"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."
{"title":"A modified Susceptible-Infected-Recovered epidemiological model","authors":"I. Bica, Zhichun Zhai, Rui Hu","doi":"10.52846/ami.v49i2.1560","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1560","url":null,"abstract":"\"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.\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75740332","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}
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.
{"title":"Δ-wavy probability distributions and Potts model","authors":"Udrea Păun","doi":"10.52846/ami.v49i2.1494","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1494","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73385341","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}
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.
{"title":"Location of zeros of a Lacunary type polynomial","authors":"Subhasis Das","doi":"10.52846/ami.v49i2.1614","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1614","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89606146","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}
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.
{"title":"A statistical evaluation of the preprocessing medical images impact on a deep learning network’s performance","authors":"R. Ivanescu","doi":"10.52846/ami.v49i2.1641","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1641","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77496018","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}
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.
{"title":"Integral inequalities for mappings whose derivatives are (h,m,s)-convex modied of second type via Katugampola integrals","authors":"B. Bayraktar, J. E. Napoles-Valdes","doi":"10.52846/ami.v49i2.1596","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1596","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88062431","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}
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。
{"title":"∆λ−statistical boundedness of order α on time scales","authors":"Büşra Nur Er, Y. Altın","doi":"10.52846/ami.v49i2.1296","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1296","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89830689","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}
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.
{"title":"On the nonhomogeneous wavelet bi-frames for reducing subspaces of Hs(K)","authors":"M. Y. Bhat","doi":"10.52846/ami.v49i2.1615","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1615","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77308205","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}
"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."
{"title":"Weigthed elliptic equation of Kirchhoff type with exponential non linear growthWeigthed elliptic equation of Kirchhoff type with exponential non linear growth","authors":"Rached Jaidane","doi":"10.52846/ami.v49i2.1572","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1572","url":null,"abstract":"\"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.\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72771114","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}
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.
{"title":"Provide a framework for problem statement in the organization's research: an AHP, ISM, and MICMAC approach","authors":"Ehsan Farzin Abdehgah, Sayedeh Babooneh Rastgooyan, C. Spulbar, Ramona Birau","doi":"10.52846/ami.v49i2.1685","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1685","url":null,"abstract":"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.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88971627","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}
"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]."
{"title":"Heteroclinic solutions for damped p-Laplacian difference equations","authors":"A. Daouas, Ameni Guefrej","doi":"10.52846/ami.v49i2.1585","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1585","url":null,"abstract":"\"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].\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86656405","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}
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