Pub Date : 2018-12-17DOI: 10.46991/pysu:a/2018.52.3.172
B. A. Sahakyan
In the paper Taylor–Maclaurin type formulas for some classes of functions are obtained. The main result of this study introduces an idea of the generalized classes of $ langle rho_j rangle $ completely monotone function. Under the various conditions $ left( sumlimits_{j=1}^{infty} dfrac{1}{rho_j} < + infty , sumlimits_{j=1}^{infty} dfrac{1}{rho_j} = + infty right) $ the terms of their representation are obtained and some related theorems are proved.
{"title":"ON A GENERALIZED FORMULA OF TAYLOR–MACLAURIN TYPE ON THE GENERALIZED COMPLETELY MONOTONE FUNCTIONS","authors":"B. A. Sahakyan","doi":"10.46991/pysu:a/2018.52.3.172","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.3.172","url":null,"abstract":"In the paper Taylor–Maclaurin type formulas for some classes of functions are obtained. The main result of this study introduces an idea of the generalized classes of $ langle rho_j rangle $ completely monotone function. Under the various conditions $ left( sumlimits_{j=1}^{infty} dfrac{1}{rho_j} < + infty , sumlimits_{j=1}^{infty} dfrac{1}{rho_j} = + infty right) $ the terms of their representation are obtained and some related theorems are proved.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73626713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-17DOI: 10.46991/pysu:a/2018.52.3.217
M. Stepanyan
Using computer simulations and simultaneous X-ray diffraction at large and small angles, the dependence of the swelling coefficient of the phospholipid bilayer on the angle between the inclination of dipole fragments and the plane of the lamella was investigated. It was shown that in this case the balance between electrostatic, repulsive and van der Waals attraction forces is a particular importance. As the dipole angle increases, the repulsive forces of the electrostatic dipole-dipole interaction increase, resulting the increase of the bilayer thickness as a function of the number of –CH-groups in the phospholipid. At a certain angle the bilayer is destroyed. It is also shown that at certain small angles the bilayer takes a minimum thickness. In this case a phase transformation takes place and the system enters the “gel”-phase.
{"title":"STUDY OF THE SWELLING OF THE PHOSPHOLIPID BILAYER, DEPENDING ON THE ANGLE BETWEEN THE INCLINATION OF THE DIPOLE FRAGMENTS AND THE PLANE OF THE LAMELLA","authors":"M. Stepanyan","doi":"10.46991/pysu:a/2018.52.3.217","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.3.217","url":null,"abstract":"Using computer simulations and simultaneous X-ray diffraction at large and small angles, the dependence of the swelling coefficient of the phospholipid bilayer on the angle between the inclination of dipole fragments and the plane of the lamella was investigated. It was shown that in this case the balance between electrostatic, repulsive and van der Waals attraction forces is a particular importance. As the dipole angle increases, the repulsive forces of the electrostatic dipole-dipole interaction increase, resulting the increase of the bilayer thickness as a function of the number of –CH-groups in the phospholipid. At a certain angle the bilayer is destroyed. It is also shown that at certain small angles the bilayer takes a minimum thickness. In this case a phase transformation takes place and the system enters the “gel”-phase.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"239 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90503957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.119
S. A. Nigiyan
In this paper the interpretation algorithms for typed and untyped functional programs are considered. Typed functional programs use variables of any order and constants of order $ leq 1 $, where constants of order 1 are strongly computable, monotonic functions with indeterminate values of arguments. The basic semantics of the typed functional program is a function with indeterminate values of arguments, which is the main component of its least solution. The interpretation algorithms of typed functional programs are based on substitutions, $ beta $-reduction and canonical $ delta $-reduction. The basic semantics of the untyped functional program is the untyped $ lambda $-term, which is defined by means of the fixed point combinator. The interpretation algorithms of untyped functional programs are based on substitutions and $ beta $-reduction. Interpretation algorithms are examined for completeness and comparability. It is investigated how the “behavior” of the interpretation algorithm changes after translation of typed functional program into untyped functional program.
