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Among other things, we prove that, for a compact K?hler-Einstein complex surface (M, J, g0) with negative scalar curvature, (i) if g1 is a Riemannian metric on M with λM(g1) = λM(g0), then
      
It is shown that the higher the slag basicity, the stronger the hydration interactions in alkaline binder compositions causing their hardening, all other things being equal.
      
It is shown that, other things being equal, the response of the system to the light wave is greatest when the period of the interference intensity pattern is of the order of twice the thickness of the layer.
      
Apparently, the calculation formulas for the rate of thermophoretic transfer have a wider range of validity than those previously obtained, all other things being equal.
      
It is demonstrated that the main factor defining the electron loss in magnetic traps in the collisionless limit is the departure of fast electrons from magnetic traps to the boundaries of the structure among other things.
      
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In the restricted predicate calculus we deal with functions, namely, the thing functions which take individuals as as values and the propositional functions i.e. predicates. Usually they take only individuals as arguments. Such a restriction seems, however, too severe. It would be better if we allow them to take also propositions as arguments. Besides, we deal also with operators, namely, quantifiers and descriptions. By the same reason, it would be better if we allow them to take also terms as their scopes...

In the restricted predicate calculus we deal with functions, namely, the thing functions which take individuals as as values and the propositional functions i.e. predicates. Usually they take only individuals as arguments. Such a restriction seems, however, too severe. It would be better if we allow them to take also propositions as arguments. Besides, we deal also with operators, namely, quantifiers and descriptions. By the same reason, it would be better if we allow them to take also terms as their scopes and to take propositional variables as the directive variables. Further, in the extended predicate calculus, we deal also with functions of higher order and operators of higher order. We usually consider them to be quite different from each other. In the present paper, we show that: First, the functions of the second order are the same as the operators ofthe first order. For example, the expression φ(A), where φ is a function of second order, and A is a two-place first order function, may also be represented as φ_(xy) A(x,y), where φ_(xy) is an operator of first order with two directive variables x and y. On the other hand, the expression lim(x→a) f(x), where lim is an operator of first order, may also be represented as lim(a,f), where lira is now a function of second order with one individual argument and one functionargument (of first order). In general, the functions of order n+1 are the same as the operators of order n. (However, see the following.) Secondly, when we apply functions of second order (i.e. operator of first order) to functions of first order to form a term or a formula, it is not that the former (of higher order) take the latter (of lower order) as arguments (so asserted by the prevailing opinion), but that the former become arguments of the latter, or at least that the former bind the empty places of the latter. Anyhow we cannot say that the latter are arguments of the former. Hence the usual expressions Axa(x) and lim(x→a) f(x) should be written as (αA and (f lira α or as Aα(i) and lim a f(i). (We stipulate that if operators should be written after the scope they must be coupled with left parentheses.) Thirdly, since the first order operators (i.e. functions of the second order) never take functions of first order as arguments, there is no room to give riseto higher functions and operators. Hence we have only individuals, propositions, functions (of first order) and operators (of first order, i.e. functions of second order). The extended predicate calculus would become much simpler.

在狭义谓词演算中我们讨论了函谓词,即以个体为值的函词和以命题为值的谓词。通常它们以个体为变目,但这种限制太严了,我们应该容许命题亦作为变目。此外,我们又讨论了量词与摹状词,它们合称约束词。根据同样理由,我们也容许它们的作用域可为项(不限于公式),它们的指导变元可为命题变元。在高级谓词演算中,我们还讨论高级函谓词和高级约束词。通常我们把高级函谓词和高级约束词看作是本质不同的。在本文中,我们指出: 第一,二级函谓词和一级约束词是一样的。例如,对二级函谓词φ及二元一级函谓词A而言,φ(A)亦可表为φ_(xy)A(x,y),这里φ_(xy)为具有两个指导变元的一级约束词。另一方面,对一级约束词lim而言,lim f(x)亦可表为lim(a,f),这里lim是二级函谓词,它有一个个体变目和一个函谓词(一级)变目。一般说来,n+1级函谓词和n级约束词是一样的(但参看下文)。其次,当我们把二级函谓词(亦即一级约束词)作用于一级函谓词以作成一项或一公式时,并不是前者(级数较高)以后者(级数较低)为变目,(这是通常的说法所断定的),而是前者填充后者的变目,至少是前者约束后者的变目,无论如何,我们不能说后者是前者的变目。因此通常...

