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    BANGNAM
    2023-01-29 12:17:05
    5 min read
    · 5:30

    Xspace 123 là gì

    This chapter illustrates the way time geometry and space geometry combines to form a solid foundation for space-time geometry. In an inhomogeneous time-varying gravitational field, the rates of clocks depend upon both position and time, and synchronization is not transitive. Consequently, synchronization must be performed continuously between all clocks and a central clock. Because of the finite speed of any signal, it takes time to synchronize a distant clock, which adds another complication. The chapter illustrates the fact that synchronization is conventional and arbitrary. It is desirable to find a method to describe physical phenomena without synchronization. The chapter also derives from the general theory of relativity (GR) a relation between lag time and other (proper) time intervals. Furthermore, the rate of a standard clock may vary with both position and time, and there is no escape from the formulation of space-time geometry in terms of local relations.

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      Complete load-deflection relationships of a rigid-plastic beam subjected to a non-symmetrically placed point load are derived. In addition to the inclusion of the effects of geometry change, the analysis considers the supports as being capable of variable combined axial and rotational restraints. As expected, the increase in load-carrying capacity with deflection can be quite large for certain support conditions.

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      There are several different kinds of glucansucrases that synthesize glucans with different structures from sucrose. Glucans that have contiguous α-1→6 linked glucose residues are known as dextrans. The dextrans differ from each other by the type of branch linkages (α-1→2, α-1→2 and α-1→4), the percentage of branching, the length of the branch chains, and their spatial arrangement. Some of these dextrans are very highly branched with 35%≈50% branch linkages. Other glucans that have contiguous α-1→3 linked glucose residues in the main chains are known as mutans, and glucans with alternating α-1→6 and α-1→3 linked glucose residues in the main chains are known as alternans. The enzymes that catalyze glucan synthesis from sucrose form covalent glucosyl- and glucanyl-enzyme complexes. They transfer the glucosyl unit to the reducing-end of the growing glucan chain by a two-site insertion mechanism. Branching of the glucans occurs when a glucan chain acts as an acceptor and attacks the covalent glucosyl- or glucanyl-enzyme complex. Glucose or glucan chain are transferred to the acceptor chain where they are attached by a branch linkage. When other carbohydrates, in addition to sucrose, are present in the enzyme digest, the enzyme transfers glucose to the carbohydrate acceptors in a secondary reaction that diverts some of the glucose from incorporation into glucan. Many carbohydrate acceptors have been recognized and the products that result are dependent on the particular enzyme and the structure of the particular acceptor.

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      Reversible Adsorption of H2 on Rh/TiO2

      Studies in Surface Science and Catalysis, Volume 17, 1983, pp. 149-161

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      Volumetric adsorption, ESR, NMR and IR measurements have been used to study the effect of H2 adsorption and desorption at 295 K on a TiO2-supported rhodium catalyst. Three situations have been differentiated along the reduction process of the samples from RhCl3/anatase to Rh (metal)utile: (a) when rhodium is stabilised as Rh a small part of the important H2 adsorption is in close interaction with the support; (b) in the situation Rh°/anatase a more substantial amount of the adsorbed hydrogen is spilt reversibly over the support; (c) H2 adsorption is small after reduction and pumping at 773 K, but a certain amount of hydrogen has been stabilised inside the rutilised support during the high-temperature treatment.

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      Some Problems of Definability in Recursive Function Theory

      Studies in Logic and the Foundations of Mathematics, Volume 46, 1967, pp. 183-201

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      This chapter discusses several problems of definability in recursive function theory. It presents several of the basic facts of elementary recursive function theory and describes several structures that have been principal objects of study in recent development of the theory. The chapter considers the notion of definability and provides a brief discussion of the open problems. The notion of recursive function is the central concept in the theory; the partial recursive functions play a fundamental technical role. They can be effectively enumerated; which means that an effective procedure exists for listing all the sets of instructions for all the partial recursive functions. The chapter describes the concepts of recursive function and partial recursive function. A few basic theorems in the elementary theory are also presented. The first theorem gives a fundamental relationship among the concepts of recursive function. The second theorem gives a technically useful characterization of recursive enumerability. The third theorem simplifies several concerns of later parts of the theory.

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      Concrete Models of Set Theory

      Studies in Logic and the Foundations of Mathematics, Volume 46, 1967, pp. 44-74

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      This chapter provides an introduction to Cohen's forcing method. It presents Cohen's basic method and a proof of the independence of the continuum hypothesis as a typical application. The chapter describes the formal system of Zernielo–Fraenkel set theory (ZF) and introduces the basic notations. The metalinguistic framework of the investigation and an arithmetisation of the object language are described in the chapter. The class of concrete models is introduced in the chapter. The chapter describes the notion of constructible closure and contains a proof that every constructibly closed inner model of a concrete ZF model M is a ZF model. Later, the notions of forcing and generic model are introduced in the chapter. By a straightforward modification, it is proved that every generic model is a ZF model. It is also proved that each of a class of axioms, which violates the general continuum hypothesis, is consistent.

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