F. Arzikulov, Furqatjon Urinboyev, Shahlo Ergasheva
In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra (mathcal{D}) and the seven-dimensional central simple commutative algebra (mathcal{C}). We prove that every local derivation of these algebras (mathcal{D}) and (mathcal{C}) is a derivation, and every 2-local derivation of these algebras (mathcal{D}) and (mathcal{C}) is also a derivation. We also prove that every local automorphism of these algebras (mathcal{D}) and (mathcal{C}) is an automorphism, and every 2-local automorphism of these algebras (mathcal{D}) and (mathcal{C}) is also an automorphism.
{"title":"A CHARACTERIZATION OF DERIVATIONS AND AUTOMORPHISMS ON SOME SIMPLE ALGEBRAS","authors":"F. Arzikulov, Furqatjon Urinboyev, Shahlo Ergasheva","doi":"10.15826/umj.2022.2.004","DOIUrl":"https://doi.org/10.15826/umj.2022.2.004","url":null,"abstract":"In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra (mathcal{D}) and the seven-dimensional central simple commutative algebra (mathcal{C}). We prove that every local derivation of these algebras (mathcal{D}) and (mathcal{C}) is a derivation, and every 2-local derivation of these algebras (mathcal{D}) and (mathcal{C}) is also a derivation. We also prove that every local automorphism of these algebras (mathcal{D}) and (mathcal{C}) is an automorphism, and every 2-local automorphism of these algebras (mathcal{D}) and (mathcal{C}) is also an automorphism.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44139315","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 introduce the concept of the (mathbb{B}_{alpha})-classical orthogonal polynomials, where (mathbb{B}_{alpha}) is the raising operator (mathbb{B}_{alpha}:=x^2 cdot {d}/{dx}+big(2(alpha-1)x+1big)mathbb{I}), with nonzero complex number (alpha) and (mathbb{I}) representing the identity operator. We show that the Bessel polynomials (B^{(alpha)}_n(x), ngeq0), where (alphaneq-{m}/{2}, mgeq -2, min mathbb{Z}), are the only (mathbb{B}_{alpha})-classical orthogonal polynomials. As an application, we present some new formulas for polynomial solution.
{"title":"BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS","authors":"B. Aloui, Jihad Souissi","doi":"10.15826/umj.2022.2.001","DOIUrl":"https://doi.org/10.15826/umj.2022.2.001","url":null,"abstract":"In this paper, we introduce the concept of the (mathbb{B}_{alpha})-classical orthogonal polynomials, where (mathbb{B}_{alpha}) is the raising operator (mathbb{B}_{alpha}:=x^2 cdot {d}/{dx}+big(2(alpha-1)x+1big)mathbb{I}), with nonzero complex number (alpha) and (mathbb{I}) representing the identity operator. We show that the Bessel polynomials (B^{(alpha)}_n(x), ngeq0), where (alphaneq-{m}/{2}, mgeq -2, min mathbb{Z}), are the only (mathbb{B}_{alpha})-classical orthogonal polynomials. As an application, we present some new formulas for polynomial solution.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46473440","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}
Regan Murugesan, Sathish Kumar Kumaravel, S. Rasappan, Wardah Abdullah Al Majrafi
The mosquito life cycle is developed mathematically with the concept of difference equation. The qualitative properties of the life-cycle are analyzed. The Lyapunov function is defined for difference equation to stabilize the system of mosquito life cycle. A novel technique is applied for deriving stability criterion, especially the back-stepping control technique is applied for discrete time system. The bifurcation analysis is also furnished for the model of mosquito life cycle. The new technique is applied in the mosquito life cycle model and its results are examined through MATLAB.
