A (Q)-polynomial Shilla graph with (b = 5) has intersection arrays ({105t,4(21t+1),16(t+1); 1,4 (t+1),84t}), (tin{3,4,19}). The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of (Q)-polynomial Shilla graphs with (b = 6) are found.
具有（b=5）的（Q）-多项式Shilla图具有相交数组（｛105t，4（21t+1），16（t+1）；1，4（t+1，84t），（t in ｛3，4，19）。证明了具有这些交数组的距离正则图是不存在的。此外，还得到了具有（b=6）的（Q）-多项式Shilla图的可行交数组。
{"title":"SHILLA GRAPHS WITH (b=5) AND (b=6)","authors":"A. Makhnev, I. Belousov","doi":"10.15826/umj.2021.2.004","DOIUrl":"https://doi.org/10.15826/umj.2021.2.004","url":null,"abstract":"A (Q)-polynomial Shilla graph with (b = 5) has intersection arrays ({105t,4(21t+1),16(t+1); 1,4 (t+1),84t}), (tin{3,4,19}). The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of (Q)-polynomial Shilla graphs with (b = 6) are found.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46130997","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}
Let ({E}_{n}) be the ring of Eisenstein integers modulo (n). We denote by (G({E}_{n})) and (G_{{E}_{n}}), the unit graph and the unitary Cayley graph of ({E}_{n}), respectively. In this paper, we obtain the value of the diameter, the girth, the clique number and the chromatic number of these graphs. We also prove that for each (n>1), the graphs (G(E_{n})) and (G_{E_{n}}) are Hamiltonian.
{"title":"UNIT AND UNITARY CAYLEY GRAPHS FOR THE RING OF EISENSTEIN INTEGERS MODULO (n)","authors":"R. Jahani-Nezhad, Ali Bahrami","doi":"10.15826/umj.2021.2.003","DOIUrl":"https://doi.org/10.15826/umj.2021.2.003","url":null,"abstract":"Let ({E}_{n}) be the ring of Eisenstein integers modulo (n). We denote by (G({E}_{n})) and (G_{{E}_{n}}), the unit graph and the unitary Cayley graph of ({E}_{n}), respectively. In this paper, we obtain the value of the diameter, the girth, the clique number and the chromatic number of these graphs. We also prove that for each (n>1), the graphs (G(E_{n})) and (G_{E_{n}}) are Hamiltonian.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44846469","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 suggest an explicit continuation formula for a solution to the Cauchy problem for the Poisson equation in a domain from its values and values of its normal derivative on a part of the boundary. We construct the continuation formula of this problem based on the Carleman--Yarmuhamedov function method.
{"title":"CARLEMAN'S FORMULA OF A SOLUTIONS OF THE POISSON EQUATION IN BOUNDED DOMAIN","authors":"É. N. Sattorov, Z. E. Ermamatova","doi":"10.15826/umj.2021.2.008","DOIUrl":"https://doi.org/10.15826/umj.2021.2.008","url":null,"abstract":"We suggest an explicit continuation formula for a solution to the Cauchy problem for the Poisson equation in a domain from its values and values of its normal derivative on a part of the boundary. We construct the continuation formula of this problem based on the Carleman--Yarmuhamedov function method.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48921503","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}
Constructions related to products of maximal linked systems (MLSs) and MLSs on the product of widely understood measurable spaces are considered (these measurable spaces are defined as sets equipped with (pi)-systems of their subsets; a (pi)-system is a family closed with respect to finite intersections). We compare families of MLSs on initial spaces and MLSs on the product. Separately, we consider the case of ultrafilters. Equipping set-products with topologies, we use the box-topology and the Tychonoff product of Stone-type topologies. The properties of compaction and homeomorphism hold, respectively.
{"title":"PRODUCTS OF ULTRAFILTERS AND MAXIMAL LINKED SYSTEMS ON WIDELY UNDERSTOOD MEASURABLE SPACES","authors":"A. Chentsov","doi":"10.15826/umj.2021.2.001","DOIUrl":"https://doi.org/10.15826/umj.2021.2.001","url":null,"abstract":"Constructions related to products of maximal linked systems (MLSs) and MLSs on the product of widely understood measurable spaces are considered (these measurable spaces are defined as sets equipped with (pi)-systems of their subsets; a (pi)-system is a family closed with respect to finite intersections). We compare families of MLSs on initial spaces and MLSs on the product. Separately, we consider the case of ultrafilters. Equipping set-products with topologies, we use the box-topology and the Tychonoff product of Stone-type topologies. The properties of compaction and homeomorphism hold, respectively.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48449253","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 nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.
