The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis ...The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.展开更多
The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we st...The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.展开更多
In this paper,a new approach is proposed to determine whether the content of an image is authentic or modified with a focus on detecting complex image tampering.Detecting image tampering without any prior information ...In this paper,a new approach is proposed to determine whether the content of an image is authentic or modified with a focus on detecting complex image tampering.Detecting image tampering without any prior information of the original image is a challenging problem since unknown diverse manipulations may have different characteristics and so do various formats of images.Our principle is that image processing,no matter how complex,may affect image quality,so image quality metrics can be used to distinguish tampered images.In particular,based on the alteration of image quality in modified blocks,the proposed method can locate the tampered areas.Referring to four types of effective no-reference image quality metrics,we obtain 13 features to present an image.The experimental results show that the proposed method is very promising on detecting image tampering and locating the locally tampered areas especially in realistic scenarios.展开更多
In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and local...In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and locally conformal pseudo-Kahler Finsler manifold,which is simply connected or whose fundamental group contains elements of nite order only,can be given a Kahler metric.展开更多
Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is ...Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.展开更多
We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone ac...We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.展开更多
In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.
文摘The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extendedEPRperfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.
基金funded by the Deanship of Scientific Research at Jouf University under Grant No.DSR-2021-03-0301supported by the Higher Education Commission of Pakistan through the National Research Program for Universities Grant No.20-16188/NRPU/R&D/HEC/20212021.
文摘The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.
基金Sponsored by the National Natural Science Foundation of China(Grant No.60971095 and No.61172109)Artificial Intelligence Key Laboratory of Sichuan Province(Grant No.2012RZJ01)the Fundamental Research Funds for the Central Universities(Grant No.DUT13RC201)
文摘In this paper,a new approach is proposed to determine whether the content of an image is authentic or modified with a focus on detecting complex image tampering.Detecting image tampering without any prior information of the original image is a challenging problem since unknown diverse manipulations may have different characteristics and so do various formats of images.Our principle is that image processing,no matter how complex,may affect image quality,so image quality metrics can be used to distinguish tampered images.In particular,based on the alteration of image quality in modified blocks,the proposed method can locate the tampered areas.Referring to four types of effective no-reference image quality metrics,we obtain 13 features to present an image.The experimental results show that the proposed method is very promising on detecting image tampering and locating the locally tampered areas especially in realistic scenarios.
基金Supported by the National Natural Science Foundation of China(Grant No.12001165)Postdoctoral Research Foundation of China(Grant No.2019M652513)Postdoctoral Research Foundation of Henan Province(Grant No.19030050).
文摘In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and locally conformal pseudo-Kahler Finsler manifold,which is simply connected or whose fundamental group contains elements of nite order only,can be given a Kahler metric.
文摘Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.
文摘We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.
文摘In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.
