Applied Mathematics and Computation最新文献

英文中文

Estimation of parameters and valuation of options written on multiple assets described by uncertain fractional differential equations 不确定分式微分方程描述的多种资产期权的参数估计和估值

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129109

Yue Xin , Yi Zhang , Idin Noorani , Farshid Mehrdoust , Jinwu Gao

This study suggests the pricing problems of options dependent on multiple assets, spread, basket, and quanto options when the asset dynamics are described by the uncertain fractional differential equation. The solutions of these option prices are analytically provided and the algorithms related to each one of these derivatives are designed. For the first time, we apply the minimum cover method to estimate the parameters of the uncertain fractional differential equations based on the real data related to the stock prices of some markets. Through the uncertain hypothesis test, we demonstrate that the estimated uncertain fractional differential equations can successfully fit the observed data. We then experimentally show that the α-paths obtained by the estimated uncertain fractional differential equations favorably cover the sample data. Finally, some numerical experiments based on the uncertain fractional differential equation estimated by the minimum cover method are accomplished to confirm the achievement of the presented results.

本研究提出了当资产动态由不确定分式微分方程描述时，取决于多种资产的期权、价差期权、一篮子期权和量子期权的定价问题。通过分析提供了这些期权价格的解，并设计了与每种衍生品相关的算法。我们首次根据一些市场股票价格的相关真实数据，应用最小覆盖法来估计不确定分式微分方程的参数。通过不确定假设检验，我们证明了估计的不确定分式微分方程能够成功拟合观测数据。然后，我们通过实验证明，由估计的不确定分数微分方程得到的 α 路径可以很好地覆盖样本数据。最后，我们基于用最小覆盖法估计的不确定分数微分方程进行了一些数值实验，以证实所展示结果的实现。

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引用次数: 0

Distance (signless) Laplacian spectra and energies of two classes of cyclic polyomino chains 两类环状多臂链的距离（无符号）拉普拉斯谱和能量

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129099

Yonghong Zhang , Ligong Wang

Let

D (G)

and

T r (G)

be the distance matrix and the diagonal matrix of vertex transmissions of a graph G, respectively. The distance Laplacian matrix and the distance signless Laplacian matrix of G are defined as

D^{L} (G) = T r (G) - D (G)

and

D^{Q} (G) = T r (G) + D (G)

, respectively. In this paper, we consider the distance Laplacian spectra and the distance signless Laplacian spectra of the linear cyclic polyomino chain

F_{n}

and the Möbius cyclic polyomino chain

M_{n}

. By utilizing the properties of circulant matrices, we give the characteristic polynomials and the eigenvalues for the distance Laplacian matrices and the distance signless Laplacian matrices of the graphs

F_{n}

and

M_{n}

, respectively. Furthermore, we provide the exactly values of the distance Laplacian energy and the distance signless Laplacian energy of the graph

F_{n}

, and the upper bounds on the distance Laplacian energy and the distance signless Laplacian energy of the graph

M_{n}

, respectively.

设 D(G) 和 Tr(G) 分别为图 G 的距离矩阵和顶点传输对角矩阵。G 的距离拉普拉斯矩阵和距离无符号拉普拉斯矩阵分别定义为 DL(G)=Tr(G)-D(G) 和 DQ(G)=Tr(G)+D(G) 。本文考虑线性循环多角体链 Fn 和莫比乌斯循环多角体链 Mn 的距离拉普拉斯谱和距离无符号拉普拉斯谱。利用循环矩阵的性质，我们分别给出了图形 Fn 和 Mn 的距离拉普拉斯矩阵和无距离拉普拉斯矩阵的特征多项式和特征值。此外，我们还分别给出了图 Fn 的距离拉普拉奇能量和无符号距离拉普拉奇能量的精确值，以及图 Mn 的距离拉普拉奇能量和无符号距离拉普拉奇能量的上限。

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引用次数: 0

Theory of Hermite and Laguerre Bessel function from the umbral point of view 从本体角度看赫米特和拉盖尔贝塞尔函数理论

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129103

M. Artioli , G. Dattoli , U. Zainab

The theoretical underpinnings of hybrid families of special functions are examined through an umbral reformulation. Our discussion encompasses diverse families of Bessel-type functions and special polynomials, all situated within a unifying umbral-algebraic formalism. The method presented capitalizes on recent advancements in the formal treatment of higher transcendental functions, enabling novel and intriguing generalizations.

