In this paper, we introduce the classes of $(omega, c)$-pseudo almost periodicfunctions and $(omega, c)$-pseudo almost automorphicfunctions. These collections include $(omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach spaces.
{"title":"(&omega,c)- PSEUDO ALMOST PERIODIC FUNCTIONS, (&omega,c)- PSEUDO ALMOST AUTOMORPHIC FUNCTIONS AND APPLICATIONS","authors":"M. T. Khalladi, M. Kostic, A. Rahmani, D. Velinov","doi":"10.22190/FUMI200421014K","DOIUrl":"https://doi.org/10.22190/FUMI200421014K","url":null,"abstract":"In this paper, we introduce the classes of $(omega, c)$-pseudo almost periodicfunctions and $(omega, c)$-pseudo almost automorphicfunctions. These collections include $(omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach spaces.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":" 22","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72384349","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 have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough $I$-convergence with both of rough $I^*$-convergence and rough $I^K$-convergence.
{"title":"ON ROUGH $I^*$ AND $I^K$-CONVERGENCE OF SEQUENCES IN NORMED LINEAR SPACES","authors":"A. Banerjee, Anirban Paul","doi":"10.22190/fumi210921038b","DOIUrl":"https://doi.org/10.22190/fumi210921038b","url":null,"abstract":"In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough $I$-convergence with both of rough $I^*$-convergence and rough $I^K$-convergence.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"28 26 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84669096","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 nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of solutions is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in Azabut.
{"title":"NONLINEAR NEUTRAL CAPUTO-FRACTIONAL DIFFERENCE EQUATIONS WITH APPLICATIONS TO LOTKA-VOLTERRA NEUTRAL MODEL","authors":"M. Mesmouli, A. Ardjouni, A. Djoudi","doi":"10.22190/FUMI2005475M","DOIUrl":"https://doi.org/10.22190/FUMI2005475M","url":null,"abstract":"In this paper, we consider a nonlinear neutral fractional difference equations. By applying Krasnoselskii's fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of solutions is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete fractional Lotka-Volterra model of neutral type. Our main results extend and generalize the results that are obtained in Azabut.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"12 4 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79354305","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 k-means problem and the algorithm of the same name are the most commonly used clustering model and algorithm. Being a local search optimization method, the k-means algorithm falls to a local minimum of the objective function (sum of squared errors) and depends on the initial solution which is given or selected randomly. This disadvantage of the algorithm can be avoided by combining this algorithm with more sophisticated methods such as the Variable Neighborhood Search, agglomerative or dissociative heuristic approaches, the genetic algorithms, etc. Aiming at the shortcomings of the k-means algorithm and combining the advantages of the k-means algorithm and rvolutionary approack, a genetic clustering algorithm with the cross-mutation operator was designed. The efficiency of the genetic algorithms with the tournament selection, one-point crossover and various mutation operators (without any mutation operator, with the uniform mutation, DBM mutation and new cross-mutation) are compared on the data sets up to 2 millions of data vectors. We used data from the UCI repository and special data set collected during the testing of the highly reliable semiconductor components. In this paper, we do not discuss the comparative efficiency of the genetic algorithms for the k-means problem in comparison with the other (non-genetic) algorithms as well as the comparative adequacy of the k-means clustering model. Here, we focus on the influence of various mutation operators on the efficiency of the genetic algorithms only.
{"title":"COMPARATIVE STUDY OF MUTATION OPERATORS IN THE GENETIC ALGORITHMS FOR THE K-MEANS PROBLEM","authors":"Ri-Zhi Li, L. Kazakovtsev","doi":"10.22190/FUMI2004091L","DOIUrl":"https://doi.org/10.22190/FUMI2004091L","url":null,"abstract":"The k-means problem and the algorithm of the same name are the most commonly used clustering model and algorithm. Being a local search optimization method, the k-means algorithm falls to a local minimum of the objective function (sum of squared errors) and depends on the initial solution which is given or selected randomly. This disadvantage of the algorithm can be avoided by combining this algorithm with more sophisticated methods such as the Variable Neighborhood Search, agglomerative or dissociative heuristic approaches, the genetic algorithms, etc. Aiming at the shortcomings of the k-means algorithm and combining the advantages of the k-means algorithm and rvolutionary approack, a genetic clustering algorithm with the cross-mutation operator was designed. The efficiency of the genetic algorithms with the tournament selection, one-point crossover and various mutation operators (without any mutation operator, with the uniform mutation, DBM mutation and new cross-mutation) are compared on the data sets up to 2 millions of data vectors. We used data from the UCI repository and special data set collected during the testing of the highly reliable semiconductor components. In this paper, we do not discuss the comparative efficiency of the genetic algorithms for the k-means problem in comparison with the other (non-genetic) algorithms as well as the comparative adequacy of the k-means clustering model. Here, we focus on the influence of various mutation operators on the efficiency of the genetic algorithms only.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90620374","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 $q$ be a positive weight function on $mathbf{R}_{+}:=[0, infty)$ which is integrable in Lebesgue's sense over every finite interval $(0,x)$ for $00$, $Q(0)=0$ and $Q(x) rightarrow infty $ as $x to infty $.Given a real or complex-valued function $f in L^{1}_{loc} (mathbf{R}_{+})$, we define $s(x):=int_{0}^{x}f(t)dt$ and$$tau^{(0)}_q(x):=s(x), tau^{(m)}_q(x):=frac{1}{Q(x)}int_0^x tau^{(m-1)}_q(t) q(t)dt,,, (x>0, m=1,2,...),$$provided that $Q(x)>0$. We say that $int_{0}^{infty}f(x)dx$ is summable to $L$ by the $m$-th iteration of weighted mean method determined by the function $q(x)$, or for short, $(overline{N},q,m)$ integrable to a finite number $L$ if$$lim_{xto infty}tau^{(m)}_q(x)=L.$$In this case, we write $s(x)rightarrow L(overline{N},q,m)$. It is known thatif the limit $lim _{x to infty} s(x)=L$ exists, then $lim _{x to infty} tau^{(m)}_q(x)=L$ also exists. However, the converse of this implicationis not always true. Some suitable conditions together with the existence of the limit $lim _{x to infty} tau^{(m)}_q(x)$, which is so called Tauberian conditions, may imply convergence of $lim _{x to infty} s(x)$. In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for $(overline{N},q,m)$ summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Ces`{a}ro summability $(C,1)$ and weighted mean method of summability $(overline{N},q)$ have been extended and generalized.
