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Location of zeros of a Lacunary type polynomial lacary型多项式的零点位置
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1614
Subhasis Das
For a given polynomial p(z) of degree n with real or complex coefficients, our basic aim has been to determine the smallest region in which all the zeros of p(z) lie. In the present paper, we have obtained a result by using Lacunary type polynomial which gives the region of zeros neither circular nor annular except in some particular cases. Our result plays an important role to reduce the region of polynomial zeros.
对于给定的n次多项式p(z),具有实系数或复系数,我们的基本目标是确定p(z)的所有零所在的最小区域。本文利用拉库纳型多项式得到了一个结果,除了某些特殊情况外,该结果给出了零的区域既不是圆的也不是环的。我们的结果对于减少多项式零区域具有重要的意义。
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引用次数: 0
A modified Susceptible-Infected-Recovered epidemiological model 一种改良的易感-感染-康复流行病学模型
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1560
I. Bica, Zhichun Zhai, Rui Hu
"Objectives This paper proposes an infectious disease model incorporating two new model compartments, hospitalization, and intensive care unit. Methods The model dynamics are analyzed using the local and global stability theory of nonlinear systems of ordinary differential equations. For the numerical simulations, we used the Rosenbrock method for stiff initial value problems. We obtained numerical simulations using MAPLE software. The returned MAPLE procedure was called only for points inside the range on which the method evaluated the numerical solution of the system with specified initial conditions. Results We proposed a new model to describe the dynamics of microparasitic infections. Numerical simulations revealed that the proposed model fitted with the expected behaviour of mi- croparasitic infections with ”acute epidemicity.” The numerical simulations showed consistency in the behaviour of the system. Conclusions The model proposed has ”robust” dynamics, supported by the global stability of its endemic state and the consistency of the numerical simulations regarding the model’s timeevolution behaviour. The introduction of the hospitalization and intensive care unit compartments in the proposed model revealed that it is essential to consider such policies in the case of ”acuteepidemicity” of microparasitic infections."
本文提出了一种包含住院和重症监护室两个新的模型室的传染病模型。方法利用常微分方程非线性系统的局部稳定性和全局稳定性理论对模型动力学进行分析。在数值模拟中,我们使用Rosenbrock方法求解刚性初值问题。我们使用MAPLE软件进行了数值模拟。返回的MAPLE过程只对该方法在给定初始条件下计算系统数值解的范围内的点调用。结果我们提出了一个描述微寄生虫感染动态的新模型。数值模拟结果表明,所提出的模型符合具有“急性流行”的交叉寄生虫感染的预期行为。数值模拟显示了系统行为的一致性。该模型具有“鲁棒”动力学,其地方性状态的全球稳定性和关于模型时间演化行为的数值模拟的一致性支持了该模型。在提出的模型中引入住院和重症监护病房的情况表明,在微寄生虫感染的“急性流行”情况下,必须考虑这些政策。
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引用次数: 0
Δ-wavy probability distributions and Potts model Δ-wavy概率分布和波茨模型
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1494
Udrea Păun
We define the wavy probability distributions on a subset and Δ-wavy probability distributions - two generalizations of the wavy probability distributions. A classification on the Δ-waviness is given. For the Δ-wavy probability distributions having normalization constant, we give a formula for this constant, to compute this constant. We show that the Potts model is a Δ-wavy probability distribution, where Δ is a partition which will be specified. For the normalization constant of Potts model, we give formulas and bounds. As to the formulas for this constant, we give two general formulas, one of them is simple while the other is more complicated, and based on independent sets, a formula for the Potts model on connected separable graphs - closed-form expressions are then obtained in several cases -, and a formula for the Potts model on graphs with a vertex of degree 2 - a recurrence relation is then obtained for the normalization constant of Potts model on Cn; the cycle graph with n vertices; the normalization constant of Ising model on Cn is computed using this relation. As to the bounds for the normalization constant, we present two ways to obtain such bounds; we illustrate these ways giving a general lower bound, and a lower bound and an upper one when the model is the Potts model on Gn,n, the square grid graph, n = 6k, k ≥ 1 - two upper bounds for the free energy per site of this model are then obtained, one of them being in the limit. A sampling method for the Δ-wavy probability distributions is given and, as a result, a sampling method for the Potts is given. This method - that for the Potts model too - has two steps, Step 1 and Step 2, when |Δ| > 1 and one step, Step 2 only, when |Δ| = 1. For the Potts model, Step 1 is, in general, difficult. As to Step 2, for the Potts model too, using the Gibbs sampler in a generalized sense, we obtain an exact (not approximate) sampling method having p + 1 steps (p + 1 substeps of Step 2), where p = |I|; I is an independent set, best, a maximum independent set, best, a maximum independent set - for the Potts model on Gn1,n2,…,nd , the d-dimensional grid graph, d ≥ 1, n1, n2,…, nd ≥ 1, n1n2·…·nd ≥ 2; we obtain an exact sampling method for half or half+1 vertices.
