Journal of Mathematical Analysis and Applications最新文献

{"title":"The truncated multidimensional moment problem: Canonical solutions","authors":"Sergey Zagorodnyuk","doi":"10.1016/j.jmaa.2025.129524","DOIUrl":"10.1016/j.jmaa.2025.129524","url":null,"abstract":"<div><div>For the truncated multidimensional moment problem we introduce a notion of a canonical solution. Namely, canonical solutions are those solutions which are generated by commuting self-adjoint extensions inside the associated Hilbert space. It is constructed a 1-1 correspondence between canonical solutions and flat extensions of the given moments (both sets may be empty). In the case of the two-dimensional moment problem (with triangular truncations) a search for canonical solutions leads to an algebraic system of equations. A notion of the index <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> of nonself-adjointness for a set of prescribed moments is introduced. The case <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> corresponds to flatness. In the case <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> we get explicit necessary and sufficient conditions for the existence of canonical solutions. These conditions are valid for arbitrary sizes of truncations. In the case <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>2</mn></math></span> we get either explicit conditions for the existence of canonical solutions or a single quadratic equation with several unknowns. Numerical examples are provided.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129524"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-isometric translation and modulation invariant Hilbert spaces","authors":"P.K. Ratnakumar ,&nbsp;Joachim Toft ,&nbsp;Jasson Vindas","doi":"10.1016/j.jmaa.2025.129530","DOIUrl":"10.1016/j.jmaa.2025.129530","url":null,"abstract":"<div><div>Let <span><math><mi>H</mi></math></span> be a Hilbert space, continuously embedded in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>, and which contains at least one non-zero element in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>. If there is a constant <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span> such that<span><span><span><math><msub><mrow><mo>‖</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mo>〈</mo><mspace></mspace><mo>⋅</mo><mspace></mspace><mo>,</mo><mi>ξ</mi><mo>〉</mo></mrow></msup><mi>f</mi><mo>(</mo><mspace></mspace><mo>⋅</mo><mspace></mspace><mo>−</mo><mi>x</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mi>H</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>H</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>f</mi><mo>∈</mo><mi>H</mi><mo>,</mo><mspace></mspace><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></math></span></span></span> then we prove that <span><math><mi>H</mi><mo>=</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>, with equivalent norms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129530"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Explicit bounds for Bell numbers and their ratios","authors":"Jerzy Grunwald,&nbsp;Grzegorz Serafin","doi":"10.1016/j.jmaa.2025.129527","DOIUrl":"10.1016/j.jmaa.2025.129527","url":null,"abstract":"<div><div>In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main results correspond to two asymptotic forms expressed by means of the Lambert <em>W</em> function. As an application, some straightforward elementary bounds are derived. Additionally, an absolute convergence rate of the ratio of consecutive Bell numbers is derived. One of the main challenges was to obtain satisfactory constants, as the Bell numbers grow rapidly, while the convergence rates are rather slow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129527"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and non-existence results for parabolic systems with an Hardy-Leray potential","authors":"Fatima Zohra Bengrine ,&nbsp;Ana Primo ,&nbsp;Giovanni Siclari","doi":"10.1016/j.jmaa.2025.129533","DOIUrl":"10.1016/j.jmaa.2025.129533","url":null,"abstract":"<div><div>In this paper we study the problem of existence or non existence of positive supersolution to the system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mfrac><mrow><mi>u</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>,</mo><mi>∇</mi><mi>v</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext> in </mtext><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>=</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mfrac><mrow><mi>v</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>∇</mi><mi>u</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext> in </mtext><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>, is a regular domain containing the origin and:</div><div><em>i</em>) <span><math><mi>f</mi><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>, <span><math><mi>i</mi><mi>i</mi><mo>)</mo></math></span> <span><math><mi>f</mi><mo>=</mo><mo>|</mo><mi>∇</mi><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>=</mo><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span>, <span><math><mi>i</mi><mi>i</mi><mi>i</mi><mo>)</mo></math></span> <span><math><mi>f</mi><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>=</mo><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span>.</div><div>According to the form of the nonlinearities, we are able to get the existence of critical curves separating the existence and the non existence regions. In the case <span><math><mi>f</mi><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><mi>g</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>, we study the Cauchy system in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></math></span>. The existence of a Fujita type exponent is deeply analyzed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129533"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Brown-Halmos theorems on the Fock-Sobolev space","authors":"Jie Qin","doi":"10.1016/j.jmaa.2025.129532","DOIUrl":"10.1016/j.jmaa.2025.129532","url":null,"abstract":"<div><div>In this paper, we generalize the Brown-Halmos theorems to the Fock-Sobolev space. We obtain that the Brown-Halmos theorems hold true on the Fock-Sobolev space for Toeplitz operators with harmonic symbols. We completely explain the difference between the geometries of the Fock and Fock-Sobolev space by using the Berezin transform.