{"title":"ANALYSIS OF THE GROWTH RATE OF FEMININE MOSQUITO THROUGH DIFFERENCE EQUATIONS","authors":"Regan Murugesan, Sathish Kumar Kumaravel, S. Rasappan, Wardah Abdullah Al Majrafi","doi":"10.15826/umj.2022.2.011","DOIUrl":"https://doi.org/10.15826/umj.2022.2.011","url":null,"abstract":"The mosquito life cycle is developed mathematically with the concept of difference equation. The qualitative properties of the life-cycle are analyzed. The Lyapunov function is defined for difference equation to stabilize the system of mosquito life cycle. A novel technique is applied for deriving stability criterion, especially the back-stepping control technique is applied for discrete time system. The bifurcation analysis is also furnished for the model of mosquito life cycle. The new technique is applied in the mosquito life cycle model and its results are examined through MATLAB.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45933220","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 the present paper, we classify abelian antipodal distance-regular graphs (Gamma) of diameter 3 with the following property: ((*)) (Gamma) has a transitive group of automorphisms (widetilde{G}) that induces a primitive almost simple permutation group (widetilde{G}^{Sigma}) on the set ({Sigma}) of its antipodal classes. There are several infinite families of (arc-transitive) examples in the case when the permutation rank ({rm rk}(widetilde{G}^{Sigma})) of (widetilde{G}^{Sigma}) equals 2 moreover, all such graphs are now known. Here we focus on the case ({rm rk}(widetilde{G}^{Sigma})=3).Under this condition the socle of (widetilde{G}^{Sigma}) turns out to be either a sporadic simple group, or an alternating group, or a simple group of exceptional Lie type, or a classical simple group. Earlier, it was shown that the family of non-bipartite graphs (Gamma) with the property ((*)) such that (rk(widetilde{G}^{Sigma})=3) and the socle of (widetilde{G}^{Sigma}) is a sporadic or an alternating group is finite and limited to a small number of potential examples. The present paper is aimed to study the case of classical simple socle for (widetilde{G}^{Sigma}). We follow a classification scheme that is based on a reduction to minimal quotients of (Gamma) that inherit the property ((*)). For each given group (widetilde{G}^{Sigma}) with simple classical socle of degree (|{Sigma}|le 2500), we determine potential minimal quotients of (Gamma), applying some previously developed techniques for bounding their spectrum and parameters in combination with the classification of primitive rank 3 groups of the corresponding type and associated rank 3 graphs. This allows us to essentially restrict the sets of feasible parameters of (Gamma) in the case of classical socle for (widetilde{G}^{Sigma}) under condition (|{Sigma}|le 2500.)
{"title":"ON SOME VERTEX-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS","authors":"L. Tsiovkina","doi":"10.15826/umj.2022.2.014","DOIUrl":"https://doi.org/10.15826/umj.2022.2.014","url":null,"abstract":"In the present paper, we classify abelian antipodal distance-regular graphs (Gamma) of diameter 3 with the following property: ((*)) (Gamma) has a transitive group of automorphisms (widetilde{G}) that induces a primitive almost simple permutation group (widetilde{G}^{Sigma}) on the set ({Sigma}) of its antipodal classes. There are several infinite families of (arc-transitive) examples in the case when the permutation rank ({rm rk}(widetilde{G}^{Sigma})) of (widetilde{G}^{Sigma}) equals 2 moreover, all such graphs are now known. Here we focus on the case ({rm rk}(widetilde{G}^{Sigma})=3).Under this condition the socle of (widetilde{G}^{Sigma}) turns out to be either a sporadic simple group, or an alternating group, or a simple group of exceptional Lie type, or a classical simple group. Earlier, it was shown that the family of non-bipartite graphs (Gamma) with the property ((*)) such that (rk(widetilde{G}^{Sigma})=3) and the socle of (widetilde{G}^{Sigma}) is a sporadic or an alternating group is finite and limited to a small number of potential examples. The present paper is aimed to study the case of classical simple socle for (widetilde{G}^{Sigma}). We follow a classification scheme that is based on a reduction to minimal quotients of (Gamma) that inherit the property ((*)). For each given group (widetilde{G}^{Sigma}) with simple classical socle of degree (|{Sigma}|le 2500), we determine potential minimal quotients of (Gamma), applying some previously developed techniques for bounding their spectrum and parameters in combination with the classification of primitive rank 3 groups of the corresponding type and associated rank 3 graphs. This allows us to essentially restrict the sets of feasible parameters of (Gamma) in the case of classical socle for (widetilde{G}^{Sigma}) under condition (|{Sigma}|le 2500.)","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48157111","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 article, we have discussed Biharmonic Green function on an infinite network and bimedian functions. We have proved some standard results in terms of supermedian and bimedian. Also, we have proved the Discrete Riquier problem in the setting of bimedian functions.
