For a distance-regular graph (Gamma) of diameter 3, the graph (Gamma_i) can be strongly regular for (i=2) or 3. J.Kulen and co-authors found the parameters of a strongly regular graph (Gamma_2) given the intersection array of the graph (Gamma) (independently, the parameters were found by A.A. Makhnev and D.V.Paduchikh). In this case, (Gamma) has an eigenvalue (a_2-c_3). In this paper, we study graphs (Gamma) with strongly regular graph (Gamma_2) and eigenvalue (theta=1). In particular, we prove that, for a (Q)-polynomial graph from a series of graphs with intersection arrays ({2c_3+a_1+1,2c_3,c_3+a_1-c_2;1,c_2,c_3}), the equality (c_3=4 (t^2+t)/(4t+4-c_2^2)) holds. Moreover, for (tle 100000), there is a unique feasible intersection array ({9,6,3;1,2,3}) corresponding to the Hamming (or Doob) graph (H(3,4)). In addition, we found parametrizations of intersection arrays of graphs with (theta_2=1) and (theta_3=a_2-c_3).
{"title":"ON DISTANCE–REGULAR GRAPHS OF DIAMETER 3 WITH EIGENVALUE (theta=1)","authors":"A. Makhnev, I. Belousov, K. S. Efimov","doi":"10.15826/umj.2022.2.010","DOIUrl":"https://doi.org/10.15826/umj.2022.2.010","url":null,"abstract":"For a distance-regular graph (Gamma) of diameter 3, the graph (Gamma_i) can be strongly regular for (i=2) or 3. J.Kulen and co-authors found the parameters of a strongly regular graph (Gamma_2) given the intersection array of the graph (Gamma) (independently, the parameters were found by A.A. Makhnev and D.V.Paduchikh). In this case, (Gamma) has an eigenvalue (a_2-c_3). In this paper, we study graphs (Gamma) with strongly regular graph (Gamma_2) and eigenvalue (theta=1). In particular, we prove that, for a (Q)-polynomial graph from a series of graphs with intersection arrays ({2c_3+a_1+1,2c_3,c_3+a_1-c_2;1,c_2,c_3}), the equality (c_3=4 (t^2+t)/(4t+4-c_2^2)) holds. Moreover, for (tle 100000), there is a unique feasible intersection array ({9,6,3;1,2,3}) corresponding to the Hamming (or Doob) graph (H(3,4)). In addition, we found parametrizations of intersection arrays of graphs with (theta_2=1) and (theta_3=a_2-c_3).","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":"47437634","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}
With a possible connection to integrals used in General Relativity, we used our contour integral method to write a closed form solution for a quadruple integral involving exponential functions and logarithm of quotient radicals. Almost all Hurwitz–Lerch Zeta functions have an asymmetrical zero distribution. All the results in this work are new.
{"title":"A QUADRUPLE INTEGRAL INVOLVING THE EXPONENTIAL LOGARITHM OF QUOTIENT RADICALS IN TERMS OF THE HURWITZ-LERCH ZETA FUNCTION","authors":"Robert Reynolds, Allan Stauffer","doi":"10.15826/umj.2022.2.013","DOIUrl":"https://doi.org/10.15826/umj.2022.2.013","url":null,"abstract":"With a possible connection to integrals used in General Relativity, we used our contour integral method to write a closed form solution for a quadruple integral involving exponential functions and logarithm of quotient radicals. Almost all Hurwitz–Lerch Zeta functions have an asymmetrical zero distribution. All the results in this work are new.","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":"43207143","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}
Nonlinear control systems presented as differential inclusions with positional impulse controls are investigated. By such a control we mean some abstract operator with the Dirac function concentrated at each time. Such a control ("running impulse"), as a generalized function, has no meaning and is formalized as a sequence of correcting impulse actions on the system corresponding to a directed set of partitions of the control interval. The system responds to such control by discontinuous trajectories, which form a network of so-called "Euler's broken lines." If, as a result of each such correction, the phase point of the object under study is on some given manifold (hypersurface), then a slip-type effect is introduced into the motion of the system, and then the network of "Euler's broken lines" is called an impulse-sliding mode. The paper deals with the problem of approximating impulse-sliding modes using sequences of continuous delta-like functions. The research is based on Yosida's approximation of set-valued mappings and some well-known facts for ordinary differential equations with impulses.