{"title":"CONTROL SYSTEM DEPENDING ON A PARAMETER","authors":"V. Ushakov, A. Ershov, A. Ushakov, O. Kuvshinov","doi":"10.15826/umj.2021.1.011","DOIUrl":"https://doi.org/10.15826/umj.2021.1.011","url":null,"abstract":"A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43150492","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 main purpose of this work is to define Rough Statistical (Lambda)-Convergence of order (alpha) ((0
本工作的主要目的是在赋范线性空间中定义粗糙统计(Lambda) -阶(alpha)((0
{"title":"SOME REMARKS ON ROUGH STATISTICAL (Lambda)-CONVERGENCE OF ORDER (alpha)","authors":"Reena Antal, Meenakshi Chawla, Vijay Kumar","doi":"10.15826/umj.2021.1.002","DOIUrl":"https://doi.org/10.15826/umj.2021.1.002","url":null,"abstract":"The main purpose of this work is to define Rough Statistical (Lambda)-Convergence of order (alpha) ((0<alphaleq1)) in normed linear spaces. We have proved some basic properties and also provided some examples to show that this method of convergence is more generalized than the rough statistical convergence. Further, we have shown the results related to statistically (Lambda)-bounded sets of order (alpha) and sets of rough statistically (Lambda)-convergent sequences of order (alpha).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43761867","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 consider a set membership estimation problem for linear non-stationary systems for which initial states belong to a compact set and uncertain disturbances in an observation equation are integrally restricted. We provethat the exact information set of the system can be approximated by a set of external ellipsoids in the absence of disturbances in the dynamic equation.There are three examples of linear systems. Two examples illustrate the main theorem of the paper, the latter one shows the possibility of generalizing the theorem to the case with disturbances in the dynamic equation.
{"title":"SET MEMBERSHIP ESTIMATION WITH A SEPARATE RESTRICTION ON INITIAL STATE AND DISTURBANCES","authors":"P. Yurovskikh","doi":"10.15826/umj.2021.1.012","DOIUrl":"https://doi.org/10.15826/umj.2021.1.012","url":null,"abstract":"We consider a set membership estimation problem for linear non-stationary systems for which initial states belong to a compact set and uncertain disturbances in an observation equation are integrally restricted. We provethat the exact information set of the system can be approximated by a set of external ellipsoids in the absence of disturbances in the dynamic equation.There are three examples of linear systems. Two examples illustrate the main theorem of the paper, the latter one shows the possibility of generalizing the theorem to the case with disturbances in the dynamic equation.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46053066","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}
Let (P(G, x)) be a chromatic polynomial of a graph (G). Two graphs (G) and (H) are called chromatically equivalent iff (P(G, x) = H(G, x)). A graph (G) is called chromatically unique if (Gsimeq H) for every (H) chromatically equivalent to (G). In this paper, the chromatic uniqueness of complete tripartite graphs (K(n_1, n_2, n_3)) is proved for (n_1 geqslant n_2 geqslant n_3 geqslant 2) and (n_1 - n_3 leqslant 5).
{"title":"ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS","authors":"P. A. Gein","doi":"10.15826/umj.2021.1.004","DOIUrl":"https://doi.org/10.15826/umj.2021.1.004","url":null,"abstract":"Let (P(G, x)) be a chromatic polynomial of a graph (G). Two graphs (G) and (H) are called chromatically equivalent iff (P(G, x) = H(G, x)). A graph (G) is called chromatically unique if (Gsimeq H) for every (H) chromatically equivalent to (G). In this paper, the chromatic uniqueness of complete tripartite graphs (K(n_1, n_2, n_3)) is proved for (n_1 geqslant n_2 geqslant n_3 geqslant 2) and (n_1 - n_3 leqslant 5).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90475614","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}
One problem focused on engineering applications is considered. It is assumed that sequential visits to megacities have been implemented. After all visits have been made, it is required to return to the starting point (a more complex dependence on the starting point is also considered). But the last requirement is not strict: some weakening of the return condition is acceptable. Under these assumptions, it is required to optimize the choice of starting point, route, and specific trajectory. The well-known dynamic programming (DP) is used for the solution. But when using DP, significant difficulties arise associated with the dependence of the terminal component of the criterion on the starting point. Starting point enumeration is required. We consider the possibility of reducing the enumeration associated with applied variants of universal (relative to the starting point) dynamic programming. Of course, this approach requires some transformation of the problem.
