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Approximation of the Meaning for Thematic Subject Headings by Simple Interpretable Representations 用简单可解释的表示法近似表达主题词的含义
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600778
R. V. Sulzhenko, B. V. Dobrov

Abstract

The paper studies methods for approximating a user labeled topics by simple representations in a text classification problem. It is assumed that in real information systems the meaning of thematic categories can be approximated by a fairly simple interpreted expression. An algorithm for constructing formulas is considered, which constructs a representation of a text topic in the form of a Boolean formula—in fact, a request to a full-text information system. The algorithm is based on an optimized selection of various logical predicates with words and terms from the thesaurus. The presented algorithm has been compared with modern machine learning techniques on real collections with noisy expert markup. The described method can be used for text classification, expert evaluation of the content of the heading, assessment of the complexity of the description of the topic, and correcting the markup.

摘要 本文研究了在文本分类问题中用简单表示法近似用户标注主题的方法。假设在实际信息系统中,主题类别的含义可以用相当简单的解释表达式来近似表示。我们考虑了一种构建公式的算法,它以布尔公式的形式构建文本主题的表示,实际上就是向全文信息系统提出请求。该算法基于从词库中优化选择各种逻辑谓词和词汇。所介绍的算法与现代机器学习技术在带有嘈杂专家标记的真实文集上进行了比较。所描述的方法可用于文本分类、标题内容的专家评估、主题描述复杂性评估以及修正标记。
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引用次数: 0
Statistical Modeling of the Cobb–Douglas Production Function: A Multiple Linear Regression Approach in Presence of Stable Distribution Noise 柯布-道格拉斯生产函数的统计建模:存在稳定分布噪声时的多元线性回归方法
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600572
B. D. Coulibaly, G. Chaibi, M. El Khomssi

Abstract

In this work, we delved into advanced modeling of economic relationships using the Cobb–Douglas production function as a theoretical foundation. Our primary goal was to develop an innovative multiple linear regression model by introducing innovations based on the (alpha)-stable distribution. By adapting the traditional multiple linear regression model, our approach incorporates the (alpha)-stable distribution to better represent the complexity of relationships between economic variables. This modification enables a better fit for asymmetric distributions and scenarios where data exhibit heavy tails. To assess the performance of our model, we applied it to real financial data. This practical step allowed us to evaluate the effectiveness and predictive capability of our approach in a real-world context, thus offering fresh perspectives for financial data analysis.

摘要 在这项工作中,我们以柯布-道格拉斯生产函数为理论基础,深入研究了经济关系的高级建模。我们的主要目标是通过引入基于 (α)-stable 分布的创新,建立一个创新的多元线性回归模型。通过调整传统的多元线性回归模型,我们的方法纳入了(α)-稳定分布,以更好地表示经济变量之间的复杂关系。这种修改能更好地拟合非对称分布和数据显示重尾的情况。为了评估模型的性能,我们将其应用于真实的金融数据。这一实际步骤使我们能够评估我们的方法在现实世界中的有效性和预测能力,从而为金融数据分析提供新的视角。
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引用次数: 0
Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions 带卷积和非线性条件的脉冲抛物整微分方程的混合问题
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s199508022460078x
A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev

Abstract

In this paper, we consider an impulsive homogeneous parabolictype partial integro-differential equation with degenerate kerneland involution. With respect to spatial variable (x) is usedDirichlet boundary value conditions and spectral problem isstudied. The Fourier method of separation of variables is applied.The countable system of nonlinear functional equations is obtainedwith respect to the Fourier coefficients of unknown function.Theorem on a unique solvability of countable system of functionalequations is proved. The method of successive approximations isused in combination with the method of contraction mapping. Theunique solution of the impulsive mixed problem is obtained in theform of Fourier series. Absolutely and uniformly convergence ofFourier series is proved.

摘要 本文考虑了一个具有退化 kerneland 内卷的脉冲同调抛物型偏积分微分方程。关于空间变量 (x) 使用了 Dirichlet 边界值条件,并研究了谱问题。应用傅里叶变量分离法,得到了关于未知函数傅里叶系数的可数非线性函数方程组,证明了可数函数方程组唯一可解性定理。结合使用了连续逼近法和收缩映射法。以傅里叶级数形式得到了脉冲混合问题的唯一解。证明了傅里叶级数的绝对均匀收敛性。
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引用次数: 0
Asymptotics of the Solution of the Cauchy Problem with an Unstable Spectrum and Prolonging Loss of Stability 具有不稳定频谱和长期失稳的考奇问题解的渐近性
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600845
D. A. Tursunov, A. S. Sadieva, K. G. Kozhobekov, E. A. Tursunov