我们定义了一个子集上的波状概率分布和Δ-wavy概率分布-波状概率分布的两种推广。在Δ-waviness上给出了分类。对于具有归一化常数的Δ-wavy概率分布,我们给出这个常数的公式,来计算这个常数。我们证明Potts模型是一个Δ-wavy概率分布,其中Δ是一个将被指定的分区。对于Potts模型的归一化常数,给出了公式和界。对于这个常数的表达式,我们给出了两个简单而复杂的一般公式,并在独立集的基础上,得到了连通可分离图上的Potts模型的一个公式——在几种情况下得到了封闭形式的表达式——和顶点为2次的图上的Potts模型的一个公式——在Cn上的Potts模型的归一化常数的递推关系;n个顶点的循环图;利用此关系式计算了Cn上Ising模型的归一化常数。对于归一化常数的边界,我们给出了两种方法来求得这样的边界;我们给出了这些方法的一般下界,以及当模型是Gn,n,方形网格图,n = 6k, k≥1的Potts模型时的下界和上界,然后得到了该模型的每个位置的自由能的两个上界,其中一个是极限。给出了Δ-wavy概率分布的抽样方法,从而给出了波茨的抽样方法。当|Δ| > 1时,这个方法也适用于Potts模型,它有两个步骤,即步骤1和步骤2;当|Δ| = 1时,只有一个步骤,即步骤2。对于Potts模型,步骤1通常是困难的。对于步骤2,对于Potts模型,使用广义的Gibbs采样器,我们得到了具有p + 1个步骤(步骤2的p + 1个子步骤)的精确(而不是近似)采样方法,其中p = |I|;I是独立集,best,最大独立集,best,最大独立集-对于Potts模型在Gn1,n2,…,nd上的d维网格图,d≥1,n1,n2,…,nd≥1,n1n2·…·nd≥2;我们得到了半顶点或半+1顶点的精确采样方法。
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引用次数: 2
A statistical evaluation of the preprocessing medical images impact on a deep learning network’s performance 医学图像预处理对深度学习网络性能影响的统计评估
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1641
R. Ivanescu
The aim of this paper is to explore the efficiency of preprocessing medical images before applying a deep learning algorithm to classify the data. The study uses a statistical framework that establishes the fact that depending on the dataset used, image preprocessing indeed decreases the computational time, without having a dropdown in performance. The dataset used in this study regard colon cancer, lung cancer, and fetal brain ultrasound scans. The study proposes a statistical performance that studies the performances of the ResNet50 deep learning network in different preprocessing scenarios.
本文的目的是探讨在应用深度学习算法对数据进行分类之前对医学图像进行预处理的效率。该研究使用了一个统计框架,根据所使用的数据集,图像预处理确实减少了计算时间,而不会降低性能。本研究使用的数据集涉及结肠癌、肺癌和胎儿脑超声扫描。本研究提出了一个统计性能,研究了ResNet50深度学习网络在不同预处理场景下的性能。
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引用次数: 1
Integral inequalities for mappings whose derivatives are (h,m,s)-convex modied of second type via Katugampola integrals 导数为(h,m,s)的映射的积分不等式-通过Katugampola积分进行第二类凸调制
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1596
B. Bayraktar, J. E. Napoles-Valdes
In this paper, using the definition of functions (h,m,s)-convex modified of second type, various extensions of the classic Hermite-Hadamard Inequality are obtained using Katugampola integrals. In addition, we show that several results known are particular cases of ours.