{"title":"ON INTERPRETATION OF TYPED AND UNTYPED FUNCTIONAL PROGRAMS","authors":"S. A. Nigiyan","doi":"10.46991/pysu:a/2018.52.2.119","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.119","url":null,"abstract":"In this paper the interpretation algorithms for typed and untyped functional programs are considered. Typed functional programs use variables of any order and constants of order $ leq 1 $, where constants of order 1 are strongly computable, monotonic functions with indeterminate values of arguments. The basic semantics of the typed functional program is a function with indeterminate values of arguments, which is the main component of its least solution. The interpretation algorithms of typed functional programs are based on substitutions, $ beta $-reduction and canonical $ delta $-reduction. The basic semantics of the untyped functional program is the untyped $ lambda $-term, which is defined by means of the fixed point combinator. The interpretation algorithms of untyped functional programs are based on substitutions and $ beta $-reduction. Interpretation algorithms are examined for completeness and comparability. It is investigated how the “behavior” of the interpretation algorithm changes after translation of typed functional program into untyped functional program.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78320195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.093
K. Navasardyan
In this paper we prove that there exist a nontrivial Franklin series and a sequence $ M_n $ such that the partial sums $ S_{M_n} (x) $ of that series converge to 0 almost everywhere and $ lambda cdot text{mes} { x : suplimits_{n}{left| S_{M_n} (x) right|} > lambda } to 0 $ as $ lambda to +infty $. This shows that the boundedness assumption of the ratio $ dfrac{ M_{n+1}}{M_n} $, used for the proofs of uniqueness theorems in earlier papers, can not be omitted.
本文证明了存在一个非平凡富兰克林级数和一个序列$ M_n $，使得该级数的部分和$ S_{M_n} (x) $几乎处处收敛于0，且$ lambda cdot text{mes} { x : suplimits_{n}{left| S_{M_n} (x) right|} > lambda } to 0 $为$ lambda to +infty $。这表明在以前的论文中用来证明唯一性定理的比率$ dfrac{ M_{n+1}}{M_n} $的有界假设是不能省略的。
{"title":"ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM","authors":"K. Navasardyan","doi":"10.46991/pysu:a/2018.52.2.093","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.093","url":null,"abstract":"In this paper we prove that there exist a nontrivial Franklin series and a sequence $ M_n $ such that the partial sums $ S_{M_n} (x) $ of that series converge to 0 almost everywhere and $ lambda cdot text{mes} { x : suplimits_{n}{left| S_{M_n} (x) right|} > lambda } to 0 $ as $ lambda to +infty $. This shows that the boundedness assumption of the ratio $ dfrac{ M_{n+1}}{M_n} $, used for the proofs of uniqueness theorems in earlier papers, can not be omitted.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"133 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85304325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.140
A. Gevorgyan, H. Avagyan
This work presents development of a method for multi-criteria decision making under uncertainty conditions based on single-attribute value functions and probabilistic distributions. The values of different criteria are modeled using normal distributions, i.e. the value of the $ i $-th criteria of the $ j $-th option is given by $ x^j_i sim mathcal{N} ({mu}^j_i, {sigma}^j_i) $ distribution. The method is evaluated and the results are analyzed on a simple example.
{"title":"A METHOD FOR MULTI-CRITERIA DECISION MAKING UNDER UNCERTAINTY","authors":"A. Gevorgyan, H. Avagyan","doi":"10.46991/pysu:a/2018.52.2.140","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.140","url":null,"abstract":"This work presents development of a method for multi-criteria decision making under uncertainty conditions based on single-attribute value functions and probabilistic distributions. The values of different criteria are modeled using normal distributions, i.e. the value of the $ i $-th criteria of the $ j $-th option is given by $ x^j_i sim mathcal{N} ({mu}^j_i, {sigma}^j_i) $ distribution. The method is evaluated and the results are analyzed on a simple example.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80742117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.101
R. Kirakosyan, S. Stepanyan
On the basis of the refined theory of orthotropic plates of variable thickness, the equations of the beam bending problem are obtained with the simultaneous action of compressive forces and transverse load. It is accepted that the edges of the beam have an elastically clamped support and the reduction of the compressive force by the support due to friction is taking into account. Passing to dimensionless quantities, a certain problem is solved. The stability of a beam is discussed. Based on the results obtained, conclusions are drawn.
{"title":"THE NON-CLASSICAL PROBLEM OF AN ELASTICALLY CLAMPED ORTHOTROPIC BEAM OF VARIABLE THICKNESS UNDER THE COMBINED ACTION OF COMPRESSIVE FORCES AND TRANSVERSE LOAD","authors":"R. Kirakosyan, S. Stepanyan","doi":"10.46991/pysu:a/2018.52.2.101","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.101","url":null,"abstract":"On the basis of the refined theory of orthotropic plates of variable thickness, the equations of the beam bending problem are obtained with the simultaneous action of compressive forces and transverse load. It is accepted that the edges of the beam have an elastically clamped support and the reduction of the compressive force by the support due to friction is taking into account. Passing to dimensionless quantities, a certain problem is solved. The stability of a beam is discussed. Based on the results obtained, conclusions are drawn.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73996508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.134
T. Z. Bezhanyan
The results of temperature measurements in the Argon discharge in plasma with acoustic perturbation are presented. Possibility of, as decreasing, so increasing of discharge temperature in several times is shown.
