Pub Date : 2022-11-13DOI: 10.15330/cmp.14.2.388-394
E. Savaş
The purpose of this paper is to introduce the concept of $lambda$-double almost statistical convergence of weight $g$, which emerges naturally from the concept of the double almost convergence and $lambda$-statistical convergence. Some interesting inclusion relations have been considered.
{"title":"On generalized double almost statistical convergence of weight $g$","authors":"E. Savaş","doi":"10.15330/cmp.14.2.388-394","DOIUrl":"https://doi.org/10.15330/cmp.14.2.388-394","url":null,"abstract":"The purpose of this paper is to introduce the concept of $lambda$-double almost statistical convergence of weight $g$, which emerges naturally from the concept of the double almost convergence and $lambda$-statistical convergence. Some interesting inclusion relations have been considered.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"45 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77367313","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}
Pub Date : 2022-11-12DOI: 10.15330/cmp.14.2.371-387
Sung Guen Kim
Let $l_{infty}^3=mathbb{R}^3$ be endowed with the supremum norm. In [Comment. Math. 2017, 57 (1), 1-7], S.G. Kim classified the extreme points of the unit ball of ${mathcal L}_s(^2l_{infty}^3)$ only using Mathematica 8, where ${mathcal L}_s(^2l_{infty}^3)$ is the space of symmetric bilinear forms on $l_{infty}^3$. It seems to be interesting and meaningful to classify the extreme points of the unit ball of ${mathcal L}_s(^2l_{infty}^3)$ without using Mathematica 8. The aim of this paper is to make such classification by mathematical calculations.
{"title":"Classification of the extreme points of ${mathcal L}_s(^2l_{infty}^3)$ by computation","authors":"Sung Guen Kim","doi":"10.15330/cmp.14.2.371-387","DOIUrl":"https://doi.org/10.15330/cmp.14.2.371-387","url":null,"abstract":"Let $l_{infty}^3=mathbb{R}^3$ be endowed with the supremum norm. In [Comment. Math. 2017, 57 (1), 1-7], S.G. Kim classified the extreme points of the unit ball of ${mathcal L}_s(^2l_{infty}^3)$ only using Mathematica 8, where ${mathcal L}_s(^2l_{infty}^3)$ is the space of symmetric bilinear forms on $l_{infty}^3$. It seems to be interesting and meaningful to classify the extreme points of the unit ball of ${mathcal L}_s(^2l_{infty}^3)$ without using Mathematica 8. The aim of this paper is to make such classification by mathematical calculations.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"21 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85794070","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}
Pub Date : 2022-09-04DOI: 10.15330/cmp.14.2.364-370
M. Dmytryshyn, L. Dmytryshyn
We establish the Bernstein and Jackson type inequalities with exact constants for estimations of best approximations by exponential type functions in Orlicz spaces $L_M(mathbb{R}^n)$. For this purpose, we use a special scale of approximation spaces $mathcal{B}_tau^s(M)$ that are interpolation spaces between the subspace $mathscr{E}_M$ of exponential type functions and the space $L_M(mathbb{R}^n)$. These approximation spaces are defined using a functional $Eleft(t,fright)$ that plays a similar role as the module of smoothness. The constants in obtained inequalities are expressed using a normalization factor $N_{vartheta,q}$ that is determined by the parameters $tau$ and $s$ of the approximation space $mathcal{B}_tau^s(M)$.
{"title":"Bernstein-Jackson-type inequalities with exact constants in Orlicz spaces","authors":"M. Dmytryshyn, L. Dmytryshyn","doi":"10.15330/cmp.14.2.364-370","DOIUrl":"https://doi.org/10.15330/cmp.14.2.364-370","url":null,"abstract":"We establish the Bernstein and Jackson type inequalities with exact constants for estimations of best approximations by exponential type functions in Orlicz spaces $L_M(mathbb{R}^n)$. For this purpose, we use a special scale of approximation spaces $mathcal{B}_tau^s(M)$ that are interpolation spaces between the subspace $mathscr{E}_M$ of exponential type functions and the space $L_M(mathbb{R}^n)$. These approximation spaces are defined using a functional $Eleft(t,fright)$ that plays a similar role as the module of smoothness. The constants in obtained inequalities are expressed using a normalization factor $N_{vartheta,q}$ that is determined by the parameters $tau$ and $s$ of the approximation space $mathcal{B}_tau^s(M)$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85501796","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}
Pub Date : 2022-08-21DOI: 10.15330/cmp.14.2.354-363
W. Ramírez, C. Cesarano
The aim of this paper is to study new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order $alpha$ and level $m$ in the variable $x$. Here the degenerate polynomials are a natural extension of the classic polynomials. In more detail, we derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. Most of the results are proved by using generating function methods.