本文利用第二类修正函数(h,m,s)-凸的定义,利用Katugampola积分得到了经典Hermite-Hadamard不等式的各种推广。此外,我们还表明,已知的几个结果是我们的特殊情况。
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引用次数: 2
∆λ−statistical boundedness of order α on time scales ∆λ−α阶在时间尺度上的统计有界性
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1296
Büşra Nur Er, Y. Altın
In this study, we introduce the notions ∆λ−statistical convergence of order α (for αϵ(0,1])  and λp−summable of order α (for αϵ(0,1]) on an arbitrary time scale. Moreover, some relations about these notions are obtained. We define ∆λ− statistically boundedness of order α (for αϵ(0,1]) on a time scale. Furthermore, We give connections between S (λ,α) T (b) , S (β,θ) T (b) and ST (b) for various sequences µ∆λ(t) and µ∆β(t) are determined in class Λ.
在本研究中,我们引入了在任意时间尺度上α阶(对于α λ(0,1))的λ -统计收敛和α阶(对于α λ(0,1))的λp -可求和的概念。此外,还得到了这些概念的一些关系。我们在时间尺度上定义了α阶(对于α λ(0,1))的∆λ−统计有界性。此外,我们给出了S (λ,α) T (b), S (β,θ) T (b)和ST (b)之间的联系,对于各种序列µ∆λ(T)和µ∆β(T)在Λ类中确定。
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引用次数: 0
Weigthed elliptic equation of Kirchhoff type with exponential non linear growthWeigthed elliptic equation of Kirchhoff type with exponential non linear growth 具有指数非线性增长的Kirchhoff型加权椭圆方程
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1572
Rached Jaidane
"This work is concerned with the existence of a positive ground state solution for the following non local weighted problem begin{equation*} displaystyle left{ begin{array}{rclll} L_{(sigma,V)}u &= & displaystyle f(x,u)& mbox{in} B u &>&0 &mbox{in }B u&=&0 &mbox{on } partial B, end{array} right. end{equation*} where $$L_{(sigma,V)}u:=g(int_{B}(sigma(x)|nabla u|^{N}+V(x)|u|^{N})dx)big[-textmd{div} (sigma(x)|nabla u|^{N-2} nabla u)+V(x)|u|^{N-2}ubig],$$ B is the unit ball of $mathbb{R}^{N}$, $ N>2$, $sigma(x)=Big(log(frac{e}{|x|})Big)^{beta(N-1)}$, $beta in[0,1)$ the singular logarithm weight , $V(x)$ is a positif continuous potential.The Kirchhoff function $g$ is positive and continuous on $(0,+infty)$. The nonlinearities are critical or subcritical growth in view of Trudinger-Moser inequalities of exponential type. We prove the existence of a positive ground state solution by using Mountain Pass theorem . In the critical case, the Euler-Lagrange function loses compactness except for a certain level. We dodge this problem by using adapted test functions to identify this level of compactness."
“这项工作涉及以下非局部加权问题begin{equation*} displaystyle left{ begin{array}{rclll} L_{(sigma,V)}u &= & displaystyle f(x,u)& mbox{in} B u &>&0 &mbox{in }B u&=&0 &mbox{on } partial B, end{array} right. end{equation*}的正基态解的存在性,其中$$L_{(sigma,V)}u:=g(int_{B}(sigma(x)|nabla u|^{N}+V(x)|u|^{N})dx)big[-textmd{div} (sigma(x)|nabla u|^{N-2} nabla u)+V(x)|u|^{N-2}ubig],$$ B是$mathbb{R}^{N}$的单位球,$ N>2$, $sigma(x)=Big(log(frac{e}{|x|})Big)^{beta(N-1)}$, $beta in[0,1)$的奇异对数权,$V(x)$是一个正连续势。Kirchhoff函数$g$在$(0,+infty)$上是正连续的。对于指数型Trudinger-Moser不等式,非线性是临界或亚临界增长。利用山口定理证明了正基态解的存在性。在临界情况下,欧拉-拉格朗日函数除某一水平外失去紧致性。我们通过使用适应的测试函数来识别这种紧凑程度,从而避免了这个问题。”
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引用次数: 2
On the nonhomogeneous wavelet bi-frames for reducing subspaces of Hs(K) 关于Hs(K)子空间约化的非齐次小波双框架
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1615
M. Y. Bhat
Ahmad and Shiekh in Filomat 34: 6(2020), 2091-2099 have constructed dual wavelet frames in Sobolev spaces on local fields of positive characteristic. We continued the study and provided the characterization of nonhomogeneous wavelet bi-frames. First of all we introduce the reducing subspaces of Sobolev spaces over local fields of prime characteristics and then provide the way to characterize the nonhomogeneous wavelet bi-frames over such fields. Our results are better than those established by Ahmad and Shiekh.
