Mikhail Mikhaylov - Academia.edu (original) (raw)
Papers by Mikhail Mikhaylov
ABSTRACT. Thoughts expressed in previous paper [3] were developed. There was shown formally that ... more ABSTRACT. Thoughts expressed in previous paper [3] were developed. There was shown formally that collection of sets ’ properties may not appear chaotically and independently on each other. Presence or absence of one leads to rise or drop of another. Contents 1. Something about “reflexivity ” of tolerances............................................................................... 1 2. Dependence of reversibility on the other relation’s properties................................................... 3
viXra, 2017
This sum for natural values is, of course, already calculated by Bernoulli himself – at least mod... more This sum for natural values is, of course, already calculated by Bernoulli himself – at least modern or relatively recent authors that deal with it usually refer to take into account Bernoulli numbers. But, apparently, this method is rather cumbersome. Therefore, there can be suggested another, easier way to do this, but without claiming of its superfluous rigidity.
It seems that statements determining features of some algebraic structures behavior are based on ... more It seems that statements determining features of some algebraic structures behavior are based on just intuitive assumptions or empiric observations and for sake of convenience (simplest example is the phrase: "let's consider 0! =1"… perhaps, just because sir I. Newton entrusted, so, why not 2, 5, 7.65-choose any). So, without logical explanation these are looking a little mysterious or sometimes even magic. This article is a humble attempt to get it straight rather formally. Some troubles may appear on the way-e.g. as it was shown earlier (in the ref. [2], for example), there are at least two binary relations having properties of idempotent equivalences-algebra's elements that may aspire to be an identity. Apparently, probable obtaining of some well-known results in the text is not an attempt of their rediscovering , but it is rather "check-points" that confirm theory validity, more by token that it was made by using of the only exceptionally formal way, while usually they are obtained rather intuitively. Usually the notion of tensor product is determined for each kind of algebraic structure-especially for modulus (in group theory it is often called direct product-but this is a matter of semantics, so, it's rather negligible). Here it is shown that tensor product may be introduced without defining of concrete algebraic structure. Without such introduction defining of algebraic operation is strongly complicated.
There was an attempt to formalize an appearance of main relation properties in contrast to the us... more There was an attempt to formalize an appearance of main relation properties in contrast to the usual one. There was paid an attention only for natural relations. In fact, such relations as "better than" are not observed here since the notion of "good" is still not defined.
Recent Advances in Mathematical Research and Computer Science Vol. 6
In this study the reasons obliging a relation to be transitive were established. Unified definiti... more In this study the reasons obliging a relation to be transitive were established. Unified definitions of different symmetry and reflexivity manifests were made. It was shown that among relations’ properties only transitivity has the direct negation.
ABSTRACT. Thoughts expressed in previous paper [3] were developed. There was shown formally that ... more ABSTRACT. Thoughts expressed in previous paper [3] were developed. There was shown formally that collection of sets ’ properties may not appear chaotically and independently on each other. Presence or absence of one leads to rise or drop of another. Contents 1. Something about “reflexivity ” of tolerances............................................................................... 1 2. Dependence of reversibility on the other relation’s properties................................................... 3
viXra, 2017
This sum for natural values is, of course, already calculated by Bernoulli himself – at least mod... more This sum for natural values is, of course, already calculated by Bernoulli himself – at least modern or relatively recent authors that deal with it usually refer to take into account Bernoulli numbers. But, apparently, this method is rather cumbersome. Therefore, there can be suggested another, easier way to do this, but without claiming of its superfluous rigidity.
It seems that statements determining features of some algebraic structures behavior are based on ... more It seems that statements determining features of some algebraic structures behavior are based on just intuitive assumptions or empiric observations and for sake of convenience (simplest example is the phrase: "let's consider 0! =1"… perhaps, just because sir I. Newton entrusted, so, why not 2, 5, 7.65-choose any). So, without logical explanation these are looking a little mysterious or sometimes even magic. This article is a humble attempt to get it straight rather formally. Some troubles may appear on the way-e.g. as it was shown earlier (in the ref. [2], for example), there are at least two binary relations having properties of idempotent equivalences-algebra's elements that may aspire to be an identity. Apparently, probable obtaining of some well-known results in the text is not an attempt of their rediscovering , but it is rather "check-points" that confirm theory validity, more by token that it was made by using of the only exceptionally formal way, while usually they are obtained rather intuitively. Usually the notion of tensor product is determined for each kind of algebraic structure-especially for modulus (in group theory it is often called direct product-but this is a matter of semantics, so, it's rather negligible). Here it is shown that tensor product may be introduced without defining of concrete algebraic structure. Without such introduction defining of algebraic operation is strongly complicated.
There was an attempt to formalize an appearance of main relation properties in contrast to the us... more There was an attempt to formalize an appearance of main relation properties in contrast to the usual one. There was paid an attention only for natural relations. In fact, such relations as "better than" are not observed here since the notion of "good" is still not defined.
Recent Advances in Mathematical Research and Computer Science Vol. 6
In this study the reasons obliging a relation to be transitive were established. Unified definiti... more In this study the reasons obliging a relation to be transitive were established. Unified definitions of different symmetry and reflexivity manifests were made. It was shown that among relations’ properties only transitivity has the direct negation.