{"title":"APPROXIMATION OF POSITIONAL IMPULSE CONTROLS FOR DIFFERENTIAL INCLUSIONS","authors":"I. Finogenko, A. Sesekin","doi":"10.15826/umj.2022.1.005","DOIUrl":"https://doi.org/10.15826/umj.2022.1.005","url":null,"abstract":"Nonlinear control systems presented as differential inclusions with positional impulse controls are investigated. By such a control we mean some abstract operator with the Dirac function concentrated at each time. Such a control (\"running impulse\"), as a generalized function, has no meaning and is formalized as a sequence of correcting impulse actions on the system corresponding to a directed set of partitions of the control interval. The system responds to such control by discontinuous trajectories, which form a network of so-called \"Euler's broken lines.\" If, as a result of each such correction, the phase point of the object under study is on some given manifold (hypersurface), then a slip-type effect is introduced into the motion of the system, and then the network of \"Euler's broken lines\" is called an impulse-sliding mode. The paper deals with the problem of approximating impulse-sliding modes using sequences of continuous delta-like functions. The research is based on Yosida's approximation of set-valued mappings and some well-known facts for ordinary differential equations with impulses.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46220080","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}
M. Nithya, C. Sugapriya, S. Selvakumar, K. Jeganathan, T. Harikrishnan
This paper explores the two-commodity (TC) inventory system in which commodities are classified as major and complementary items. The system allows a customer who has purchased a free product to conduct Bernoulli trials at will. Under the Bernoulli schedule, any entering customer will quickly enter an orbit of infinite capability during the stock-out time of the major item. The arrival of a retrial customer in the system follows a classical retrial policy. These two products' re-ordering process occurs under the ((s, Q)) and instantaneous ordering policies for the major and complimentary items, respectively. A comprehensive analysis of the retrial queue, including the system's stability and the steady-state distribution of the retrial queue with the stock levels of two commodities, is carried out. The various system operations are measured under the stability condition. Finally, numerical evidence has shown the benefits of the proposed model under different random situations.
{"title":"A MARKOVIAN TWO COMMODITY QUEUEING–INVENTORY SYSTEM WITH COMPLIMENT ITEM AND CLASSICAL RETRIAL FACILITY","authors":"M. Nithya, C. Sugapriya, S. Selvakumar, K. Jeganathan, T. Harikrishnan","doi":"10.15826/umj.2022.1.009","DOIUrl":"https://doi.org/10.15826/umj.2022.1.009","url":null,"abstract":"This paper explores the two-commodity (TC) inventory system in which commodities are classified as major and complementary items. The system allows a customer who has purchased a free product to conduct Bernoulli trials at will. Under the Bernoulli schedule, any entering customer will quickly enter an orbit of infinite capability during the stock-out time of the major item. The arrival of a retrial customer in the system follows a classical retrial policy. These two products' re-ordering process occurs under the ((s, Q)) and instantaneous ordering policies for the major and complimentary items, respectively. A comprehensive analysis of the retrial queue, including the system's stability and the steady-state distribution of the retrial queue with the stock levels of two commodities, is carried out. The various system operations are measured under the stability condition. Finally, numerical evidence has shown the benefits of the proposed model under different random situations.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46183422","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 monopolistic competition model with producer-retailer-consumers two-level interaction. The industry is organized according to the Dixit–Stiglitz model. The retailer is the only monopolist. A quadratic utility function represents consumer preferences. We consider the case of the retailer's leadership; namely, we study two types of behavior: with and without the free entry condition. Earlier, we obtained the result: to increase social welfare and/or consumer surplus, the government needs to subsidize (not tax!) retailers. In the presented paper, we develop these results for the situation when the producer imposes an entrance fee for retailers.
{"title":"MONOPOLISTIC COMPETITION MODEL WITH ENTRANCE FEE","authors":"O. Tilzo","doi":"10.15826/umj.2022.1.010","DOIUrl":"https://doi.org/10.15826/umj.2022.1.010","url":null,"abstract":"We study the monopolistic competition model with producer-retailer-consumers two-level interaction. The industry is organized according to the Dixit–Stiglitz model. The retailer is the only monopolist. A quadratic utility function represents consumer preferences. We consider the case of the retailer's leadership; namely, we study two types of behavior: with and without the free entry condition. Earlier, we obtained the result: to increase social welfare and/or consumer surplus, the government needs to subsidize (not tax!) retailers. In the presented paper, we develop these results for the situation when the producer imposes an entrance fee for retailers.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43938102","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 are introducing certain subfamilies of holomorphic functions and making an attempt to obtain an upper bound (UB) to the second and third order Hankel determinants by applying certain lemmas, Toeplitz determinants, for the normalized analytic functions belong to these classes, defined on the open unit disc in the complex plane. For one of the inequality, we have obtained sharp bound.