Abstract

The article is devoted to construct a complete asymptotic expansion of the solution to the Cauchy problem for a linear analytical system of singularly perturbed ordinary differential equations of the first order. The peculiarities of the Cauchy problem are that a small parameter is present in front of the derivative, and the stability conditions are violated in the region under consideration. By modifying the method of boundary functions, a formal asymptotic expansion of the solution to the Cauchy problem is constructed. The remainder term of the expansion is estimated by the idea of L.S. Pontryagin entering the complex plane.

摘要 本文致力于构建一阶奇异扰动常微分方程线性解析系统的 Cauchy 问题解的完整渐近展开。Cauchy 问题的特殊性在于导数前存在一个小参数,并且在所考虑的区域内违反了稳定性条件。通过修改边界函数方法,构建了 Cauchy 问题解的形式渐近展开。根据 L.S. Pontryagin 进入复平面的思想,对扩展的余项进行了估计。
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引用次数: 0
Derivation of a Controllability Criteria for a Linear Singularly Perturbed Discrete System with Small Step 小步长线性奇异扰动离散系统可控性标准的推导
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600547
B. Y. Ashirbaev, T. K. Yuldashev

Abstract

The article is devoted to study of controllability properties of a linear singularly perturbed discrete system with a small step. It is used the Gram operator, which transforms an infinite-dimensional space into a finite-dimensional one, and based on the separation of state variables of a linear discrete singularly perturbed system with a small step. The controllability criteria for this discrete system is derived.

摘要 本文致力于研究具有小步长的线性奇异扰动离散系统的可控性。文章使用了将无穷维空间转换为有限维空间的格拉姆算子,并基于具有小步长的线性离散奇异扰动系统的状态变量分离。得出了该离散系统的可控性标准。
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引用次数: 0
Some Aspects of Remote State Restoring in State Transfer Governed by XXZ-Hamiltonian 由 XXZ-Hamiltonian 控制的状态转移中远程状态恢复的几个方面
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600596
G. A. Bochkin, S. I. Doronin, E. B. Fel’dman, E. I. Kuznetsova, I. D. Lazarev, A. N. Pechen, A. I. Zenchuk

Abstract

We consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length.

摘要 我们考虑了一个自旋系统中零阶相干矩阵(PTZ)的远程状态恢复和完美转移问题,该自旋系统受守恒激励数的 XXZ-哈密顿支配。恢复工具由哈密顿中的几个非零拉莫尔频率表示。为了简化分析,我们使用了两种近似模型,包括拉莫尔频率的阶跃型或脉冲型时间依赖性。我们研究了多达 20 个节点的自旋链中的恢复。在研究 PTZ 时,我们考虑了之字形和矩形配置,并利用通信线路的几何参数以及扩展接收器的特殊单元变换优化了 0 阶相干矩阵的传输。总体观察结果表明,XXZ 链比 XX 链需要更长的状态转移时间,这一点在最近邻近似下的演化分析研究中得到了证实。我们证明了状态转移时间随自旋链长度呈指数增长。
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引用次数: 0
On the Non-local Problem for a Boussinesq Type Equations 关于布森斯克方程的非局部问题
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600808
Kh. T. Dekhkonov, Yu. E. Fayziev, R. R. Ashurov

Abstract

The problem of finding a solution, satisfying the non-local condition (u(xi_{0})=alpha u(+0)+varphi) in time for the Boussinesq type equation of the form (u_{tt}+Au_{tt}+Au=f) is studied in the article. Here (alpha) and (xi_{0}), (xi_{0}in(0,T],) are the given numbers, (A:Hrightarrow H) is the self-adjoint, unbounded, positive operator defined in the Hilbert separable space (H). By using the Fourier method, it was shown that the solution to the problem exists and is unique. The effect of parameter (alpha) on the existence and uniqueness of the solution is studied in the article. The inverse problem of determining the right-hand side of the equation is also considered.

