This paper presents the complex dynamics synthesis of the combat dy-namics series called tensor-centric warfare (TCW;for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of c...This paper presents the complex dynamics synthesis of the combat dy-namics series called tensor-centric warfare (TCW;for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of classical Lanchester-type combat equations, entropic Lie-dragging and commutators for modeling warfare uncertainty and symmetry, and various delta-strikes and missiles (both deterministic and random). The present paper gives a unique synthesis of the Red vs. Blue vectorfields into a single complex battle-vectorfield, using dynamics on Kähler manifolds as a rigorous framework for extending the TCW concept. The global Kähler dynamics framework, with its rigorous underpinning called the Kähler-Ricci flow, provides not only a new insight into the “geometry of warfare”, but also into the “physics of warfare”, in terms of Lagrangian and Hamiltonian structures of the battlefields. It also provides a convenient and efficient computational framework for entropic wargaming.展开更多
In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly, we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new m...In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly, we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type.展开更多
In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strateg...In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.展开更多
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then t...Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton＇s equations was obtained, and so on.展开更多
The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics...The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential展开更多
Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so o...Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.展开更多
In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex ...In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.展开更多
In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.
Kahler’s disease or “multiple myeloma” is a cancerous disease of the bone marrow. It may appear straightaway in its multiple myeloma form or in the form of solitary bone plasmacytoma or extra bone plasmacytoma. In ...Kahler’s disease or “multiple myeloma” is a cancerous disease of the bone marrow. It may appear straightaway in its multiple myeloma form or in the form of solitary bone plasmacytoma or extra bone plasmacytoma. In the extra bone form, its orbital location as the first symptom is exceptional. Our case concerned a 49-year-old female patient without significant medical history who was followed for 6 months for a voluminous left exophthalmos. This ocular symptomatology was accompanied six months after by acute bone pains in the spine and pelvis then by a pathological fracture of the left trochanter. Histological assessment during the treatment showed the diagnosis of Kahler’s disease. The serum calcium was 106 mmol/l, a blood level of chloride to 96 mmol/l, of potassium to 5.36 mmol/l, of sodium to 136 mmol/l. The 24-hour proteinuria was 0.30 g/l and indicated renal impairment. The patient had anemia with a hemoglobin level to 8.8 g/l. Tumor markers were normal;in particular the CA was 13.148, ACE-2 to 1.013 ng/ml and CA19-9 to 5.029 IU/ml. The patient was transferred to a specialized unit but died before the start of treatment. Thus any isolated exophthalmos or accompanied by bone signs must systematically suggest Kahler’s disease and make undertake investigations in this direction. It is on this condition that an early management of the disease can improve the prognosis of the disease and prolong the patient’s life.展开更多
In this paper,we first solve the Dirichlet problem forα-Hermite-Yang-Mills-Higgs equations on I_(±)-Higgs bundles over a compact generalized Kahler manifold.Then we prove that theα-semi-stability on I_(±)-...In this paper,we first solve the Dirichlet problem forα-Hermite-Yang-Mills-Higgs equations on I_(±)-Higgs bundles over a compact generalized Kahler manifold.Then we prove that theα-semi-stability on I_(±)-Higgs bundles over closed generalized Kahler manifolds implies the existence of approximateα-Hermite-Yang-Mills-Higgs structure.展开更多
In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more...In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more complicated than what they have thought.We shall also give some detail calculations and found that our results fit quite well with earlier papers of the first author,one of them with X.X.Chen.展开更多
In this paper we discuss Newtonian Mechanics on Kahler Manifold, and also givefoe complex mathematical aspects of Newton's law, the law of kinetic energy, the lawof kinetic quantity,the equation of motion and the ...In this paper we discuss Newtonian Mechanics on Kahler Manifold, and also givefoe complex mathematical aspects of Newton's law, the law of kinetic energy, the lawof kinetic quantity,the equation of motion and the 'general equation of dynamics',and so on.展开更多
文摘This paper presents the complex dynamics synthesis of the combat dy-namics series called tensor-centric warfare (TCW;for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of classical Lanchester-type combat equations, entropic Lie-dragging and commutators for modeling warfare uncertainty and symmetry, and various delta-strikes and missiles (both deterministic and random). The present paper gives a unique synthesis of the Red vs. Blue vectorfields into a single complex battle-vectorfield, using dynamics on Kähler manifolds as a rigorous framework for extending the TCW concept. The global Kähler dynamics framework, with its rigorous underpinning called the Kähler-Ricci flow, provides not only a new insight into the “geometry of warfare”, but also into the “physics of warfare”, in terms of Lagrangian and Hamiltonian structures of the battlefields. It also provides a convenient and efficient computational framework for entropic wargaming.
文摘In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly, we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type.
文摘In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.
文摘Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton＇s equations was obtained, and so on.
文摘The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential
文摘Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.
基金Project supported by the National Natural Science Foundation of China (10271106)
文摘In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.
基金The NSF(11101352) of ChinaNew Century Talent Project of Yangzhou University,Fund of Jiangsu University of Technology(KYY 13005)Qing Lan Project
文摘In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.
文摘Kahler’s disease or “multiple myeloma” is a cancerous disease of the bone marrow. It may appear straightaway in its multiple myeloma form or in the form of solitary bone plasmacytoma or extra bone plasmacytoma. In the extra bone form, its orbital location as the first symptom is exceptional. Our case concerned a 49-year-old female patient without significant medical history who was followed for 6 months for a voluminous left exophthalmos. This ocular symptomatology was accompanied six months after by acute bone pains in the spine and pelvis then by a pathological fracture of the left trochanter. Histological assessment during the treatment showed the diagnosis of Kahler’s disease. The serum calcium was 106 mmol/l, a blood level of chloride to 96 mmol/l, of potassium to 5.36 mmol/l, of sodium to 136 mmol/l. The 24-hour proteinuria was 0.30 g/l and indicated renal impairment. The patient had anemia with a hemoglobin level to 8.8 g/l. Tumor markers were normal;in particular the CA was 13.148, ACE-2 to 1.013 ng/ml and CA19-9 to 5.029 IU/ml. The patient was transferred to a specialized unit but died before the start of treatment. Thus any isolated exophthalmos or accompanied by bone signs must systematically suggest Kahler’s disease and make undertake investigations in this direction. It is on this condition that an early management of the disease can improve the prognosis of the disease and prolong the patient’s life.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11971253,11625106,11801535,11721101)the Natural Science Foundation of Anhui Province(Grant No.1908085QA04)Partially Supported by the Project“Analysis and Geometry on Bundle”of Ministry of Science and Technology of the People’s Republic of China(Grant No.SQ2020YFA070080)。
文摘In this paper,we first solve the Dirichlet problem forα-Hermite-Yang-Mills-Higgs equations on I_(±)-Higgs bundles over a compact generalized Kahler manifold.Then we prove that theα-semi-stability on I_(±)-Higgs bundles over closed generalized Kahler manifolds implies the existence of approximateα-Hermite-Yang-Mills-Higgs structure.
基金Supported by National Natural Science Foundation of China(Grant No.12171140).
文摘In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more complicated than what they have thought.We shall also give some detail calculations and found that our results fit quite well with earlier papers of the first author,one of them with X.X.Chen.
文摘In this paper we discuss Newtonian Mechanics on Kahler Manifold, and also givefoe complex mathematical aspects of Newton's law, the law of kinetic energy, the lawof kinetic quantity,the equation of motion and the 'general equation of dynamics',and so on.