{"title":"ON ROUTING PROBLEM WITH STARTING POINT OPTIMIZATION","authors":"A. Chentsov, P. Chentsov","doi":"10.15826/umj.2020.2.005","DOIUrl":"https://doi.org/10.15826/umj.2020.2.005","url":null,"abstract":"One problem focused on engineering applications is considered. It is assumed that sequential visits to megacities have been implemented. After all visits have been made, it is required to return to the starting point (a more complex dependence on the starting point is also considered). But the last requirement is not strict: some weakening of the return condition is acceptable. Under these assumptions, it is required to optimize the choice of starting point, route, and specific trajectory. The well-known dynamic programming (DP) is used for the solution. But when using DP, significant difficulties arise associated with the dependence of the terminal component of the criterion on the starting point. Starting point enumeration is required. We consider the possibility of reducing the enumeration associated with applied variants of universal (relative to the starting point) dynamic programming. Of course, this approach requires some transformation of the problem.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44531534","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, the local density ((l d)) and the local weak density ((l w d)) in the space of permutation degree as well as the cardinal and topological properties of Hattori spaces are studied. In other words, we study the properties of the functor of permutation degree (S P^{n}) and the subfunctor of permutation degree (S P_{G}^{n}), (P) is the cardinal number of topological spaces. Let (X) be an infinite (T_{1})-space. We prove that the following propositions hold.(1) Let (Y^{n} subset X^{n}); (A) if (d, left(Y^{n} right)=d, left(X^{n} right)), then (d, left(S P^{n} Yright)=d, left(SP^{n} Xright)); (B) if (l w d, left(Y^{n} right)=l w d, left(X^{n} right)), then (l w d, left(S P^{n} Yright)=l w d, left(S P^{n} Xright)). (2) Let (Ysubset X); (A) if (l d ,(Y)=l d ,(X)), then (l d, left(S P^{n} Yright)=l d, left(S P^{n} Xright)); (B) if (w d ,(Y)=w d ,(X)), then (w d, left(S P^{n} Yright)=w d, left(S P^{n} Xright)).(3) Let (n) be a positive integer, and let (G) be a subgroup of the permutation group (S_{n}). If (X) is a locally compact (T_{1})-space, then (S P^{n} X, , S P_{G}^{n} X), and (exp _{n} X) are (k)-spaces.(4) Let (n) be a positive integer, and let (G) be a subgroup of the permutation group (S_{n}). If (X) is an infinite (T_{1})-space, then (n ,pi ,w left(Xright)=n , pi ,w left(S P^{n} X right)=n ,pi ,w left(S P_{G}^{n} X right)=n ,pi ,w left(exp _{n} X right)).We also have studied that the functors (SP^{n},) (SP_{G}^{n} ,) and (exp _{n} ) preserve any (k)-space. The functors (SP^{2}) and (SP_{G}^{3}) do not preserve Hattori spaces on the real line. Besides, it is proved that the density of an infinite (T_{1})-space (X) coincides with the densities of the spaces (X^{n}), (,S P^{n} X), and (exp _{n} X). It is also shown that the weak density of an infinite (T_{1})-space (X) coincides with the weak densities of the spaces (X^{n}), (,S P^{n} X), and (exp _{n} X).
