We provide a direct proof of the Seidel representation in the quantum K-theory QK(Gr(k,n))b...On Seidel representation in quantum K-theory of Grassmannians.Changzheng Li,Zhaoyang Liu,Jiayu Song&Mingzhi Yang.Abstract We provide a direct proof of the Seidel representation in the quantum K-theory QK(Gr(k,n))by studying projected Gromov-Witten varieties concretely.As applications,we give an alternative proof of the K-theoretic quantum Pieri rule by Buch and Mihalcea(2011),reduce certain quantum Schubert structure constants of higher degree to classical Littlewood-Richardson coefficients for K(Gr(k,n)),and provide a quantum LittlewoodRichardson rule for QK(Gr(3,n)).展开更多
基金Supported by the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2019MS01023)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZZ19209,NJZY20198).
文摘In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.
文摘In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.
文摘The current study provides a quantum calculus-based medical image enhancement technique that dynamically chooses the spatial distribution of image pixel intensity values.The technique focuses on boosting the edges and texture of an image while leaving the smooth areas alone.The brain Magnetic Resonance Imaging(MRI)scans are used to visualize the tumors that have spread throughout the brain in order to gain a better understanding of the stage of brain cancer.Accurately detecting brain cancer is a complex challenge that the medical system faces when diagnosing the disease.To solve this issue,this research offers a quantum calculus-based MRI image enhancement as a pre-processing step for brain cancer diagnosis.The proposed image enhancement approach improves images with low gray level changes by estimating the pixel’s quantum probability.The suggested image enhancement technique is demonstrated to be robust and resistant to major quality changes on a variety ofMRIscan datasets of variable quality.ForMRI scans,the BRISQUE“blind/referenceless image spatial quality evaluator”and the NIQE“natural image quality evaluator”measures were 39.38 and 3.58,respectively.The proposed image enhancement model,according to the data,produces the best image quality ratings,and it may be able to aid medical experts in the diagnosis process.The experimental results were achieved using a publicly available collection of MRI scans.
文摘This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.
文摘On Seidel representation in quantum K-theory of Grassmannians.Changzheng Li,Zhaoyang Liu,Jiayu Song&Mingzhi Yang.Abstract We provide a direct proof of the Seidel representation in the quantum K-theory QK(Gr(k,n))by studying projected Gromov-Witten varieties concretely.As applications,we give an alternative proof of the K-theoretic quantum Pieri rule by Buch and Mihalcea(2011),reduce certain quantum Schubert structure constants of higher degree to classical Littlewood-Richardson coefficients for K(Gr(k,n)),and provide a quantum LittlewoodRichardson rule for QK(Gr(3,n)).