在狭义谓词演算中我们讨论了函谓词,即以个体为值的函词和以命题为值的谓词。通常它们以个体为变目,但这种限制太严了,我们应该容许命题亦作为变目。此外,我们又讨论了量词与摹状词,它们合称约束词。根据同样理由,我们也容许它们的作用域可为项(不限于公式),它们的指导变元可为命题变元。在高级谓词演算中,我们还讨论高级函谓词和高级约束词。通常我们把高级函谓词和高级约束词看作是本质不同的。在本文中,我们指出: 第一,二级函谓词和一级约束词是一样的。例如,对二级函谓词φ及二元一级函谓词A而言,φ(A)亦可表为φ_(xy)A(x,y),这里φ_(xy)为具有两个指导变元的一级约束词。另一方面,对一级约束词lim而言,lim f(x)亦可表为lim(a,f),这里lim是二级函谓词,它有一个个体变目和一个函谓词(一级)变目。一般说来,n+1级函谓词和n级约束词是一样的(但参看下文)。其次,当我们把二级函谓词(亦即一级约束词)作用于一级函谓词以作成一项或一公式时,并不是前者(级数较高)以后者(级数较低)为变目,(这是通常的说法所断定的),而是前者填充后者的变目,至少是前者约束后者的变目,无论如何,我们不能说后者是前者的变目。因此通常的表达式Axα(x)和limf(x)应该写成(αA和(flima,或写成Aα(i)和lim af(i)。(我们约定,约束词应依序约束)。第三,由于二级函谓词永不以一级函谓词为变目,也就没有产生更高级函谓词的可能。因此,我们只有个体、命题、(一级)函谓词和(一级)约束词四者,因此广义谓词演算也就变得更简单了。

The article deals with the relationships between the aggregate and system. The author holds that both the system and the aggregate are composed of a number of parts which reach a rudimentary quantity, that they share such characteristics that the whole is bigger that the sum of the parts, and that they are things of diff erentkinds, however. Besides, the author offers a strict definition of aggregate and explains the reasons for formation of the aggregate characteristics, Also discussed are the transformation...

The article deals with the relationships between the aggregate and system. The author holds that both the system and the aggregate are composed of a number of parts which reach a rudimentary quantity, that they share such characteristics that the whole is bigger that the sum of the parts, and that they are things of diff erentkinds, however. Besides, the author offers a strict definition of aggregate and explains the reasons for formation of the aggregate characteristics, Also discussed are the transformation and the relationships between the aggregate and the system.

本文从部分与整体的内在联系、部分在整体中的作用的角度探讨了集合体与系统的关系,指出:系统与集合体都是由达到一个起码数量的若干部分之和的特性;但系统对部分有较严格的量的规定性和结合方式的规定性,构成系统的部分可以是子系统或不同性质的部分,构成集合体的部分则是同类性质的个体。所以集合体与系统是两种不同的事物。

Abstract Aristotle's law of identity evades contradictions and neglects the fact that things in nature are various, different and diverse. The law in fact was a rigid, impractical dogma, which has been harmful in history and cannotmeet the current needs of scientific and technological development and social change Hegal's law of initial identity and secondary diversity makes up the fault of the law of identity on the aspect of "diversity".But Hegal's law emphasizes contradiction and contrariety and overlooks...

Abstract Aristotle's law of identity evades contradictions and neglects the fact that things in nature are various, different and diverse. The law in fact was a rigid, impractical dogma, which has been harmful in history and cannotmeet the current needs of scientific and technological development and social change Hegal's law of initial identity and secondary diversity makes up the fault of the law of identity on the aspect of "diversity".But Hegal's law emphasizes contradiction and contrariety and overlooks the pluralistic, multipolra and diverse qualities of phenomena in nature and ignores the balance between them. the law of identity of diversity, based on the prin-ciple "logic is under constant development", modifies aad advances the two previous laws so as to meet the needs of the present.

亚里士多德的“同一律”是人们进行正常逻辑思维的十分重要的基本规范,在认识史上起了重大作用。但其躲开矛盾,回避万事万物有异、是异、多异的僵死空洞教条方法,在历史上害处甚多,更不相应今日科技水平与社会变革的现实需要。黑格尔辩证逻辑以“一同二异律”弥补了“同一律”在“异”上的缺陷,但其只重矛盾、对立,忽视事物现象的多元多极多异及协同平衡。“同一多异律”从“逻辑是发展的”出发,改善发展了前两律,立一新律以应时代之需。

 
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