在本文中，局部密度 ((l d)) 和局部弱密度 ((l w d)) 在置换度空间中，研究了服部空间的基数性质和拓扑性质。换句话说，我们研究了置换度函子的性质 (S P^{n}) 和置换度的子函子 (S P_{G}^{n})， (P) 是拓扑空间的基数。让 (X) 是无限的 (T_{1})-space。我们证明下列命题成立:(1)设 (Y^{n} subset X^{n});(A)如果 (d, left(Y^{n} right)=d, left(X^{n} right))那么， (d, left(S P^{n} Yright)=d, left(SP^{n} Xright));(B)如果 (l w d, left(Y^{n} right)=l w d, left(X^{n} right))那么， (l w d, left(S P^{n} Yright)=l w d, left(S P^{n} Xright))． (2)让 (Ysubset X);(A)如果 (l d ,(Y)=l d ,(X))那么， (l d, left(S P^{n} Yright)=l d, left(S P^{n} Xright));(B)如果 (w d ,(Y)=w d ,(X))那么， (w d, left(S P^{n} Yright)=w d, left(S P^{n} Xright))(3)让 (n) 是一个正整数，令 (G) 是置换群的子群 (S_{n})． 如果 (X) 是一个局部契约 (T_{1})-空格，那么 (S P^{n} X, , S P_{G}^{n} X)，和 (exp _{n} X) 是 (k)-空格。(4 (n) 是一个正整数，令 (G) 是置换群的子群 (S_{n})． 如果 (X) 是无限的 (T_{1})-空格，那么 (n ,pi ,w left(Xright)=n , pi ,w left(S P^{n} X right)=n ,pi ,w left(S P_{G}^{n} X right)=n ,pi ,w left(exp _{n} X right))我们也学过函子 (SP^{n},) (SP_{G}^{n} ,) 和 (exp _{n} ) 保留任何 (k)-space。函子 (SP^{2}) 和 (SP_{G}^{3}) 不要在实线上保留服部空间。此外，还证明了一个无限大的密度 (T_{1})-space (X) 与空间的密度一致 (X^{n})， (,S P^{n} X)，和 (exp _{n} X)． 还证明了一个无穷大的弱密度 (T_{1})-space (X) 与空间的弱密度相吻合 (X^{n})， (,S P^{n} X)，和 (exp _{n} X)．
{"title":"THE LOCAL DENSITY AND THE LOCAL WEAK DENSITY IN THE SPACE OF PERMUTATION DEGREE AND IN HATTORI SPACE","authors":"T. Yuldashev, F. Mukhamadiev","doi":"10.15826/umj.2020.2.011","DOIUrl":"https://doi.org/10.15826/umj.2020.2.011","url":null,"abstract":"In this paper, the local density ((l d)) and the local weak density ((l w d)) in the space of permutation degree as well as the cardinal and topological properties of Hattori spaces are studied. In other words, we study the properties of the functor of permutation degree (S P^{n}) and the subfunctor of permutation degree (S P_{G}^{n}), (P) is the cardinal number of topological spaces. Let (X) be an infinite (T_{1})-space. We prove that the following propositions hold.(1) Let (Y^{n} subset X^{n}); (A) if (d, left(Y^{n} right)=d, left(X^{n} right)), then (d, left(S P^{n} Yright)=d, left(SP^{n} Xright)); (B) if (l w d, left(Y^{n} right)=l w d, left(X^{n} right)), then (l w d, left(S P^{n} Yright)=l w d, left(S P^{n} Xright)). (2) Let (Ysubset X); (A) if (l d ,(Y)=l d ,(X)), then (l d, left(S P^{n} Yright)=l d, left(S P^{n} Xright)); (B) if (w d ,(Y)=w d ,(X)), then (w d, left(S P^{n} Yright)=w d, left(S P^{n} Xright)).(3) Let (n) be a positive integer, and let (G) be a subgroup of the permutation group (S_{n}). If (X) is a locally compact (T_{1})-space, then (S P^{n} X, , S P_{G}^{n} X), and (exp _{n} X) are (k)-spaces.(4) Let (n) be a positive integer, and let (G) be a subgroup of the permutation group (S_{n}). If (X) is an infinite (T_{1})-space, then (n ,pi ,w left(Xright)=n , pi ,w left(S P^{n} X right)=n ,pi ,w left(S P_{G}^{n} X right)=n ,pi ,w left(exp _{n} X right)).We also have studied that the functors (SP^{n},) (SP_{G}^{n} ,) and (exp _{n} ) preserve any (k)-space. The functors (SP^{2}) and (SP_{G}^{3}) do not preserve Hattori spaces on the real line. Besides, it is proved that the density of an infinite (T_{1})-space (X) coincides with the densities of the spaces (X^{n}), (,S P^{n} X), and (exp _{n} X). It is also shown that the weak density of an infinite (T_{1})-space (X) coincides with the weak densities of the spaces (X^{n}), (,S P^{n} X), and (exp _{n} X).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48333613","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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