通过本构重述，研究了特殊函数混合族的理论基础。我们的讨论涵盖了贝塞尔型函数和特殊多项式的各种族，它们都位于统一的本构-代数形式主义中。所提出的方法利用了最近在高超函数形式处理方面取得的进展，实现了新颖而有趣的概括。

引用次数: 0

A global approximation method for second-kind nonlinear integral equations 第二类非线性积分方程的全局近似法

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129094

Luisa Fermo , Anna Lucia Laguardia , Concetta Laurita , Maria Grazia Russo

A global approximation method of Nyström type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first occurrence, the method uses a Gauss-Legendre rule whereas in the second one resorts to a product rule based on Legendre nodes. Stability and convergence are proved in functional spaces equipped with the uniform norm and several numerical tests are given to show the good performance of the proposed method. An application to the interior Neumann problem for the Laplace equation with nonlinear boundary conditions is also considered.

本论文探讨了一种 Nyström 类型的全局近似方法，用于数值求解一类第二类非线性积分方程。该方法同时考虑了光滑核和弱奇异核的情况。在第一种情况下，该方法使用高斯-勒让德规则，而在第二种情况下，则使用基于勒让德节点的乘积规则。在配有统一规范的函数空间中，证明了稳定性和收敛性，并给出了几个数值测试，以显示所提方法的良好性能。此外，还考虑了对具有非线性边界条件的拉普拉斯方程的内部诺依曼问题的应用。

引用次数: 0

Contagion probability in linear threshold model 线性阈值模型中的传染概率

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129090

Ying Ying Keng , Kiam Heong Kwa

<div><div>We study a linear threshold model on a simple undirected connected network G where each non-seed becomes active if and only if the proportion of its active neighbors exceeds its adoption threshold. Each threshold function <math><mi>ϕ</mi><mo>:</mo><mi>V</mi><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math> is viewed as a point <math><mo>(</mo><mi>ϕ</mi><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><mo>…</mo><mo>,</mo><mi>ϕ</mi><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>)</mo></math> in the n-cube <math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mi>n</mi></mrow></msup></math>, where <math><mi>V</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></math> is the set of nodes in G. We define ϕ as a contagious point of a subset S of nodes if it can induce full contagion from S. Consequently, the volume of the set of contagious points of S in <math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mi>n</mi></mrow></msup></math> represents the probability of full contagion from S when the adoption threshold of each node is independently and uniformly distributed in <math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math>, which we term the contagion probability of S and denote by <math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></math>. We derive an explicit formula for <math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></math>, showing that <math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></math> is determined by how likely S can produce full contagion exclusively through each spanning tree of the quotient graph <math><msub><mrow><mi>G</mi></mrow><mrow><mi>S</mi></mrow></msub></math> of G in which S is treated as a single node. Besides, we compare <math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></math> with the contagion threshold of S, which is denoted by <math><msub><mrow><mi>q</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo></math> and is the probability of full contagion from S when all nodes share a common adoption threshold q chosen uniformly at random from <math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math>. We show that the presence of a cycle in <math><msub><mrow><mi>G</mi>

我们研究的是一个简单无向连接网络 G 上的线性阈值模型，在该模型中，当且仅当其活跃邻居的比例超过其采用阈值时，每个非种子才会变得活跃。我们将每个阈值函数 ϕ:V→[0,1] 视为 n 立方体 [0,1]n 中的一个点 (j(v1),...,j(vn))，其中 V={v1,...vn} 是 G 中的节点集。因此，S 的传染点集合在 [0,1]n 中的体积表示当每个节点的采用阈值在 [0,1] 中独立均匀分布时，从 S 完全传染的概率，我们称之为 S 的传染概率，用 pc(S) 表示。我们推导出 pc(S)的明确公式，表明 pc(S)取决于 S 通过 G 的商图 GS 的每棵生成树（其中 S 被视为单个节点）产生完全传染的可能性。此外，我们还将 pc(S)与 S 的传染阈值进行了比较，传染阈值用 qc(S)表示，是所有节点共享从 [0,1] 中均匀随机选择的共同采用阈值 q 时，S 产生完全传染的概率。我们的研究表明，GS 中循环的存在是 pc(S) 超过 qc(S) 的必要条件，但不是充分条件，这表明允许阈值异质性并不总能增加完全传染的机会。我们的框架可以扩展到研究各种阈值设置下的传染。