{"title":"HANKEL DETERMINANT OF CERTAIN ORDERS FOR SOME SUBCLASSES OF HOLOMORPHIC FUNCTIONS","authors":"D. Vamshee Krishna, D. Shalini","doi":"10.15826/umj.2022.1.011","DOIUrl":"https://doi.org/10.15826/umj.2022.1.011","url":null,"abstract":"In this paper, we are introducing certain subfamilies of holomorphic functions and making an attempt to obtain an upper bound (UB) to the second and third order Hankel determinants by applying certain lemmas, Toeplitz determinants, for the normalized analytic functions belong to these classes, defined on the open unit disc in the complex plane. For one of the inequality, we have obtained sharp bound.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43387782","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 induced (nK_2) decomposition of infinite square grids and hexagonal grids are described here. We use the multi-level distance edge labeling as an effective technique in the decomposition of square grids. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. Only non-negative integers are used for labeling. The proposed partitioning technique per the edge labels to get the induced (nK_2) decomposition of the ladder graph is the square grid and the hexagonal grid.
{"title":"INDUCED (nK_{2}) DECOMPOSITION OF INFINITE SQUARE GRIDS AND INFINITE HEXAGONAL GRIDS","authors":"D. Deepthy, J. Kureethara","doi":"10.15826/umj.2022.1.003","DOIUrl":"https://doi.org/10.15826/umj.2022.1.003","url":null,"abstract":"The induced (nK_2) decomposition of infinite square grids and hexagonal grids are described here. We use the multi-level distance edge labeling as an effective technique in the decomposition of square grids. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. Only non-negative integers are used for labeling. The proposed partitioning technique per the edge labels to get the induced (nK_2) decomposition of the ladder graph is the square grid and the hexagonal grid.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46153266","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 solution of the Cauchy problem for the vector Burgers equation with a small parameter of dissipation (varepsilon) in the (4)-dimensional space-time is studied: $$ mathbf{u}_t + (mathbf{u}nabla) mathbf{u} = varepsilon triangle mathbf{u}, quad u_{nu} (mathbf{x}, -1, varepsilon) = - x_{nu} + 4^{-nu}(nu + 1) x_{nu}^{2nu + 1}, $$ With the help of the Cole–Hopf transform (mathbf{u} = - 2 varepsilon nabla ln H,) the exact solution and its leading asymptotic approximation, depending on six space-time scales, near a singular point are found. A formula for the growth of partial derivatives of the components of the vector field (mathbf{u}) on the time interval from the initial moment to the singular point, called the formula of the gradient catastrophe, is established: $$ frac{partial u_{nu} (0, t, varepsilon)}{partial x_{nu}} = frac{1}{t} left[ 1 + O left( varepsilon |t|^{- 1 - 1/nu} right) right]!, quad frac{t}{varepsilon^{nu /(nu + 1)} } to -infty, quad t to -0.$$The asymptotics of the solution far from the singular point, involving a multistep reconstruction of the space-time scales, is also obtained: $$ u_{nu} (mathbf{x}, t, varepsilon) approx - 2 left( frac{t}{nu + 1} right)^{1/2nu} tanh left[ frac{x_{nu}}{varepsilon} left( frac{t}{nu + 1} right)^{1/2nu} right]!, quad frac{t}{varepsilon^{nu /(nu + 1)} } to +infty. $$
研究了具有小耗散参数的向量Burgers方程在（4）维时空中的Cauchy问题的解：$$mathbf{u}_t+（mathbf｛u｝nabla）mathbf{u｝=varepsilontrianglemathbf｛u}，quad u_｛nu｝找到。建立了向量场（mathbf｛u｝）分量在从初始时刻到奇异点的时间间隔上的偏导数增长的公式，称为梯度突变公式：$$frac｛partial u_｛u｝（0，t，varepsilon）｝｛ partial x_｛nu｝＝frac{1｝{t｝left[1+Oleft（varepsilion|t|^｛-1/nu｝right）right]！，quadfrac｛t｝｛varepsilon^｛nu/（nu+1）｝｝to-infty，quad t to-0.$$解的渐近性远离奇异点，涉及时空尺度的多步重建，也得到：$$u_｛nu｝（mathbf｛x｝，t，varepsilon）approxy-2left（frac｛t｝｛nu+1｝right）^｛1/2nu｝tanhleft[frac｛x_｛ nu｝｝！，quadfrac｛t｝｛varepsilon^｛nu/（nu+1）｝｝到+infty$$
