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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika最新文献

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On the Baillie PSW-conjecture 关于贝利 PSW 猜想
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-24 DOI: 10.26907/0021-3446-2024-4-80-88
Sh. T. Ishmukhametov, B. Mubarakov, R. Rubtsova, E. V. Oleynikova
{"title":"On the Baillie PSW-conjecture","authors":"Sh. T. Ishmukhametov, B. Mubarakov, R. Rubtsova, E. V. Oleynikova","doi":"10.26907/0021-3446-2024-4-80-88","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-80-88","url":null,"abstract":"The Baillie PSW hypothesis was formulated in 1980 and was named after the authors R. Baillie, C. Pomerance, J. Selfridge and S. Wagstaff. The hypothesis is related to the problem of the existence of odd numbers n equiv pm 2 (mod 5), which are both Fermat and Lucas-pseudoprimes (in short, FL-pseudoprimes). A Fermat pseudoprime to base a is a composite number n satisfying the condition an - 1 equiv 1 (mod n). Base a is chosen to be equal to 2. A Lucas pseudoprime is a composite n satisfying Fn - e(n) equiv 0 (mod n), where n(e) is the Legendre symbol e(n) = bigl( n 5 bigr) , Fm the mth term of the Fibonacci series. According to Baillie’s PSW conjecture, there are no FL-pseudoprimes. If the hypothesis is true, the combined primality test checking Fermat and Lucas conditions for odd numbers not divisible by 5 gives the correct answer for all numbers of the form n equiv pm 2 (mod 5), which generates a new deterministic polynomial primality test detecting the primality of 60 percent of all odd numbers in just two checks. In this work, we continue the study of FL-pseudoprimes, started in our article \"On a combined primality test\" published in the journal \"Izvestia VUZov.Matematika\" No. 12 in 2022. We have established new restrictions on probable FL-pseudoprimes and described new algorithms for checking FL-primality, and with the help of them we proved the absence of such numbers up to the boundary B = 1021, which is more than 30 times larger than the previously known boundary 264 found by J. Gilchrist in 2013. An inaccuracy in the formulation of theorem 4 in the mentioned article has also been corrected.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"33 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140661274","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}
引用次数: 0
Sharpening of Tur´an-type inequality for polynomials 锐化多项式的 Tur´an 型不等式
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-24 DOI: 10.26907/0021-3446-2024-4-39-46
N. A. Rather, A. Bhat, M. Shafi
{"title":"Sharpening of Tur´an-type inequality for polynomials","authors":"N. A. Rather, A. Bhat, M. Shafi","doi":"10.26907/0021-3446-2024-4-39-46","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-39-46","url":null,"abstract":"For the polynomial P(z) = n sum j=0 cjzj of degree n having all its zeros in | z| leq k, k geq 1, V. Jain in “On the derivative of a polynomial”, Bull. Math. Soc. Sci. Math. Roumanie Tome 59, 339–347 (2016) proved that max | z| =1 | P prime (z)| geq n biggl( | c0| + | cn| kn+1 | c0| (1 + kn+1) + | cn| (kn+1 + k2n) biggr) max | z| =1 | P(z)| . In this paper we strengthen the above inequality and other related results for the polynomials of degree n geq 2.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"27 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140661844","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}
引用次数: 0
On infinite spectra of oscillation exponents of third order linear differential equations 论三阶线性微分方程振荡指数的无限谱
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-24 DOI: 10.26907/0021-3446-2024-4-47-66
A. K. Aydamir Khazretovich Stash
{"title":"On infinite spectra of oscillation exponents of third order linear differential equations","authors":"A. K. Aydamir Khazretovich Stash","doi":"10.26907/0021-3446-2024-4-47-66","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-47-66","url":null,"abstract":"The research topic of this work is at the junction of the theory of Lyapunov exponents and oscillation theory. In this paper, we study the spectra (i.e., the sets of different values on nonzero solutions) of the exponents of oscillation of signs (strict and nonstrict), zeros, roots, and hyperroots of linear homogeneous differential equations with coefficients continuous on the positive semi-axis. In the first part of the paper, we build a third order linear differential equation with the following property: the spectra of all upper and lower strong and weak exponents of oscillation of strict and non-strict signs, zeros, roots and hyper roots contain a countable set of different essential values, both metrically and topologically. Moreover, all these values are implemented on the same sequence of solutions of the constructed equation, that is, for each solution from this sequence, all of the oscillation exponents coincide with each other. In the construction of the indicated equation and in the proof of the required results, we used analytical methods of the qualitative theory of differential equations and methods from the theory of perturbations of solutions of linear differential equations, in particular, the author’s technique for controlling the fundamental system of solutions of such equations in one special case. In the second part of the paper, the existence of a third order linear differential equation with continuum spectra of the oscillation exponents is established, wherein the spectra of all oscillation exponents fill the same segment of the number axis with predetermined arbitrary positive incommensurable ends. It turned out that for each solution of the constructed differential equation, all of the oscillation exponents coincide with each other. The obtained results are theoretical in nature, they expand our understanding of the possible spectra of oscillation exponents of linear homogeneous differential equations.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"64 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140663993","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}
引用次数: 0
On undecidability of unary non-nested PFP-operators for one successor function theory 论单后继函数理论中一元非嵌套 PFP 运算符的不可判定性
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-24 DOI: 10.26907/0021-3446-2024-4-89-93
V. Sekorin
