A semigroup S is called an E-inversive if for every aS there exists x in S Such that axE(s), where E(s) is the set of all idempotents of S, introduced by G.Thierrin. The concept of sub direct product of two E-inversive semigroups introduced by H. Mitsch by using the concept of sub homomorphism of inverse semigroups introduced by Mc Alisterand N.R.Reilly. The semidirect of two E-inversive semigroups introduced by F.Catino and M.M.Miccoli. In this paper we study some special identities in an E-inversive semigroup and we present preliminaries and basic concepts of E-inversive semigroups.
{"title":"E-Inversive Semigroups With the Identity ABC = AC","authors":"P. S. Reddy, Kassaw Benebere","doi":"10.2139/ssrn.3390372","DOIUrl":"https://doi.org/10.2139/ssrn.3390372","url":null,"abstract":"A semigroup S is called an E-inversive if for every aS there exists x in S Such that axE(s), where E(s) is the set of all idempotents of S, introduced by G.Thierrin. The concept of sub direct product of two E-inversive semigroups introduced by H. Mitsch by using the concept of sub homomorphism of inverse semigroups introduced by Mc Alisterand N.R.Reilly. The semidirect of two E-inversive semigroups introduced by F.Catino and M.M.Miccoli. In this paper we study some special identities in an E-inversive semigroup and we present preliminaries and basic concepts of E-inversive semigroups.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126356358","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}
This paper discusses the wave description in biology, chemistry and economics. Using quantum mechanics to study social processes, it was shown that the economic waves of N. Kondratiev are theoretically derived from the quantum theory of the development of science and society. The use of Heisenberg’s uncertainty principle for social phenomena shows that the development of society is conceptually probabilistic in nature and cannot be strictly predicted in principle (given the mathematical formula). The rejection of the “time arrow�? at the quantum level leads to the conclusion that “time in our world�? is a definite “averaging and transformation�? of periodic quantum processes at the fundamental level. It also shows the impossibility of achieving technological singularity and the creation of artificial intelligence like human.
{"title":"Quantum Theory of the Development of Science, Economic and Society","authors":"V. Bezverkhniy, Vitaliy Bezverkhniy","doi":"10.2139/ssrn.3367633","DOIUrl":"https://doi.org/10.2139/ssrn.3367633","url":null,"abstract":"This paper discusses the wave description in biology, chemistry and economics. Using quantum mechanics to study social processes, it was shown that the economic waves of N. Kondratiev are theoretically derived from the quantum theory of the development of science and society. The use of Heisenberg’s uncertainty principle for social phenomena shows that the development of society is conceptually probabilistic in nature and cannot be strictly predicted in principle (given the mathematical formula). The rejection of the “time arrow�? at the quantum level leads to the conclusion that “time in our world�? is a definite “averaging and transformation�? of periodic quantum processes at the fundamental level. It also shows the impossibility of achieving technological singularity and the creation of artificial intelligence like human.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115775979","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}
Thе nеw agе tеchniquеs of cloud computing for procеssing of data is gеnеrally scalablе and sеcurе and to a grеat еxtеnt attracts thе infrastructurе to support big data applications. Howеvеr, thе privacy issuеs posе hindrancе for using thе cloud platforms. Numеrous tеchniquеs arе lеarnt for prеsеrvation of privacy whеrеin data usability and data obfuscation is considеrеd but failеd in balancing thе data privacy and data utility. Naturе-inspirеd mеtahеuristic algorithms arе simplе and flеxiblе and thus now-a-days popular among rеsеarchеrs. Thеsе naturе-inspirеd algorithms arе analysеd in tеrms of thеir kеy fеaturеs likе thеir divеrsity and adaptation, еxploration and еxploitation, and attractions and diffusion mеchanisms. This papеr proposеs an anonymization basеd privacy prеsеrvation modеl using k-anonymization critеria and intеgration of two algorithms - Grеy wolf optimizеr and Cat Swarm Optimization, for attaining privacy prеsеrvation in big data bеforе providing thе data to thе cloud platform. Thе anonymization tеchniquе is procеssеd by adapting k- anonymization critеria for duplicating k-rеcords from thе original databasе. New technique will rеvеal only thе еssеntial dеtails to thе еnd usеrs by hiding thе confidеntial information to offеr a sеcurеd communication. To attain balancе bеtwееn privacy and utility, thе fitnеss function is formulatеd and thе proposеd tеchniquе is comparеd with various еxisting tеchniquеs basеd on thе pеrformancе mеtrics - Classification accuracy and Information loss.