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129532"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of reciprocal sums of hyperbolic functions using quasimodular forms","authors":"Wei Wang","doi":"10.1016/j.jmaa.2025.129526","DOIUrl":"10.1016/j.jmaa.2025.129526","url":null,"abstract":"<div><div>This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. Using complex multiplication theory, the structure of the rings of modular forms and quasimodular forms, and certain differential operators defined on these rings, this paper gives a systematic method for computing the values of these series at CM points. This paper also expresses the generalized reciprocal sums of Fibonacci numbers as the special values of the series mentioned above. Thus it gives some algebraic independence results about the generalized reciprocal sums of Fibonacci numbers.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129526"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Zhang-Yang's open question about iterative roots of PM functions of height 1 (II): Decreasing case","authors":"Siyi Zhao ,&nbsp;Liu Liu ,&nbsp;Weinian Zhang","doi":"10.1016/j.jmaa.2025.129517","DOIUrl":"10.1016/j.jmaa.2025.129517","url":null,"abstract":"<div><div>A Zhang-Yang's open question reads: Does a PM function <em>F</em> with height <span><math><mi>H</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span> have an iterative root <em>f</em> of order <span><math><mi>n</mi><mo>≤</mo><mi>N</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span> if the ‘characteristic endpoints condition’ is not satisfied? This question was answered in the case that <em>F</em> is strictly increasing on its characteristic interval <span><math><mi>K</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></span>. However, a more difficult case is that <em>F</em> is strictly decreasing on <span><math><mi>K</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></span>. In this paper we discuss the decreasing case, giving existence of <em>f</em> of order <span><math><mi>n</mi><mo>&lt;</mo><mi>N</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></span> with <span><math><mi>H</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>n</mi></math></span> and of order <span><math><mi>n</mi><mo>≤</mo><mi>N</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span> with <span><math><mi>H</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129517"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes revisited: Boundary-layer-in-time effects","authors":"Grigory Panasenko ,&nbsp;Igor Pažanin ,&nbsp;Borja Rukavina","doi":"10.1016/j.jmaa.2025.129519","DOIUrl":"10.1016/j.jmaa.2025.129519","url":null,"abstract":"<div><div>In this paper, we revisit the problem of the time-dependent micropolar fluid flow in a thin pipe system considered in Pažanin et al. (2024) <span><span>[29]</span></span>. We remove the restriction that the inflow/outflow and the external source functions vanish for small values of time and extend the analysis to non-homogeneous initial conditions. This requires the construction of the boundary-layer-in-time and the boundary-layer-in-space-and-in-time correctors in the asymptotic expansion of the solution. Consequently, we propose a new asymptotic approximation of higher order of accuracy for a general case with strong coupling between velocity and microrotation. The error estimates are also proved justifying the use of the derived effective model and indicating its range of applicability.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129519"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the asymptotic analysis of lazy reinforced random walks: A martingale approach","authors":"Manuel González-Navarrete ,&nbsp;Rodrigo Lambert ,&nbsp;Víctor Hugo Vázquez-Guevara","doi":"10.1016/j.jmaa.2025.129520","DOIUrl":"10.1016/j.jmaa.2025.129520","url":null,"abstract":"<div><div>We provide a comprehensive characterization of the limiting behavior of lazy reinforced random walks (LRRW's). These random walks exhibit three distinct phases: diffusive, critical, and superdiffusive. Using a martingale theory approach, we establish proper versions of the law of large numbers, the almost sure convergence to even moments of Gaussian distribution, the law of the iterated logarithm, the almost sure central limit theorem, and the functional central limit theorem for the diffusive and critical regimes. In the superdiffusive regime, we demonstrate strong convergence to a random variable, as well as a central limit theorem and a law of the iterated logarithm for the fluctuations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129520"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Most of the minimization problems have a unique solution","authors":"Ľubica Holá","doi":"10.1016/j.jmaa.2025.129523","DOIUrl":"10.1016/j.jmaa.2025.129523","url":null,"abstract":"<div><div>Let <em>X</em> be a Tychonoff topological space, <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> be the space of continuous real-valued functions defined on <em>X</em> and <span><math><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> be the space of all nonempty compact subsets of <em>X</em>. Define the multifunction argmin<span><math><mo>:</mo><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>×</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>→</mo><mi>X</mi></math></span> as follows: argmin <span><math><mo>(</mo><mi>f</mi><mo>,</mo><mi>K</mi><mo>)</mo><mo>=</mo><mo>{</mo><mi>x</mi><mo>∈</mo><mi>K</mi><mo>:</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>:</mo><mi>y</mi><mo>∈</mo><mi>K</mi><mo>}</mo><mo>}</mo></math></span>. Let <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>U</mi></mrow></msub></math></span> be the topology of uniform convergence on <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span> the Vietoris topology on <span><math><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. We prove that argmin<span><math><mo>:</mo><mo>(</mo><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>U</mi></mrow></msub><mo>)</mo><mo>×</mo><mo>(</mo><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>)</mo><mo>→</mo><mi>X</mi></math></span> is minimal usco and extend Kenderov's generic optimization theorem to Tychonoff almost Čech-complete spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129523"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}