给出了声扰动下等离子体氩气放电温度的测量结果。给出了放电温度在几次内随温度降低或升高的可能性。
{"title":"MEASUREMENT OF DISCHARGES TEMPERATURE IN LOW-TEMPERATURE ACOUSTOPLASMA","authors":"T. Z. Bezhanyan","doi":"10.46991/pysu:a/2018.52.2.134","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.134","url":null,"abstract":"The results of temperature measurements in the Argon discharge in plasma with acoustic perturbation are presented. Possibility of, as decreasing, so increasing of discharge temperature in several times is shown.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84795885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.109
D. Grigoryan
In the paper the interpretation algorithms of typed functional programs are considered. The interpretation algorithm is based on substitution, $ beta $-reduction and canonical $ delta $-reduction. It is shown that seven known interpretation algorithms (FS (of full substitution), PES (of parallel external substitution), LES (of left external substitution), PIS (of parallel inner substitution), LIS (of left inner substitution), ACT (active algorithm), PAS (passive algorithm)) are pairwise incomparable with respect to undefined value ($ perp $-incomparable).
{"title":"ON INCOMPARABILITY OF INTERPRETATION ALGORITHMS OF TYPED FUNCTIONAL PROGRAMS WITH RESPECT TO UNDEFINED VALUE","authors":"D. Grigoryan","doi":"10.46991/pysu:a/2018.52.2.109","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.109","url":null,"abstract":"In the paper the interpretation algorithms of typed functional programs are considered. The interpretation algorithm is based on substitution, $ beta $-reduction and canonical $ delta $-reduction. It is shown that seven known interpretation algorithms (FS (of full substitution), PES (of parallel external substitution), LES (of left external substitution), PIS (of parallel inner substitution), LIS (of left inner substitution), ACT (active algorithm), PAS (passive algorithm)) are pairwise incomparable with respect to undefined value ($ perp $-incomparable).","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74750016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.088
N. Mirzakhanyan, H. Piliposyan
In the paper an answer to a problem posed by A.I. Sozutov in the Kourovka Notebook is given. The solution is based on some modification of the method that was proposed for constructing a non-abelian analogue of the additive group of rational numbers, i.e. a group whose center is an infinite cyclic group and any two non-trivial subgroups of which have a non-trivial intersection.
{"title":"ON A QUESTION OF A. SOZUTOV","authors":"N. Mirzakhanyan, H. Piliposyan","doi":"10.46991/pysu:a/2018.52.2.088","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.088","url":null,"abstract":"In the paper an answer to a problem posed by A.I. Sozutov in the Kourovka Notebook is given. The solution is based on some modification of the method that was proposed for constructing a non-abelian analogue of the additive group of rational numbers, i.e. a group whose center is an infinite cyclic group and any two non-trivial subgroups of which have a non-trivial intersection.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84053631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.46991/pysu:a/2018.52.2.077
A. Hovhannisyan, A. Kamalyan, H. A. Kamalyan
In the present paper the connection between a class of systems of differential equations and integral operators with semi-separable kernel is established. Using a matrix of the system the inverse to a given integral operator is constructed. Moreover by putting some additional conditions on the kernel of integral operator and by the help of inverse of integral operator a fundamental matrix of the system is constructed.
{"title":"ON A CONNECTION BETWEEN A CLASS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRAL OPERATORS WITH SEMI-SEPARABLE KERNEL","authors":"A. Hovhannisyan, A. Kamalyan, H. A. Kamalyan","doi":"10.46991/pysu:a/2018.52.2.077","DOIUrl":"https://doi.org/10.46991/pysu:a/2018.52.2.077","url":null,"abstract":"In the present paper the connection between a class of systems of differential equations and integral operators with semi-separable kernel is established. Using a matrix of the system the inverse to a given integral operator is constructed. Moreover by putting some additional conditions on the kernel of integral operator and by the help of inverse of integral operator a fundamental matrix of the system is constructed.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"201 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78490012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：