Examples and Counterexamples最新文献

{"title":"Taper-based scattering formulation of the Helmholtz equation to improve the training process of Physics-Informed Neural Networks","authors":"W. Dörfler,&nbsp;M. Elasmi,&nbsp;T. Laufer","doi":"10.1016/j.exco.2025.100210","DOIUrl":"10.1016/j.exco.2025.100210","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) face significant challenges when applied to problems governed by the Helmholtz equation, primarily due to its indefinite structure and the well-known spectral bias of neural networks. These issues become particularly pronounced at high wavenumbers. To address this, we propose a novel stabilization strategy that improves the learning capabilities of PINNs by recasting the original boundary value problem into an equivalent one that is more amenable to training. Specifically, we reformulate the model problem by decomposing the total wave into a tapered continuation of the incoming wave and a residual scattered field. This allows for the introduction of an inhomogeneity in the boundary value problem, which improves the flow of information during backpropagation. To illustrate the issue and highlight the effectiveness of our approach, we consider a simplified scattering problem involving an incident wave at the junction of two semi-infinite waveguides, a fundamental setting in communication technology. The numerical results presented are in accordance with the expected behavior, paving the way for a possible alternative approach to predict scattering problems using PINNs.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"9 ","pages":"Article 100210"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799023","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}

{"title":"Almost automorphic and pseudo almost periodic solutions to damped Euler–Lagrange equations","authors":"Bouadi Abdelkader ,&nbsp;Boudjema Souhila ,&nbsp;Houmia Anouar","doi":"10.1016/j.exco.2025.100211","DOIUrl":"10.1016/j.exco.2025.100211","url":null,"abstract":"<div><div>This paper investigates the existence of almost automorphic, asymptotically almost automorphic, pseudo almost automorphic, and pseudo almost periodic solutions to damped Euler–Lagrange equations. The analysis relies on a variational framework and the continuity properties of Nemytskii operators. Both autonomous and non-autonomous cases, including external forcing terms, are addressed. A central result shows that the set of forcing functions leading to almost automorphic solutions is dense with respect to a suitable norm. The main contribution of this work lies in extending classical existence results for almost periodic solutions to more general classes of functions, thereby emphasizing the robustness and generality of such behaviors in variational systems.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"9 ","pages":"Article 100211"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145719100","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}

{"title":"Some new relations between Sombor index and graph energy","authors":"Abujafar Mandal,&nbsp;Sk. Md. Abu Nayeem","doi":"10.1016/j.exco.2026.100213","DOIUrl":"10.1016/j.exco.2026.100213","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be a graph with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; being vertices and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; being the corresponding vertex degrees. The Sombor index of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is denoted by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and is defined by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; means there exists an edge between the vertices &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. Among many other aspects of this index, the relationship of the Sombor index with adjacency graph energy has been studied by many researchers. In this paper, first, we improve the bounds of the second Zagreb index, which is better than the previous existing bounds, and using that result, we establish a relation between the Sombor index and adjacency graph energy. The extended adjacency matrix of a graph of order &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; real matrix whose &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;-th element will be &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and 0 otherwise. The extended energy is the aggregate of the absolute values of the eigenvalues of this matrix. Finally, we establish a relationship between the Sombor index and the extended energy. We find an upper and a lower bound of the Sombor index in terms of the extended energy, order of the graph &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, size of the graph &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, maximum degree &lt;span&gt;&lt;ma","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"9 ","pages":"Article 100213"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077662","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}

{"title":"Applications of the (q,τ)-Gamma function in fractional calculus and special functions","authors":"Shaher Momani ,&nbsp;Rabha W. Ibrahim","doi":"10.1016/j.exco.2025.100212","DOIUrl":"10.1016/j.exco.2025.100212","url":null,"abstract":"<div><div>The <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span>-Gamma function provides a two-parameter extension of the classical and <span><math><mi>q</mi></math></span>-deformed Gamma functions, enabling enhanced modeling of memory and scaling effects in fractional calculus and special functions. This paper presents the definition, key properties, and computational aspects of the <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span>-Gamma function Applications in generalized fractional derivatives, integral transforms, and <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span>-special polynomials are described, with selected examples and discussion of future directions.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"9 ","pages":"Article 100212"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927219","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}