{"title":"On undecidability of unary non-nested PFP-operators for one successor function theory","authors":"V. Sekorin","doi":"10.26907/0021-3446-2024-4-89-93","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-89-93","url":null,"abstract":"We investigate the decidability of first-order logic extensions. For example, it is established in A. S. Zolotov’s works that a logic with a unary transitive closure operator for the one successor theory is decidable. We show that in a similar case, a logic with a unary partial fixed point operator is undecidable. For this purpose, we reduce the halting problem for the counter machine to the problem of truth of the underlying formula. This reduction uses only one unary non-nested partial fixed operator that is applied to a universal or existential formula.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"2 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664702","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}
引用次数: 0
Variation and λ-jump inequalities on Hp spaces Hp 空间上的变式和λ-跳跃不等式
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-22 DOI: 10.26907/0021-3446-2024-4-15-19
S. Demir
{"title":"Variation and λ-jump inequalities on Hp spaces","authors":"S. Demir","doi":"10.26907/0021-3446-2024-4-15-19","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-15-19","url":null,"abstract":"Let phi in S with int phi (x) dx = 1, and define phi t(x) = 1 tn phi Bigl( x t Bigr) , and denote the function family { phi tast f(x)} t>0 by Phi ast f(x). Let scrJ be a subset of BbbR (or more generally an ordered index set), and suppose that there exists a constant C1 such that sum tin scrJ | ^phi t(x)| 2 < C1 for all x in BbbR n. Then i) There exists a constant C2 > 0 such that | V2(Phi ast f)| Lp leq C2| f| Hp, n n + 1 < p leq 1 for all f in Hp(BbbR n), n n + 1 < p leq 1. ii) The lambda -jump operator Nlambda (Phi ast f) satisfies | lambda [Nlambda (Phi ast f)]1/2| Lp leq C3| f| Hp, n n + 1 < p leq 1, uniformly in lambda > 0 for some constant C3 > 0.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"92 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140676793","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}
引用次数: 0
On the existence of an eigenvalue of the generalized Friedrichs model 论广义弗里德里希模型特征值的存在性
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-22 DOI: 10.26907/0021-3446-2024-4-31-38
M. I. Muminov, U. R. Shadiev
{"title":"On the existence of an eigenvalue of the generalized Friedrichs model","authors":"M. I. Muminov, U. R. Shadiev","doi":"10.26907/0021-3446-2024-4-31-38","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-31-38","url":null,"abstract":"We consider a family of bounded self-adjoint matrix operators (generalized Friedrichs models) acting on the direct sum of one-particle and two-particle subspaces of the Fock space. Conditions for the existence of eigenvalues of the matrix operators are obtained.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"5 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140674452","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}
引用次数: 0
Conditions for the existence of power solutions to a linear difference equation with constant coefficients 常数线性差分方程幂级数解存在的条件
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-22 DOI: 10.26907/0021-3446-2024-4-20-30
V. E. Kruglov
{"title":"Conditions for the existence of power solutions to a linear difference equation with constant coefficients","authors":"V. E. Kruglov","doi":"10.26907/0021-3446-2024-4-20-30","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-20-30","url":null,"abstract":"With the help of the formula for the general solution of a difference equation with constant coefficients, it is shown that the set of solutions to this equation contains classical solutions of the type kmλk. We present necessary and sufficient conditions on the coefficients of the equation and the initial parameters under which such solutions are obtained.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"21 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140674072","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}
引用次数: 0
On decompositions and transitive actions of nilpotent Lie groups 论零能李群的分解和反式作用
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-22 DOI: 10.26907/0021-3446-2024-4-3-14
V. Gorbatsevich
{"title":"On decompositions and transitive actions of nilpotent Lie groups","authors":"V. Gorbatsevich","doi":"10.26907/0021-3446-2024-4-3-14","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-4-3-14","url":null,"abstract":"The article considers decompositions of nilpotent Lie algebras and nilpotent Lie groups, and connections between them. Also, descriptions of irreducible transitive actions of nilpotent Lie groups on the plane and on three-dimensional space are given.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"58 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140675809","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}
引用次数: 0
Spectral relations for a matrix model in fermionic Fock space 费米子 Fock 空间矩阵模型的谱关系
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-09 DOI: 10.26907/0021-3446-2024-3-91-96
T. Rasulov, D. E. Ismoilova
{"title":"Spectral relations for a matrix model in fermionic Fock space","authors":"T. Rasulov, D. E. Ismoilova","doi":"10.26907/0021-3446-2024-3-91-96","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-91-96","url":null,"abstract":"","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140724247","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}
引用次数: 0
Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions 周期性无限间隙函数类中带有附加项的正弦-戈登类方程的积分问题
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-09 DOI: 10.26907/0021-3446-2024-3-70-83
A. B. Khasanov, Khasun Normurodov
{"title":"Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions","authors":"A. B. Khasanov, Khasun Normurodov","doi":"10.26907/0021-3446-2024-3-70-83","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-70-83","url":null,"abstract":"In this paper, the inverse spectral problem method is used to integrate a nonlinear sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin equations and the first trace formula satisfies sine-Gordon-type equations with an additional term.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"105 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140725766","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}
引用次数: 0
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