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Rayleigh–Ritz Operator in Inverse Problems for Higher Order Multilinear Nonautonomous Evolution Equations 高阶多线性非自治演化方程逆问题中的雷利-里兹算子
Siberian Advances in Mathematics
Pub Date : 2023-12-14 DOI: 10.1134/s1055134423040053
A. V. Lakeyev, Yu. E. Linke, V. A. Rusanov

Abstract

We study solvability questions for the problem on realization of operator functions foran invariant polylinear regulator of a higher-order differential system in an infinite-dimensionalseparable Hilbert space. This is a nonstationary coefficient-operator inverse problem formultilinear evolution equations whose dynamic order is higher than one (notice thatnonautomonous hyperbolic systems belong to this class of problems). We analyze semiadditivityand continuity for a nonlinear Rayleigh–Ritz functional operator and obtain an analytic model ofan invariant polylinear regulator. This model allows us to combine two bundles of trajectorycurves induced by different invariant polylinear regulators in a differential system and obtaina family of admissible solutions of the initial differential system in terms of an invariant polylinearaction. The obtained results can be applied in the general qualitative theory of nonlinearinfinite-dimensional adaptive control systems described by higher-order multilinearnonautonomous differential systems (including neuromodelling).

研究了无限维可分离Hilbert空间中高阶微分系统不变多线性调节器算子函数实现问题的可解性问题。这是一个动态阶次高于1的非平稳系数算子逆问题公式线性演化方程(注意非自治双曲系统属于这类问题)。本文分析了一类非线性Rayleigh-Ritz泛函算子的半可加性和连续性，得到了一类不变多线性调节器的解析模型。该模型允许我们将微分系统中由不同的不变多线性调节器诱导的两束轨迹曲线组合在一起，并在不变多线性作用下得到初始微分系统的一系列可容许解。所得结果可应用于由高阶多线性非自治微分系统(包括神经建模)描述的非线性无限维自适应控制系统的一般定性理论。
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引用次数: 0
Reconstruction of Parameters of a Set of Radiant Points from Their Images 从辐射点图像重建辐射点集合参数
Siberian Advances in Mathematics
Pub Date : 2023-12-14 DOI: 10.1134/s1055134423040028
E. Yu. Derevtsov

Abstract

Within the framework of geometric tomography, inverse problems of photometry, waveoptics, and discrete tomography, we study questions on reconstruction of the spatial location andluminosity of a discrete distribution of radiant sources from its images obtained with the use ofa small number of optical systems. We analyze the problem on finding geometric parameters ofsuch a distribution and describe sources of ambiguity. We consider the inverse problem onreconstruction of a discrete distribution that consists of incoherent and monochromatic sourcesand suggest uniqueness criteria for its solution. We also suggest a constructive approach tonumerical solution of the inverse problem on reconstruction of the coordinates and luminosity ofa family of radiant pinpoint sources from their images.

摘要在几何层析成像、光度反演、波光学和离散层析成像的框架下，研究了利用少量光学系统获得的离散辐射源图像重建其空间位置和亮度的问题。我们分析了寻找这种分布的几何参数的问题，并描述了歧义的来源。我们考虑了由非相干单色源组成的离散分布的反演问题，并给出了其解的唯一性准则。我们还提出了一种建设性的方法来数值解决从图像中重建一类辐射定点光源的坐标和亮度的反问题。
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引用次数: 0
Sharply Transitive Representations of the Algebra $$sl_3(mathbb{R})$$ 代数$$sl_3(mathbb{R})$$的锐传递表示
Siberian Advances in Mathematics
Pub Date : 2023-12-14 DOI: 10.1134/s1055134423040077
M. V. Neshchadim, A. A. Simonov

Abstract

We consider local sharply transitive representations of the algebra (sl_3(mathbb {R}) ) in the space of local vector fields with analyticcoefficients in ( mathbb {R}^{8}) that are defined ina neighborhood of the origin. We find a system of differential equations that describes suchrepresentations.

摘要:我们考虑在原点附近定义的具有解析系数( mathbb {R}^{8})的局部向量场空间中代数(sl_3(mathbb {R}) )的局部锐传递表示。我们找到了一个描述这种表示的微分方程组。
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引用次数: 0
Estimates of Solutions in a Model of Antiviral Immune Response 抗病毒免疫反应模型中的解决方案估算
Siberian Advances in Mathematics
Pub Date : 2023-12-14 DOI: 10.1134/s1055134423040089
M. A. Skvortsova

Abstract

We consider a model of antiviral immune response suggested by G.I. Marchuk. The modelis described by a system of differential equations with several delays. We study asymptoticstability for a stationary solution of the system that corresponds to a completely healthyorganism. We estimate the attraction set of this stationary solution. We also find estimates ofsolutions characterizing the stabilization rate at infinity. A Lyapunov–Krasovskiĭfunctional is used in the proof.

摘要 我们考虑了 G.I. Marchuk 提出的抗病毒免疫反应模型。该模型由一个具有多个延迟的微分方程系统描述。我们研究了与完全健康生物体相对应的系统静止解的渐近稳定性。我们估计了该静止解的吸引集。我们还找到了表征无穷大时稳定率的解的估计值。证明中使用了 Lyapunov-Krasovskiĭ 函数。
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引用次数: 0
Negative Numberings in Admissible Sets. I 可容许集合中的负数。I
Siberian Advances in Mathematics
Pub Date : 2023-12-14 DOI: 10.1134/s105513442304003x
I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faĭzrakhmanov

Abstract

We construct an admissible set (mathbb {A}) such thatthe family of all ( mathbb {A})-computably enumerable sets possessesa negative computable (mathbb {A})-numbering but lacks positive computable (mathbb {A})-numberings. We also discuss the question on existence of minimal negative (mathbb {A} )-numberings.

构造了一个容许集(mathbb {A})，使得所有的( mathbb {A}) -可计算枚举集合族具有负可计算的(mathbb {A}) -编号，但缺乏正可计算的(mathbb {A}) -编号。讨论了最小负(mathbb {A} ) -数的存在性问题。
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引用次数: 0
Optimal Recovery of a Function Holomorphic in a Polydisc from Its Approximate Values on a Part of the Skeleton 从骨架部分上的近似值优化恢复多圆盘中的全形函数
Siberian Advances in Mathematics
Pub Date : 2023-12-01 DOI: 10.1134/s1055134423040016
R. R. Akopyan
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引用次数: 0
An Extension of a Theorem of Neumann Neumann定理的一个推广
Siberian Advances in Mathematics
Pub Date : 2023-08-01 DOI: 10.1134/S1055134423030045
V. Durnev, A. Zetkina
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引用次数: 0
Stability of Solutions of Delay Differential Equations 时滞微分方程解的稳定性
Siberian Advances in Mathematics
Pub Date : 2023-08-01 DOI: 10.1134/S1055134423030094
T. Yskak
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引用次数: 0
On Location of the Matrix Spectrum with Respect to a Parabola 关于矩阵谱相对于抛物线的定位
Siberian Advances in Mathematics
Pub Date : 2023-08-01 DOI: 10.1134/S1055134423030033
G. Demidenko, V. Prokhorov
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引用次数: 0
On a Boundary Value Problem for a Pseudohyperbolic Equation 关于一类伪双曲型方程的边值问题
Siberian Advances in Mathematics
Pub Date : 2023-08-01 DOI: 10.1134/S1055134423030082
V. Shemetova
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引用次数: 0
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