设$q$是$mathbf{R}_{+}:=[0, infty)$上的一个正权函数，在Lebesgue意义上在每一个有限区间上可积$(0,x)$对于$00$, $Q(0)=0$和$Q(x) rightarrow infty $为$x to infty $。给定一个实数或复值函数$f in L^{1}_{loc} (mathbf{R}_{+})$，我们定义$s(x):=int_{0}^{x}f(t)dt$和$$tau^{(0)}_q(x):=s(x), tau^{(m)}_q(x):=frac{1}{Q(x)}int_0^x tau^{(m-1)}_q(t) q(t)dt,,, (x>0, m=1,2,...),$$，假设$Q(x)>0$。我们说$int_{0}^{infty}f(x)dx$可以通过由函数$q(x)$确定的$m$ -次迭代加权平均方法求和到$L$，或者简而言之，$(overline{N},q,m)$可积到一个有限数$L$如果$$lim_{xto infty}tau^{(m)}_q(x)=L.$$在这种情况下，我们写$s(x)rightarrow L(overline{N},q,m)$。已知，如果极限$lim _{x to infty} s(x)=L$存在，则$lim _{x to infty} tau^{(m)}_q(x)=L$也存在。然而，这一含义的反面并不总是正确的。一些适当的条件，加上极限$lim _{x to infty} tau^{(m)}_q(x)$的存在，即所谓的Tauberian条件，可以暗示$lim _{x to infty} s(x)$的收敛性。本文给出了$(overline{N},q,m)$实值或复值函数可和积分的生成函数的单侧和双侧Tauberian条件及其推广。推广和推广了关于Cesàro可和性$(C,1)$和可和性的加权平均法$(overline{N},q)$的经典型陶培尔定理。
{"title":"TAUBERIAN THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY OF INTEGRALS","authors":"Ibrahim Çanak, Firat Ozsarac","doi":"10.1063/1.5136127","DOIUrl":"https://doi.org/10.1063/1.5136127","url":null,"abstract":"Let $q$ be a positive weight function on $mathbf{R}_{+}:=[0, infty)$ which is integrable in Lebesgue's sense over every finite interval $(0,x)$ for $00$, $Q(0)=0$ and $Q(x) rightarrow infty $ as $x to infty $.Given a real or complex-valued function $f in L^{1}_{loc} (mathbf{R}_{+})$, we define $s(x):=int_{0}^{x}f(t)dt$ and$$tau^{(0)}_q(x):=s(x), tau^{(m)}_q(x):=frac{1}{Q(x)}int_0^x tau^{(m-1)}_q(t) q(t)dt,,, (x>0, m=1,2,...),$$provided that $Q(x)>0$. We say that $int_{0}^{infty}f(x)dx$ is summable to $L$ by the $m$-th iteration of weighted mean method determined by the function $q(x)$, or for short, $(overline{N},q,m)$ integrable to a finite number $L$ if$$lim_{xto infty}tau^{(m)}_q(x)=L.$$In this case, we write $s(x)rightarrow L(overline{N},q,m)$. It is known thatif the limit $lim _{x to infty} s(x)=L$ exists, then $lim _{x to infty} tau^{(m)}_q(x)=L$ also exists. However, the converse of this implicationis not always true. Some suitable conditions together with the existence of the limit $lim _{x to infty} tau^{(m)}_q(x)$, which is so called Tauberian conditions, may imply convergence of $lim _{x to infty} s(x)$. In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for $(overline{N},q,m)$ summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Ces`{a}ro summability $(C,1)$ and weighted mean method of summability $(overline{N},q)$ have been extended and generalized. ","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"40 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81476903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to prove common fixed point theorems for multivalued contraction of Wordowski type, by using the concept of subsequential continuity in the setting of set valued context contractions with compatibility. We have also given an example and an application to integral inclusions of Fredholm type to support our results.