引用次数: 0

Component connectivity of wheel networks 车轮网络的组件连通性

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129096

Guozhen Zhang , Xin Liu , Dajin Wang

The r-component connectivity

c κ_{r} (G)

of a noncomplete graph G is the size of a minimum set of vertices, whose deletion disconnects G such that the remaining graph has at least r components. When

r = 2

c κ_{r} (G)

is reduced to the classic notion of connectivity

κ (G)

. So

c κ_{r} (G)

is a generalization of

κ (G)

, and is therefore a more general and more precise measurement for the reliability of large interconnection networks. The m-dimensional wheel network

C W_{m}

was first proposed by Shi and Lu in 2008 as a potential model for the interconnection network [19], and has been getting increasing attention recently. It belongs to the category of Cayley graphs, and possesses some properties desirable for interconnection networks. In this paper, we determine the r-component connectivity of the wheel network for

r = 3, 4, 5

. We prove that

c κ_{3} (C W_{m}) = 4 m - 7

for

m \geq 5

c κ_{4} (C W_{m}) = 6 m - 13

and

c κ_{5} (C W_{m}) = 8 m - 20

for

m \geq 6

非完整图 G 的 r 分量连通性 cκr(G)是最小顶点集的大小，删除这些顶点集可以断开 G 的连接，使剩余的图至少有 r 个分量。当 r=2 时，cκr(G) 简化为连通性 κ(G) 的经典概念。因此，cκr(G) 是对κ(G) 的广义概括，因而是对大型互连网络可靠性的更广义、更精确的测量。m 维轮状网络 CWm 由 Shi 和 Lu 于 2008 年首次提出，是互联网络的潜在模型[19]，近来受到越来越多的关注。它属于 Cayley 图的范畴，具有互连网络所需的一些特性。本文确定了 r=3,4,5 时车轮网络的 r 分量连通性。我们证明，当 m≥5 时，cκ3(CWm)=4m-7；当 m≥6 时，cκ4(CWm)=6m-13；当 m≥6 时，cκ5(CWm)=8m-20。

引用次数: 0

Two-disjoint-cycle-cover pancyclicity of split-star networks 分裂星型网络的两两相接-循环-覆盖泛周期性

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129085

Hao Li , Liting Chen , Mei Lu

Pancyclicity is a stronger property than Hamiltonicity. In 1973, Bondy stated his celebrated meta-conjecture. Since then, problems related to pancyclicity have attracted a lot of attentions and interests of researchers. A connected graph G is two-disjoint-cycle-cover

[t_{1}, t_{2}]

-pancyclic or briefly 2-DCC

[t_{1}, t_{2}]

-pancyclic if for any positive integer t with

t \in [t_{1}, t_{2}]

, there are two vertex-disjoint cycles

C_{1}

and

C_{2}

in G satisfying

| V (C_{1}) | = t

and

| V (C_{2}) | = | V (G) | - t

. In this paper, it is proved that the n-dimensional split-star network

S_{n}^{2}

is 2-DCC

[3, ⌊ \frac{n!}{2} ⌋]

-pancyclic when

n \geq 3

Pancyclicity 是比 Hamiltonicity 更强的性质。1973 年，邦迪提出了著名的元猜想。从那时起，与泛周期性相关的问题引起了研究者的广泛关注和兴趣。如果对于任意正整数 t（t∈[t1,t2]），G 中存在满足 |V(C1)|=t 和 |V(C2)|=|V(G)|-t 的两个顶点相交循环 C1 和 C2，则连通图 G 是双相交循环覆盖 [t1,t2]-pancyic 或简述为 2-DCC [t1,t2]-pancyic 。本文证明，当 n≥3 时，n 维分裂星形网络 Sn2 是 2-DCC [3,⌊n!2⌋]-泛循环的。

引用次数: 0

A FFT-based DDSIIM solver for elliptic interface problems with discontinuous coefficients on arbitrary domains and its error analysis 基于 FFT 的 DDSIIM 求解器，用于求解任意域上系数不连续的椭圆界面问题及其误差分析

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129086

Jianjun Chen , Yuxuan Wang , Weiyi Wang , Zhijun Tan

In this study, we propose a fast FFT-based domain decomposition simplified immersed interface method (DDSIIM) solver for addressing elliptic interface problems characterized by fully discontinuous coefficients on arbitrary domains. The method involves decomposing the original elliptic interface problem along the interfaces, resulting in sub-problems defined on subdomains embedded within larger regular domains. By utilizing a variety of novel solution extension schemes and augmented variable strategies, each sub-problem is transformed into a straightforward elliptic interface problem with constant coefficients on a regular domain, interconnected through augmented equations. The interconnected sub-interface problems are initially resolved by solving for the augmented variables using GMRES, which does not depend on mesh size, followed by the application of the fast FFT-based SIIM in each GMRES iteration. Rigorous error estimates are derived to ensure global second-order accuracy in both the discrete

L^{2}

-norm and the maximum norm. A large number of numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed DDSIIM solver.