{"title":"Some new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials","authors":"W. Ramírez, C. Cesarano","doi":"10.15330/cmp.14.2.354-363","DOIUrl":"https://doi.org/10.15330/cmp.14.2.354-363","url":null,"abstract":"The aim of this paper is to study new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order $alpha$ and level $m$ in the variable $x$. Here the degenerate polynomials are a natural extension of the classic polynomials. In more detail, we derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. Most of the results are proved by using generating function methods.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"20 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74422025","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}
Pub Date : 2022-08-19DOI: 10.15330/cmp.15.2.331-355
O. Gutik, O. Popadiuk
We study the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$, which is introduced in the paper [Visnyk Lviv Univ. Ser. Mech.-Mat. 2020, 90, 5-19 (in Ukrainian)], in the case when the ${omega}$-closed family $mathscr{F}_n$ generated by the set ${0,1,ldots,n}$. We show that the Green relations $mathscr{D}$ and $mathscr{J}$ coincide in $boldsymbol{B}_{omega}^{mathscr{F}_n}$, the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ is isomorphic to the semigroup $mathscr{I}_omega^{n+1}(overrightarrow{mathrm{conv}})$ of partial convex order isomorphisms of $(omega,leqslant)$ of the rank $leqslant n+1$, and $boldsymbol{B}_{omega}^{mathscr{F}_n}$ admits only Rees congruences. Also, we study shift-continuous topologies on the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$. In particular, we prove that for any shift-continuous $T_1$-topology $tau$ on the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ every non-zero element of $boldsymbol{B}_{omega}^{mathscr{F}_n}$ is an isolated point of $(boldsymbol{B}_{omega}^{mathscr{F}_n},tau)$, $boldsymbol{B}_{omega}^{mathscr{F}_n}$ admits the unique compact shift-continuous $T_1$-topology, and every $omega_{mathfrak{d}}$-compact shift-continuous $T_1$-topology is compact. We describe the closure of the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ in a Hausdorff semitopological semigroup and prove the criterium when a topological inverse semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ is $H$-closed in the class of Hausdorff topological semigroups.
{"title":"On the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$, which is generated by the family $mathscr{F}_n$ of finite bounded intervals of $omega$","authors":"O. Gutik, O. Popadiuk","doi":"10.15330/cmp.15.2.331-355","DOIUrl":"https://doi.org/10.15330/cmp.15.2.331-355","url":null,"abstract":"We study the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$, which is introduced in the paper [Visnyk Lviv Univ. Ser. Mech.-Mat. 2020, 90, 5-19 (in Ukrainian)], in the case when the ${omega}$-closed family $mathscr{F}_n$ generated by the set ${0,1,ldots,n}$. We show that the Green relations $mathscr{D}$ and $mathscr{J}$ coincide in $boldsymbol{B}_{omega}^{mathscr{F}_n}$, the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ is isomorphic to the semigroup $mathscr{I}_omega^{n+1}(overrightarrow{mathrm{conv}})$ of partial convex order isomorphisms of $(omega,leqslant)$ of the rank $leqslant n+1$, and $boldsymbol{B}_{omega}^{mathscr{F}_n}$ admits only Rees congruences. Also, we study shift-continuous topologies on the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$. In particular, we prove that for any shift-continuous $T_1$-topology $tau$ on the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ every non-zero element of $boldsymbol{B}_{omega}^{mathscr{F}_n}$ is an isolated point of $(boldsymbol{B}_{omega}^{mathscr{F}_n},tau)$, $boldsymbol{B}_{omega}^{mathscr{F}_n}$ admits the unique compact shift-continuous $T_1$-topology, and every $omega_{mathfrak{d}}$-compact shift-continuous $T_1$-topology is compact. We describe the closure of the semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ in a Hausdorff semitopological semigroup and prove the criterium when a topological inverse semigroup $boldsymbol{B}_{omega}^{mathscr{F}_n}$ is $H$-closed in the class of Hausdorff topological semigroups.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88231837","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}
Pub Date : 2022-08-07DOI: 10.15330/cmp.14.2.345-353
M. Semko, L. Skaskiv, O. A. Yarovaya
Let $L$ be an algebra over a field $F$. Then $L$ is called a left Leibniz algebra, if its multiplication operation $[-,-]$ additionally satisfies the so-called left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,cin L$. A linear transformation $f$ of a Leibniz algebra $L$ is called a derivation of an algebra $L$, if $f([a,b])=[f(a),b]+[a,f(b)]$ for all elements $a,bin L$. It is well known that the set of all derivations $mathrm{Der}(L)$ of a Leibniz algebra $L$ is a subalgebra of the Lie algebra $mathrm{End}_{F}(L)$ of all linear transformations of an algebra $L$. The algebras of derivations of Leibniz algebras play an important role in the study of structure of Leibniz algebras. Their role is similar to that played by groups of automorphisms in the study of group structure. In this paper, a complete description of the algebra of derivations of nilpotent cyclic Leibniz algebra is obtained. In particular, it was proved that this algebra is metabelian and supersoluble Lie algebra, and its dimension is equal to the dimension of an algebra $L$.