{"title":"BIHARMONIC GREEN FUNCTION AND BISUPERMEDIAN ON INFINITE NETWORKS","authors":"Manivannan Varadha Raj, Venkataraman Madhu","doi":"10.15826/umj.2022.2.015","DOIUrl":"https://doi.org/10.15826/umj.2022.2.015","url":null,"abstract":"In this article, we have discussed Biharmonic Green function on an infinite network and bimedian functions. We have proved some standard results in terms of supermedian and bimedian. Also, we have proved the Discrete Riquier problem in the setting of bimedian functions.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46810080","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}
S. Kosari, S. M. Sheikholeslami, M. Chellali, M. Hajjari
A restrained Roman dominating function (RRD-function) on a graph (G=(V,E)) is a function (f) from (V) into ({0,1,2}) satisfying: (i) every vertex (u) with (f(u)=0) is adjacent to a vertex (v) with (f(v)=2); (ii) the subgraph induced by the vertices assigned 0 under (f) has no isolated vertices. The weight of an RRD-function is the sum of its function value over the whole set of vertices, and the restrained Roman domination number is the minimum weight of an RRD-function on (G.) In this paper, we begin the study of the restrained Roman reinforcement number (r_{rR}(G)) of a graph (G) defined as the cardinality of a smallest set of edges that we must add to the graph to decrease its restrained Roman domination number. We first show that the decision problem associated with the restrained Roman reinforcement problem is NP-hard. Then several properties as well as some sharp bounds of the restrained Roman reinforcement number are presented. In particular it is established that (r_{rR}(T)=1) for every tree (T) of order at least three.
{"title":"RESTRAINED ROMAN REINFORCEMENT NUMBER IN GRAPHS","authors":"S. Kosari, S. M. Sheikholeslami, M. Chellali, M. Hajjari","doi":"10.15826/umj.2022.2.007","DOIUrl":"https://doi.org/10.15826/umj.2022.2.007","url":null,"abstract":"A restrained Roman dominating function (RRD-function) on a graph (G=(V,E)) is a function (f) from (V) into ({0,1,2}) satisfying: (i) every vertex (u) with (f(u)=0) is adjacent to a vertex (v) with (f(v)=2); (ii) the subgraph induced by the vertices assigned 0 under (f) has no isolated vertices. The weight of an RRD-function is the sum of its function value over the whole set of vertices, and the restrained Roman domination number is the minimum weight of an RRD-function on (G.) In this paper, we begin the study of the restrained Roman reinforcement number (r_{rR}(G)) of a graph (G) defined as the cardinality of a smallest set of edges that we must add to the graph to decrease its restrained Roman domination number. We first show that the decision problem associated with the restrained Roman reinforcement problem is NP-hard. Then several properties as well as some sharp bounds of the restrained Roman reinforcement number are presented. In particular it is established that (r_{rR}(T)=1) for every tree (T) of order at least three.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46192973","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}
A. I. Kristiana, M. Hidayat, R. Adawiyah, D. Dafik, S. Setiawani, R. Alfarisi
Let (G=(V,E)) be a graph with a vertex set (V) and an edge set (E). The graph (G) is said to be with a local irregular vertex coloring if there is a function (f) called a local irregularity vertex coloring with the properties: (i) (l:(V(G)) to { 1,2,...,k } ) as a vertex irregular (k)-labeling and (w:V(G)to N,) for every (uv in E(G),) ({w(u)neq w(v)}) where (w(u)=sum_{vin N(u)}l(i)) and (ii) (mathrm{opt}(l)=min{ max { l_{i}: l_{i} text{is a vertex irregular labeling}}}). The chromatic number of the local irregularity vertex coloring of (G) denoted by (chi_{lis}(G)), is the minimum cardinality of the largest label over all such local irregularity vertex colorings. In this paper, we study a local irregular vertex coloring of (P_mbigodot G) when (G) is a family of tree graphs, centipede (C_n), double star graph ((S_{2,n})), Weed graph ((S_{3,n})), and (E) graph ((E_{3,n})).