{"title":"FIXED POINT THEOREMS FOR SUBSEQUENTIALLY MULTI-VALUED F_delta -CONTRACTIONS IN METRIC SPACES","authors":"S. Beloul, Heddi Kaddouri","doi":"10.22190/FUMI2002379B","DOIUrl":"https://doi.org/10.22190/FUMI2002379B","url":null,"abstract":"The aim of this paper is to prove common fixed point theorems for multivalued contraction of Wordowski type, by using the concept of subsequential continuity in the setting of set valued context contractions with compatibility. We have also given an example and an application to integral inclusions of Fredholm type to support our results.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"84 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88757345","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 star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.
{"title":"ON STAR COLORING OF DEGREE SPLITTING OF COMB PRODUCT GRAPHS","authors":"Ulagammal Subramanian, V. Joseph","doi":"10.22190/FUMI2002507S","DOIUrl":"https://doi.org/10.22190/FUMI2002507S","url":null,"abstract":"A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"19 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73983628","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(n) and q(n) be nondecreasing sequence of positive integers such that p(n) < q(n) and limn→∞ q(n) = ∞ holds. For any r ∈ Z^+, we define D_p,q^+r- statistical convergence of ∆^+r x where ∆^+r is r- th difference of the sequence (x_n). The main results in this paper consist in determining sets of sequences χ and χ' of the form [D_ p^q]_0 α satisfying χ ⊂ [D_p^q]_0(∆^+r ) ⊂ χ ' and sets φ and φ' of the form [D_p^q]_α satisfying φ ≤ [D_p^q]_∞(∆^+r ) ≤ φ' .
{"title":"THE D_p^q (∆^+r )-STATISTICAL CONVERGENCE","authors":"Neslihan Boztaş, M. Küçükaslan","doi":"10.22190/FUMI2002405B","DOIUrl":"https://doi.org/10.22190/FUMI2002405B","url":null,"abstract":"Let p(n) and q(n) be nondecreasing sequence of positive integers such that p(n) < q(n) and limn→∞ q(n) = ∞ holds. For any r ∈ Z^+, we define D_p,q^+r- statistical convergence of ∆^+r x where ∆^+r is r- th difference of the sequence (x_n). The main results in this paper consist in determining sets of sequences χ and χ' of the form [D_ p^q]_0 α satisfying χ ⊂ [D_p^q]_0(∆^+r ) ⊂ χ ' and sets φ and φ' of the form [D_p^q]_α satisfying φ ≤ [D_p^q]_∞(∆^+r ) ≤ φ' .","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"55 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91378782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For a graph $G$ and any $vin V(G)$, $E_{G}(v)$ is the set of all edges incident with $v$. A function $f:E(G)rightarrow {-1,1}$ is called a signed matching of $G$ if $sum_{ein E(v)}f(e) leq 1$ for every $ {vin V(G)}$. For a signed matching $x$, set $x(E(G))=sum_{ein E(G))}x(e)$. The signed matching number of $G$, denoted by $beta_1'(G)$, is the maximum $x(E(G))$ where the maximum is taken over all signed matching over $G$. In this paper we obtain the signed matching number of some families of graphs and study the signed matching number of subdivision and edge deletion of edges of graph.
{"title":"ON THE SIGNED MATCHINGS OF GRAPHS","authors":"S. Javan, H. Maimani","doi":"10.22190/FUMI2002541J","DOIUrl":"https://doi.org/10.22190/FUMI2002541J","url":null,"abstract":"For a graph $G$ and any $vin V(G)$, $E_{G}(v)$ is the set of all edges incident with $v$. A function $f:E(G)rightarrow {-1,1}$ is called a signed matching of $G$ if $sum_{ein E(v)}f(e) leq 1$ for every $ {vin V(G)}$. For a signed matching $x$, set $x(E(G))=sum_{ein E(G))}x(e)$. The signed matching number of $G$, denoted by $beta_1'(G)$, is the maximum $x(E(G))$ where the maximum is taken over all signed matching over $G$. In this paper we obtain the signed matching number of some families of graphs and study the signed matching number of subdivision and edge deletion of edges of graph.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"116 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87697306","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 have introduced diamond $phi_{h-s, mathbb{T}}$ derivative and diamond $phi_{h-s,mathbb{T}}$ integral on an arbitrary time scale. Moreover, various interconnections with the notion of classes of convex functions about these new concepts are also discussed.
{"title":"SOME CLASSES OF CONVEX FUNCTIONS ON TIME SCALES","authors":"Fagbemigun Opeyemi Bosede, Adesanmi Alao Mogbademu","doi":"10.22190/FUMI2001011B","DOIUrl":"https://doi.org/10.22190/FUMI2001011B","url":null,"abstract":"We have introduced diamond $phi_{h-s, mathbb{T}}$ derivative and diamond $phi_{h-s,mathbb{T}}$ integral on an arbitrary time scale. Moreover, various interconnections with the notion of classes of convex functions about these new concepts are also discussed.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"11 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84183718","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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