{"title":"On the derivations of cyclic Leibniz algebras","authors":"M. Semko, L. Skaskiv, O. A. Yarovaya","doi":"10.15330/cmp.14.2.345-353","DOIUrl":"https://doi.org/10.15330/cmp.14.2.345-353","url":null,"abstract":"Let $L$ be an algebra over a field $F$. Then $L$ is called a left Leibniz algebra, if its multiplication operation $[-,-]$ additionally satisfies the so-called left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,cin L$. A linear transformation $f$ of a Leibniz algebra $L$ is called a derivation of an algebra $L$, if $f([a,b])=[f(a),b]+[a,f(b)]$ for all elements $a,bin L$. It is well known that the set of all derivations $mathrm{Der}(L)$ of a Leibniz algebra $L$ is a subalgebra of the Lie algebra $mathrm{End}_{F}(L)$ of all linear transformations of an algebra $L$. The algebras of derivations of Leibniz algebras play an important role in the study of structure of Leibniz algebras. Their role is similar to that played by groups of automorphisms in the study of group structure. \u0000In this paper, a complete description of the algebra of derivations of nilpotent cyclic Leibniz algebra is obtained. In particular, it was proved that this algebra is metabelian and supersoluble Lie algebra, and its dimension is equal to the dimension of an algebra $L$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88580242","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}
Pub Date : 2022-08-06DOI: 10.15330/cmp.14.2.332-344
A. Harir, S. Melliani, L. S. Chadli
This article is related to present and solve the theory of fractional hybrid differential equations with fuzzy initial values involving the fuzzy Riemann-Liouville fractional differential operators of order $0 < q < 1$. For the concerned presentation, we study the existence and uniqueness of a fuzzy solution are brought in detail basing on the concept of generalized division of fuzzy numbers. We have developed and investigated a fuzzy solution of a fuzzy fractional hybrid differential equation. At the end we have given an example is provided to illustrate the theory.
{"title":"Fuzzy fractional hybrid differential equations","authors":"A. Harir, S. Melliani, L. S. Chadli","doi":"10.15330/cmp.14.2.332-344","DOIUrl":"https://doi.org/10.15330/cmp.14.2.332-344","url":null,"abstract":"This article is related to present and solve the theory of fractional hybrid differential equations with fuzzy initial values involving the fuzzy Riemann-Liouville fractional differential operators of order $0 < q < 1$. For the concerned presentation, we study the existence and uniqueness of a fuzzy solution are brought in detail basing on the concept of generalized division of fuzzy numbers. We have developed and investigated a fuzzy solution of a fuzzy fractional hybrid differential equation. At the end we have given an example is provided to illustrate the theory.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"56 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87759010","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}
Pub Date : 2022-07-27DOI: 10.15330/cmp.14.2.327-331
O. Fotiy, A. Gumenchuk, M. M. Popov
The classical Kantorovich theorem asserts the existence and uniqueness of a linear extension of a positive additive mapping, defined on the positive cone $E^+$ of a Riesz space $E$ taking values in an Archimedean Riesz space $F$, to the entire space $E$. We prove that, if $E$ has the principal projection property and $F$ is Dedekind $sigma$-complete then for every $e in E^+$ every positive finitely additive $F$-valued measure defined on the Boolean algebra $mathfrak{F}_e$ of fragments of $e$ has a unique positive linear extension to the ideal $E_e$ of $E$ generated by $e$. If, moreover, the measure is $tau$-continuous then the linear extension is order continuous.