设（G=（V，E））是一个具有顶点集（V）和边集（E）的图。如果存在一个称为局部不规则顶点着色的函数（f），其性质为：（i）（l:（V（G）） to ｛1,2，…，k｝）作为顶点不规则（k）标记，并且对于E（G）中的每一个（uv，)其中（w（u）=sum_｛v in N（u）｝l（i））和（ii）。由（chi_｛lis｝（G））表示的（G）的局部不规则顶点着色的色数，是最大标签在所有此类局部不规则点着色上的最小基数。本文研究了当（G）是树图、蜈蚣图（C_n）、双星图（S_{2，n}）、Weed图（S_｛3，n｝）和图（E_{3，n}）的一个族时（P_m bigodot G）的局部不规则顶点着色。
{"title":"ON LOCAL IRREGULARITY OF THE VERTEX COLORING OF THE CORONA PRODUCT OF A TREE GRAPH","authors":"A. I. Kristiana, M. Hidayat, R. Adawiyah, D. Dafik, S. Setiawani, R. Alfarisi","doi":"10.15826/umj.2022.2.008","DOIUrl":"https://doi.org/10.15826/umj.2022.2.008","url":null,"abstract":"Let (G=(V,E)) be a graph with a vertex set (V) and an edge set (E). The graph (G) is said to be with a local irregular vertex coloring if there is a function (f) called a local irregularity vertex coloring with the properties: (i) (l:(V(G)) to { 1,2,...,k } ) as a vertex irregular (k)-labeling and (w:V(G)to N,) for every (uv in E(G),) ({w(u)neq w(v)}) where (w(u)=sum_{vin N(u)}l(i)) and (ii) (mathrm{opt}(l)=min{ max { l_{i}: l_{i} text{is a vertex irregular labeling}}}). The chromatic number of the local irregularity vertex coloring of (G) denoted by (chi_{lis}(G)), is the minimum cardinality of the largest label over all such local irregularity vertex colorings. In this paper, we study a local irregular vertex coloring of (P_mbigodot G) when (G) is a family of tree graphs, centipede (C_n), double star graph ((S_{2,n})), Weed graph ((S_{3,n})), and (E) graph ((E_{3,n})). ","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41942417","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 study the sharp inequality between the uniform norm and (L^p(0,pi/2))-norm of polynomials in the system (mathscr{C}={cos (2k+1)x}_{k=0}^infty) of cosines with odd harmonics. We investigate the limit behavior of the best constant in this inequality with respect to the order (n) of polynomials as (ntoinfty) and provide a characterization of the extremal polynomial in the inequality for a fixed order of polynomials.
{"title":"ON ONE INEQUALITY OF DIFFERENT METRICS FOR TRIGONOMETRIC POLYNOMIALS","authors":"V. Arestov, M. Deikalova","doi":"10.15826/umj.2022.2.003","DOIUrl":"https://doi.org/10.15826/umj.2022.2.003","url":null,"abstract":"We study the sharp inequality between the uniform norm and (L^p(0,pi/2))-norm of polynomials in the system (mathscr{C}={cos (2k+1)x}_{k=0}^infty) of cosines with odd harmonics. We investigate the limit behavior of the best constant in this inequality with respect to the order (n) of polynomials as (ntoinfty) and provide a characterization of the extremal polynomial in the inequality for a fixed order of polynomials.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49379734","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 present work mainly probes into the existence and uniqueness of periodic solutions for a class of second-order neutral differential equations with multiple delays. Our approach is based on using Banach and Krasnoselskii's fixed point theorems as well as the Green's function method. Besides, two examples are exhibited to validate the effectiveness of our findings which complement and extend some relevant ones in the literature.
{"title":"PERIODIC SOLUTIONS OF A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DIFFERENT DELAYS","authors":"R. Khemis, A. Ardjouni, Ahlème Bouakkaz","doi":"10.15826/umj.2022.2.006","DOIUrl":"https://doi.org/10.15826/umj.2022.2.006","url":null,"abstract":"The present work mainly probes into the existence and uniqueness of periodic solutions for a class of second-order neutral differential equations with multiple delays. Our approach is based on using Banach and Krasnoselskii's fixed point theorems as well as the Green's function method. Besides, two examples are exhibited to validate the effectiveness of our findings which complement and extend some relevant ones in the literature.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45736513","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 consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.
{"title":"APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION","authors":"A. Benchaabane","doi":"10.15826/umj.2022.2.005","DOIUrl":"https://doi.org/10.15826/umj.2022.2.005","url":null,"abstract":"In this paper we consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45384002","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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