Abstract The problem of finding a solution, satisfying the non-local condition (u(xi_{0})=alpha u(+0)+varphi) in time for the Boussinesq type equation of the form (u_{tt}+Au_{tt}+Au=f) is studied in the article.这里(alpha)和(xi_{0}), (xi_{0}in(0,T],)是给定的数,(A:Hrightarrow H) 是定义在希尔伯特可分离空间 (H)中的自交、无界、正算子。通过使用傅立叶方法,证明了问题的解是存在的,并且是唯一的。文章研究了参数 (α)对解的存在性和唯一性的影响。还考虑了确定方程右边的逆问题。
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引用次数: 0
A 2D Convolution Kernel Determination Problem for the Time-Fractional Diffusion Equation 时间-分数扩散方程的二维卷积核确定问题
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600857
D. K. Durdiev, M. Akylbayev, Zh. Maxumova, A. Iskakova

Abstract

In this article, two dimensional inverse problem of determining convolution kernel in the fractional diffusion equation with the time-fractional Caputo derivative is studied. To represent the solution of the direct problem, the fundamental solution of the time-fractional diffusion equation with Riemann–Liouville derivative is constructed. Using the formulas of asymptotic expansions for the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel function, which was used for studying the inverse problem. The inverse problem is reduced to the equivalent integral equation of the Volterra type. The local existence and global uniqueness results are proven by the aid of fixed point argument in suitable functional classes. Also the stability estimate is obtained.

摘要 本文研究了具有时间分数卡普托导数的分数扩散方程中确定卷积核的二维反问题。为了表示直接问题的解,构建了具有黎曼-刘维尔导数的时间分数扩散方程的基本解。利用基本解及其导数的渐近展开公式,可以根据未知核函数的规范得到直接问题解的估计值,该估计值用于研究逆问题。逆问题被简化为 Volterra 类型的等价积分方程。借助适当函数类的定点论证,证明了局部存在性和全局唯一性结果。同时还获得了稳定性估计。
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引用次数: 0
D-Stability, Strong D-Stability and $$mu$$ -Values D 级稳定性、强 D 级稳定性和 $$mu$ - 值
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600754
Mutti-Ur Rehman, Tulkin H. Rasulov, Fouzia Amir

Abstract

In this article, we present some connections between the notation of D-stability, Strong D-stability, and structured singular values known as (mu)-values for square matrices.

摘要 在本文中,我们介绍了 D-稳定性、强 D-稳定性和结构奇异值之间的一些联系,这些奇异值被称为方阵的 (mu)-值。
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引用次数: 0
On Mean Field Stochastic Differential Equations Driven by $$G$$ -Brownian Motion with Averaging Principle 带平均原则的$$G$$布朗运动驱动的平均场随机微分方程
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600985
A. B. Touati, H. Boutabia, A. Redjil

Abstract

In a sublinear space (left(Omega,mathcal{H},widehat{mathbb{E}}right)), we consider Mean Field stochastic differential equations ((G)-MFSDEs in short), called also (G)-McKean–Vlasov stochastic differential equations, which are SDEs where coefficients depend not only on the state of the unknown process but also on its law. We mean by law of a random variable (X) on (left(Omega,mathcal{H},widehat{mathbb{E}}right)), the set (left{P_{X}:Pinmathcal{P}right}), where (P_{X}) is the law of (X) with respect to (P) and (mathcal{P}) is the family of probabilities associated to the sublinear expectation (widehat{mathbb{E}}). In this paper, we study the existence and uniqueness of the solution of (G)-MFSDE by using the fixed point theorem. To this end, we introduce a new type Kantorovich metric between subsets of laws and adapted Lipchitz and linear growth conditions. Furthermore, we prove the validity of the averaging principle and obtain convergence theorem where the solution of the averaged (G)-MFSDE converges to that of the standard one in the mean square sense.

Abstract In a sublinear space (left(Omega,mathcal{H},widehatmathbb{E}}right)),we consider Mean Field stochastic differential equations (简称(G)-MFSDEs), called also (G)-McKean-Vlasov stochastic differential equations, which are SDEs where cofficients depend on not only the state of unknown process but also on its law.我们所说的随机变量(X)的规律是指(left(Omega,mathcal{H},widehat{mathbb{E}}right))上的集合(left{P_{X}:其中,(P_{X})是(X)关于(P)的规律,而(mathcal{P})是与亚线性期望(widehat{mathbb{E}})相关的概率族。本文利用定点定理研究了 (G)-MFSDE 解的存在性和唯一性。为此,我们在定律子集之间引入了一种新型康托洛维奇度量,并调整了李普希兹条件和线性增长条件。此外,我们证明了平均原理的有效性,并得到了收敛定理,即平均 (G)-MFSDE 的解在均方意义上收敛于标准解。
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引用次数: 0
期刊
Lobachevskii Journal of Mathematics
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