This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector ident...This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.展开更多
A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components o...A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.展开更多
Slodkowski joint spectrum is similar to Taylor joint spectrum, but it has more important meaning in theory and application. In this paper we characterize Slodkowski joint spectrum and generalize some results about ten...Slodkowski joint spectrum is similar to Taylor joint spectrum, but it has more important meaning in theory and application. In this paper we characterize Slodkowski joint spectrum and generalize some results about tensor product.展开更多
We propose the basis for a rigorous approach to modeling combat, specifically under conditions of complexity and uncertainty. The proposed basis is a tensorial generalization of earlier Lanchester-type equations, insp...We propose the basis for a rigorous approach to modeling combat, specifically under conditions of complexity and uncertainty. The proposed basis is a tensorial generalization of earlier Lanchester-type equations, inspired by the contemporary debate in defence and military circles around how to best utilize information and communications systems in military operations, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). Despite attracting considerable interest and spawning several efforts to develop sound theoretical frameworks for informing force design decision-making, the development of good frameworks for analytically modeling combat remains anything but decided. Using a simple combat scenario, we first develop a tensor generalization of the Lanchester square law, and then extend it to also include the Lanchester linear law, which represents the effect of suppressive fire. We also add on-off control inputs, and discuss the results of a simple simulation of the final model using our small scenario.展开更多
Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ com...Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φ▽ξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.展开更多
In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detectio...In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.展开更多
In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to...In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.展开更多
General relativity of Einstein’s theory and Quantum physics theory are excellent pillars that explain much modern physics. Understanding the relation between these theories is still a theoretical physics central open...General relativity of Einstein’s theory and Quantum physics theory are excellent pillars that explain much modern physics. Understanding the relation between these theories is still a theoretical physics central open question. Over last several decades, works in this direction have led to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, one of its solutions such as a real solution is studied in our last article. In this paper, complex TOUGMA’s metric is studied, particularly the physics concepts that this metric implies such as light geodesic and metric’s impacts at r = 0. The first time, we studied the fact of r = 0 and its limits, secondly, we consider a zero length light geodesic is a geodesic and ended by studying it mathematically. These underlying principles study, those various phenomena in universe are interconnected logic leading to develop new technologies for example: news engines, telecommunication networks. This study’s applications are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics, Multiverse. Mostly this study lets us to know the quantum relativity universe behaviors.展开更多
Einstein’s General relativity theory and Quantum physics are the main pillars for explaining most modern physics. Obtaining these theories relation between them remains a theoretical physics main question. In the las...Einstein’s General relativity theory and Quantum physics are the main pillars for explaining most modern physics. Obtaining these theories relation between them remains a theoretical physics main question. In the last most decades, works are leading to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, and one of these solutions, mostly a real solution is studied in our last article. In this work, complex TOUGMA’s metric is studied, such as the physics concepts implied by this metric, mainly material bodies geodesics orbits. We studied the fact material bodies’ orbits and their limits. This study of the underlying principles and various phenomena in universe are interconnected logic leading to new technologies development such as news engines and telecommunication networks. The applications of this study are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics and Multiverse. Mostly this study allows us to know the behaviors of matter in the quantum relativity universe. Universe.展开更多
This paper constructs and studies a nonlinear multivariate regression-tensor model for substantiation of necessary/sufficient conditions of optimization of technological calculation of multifactor physical and chemica...This paper constructs and studies a nonlinear multivariate regression-tensor model for substantiation of necessary/sufficient conditions of optimization of technological calculation of multifactor physical and chemical process of hardening of complex composite media for metal coatings. An adaptive a posteriori procedure for parametric formation of the target quality functional of integrative physical and mechanical properties of the designed metal coating has been proposed. The results of the research may serve as elements of a mathematical language when creating automated design of precision nanotechnologies for surface hardening of complex composite metal coatings on the basis of complex tribological and anticorrosive tests.展开更多
文摘This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.20204007 and 50390090)the Doctoral Foundation of National Education Committee of China(No.20030248008)the 863 Project of China(No.2002AA336120).
文摘A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.
文摘Slodkowski joint spectrum is similar to Taylor joint spectrum, but it has more important meaning in theory and application. In this paper we characterize Slodkowski joint spectrum and generalize some results about tensor product.
文摘We propose the basis for a rigorous approach to modeling combat, specifically under conditions of complexity and uncertainty. The proposed basis is a tensorial generalization of earlier Lanchester-type equations, inspired by the contemporary debate in defence and military circles around how to best utilize information and communications systems in military operations, including the distributed C4ISR system (Command, Control, Communications, Computing, Intelligence, Surveillance and Reconnaissance). Despite attracting considerable interest and spawning several efforts to develop sound theoretical frameworks for informing force design decision-making, the development of good frameworks for analytically modeling combat remains anything but decided. Using a simple combat scenario, we first develop a tensor generalization of the Lanchester square law, and then extend it to also include the Lanchester linear law, which represents the effect of suppressive fire. We also add on-off control inputs, and discuss the results of a simple simulation of the final model using our small scenario.
文摘Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φ▽ξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.
文摘In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.
文摘In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.
文摘General relativity of Einstein’s theory and Quantum physics theory are excellent pillars that explain much modern physics. Understanding the relation between these theories is still a theoretical physics central open question. Over last several decades, works in this direction have led to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, one of its solutions such as a real solution is studied in our last article. In this paper, complex TOUGMA’s metric is studied, particularly the physics concepts that this metric implies such as light geodesic and metric’s impacts at r = 0. The first time, we studied the fact of r = 0 and its limits, secondly, we consider a zero length light geodesic is a geodesic and ended by studying it mathematically. These underlying principles study, those various phenomena in universe are interconnected logic leading to develop new technologies for example: news engines, telecommunication networks. This study’s applications are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics, Multiverse. Mostly this study lets us to know the quantum relativity universe behaviors.
文摘Einstein’s General relativity theory and Quantum physics are the main pillars for explaining most modern physics. Obtaining these theories relation between them remains a theoretical physics main question. In the last most decades, works are leading to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, and one of these solutions, mostly a real solution is studied in our last article. In this work, complex TOUGMA’s metric is studied, such as the physics concepts implied by this metric, mainly material bodies geodesics orbits. We studied the fact material bodies’ orbits and their limits. This study of the underlying principles and various phenomena in universe are interconnected logic leading to new technologies development such as news engines and telecommunication networks. The applications of this study are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics and Multiverse. Mostly this study allows us to know the behaviors of matter in the quantum relativity universe. Universe.
文摘This paper constructs and studies a nonlinear multivariate regression-tensor model for substantiation of necessary/sufficient conditions of optimization of technological calculation of multifactor physical and chemical process of hardening of complex composite media for metal coatings. An adaptive a posteriori procedure for parametric formation of the target quality functional of integrative physical and mechanical properties of the designed metal coating has been proposed. The results of the research may serve as elements of a mathematical language when creating automated design of precision nanotechnologies for surface hardening of complex composite metal coatings on the basis of complex tribological and anticorrosive tests.