在本研究中，我们提出了一种基于 FFT 的快速域分解简化沉浸界面法 (DDSIIM) 求解器，用于解决任意域上以完全不连续系数为特征的椭圆界面问题。该方法涉及沿界面分解原始椭圆界面问题，从而在嵌入较大规则域的子域上定义子问题。通过利用各种新颖的求解扩展方案和增强变量策略，每个子问题都被转化为常规域上具有常数系数的直接椭圆界面问题，并通过增强方程相互连接。相互连接的子界面问题最初是通过使用 GMRES（不依赖于网格大小）求解增强变量来解决的，然后在每次 GMRES 迭代中应用基于 FFT 的快速 SIIM。我们得出了严格的误差估计值，以确保离散 L2 准则和最大准则的全局二阶精度。本文列举了大量数值示例，以证明所提出的 DDSIIM 求解器的有效性和准确性。

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引用次数: 0

Radio labelling of two-branch trees 双枝树的无线电标记

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129097

Devsi Bantva , Samir Vaidya , Sanming Zhou

A radio labelling of a graph G is a mapping

f : V (G) \to {0, 1, 2, \dots}

such that

| f (u) - f (v) | \geq diam (G) + 1 - d (u, v)

for every pair of distinct vertices

u, v

of G, where

diam (G)

is the diameter of G and

d (u, v)

is the distance between u and v in G. The radio number

rn (G)

of G is the smallest integer k such that G admits a radio labelling f with

\max {f (v) : v \in V (G)} = k

. The weight of a tree T from a vertex

v \in V (T)

is the sum of the distances in T from v to all other vertices, and a vertex of T achieving the minimum weight is called a weight centre of T. It is known that any tree has one or two weight centres. A tree is called a two-branch tree if the removal of all its weight centres results in a forest with exactly two components. In this paper we obtain a sharp lower bound for the radio number of two-branch trees which improves a known lower bound for general trees. We also give a necessary and sufficient condition for this improved lower bound to be achieved. Using these results, we determine the radio number of two families of level-wise regular two-branch trees.

图 G 的无线电标注是一个映射 f:V(G)→{0,1,2,...}，对于 G 的每一对不同顶点 u,v，|f(u)-f(v)|≥diam(G)+1-d(u,v)，其中 diam(G) 是 G 的直径，d(u,v) 是 u 和 v 在 G 中的距离。G 的无线电数 rn(G) 是最小的整数 k，使得 G 允许最大{f(v):v∈V(G)}=k 的无线电标签 f。一棵树 T 从顶点 v∈V(T) 出发的权重是 T 中 v 到所有其他顶点的距离之和，T 中权重最小的顶点称为 T 的权重中心。如果去掉所有的权重中心，得到的森林只有两个部分，那么这棵树就叫做双枝树。在本文中，我们获得了双枝树无线电数的一个尖锐下限，它改进了已知的一般树的下限。我们还给出了实现这一改进下限的必要条件和充分条件。利用这些结果，我们确定了两系平移正则双分支树的无线电数。

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引用次数: 0

Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations 嵌套模糊求和形式的参数化线性矩阵不等式的宽松条件

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-09 DOI: 10.1016/j.amc.2024.129079

Do Wan Kim , Donghwan Lee

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.

本研究旨在探讨参数化线性矩阵不等式（PLMI）的较低保守条件，这些不等式被表述为嵌套模糊求和。此类 PLMI 通常出现在高木-菅野（T-S）模糊系统的稳定性分析和控制设计问题中。利用算术和几何均值加权不等式（AM-GM 不等式），我们为 PLMIs 开发了新的、不太保守的线性矩阵不等式。这种方法使我们能够有效地处理具有相交指数的成员函数乘积。通过实证案例研究，我们证明了与文献中的现有方法相比，我们提出的条件产生的结果不那么保守。

引用次数: 0

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