{"title":"EVOLUTION OF A MULTISCALE SINGULARITY OF THE SOLUTION OF THE BURGERS EQUATION IN THE 4-DIMENSIONAL SPACE–TIME","authors":"Sergey V. Zakharov","doi":"10.15826/umj.2022.1.012","DOIUrl":"https://doi.org/10.15826/umj.2022.1.012","url":null,"abstract":"The solution of the Cauchy problem for the vector Burgers equation with a small parameter of dissipation (varepsilon) in the (4)-dimensional space-time is studied: $$ mathbf{u}_t + (mathbf{u}nabla) mathbf{u} = varepsilon triangle mathbf{u}, quad u_{nu} (mathbf{x}, -1, varepsilon) = - x_{nu} + 4^{-nu}(nu + 1) x_{nu}^{2nu + 1}, $$ With the help of the Cole–Hopf transform (mathbf{u} = - 2 varepsilon nabla ln H,) the exact solution and its leading asymptotic approximation, depending on six space-time scales, near a singular point are found. A formula for the growth of partial derivatives of the components of the vector field (mathbf{u}) on the time interval from the initial moment to the singular point, called the formula of the gradient catastrophe, is established: $$ frac{partial u_{nu} (0, t, varepsilon)}{partial x_{nu}} = frac{1}{t} left[ 1 + O left( varepsilon |t|^{- 1 - 1/nu} right) right]!, quad frac{t}{varepsilon^{nu /(nu + 1)} } to -infty, quad t to -0.$$The asymptotics of the solution far from the singular point, involving a multistep reconstruction of the space-time scales, is also obtained: $$ u_{nu} (mathbf{x}, t, varepsilon) approx - 2 left( frac{t}{nu + 1} right)^{1/2nu} tanh left[ frac{x_{nu}}{varepsilon} left( frac{t}{nu + 1} right)^{1/2nu} right]!, quad frac{t}{varepsilon^{nu /(nu + 1)} } to +infty. $$","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42501887","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 set (S) of vertices in a connected graph (G=(V,E)) is called a signal set if every vertex not in (S) lies on a signal path between two vertices from (S). A set (S) is called a double signal set of (G) if (S) if for each pair of vertices (x,y in G) there exist (u,v in S) such that (x,y in L[u,v]). The double signal number (mathrm{dsn},(G)) of (G) is the minimum cardinality of a double signal set. Any double signal set of cardinality (mathrm{dsn},(G)) is called (mathrm{dsn})-set of (G). In this paper we introduce and initiate some properties on double signal number of a graph. We have also given relation between geodetic number, signal number and double signal number for some classes of graphs.
如果不在(S)中的每个顶点都位于来自(S)的两个顶点之间的信号路径上，则连通图(G=(V,E))中的顶点集合(S)称为信号集。集合(S)被称为双信号集(G)，如果(S)如果对于每一对顶点(x,y in G)存在(u,v in S)，使得(x,y in L[u,v])。(G)的双信号数(mathrm{dsn},(G))是双信号集的最小基数。基数为(mathrm{dsn},(G))的任何双信号集称为(mathrm{dsn}) - (G)集。本文引入并初始化了图的双信号数的一些性质。给出了几类图的测地数、信号数和双信号数之间的关系。
{"title":"ON DOUBLE SIGNAL NUMBER OF A GRAPH","authors":"X. Lenin Xaviour, S. Ancy Mary","doi":"10.15826/umj.2022.1.007","DOIUrl":"https://doi.org/10.15826/umj.2022.1.007","url":null,"abstract":"A set (S) of vertices in a connected graph (G=(V,E)) is called a signal set if every vertex not in (S) lies on a signal path between two vertices from (S). A set (S) is called a double signal set of (G) if (S) if for each pair of vertices (x,y in G) there exist (u,v in S) such that (x,y in L[u,v]). The double signal number (mathrm{dsn},(G)) of (G) is the minimum cardinality of a double signal set. Any double signal set of cardinality (mathrm{dsn},(G)) is called (mathrm{dsn})-set of (G). In this paper we introduce and initiate some properties on double signal number of a graph. We have also given relation between geodetic number, signal number and double signal number for some classes of graphs.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43193381","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 present some fixed point results for multivalued non-self mappings. We generalize the fixed point theorem due to Altun and Minak [2] by using Jleli and Sameti [9] (vartheta)-contraction. To validate the results proved here, we provide an appropriate application of our main result.
{"title":"FIXED POINT THEOREM FOR MULTIVALUED NON-SELF MAPPINGS SATISFYING JS-CONTRACTION WITH AN APPLICATION","authors":"David Aron, Santosh Kumar","doi":"10.15826/umj.2022.1.001","DOIUrl":"https://doi.org/10.15826/umj.2022.1.001","url":null,"abstract":"In this paper, we present some fixed point results for multivalued non-self mappings. We generalize the fixed point theorem due to Altun and Minak [2] by using Jleli and Sameti [9] (vartheta)-contraction. To validate the results proved here, we provide an appropriate application of our main result.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44991896","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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