This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself propos...This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself proposes a complete physical and mathematical blueprint of the brain’s OS. A first addition to the book (see Chapters 5 to 10 below) concerns the relation between the afore-mentioned blueprint and the more than 2000-year-old so-called fundamental laws of thought of logic and philosophy, which came to be viewed as being three (3) in number, namely the laws of 1) Identity, 2) Contradiction, and 3) the Excluded Middle. The blueprint and the laws cannot both be the final foundation of the brain’s OS. The design of the present paper is to interpret the laws in strictly mathematical terms in light of the blueprint. This addition constitutes the bulk of the present article. Chapters 5 to 8 set the stage. Chapters 9 and 10 present a detailed mathematical analysis of the laws. A second addition to the book (Chapter 11) concerns the distinction between the laws and the axioms of the brain’s OS. Laws are part of physics. Axioms are part of mathematics. Since the theory of the brain’s OS involves both physics and mathematics, it exhibits both laws and axioms. A third addition (Chapter 12) to the book involves an additional flavor of digitality in the brain’s OS. In the book, there are five (5). But brain chemistry requires a sixth. It will be called Existence Digitality. A fourth addition (Chapter 13) concerns reflections on the role of imagination in theories of physics in light of the ignorance of deeper causes. Chapters 1 to 4 present preliminary matter, for the most part a brief survey of general concepts derived from what is in the book [1]. Some historical notes are gathered at the end in Chapter 14.展开更多
Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures...Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln（Cq^-） are determined.展开更多
Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on...Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.展开更多
文摘This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself proposes a complete physical and mathematical blueprint of the brain’s OS. A first addition to the book (see Chapters 5 to 10 below) concerns the relation between the afore-mentioned blueprint and the more than 2000-year-old so-called fundamental laws of thought of logic and philosophy, which came to be viewed as being three (3) in number, namely the laws of 1) Identity, 2) Contradiction, and 3) the Excluded Middle. The blueprint and the laws cannot both be the final foundation of the brain’s OS. The design of the present paper is to interpret the laws in strictly mathematical terms in light of the blueprint. This addition constitutes the bulk of the present article. Chapters 5 to 8 set the stage. Chapters 9 and 10 present a detailed mathematical analysis of the laws. A second addition to the book (Chapter 11) concerns the distinction between the laws and the axioms of the brain’s OS. Laws are part of physics. Axioms are part of mathematics. Since the theory of the brain’s OS involves both physics and mathematics, it exhibits both laws and axioms. A third addition (Chapter 12) to the book involves an additional flavor of digitality in the brain’s OS. In the book, there are five (5). But brain chemistry requires a sixth. It will be called Existence Digitality. A fourth addition (Chapter 13) concerns reflections on the role of imagination in theories of physics in light of the ignorance of deeper causes. Chapters 1 to 4 present preliminary matter, for the most part a brief survey of general concepts derived from what is in the book [1]. Some historical notes are gathered at the end in Chapter 14.
基金supported by NSF of China(11071187)Innovation Program of Shanghai Municipal Education Commission(09YZ336)
文摘Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln（Cq^-） are determined.
基金This work is partially supported by NNSF of China(10671124)the Specialized Research Fund for the Doctoral Program of Higher Education(20040247024).
文摘Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.
基金Supported by National Natural Science Foundation of China(11971315,11871249)Scientific Research Project of Huzhou University(The structures and representations of several types of infinite dimensional Lie algebras)
