Vestnik St Petersburg University-Mathematics最新文献_第2页

Extremal Problems of Turán-type Involving the Location of All Zeros of a Class of Rational Functions 涉及一类有理函数所有零点位置的图兰型极值问题

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-05-20 DOI: 10.1134/s1063454124700122

M. Y. Mir, S. L. Wali, W. M. Shah

引用次数: 0

Stability of Floating of Vessels with Cross Sections in the Form of Elliptical and Hyperbolic Segments 横截面为椭圆形和双曲线形的船只的漂浮稳定性

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010126

A. S. Smirnov, I. A. Kravchinsky

{"title":"Stability of Floating of Vessels with Cross Sections in the Form of Elliptical and Hyperbolic Segments","authors":"A. S. Smirnov, I. A. Kravchinsky","doi":"10.1134/s1063454124010126","DOIUrl":"https://doi.org/10.1134/s1063454124010126","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Two problems on the stability of the trivial equilibrium position of floating vessels with cross sections in the form of elliptic and hyperbolic segments are considered. Examples on the stability of floating bodies are reviewed, and the key principles of its investigation by analytical statics methods are outlined. For each of the presented problems, by means of quite serious mathematical constructions, an exact expression for the potential energy is obtained within the accepted configuration, and its quadratic approximation near the equilibrium state under study is calculated. On its basis, the stability conditions of the equilibrium state in terms of three dimensionless parameters are determined and the limiting cases are also analyzed. The intermediate expressions and final results obtained as a result of discussion of each of the problems are compared, and their common and distinctive features are identified. The found solutions are illustrated as families of boundaries of stability regions on the plane of two dimensionless parameters at different values of the third parameter. These results are of fundamental theoretical importance and can prove useful for practical applications.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"101 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630725","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

Orbital Precession in the Restricted Three-Body Problem: Exact Representations 受限三体问题中的轨道前冲：精确表示法

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010047

A. A. Berezina

引用次数: 0

A Survey of Results of St. Petersburg State University Research School on Nonlinear Partial Differential Equations. I 圣彼得堡国立大学非线性偏微分方程研究学院成果概览》。I

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010035

D. E. Apushkinskaya, A. A. Arkhipova, A. I. Nazarov, V. G. Osmolovskii, N. N. Uraltseva

引用次数: 0

Closure Lemmas for Interval Translation Mappings 区间转换映射的封闭定理

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010084

A. D. Krivovicheva

引用次数: 0

Periodic Perturbations of Oscillators on a Plane 平面上振荡器的周期性扰动

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010059

Yu. N. Bibikov, E. V. Vasil’eva

{"title":"Periodic Perturbations of Oscillators on a Plane","authors":"Yu. N. Bibikov, E. V. Vasil’eva","doi":"10.1134/s1063454124010059","DOIUrl":"https://doi.org/10.1134/s1063454124010059","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The results of research carried out in the 21st century at the Department of Differential Equations of St. Petersburg State University are reviewed. The subject of study is the problem of stability of the zero solution to the second-order equation describing periodic perturbations of the oscillator with a nonlinear restoring force under reversible and conservative perturbations. Such perturbations are classified as transcendental perturbations, for which the solution of the problem of stability requires taking into account all terms in the expansion in a series of the right-hand side of the equation. The problem of stability under transcendental perturbations was formulated in 1893 by A.M. Lyapunov. The results regarding stability presented in this review were obtained using the methods of KAM theory: perturbations of the oscillator with infinitely small and infinitely large oscillation frequencies were considered; conditions for the existence of quasi-periodic solutions in any vicinity of the time axis are determined, from which the stability (not asymptotic) of the zero solution of the perturbed equation follows; and the conditions are found for the stability of the zero solution for a Hamiltonian system with two degrees of freedom, the unperturbed part of which is described by a pair of oscillators (in this case conservative perturbations are considered).</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627176","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

Characteristics of Convergence and Stability of Some Methods for Inverting the Laplace Transform 反拉普拉斯变换的一些方法的收敛性和稳定性特征

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010096

A. V. Lebedeva, V. M. Ryabov

引用次数: 0

Remarks and a Generalization of the Hegedüs–Szilágyi Fixed Point Theorem 赫格杜斯-齐拉吉定点定理的注释与推广

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010138

Y. Touail, D. Moutawakil

引用次数: 0

Inverse Problem for a Non-Homogeneous Integro-Differential Equation of the Hyperbolic Type 双曲型非均质积分微分方程的逆问题

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010114

J. Sh. Safarov

{"title":"Inverse Problem for a Non-Homogeneous Integro-Differential Equation of the Hyperbolic Type","authors":"J. Sh. Safarov","doi":"10.1134/s1063454124010114","DOIUrl":"https://doi.org/10.1134/s1063454124010114","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The inverse problem of determining the solution and one-dimensional kernel of the integral term in an inhomogeneous integro-differential equation of hyperbolic type from the conditions that make up the direct problem and some additional condition is considered. First, the direct problem is investigated, while the kernel of the integral term is assumed to be known. By integrating over the characteristics, the given integro-differential equation is reduced to a Volterra integral equation of the second kind and is solved by the method of successive approximations. Further, using additional information about the solution of the direct problem, we obtain an integral equation with respect to the kernel of the integral <i>h</i>(<i>t</i>) of the integral term. Using additional information about the solution of the direct problem, we obtain an integral equation of the second kind with respect to the kernel of the integral h(t) of the integral term. Thus, the problem is reduced to solving a system of integral equations of the Volterra type of the second kind. The resulting system is written as an operator equation. To prove the global, unique solvability of this problem, the method of contraction mappings in the space of continuous functions with weighted norms is used. In addition the theorem of the conditional stability of the solution of the inverse problem is proved, while the method of estimating integrals and Gronwall’s inequality is used.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627182","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

Damping Oscillations of a Cylinder with a Coaxial Disk and a Stabilizer 带有同轴盘和稳定器的圆柱体的阻尼振动

IF 0.2

Vestnik St Petersburg University-Mathematics Pub Date : 2024-04-18 DOI: 10.1134/s1063454124010060

D. V. Kaufman, A. N. Ryabinin

{"title":"Damping Oscillations of a Cylinder with a Coaxial Disk and a Stabilizer","authors":"D. V. Kaufman, A. N. Ryabinin","doi":"10.1134/s1063454124010060","DOIUrl":"https://doi.org/10.1134/s1063454124010060","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Damped rotational oscillations of a cylinder equipped with a coaxial disk in the head part and a stabilizer in the tail part are studied. The elongation of the cylinder (the ratio of its length to diameter) is nine. The cylinder is mounted in the test section of the low-velocity wind tunnel with a wire suspension containing steel springs. In the equilibrium position, the cylinder axis is horizontal and parallel to the velocity vector of the incoming flow. A semiconductor strain gauge is attached to one of the suspension springs, which measures the time dependence of spring tension during oscillations. The output voltage of the strain gauge is sent to a PC oscilloscope, the digital signal of which is transmitted to the computer. After calibration of the device, the frequency and amplitude of damped rotational oscillations around the horizontal axis passing through the center of the cylinder and perpendicular to the velocity vector of the incoming flow were determined. The air flow enhances the rate of the damping of rotational oscillations of the cylinder. The air flow effect is described by analogues of rotational derivatives, which, in the case of bluff bodies, depend on the amplitude of the oscillations of the inclination angle of the body and on the amplitude of the angular velocity. A simple model of the effect of a stabilizer on rotational derivatives is proposed.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"2014 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630313","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