Ahmad和sheikh在Filomat 34(2020), 2091-2099中构造了Sobolev空间中正特征域的对偶小波帧。我们继续研究并提供了非齐次小波双框架的表征。首先在素数特征局部域上引入Sobolev空间的约简子空间,然后给出了在这些域上刻画非齐次小波双帧的方法。我们的结果比Ahmad和sheikh建立的结果要好。
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引用次数: 0
Heteroclinic solutions for damped p-Laplacian difference equations 阻尼p-拉普拉斯差分方程的异斜解
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1585
A. Daouas, Ameni Guefrej
"In this paper, we investigate the existence of heteroclinic solutions for a class of p-Laplacian difference equations with a parameter. The proof of the main theorem is variational and based on the use of the Mountain Pass Theorem. Our results successfully improve recent ones in the literature and partially answer an open problem proposed by Cabada and Tersian in [23]."
本文研究了一类带参数的p-拉普拉斯差分方程异斜解的存在性。主要定理的证明是变分的,并基于山口定理的使用。我们的结果成功地改进了最近的文献,并部分回答了Cabada和Tersian在b[23]中提出的一个开放问题。”
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引用次数: 0
Provide a framework for problem statement in the organization's research: an AHP, ISM, and MICMAC approach 为组织研究中的问题陈述提供一个框架:AHP、ISM和MICMAC方法
IF 1 Q3 MATHEMATICS Pub Date : 2022-12-24 DOI: 10.52846/ami.v49i2.1685
Ehsan Farzin Abdehgah, Sayedeh Babooneh Rastgooyan, C. Spulbar, Ramona Birau
The aim is to provide a framework for statement organizational research problems. State the problem is the most important reason for the researcher to choose the subject. Although research has been done on the characteristics of expression of research problems, but in organizational research, no framework for expressing the problem has been provided. The method used in this research is grounded theory followed by the ISM-MICMAC approach for modelling. The findings of this study identify the components of problem statement in organizational research and modelling them. Due to the large number of indicators, first nine indicators of higher importance were identified, which had much more weight than other indicators. These indicators were then compared and prioritized again by other experts. Based on the level of importance of these indicators, a model is presented and it is determined what position each of these indicators is in terms of Degree of dependence and Influence rate. The researcher can easily use this information to provide an acceptable problem statement and the editors will have a good assessment tool.
其目的是为陈述组织研究问题提供一个框架。陈述问题是研究者选择课题的最重要的原因。虽然对研究问题的表达特征进行了研究,但在组织研究中,没有提供问题表达的框架。本研究使用的方法是扎根理论,然后是ISM-MICMAC建模方法。本研究的发现确定了组织研究中问题陈述的组成部分并对其进行建模。由于指标数量较多,确定了重要性较高的前9个指标,其权重远高于其他指标。然后由其他专家对这些指标进行比较并再次确定优先级。根据这些指标的重要程度,提出了一个模型,并确定了这些指标在依赖程度和影响率方面的位置。研究人员可以很容易地使用这些信息来提供一个可接受的问题陈述,编辑将有一个很好的评估工具。
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引用次数: 0
期刊
Annals of the University of Craiova-Mathematics and Computer Science Series
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