经典的Kantorovich定理断言了一个正加性映射的线性扩展的存在唯一性，该映射定义在Riesz空间$E$的正锥$E^+$上，取阿基米德Riesz空间$F$中的值，到整个空间$E$。我们证明了，如果$E$具有主投影性质，且$F$是Dedekind $sigma$ -complete，那么对于$e in E^+$，对于$e$的片段的布尔代数$mathfrak{F}_e$上定义的每一个正有限可加的$F$值测度，对$e$生成的$E$的理想$E_e$有唯一的正线性扩展。此外，如果测度是$tau$ -连续的，则线性扩展是阶连续的。
{"title":"More on the extension of linear operators on Riesz spaces","authors":"O. Fotiy, A. Gumenchuk, M. M. Popov","doi":"10.15330/cmp.14.2.327-331","DOIUrl":"https://doi.org/10.15330/cmp.14.2.327-331","url":null,"abstract":"The classical Kantorovich theorem asserts the existence and uniqueness of a linear extension of a positive additive mapping, defined on the positive cone $E^+$ of a Riesz space $E$ taking values in an Archimedean Riesz space $F$, to the entire space $E$. We prove that, if $E$ has the principal projection property and $F$ is Dedekind $sigma$-complete then for every $e in E^+$ every positive finitely additive $F$-valued measure defined on the Boolean algebra $mathfrak{F}_e$ of fragments of $e$ has a unique positive linear extension to the ideal $E_e$ of $E$ generated by $e$. If, moreover, the measure is $tau$-continuous then the linear extension is order continuous.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"115 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80626358","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}
Pub Date : 2022-07-26DOI: 10.15330/cmp.14.2.304-326
O. Stanzhytskyi, R. E. Uteshova, M. Mukash, V. Mogylova
The method of averaging is applied to study the existence of solutions of boundary value problems for systems of differential equations with non-fixed moments of impulse action. It is shown that if an averaged boundary value problem has a solution, then the original problem is solvable as well. Here the averaged problem for the impulsive system is a simpler problem of ordinary differential equations.
{"title":"Application of the method of averaging to boundary value problems for differential equations with non-fixed moments of impulse","authors":"O. Stanzhytskyi, R. E. Uteshova, M. Mukash, V. Mogylova","doi":"10.15330/cmp.14.2.304-326","DOIUrl":"https://doi.org/10.15330/cmp.14.2.304-326","url":null,"abstract":"The method of averaging is applied to study the existence of solutions of boundary value problems for systems of differential equations with non-fixed moments of impulse action. It is shown that if an averaged boundary value problem has a solution, then the original problem is solvable as well. Here the averaged problem for the impulsive system is a simpler problem of ordinary differential equations.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"49 s172","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72386035","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}
Pub Date : 2022-06-30DOI: 10.15330/cmp.14.1.289-298
D. Soybaş, S. Joshi, H. Pawar
The aim of present paper is to find out different interesting properties and characterization of unified class $P_{gamma}(A, B, alpha,sigma)$ of prestarlike functions with negative coefficients in the unit disc $U$. Furthermore, distortion theorems involving a generalized fractional integral operator involving well-known Fox's $H$-function for functions in this class are proved.
{"title":"On generalized fractional integral operator involving Fox's $H$-function and its applications to unified subclass of prestarlike functions with negative coefficients","authors":"D. Soybaş, S. Joshi, H. Pawar","doi":"10.15330/cmp.14.1.289-298","DOIUrl":"https://doi.org/10.15330/cmp.14.1.289-298","url":null,"abstract":"The aim of present paper is to find out different interesting properties and characterization of unified class $P_{gamma}(A, B, alpha,sigma)$ of prestarlike functions with negative coefficients in the unit disc $U$. Furthermore, distortion theorems involving a generalized fractional integral operator involving well-known Fox's $H$-function for functions in this class are proved.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"150 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77394696","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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