{"title":"When long-term coexistence fails: Finite time extinction in a nonlinear model","authors":"Kwadwo Antwi-Fordjour","doi":"10.1016/j.exco.2025.100205","DOIUrl":"10.1016/j.exco.2025.100205","url":null,"abstract":"<div><div>In this note, we revisit the predator–prey model with a square root functional response and prey refuge, originally analyzed by Chen and Wang (2018). While the original study asserted the global stability of the coexistence equilibrium under specific conditions, we provide an alternative mathematical proof showing that the prey population can go extinct in finite time. We refine the analytical framework, present an exact extinction criterion, and illustrate our findings with a concrete example: fixed parameter values and initial conditions that satisfy the finite-time extinction condition. Both the analytical and numerical results confirm that extinction occurs in finite time, challenging prior long-term coexistence claims. Our findings underscore the importance of incorporating behavioral dynamics, such as prey aggregation in refuge areas, into ecological models.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"8 ","pages":"Article 100205"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465968","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}

{"title":"Multiple rogue waves solutions for a (3 + 1)-dimensional nonlinear wave in liquid with gas bubbles via Hirota bilinear equation method","authors":"Mohamed M. Awad ,&nbsp;A.A. Elsadany ,&nbsp;Mohammed K. Elboree","doi":"10.1016/j.exco.2025.100202","DOIUrl":"10.1016/j.exco.2025.100202","url":null,"abstract":"<div><div>In this study, we employ a symbolic computation approach to construct various rogue wave solutions of the (3+1)-dimensional nonlinear wave equation modeling wave propagation in a liquid medium containing gas bubbles. Through the application of the Hirota bilinear method, we systematically derive first-order, second-order, and third-order rogue wave solutions. By selecting appropriate parameter values, we generate graphical illustrations that reveal the structural features and interaction dynamics of these rogue waves. A variety of soliton solutions were obtained from the analysis. Upon plotting these solutions, several rogue wave solutions emerged and periodic waveforms. These results are visually represented through two-dimensional, three-dimensional, and contour plots to highlight the different features and behaviors of each solution. The analysis enhances our understanding of rogue wave behavior within the context of the modeled physical system.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"8 ","pages":"Article 100202"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219497","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}

{"title":"On a “grouplike” family of quasigroups","authors":"Ahmed Al Fares ,&nbsp;Gizem Karaali","doi":"10.1016/j.exco.2025.100200","DOIUrl":"10.1016/j.exco.2025.100200","url":null,"abstract":"<div><div>Quasigroups are algebraic structures in which divisibility is always defined. This paper illustrates some similarities and differences between quasigroup theory and group theory, by singling out a special family of quasigroups which seem to be most “grouplike”.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"8 ","pages":"Article 100200"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157221","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}

{"title":"Lipschitz continuous points of functions on an interval","authors":"Zhekai Shen","doi":"10.1016/j.exco.2025.100194","DOIUrl":"10.1016/j.exco.2025.100194","url":null,"abstract":"<div><div>In this paper, we address the problem of finding functions with predetermined Lipschitz continuous points. More precisely, given <span><math><mrow><mi>A</mi><mo>⊆</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>, we are interested in the existence of function <span><math><mrow><mi>f</mi><mo>:</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>→</mo><mi>R</mi></mrow></math></span> which is Lipschitz continuous exactly on <span><math><mi>A</mi></math></span>. Our result is related to Liouville numbers.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"8 ","pages":"Article 100194"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631377","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}

{"title":"Logistic equation on time scales","authors":"Márcia Lemos-Silva,&nbsp;Delfim F.M. Torres","doi":"10.1016/j.exco.2025.100197","DOIUrl":"10.1016/j.exco.2025.100197","url":null,"abstract":"<div><div>We propose a new dynamic logistic equation that, in contrast with the one available in the literature, preserves the non-negativity of its solutions, which is an essential property for biological meaning. We derive the exact solution of the proposed model and analyze its behavior on arbitrary time scales. Finally, we illustrate our results with concrete examples. Our key novelty is: the model’s ability to maintain positivity across general time scales and its dynamic consistency with the classical logistic equation.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"8 ","pages":"Article 100197"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060624","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}

{"title":"A local saddle point for the hyperbolic augmented Lagrangian function","authors":"Lennin Mallma Ramirez ,&nbsp;Nelson Maculan ,&nbsp;Adilson Elias Xavier ,&nbsp;Vinicius Layter Xavier","doi":"10.1016/j.exco.2025.100195","DOIUrl":"10.1016/j.exco.2025.100195","url":null,"abstract":"<div><div>In this paper, we study the hyperbolic augmented Lagrangian function, which is based on the hyperbolic penalty function. We ensure the existence of a local saddle point for the hyperbolic augmented Lagrangian function in nonconvex constrained optimization problems by considering the classical second-order sufficiency conditions. Finally, we present some computational illustrations of the theory proposed in this work.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"8 ","pages":"Article 100195"},"PeriodicalIF":0.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144827609","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}