{"title":"A Novel Technique for Privacy Preservation Using K-Anonymization and Nature Inspired Optimization Algorithms","authors":"S. Madan, Puneet Goswami","doi":"10.2139/ssrn.3357276","DOIUrl":"https://doi.org/10.2139/ssrn.3357276","url":null,"abstract":"Thе nеw agе tеchniquеs of cloud computing for procеssing of data is gеnеrally scalablе and sеcurе and to a grеat еxtеnt attracts thе infrastructurе to support big data applications. Howеvеr, thе privacy issuеs posе hindrancе for using thе cloud platforms. Numеrous tеchniquеs arе lеarnt for prеsеrvation of privacy whеrеin data usability and data obfuscation is considеrеd but failеd in balancing thе data privacy and data utility. Naturе-inspirеd mеtahеuristic algorithms arе simplе and flеxiblе and thus now-a-days popular among rеsеarchеrs. Thеsе naturе-inspirеd algorithms arе analysеd in tеrms of thеir kеy fеaturеs likе thеir divеrsity and adaptation, еxploration and еxploitation, and attractions and diffusion mеchanisms. This papеr proposеs an anonymization basеd privacy prеsеrvation modеl using k-anonymization critеria and intеgration of two algorithms - Grеy wolf optimizеr and Cat Swarm Optimization, for attaining privacy prеsеrvation in big data bеforе providing thе data to thе cloud platform. Thе anonymization tеchniquе is procеssеd by adapting k- anonymization critеria for duplicating k-rеcords from thе original databasе. New technique will rеvеal only thе еssеntial dеtails to thе еnd usеrs by hiding thе confidеntial information to offеr a sеcurеd communication. To attain balancе bеtwееn privacy and utility, thе fitnеss function is formulatеd and thе proposеd tеchniquе is comparеd with various еxisting tеchniquеs basеd on thе pеrformancе mеtrics - Classification accuracy and Information loss.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125190271","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}
It is commonly believed that the visual system requires oculomotor information to perceive depth from binocular disparity. However, any effect of the oculomotor information on depth perception is too restricted to explain depth perception under natural viewing conditions. In this study, I describe a computational model that can recover depth from a stereo-pair of retinal images without using any oculomotor information. The model shows that, at least from a computational perspective, any oculomotor information is not necessary for perceiving depth from the stereo retinal images.
{"title":"A Computational Model that Recovers Depth from Stereo-Input without Using Any Oculomotor Information","authors":"T. Sawada","doi":"10.2139/ssrn.3354468","DOIUrl":"https://doi.org/10.2139/ssrn.3354468","url":null,"abstract":"It is commonly believed that the visual system requires oculomotor information to perceive depth from binocular disparity. However, any effect of the oculomotor information on depth perception is too restricted to explain depth perception under natural viewing conditions. In this study, I describe a computational model that can recover depth from a stereo-pair of retinal images without using any oculomotor information. The model shows that, at least from a computational perspective, any oculomotor information is not necessary for perceiving depth from the stereo retinal images.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122046777","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 discuss special types of the factorization method for the so-called β-difference hypergeometric equation, and then illustrate them by solving or transforming difference and q-difference hypergeometric equations, including the Askey-Wilson second order q-difference equation.
{"title":"The Factorization Method for the β-Difference Hypergeometric Equation","authors":"G. Bangerezako","doi":"10.2139/ssrn.3351635","DOIUrl":"https://doi.org/10.2139/ssrn.3351635","url":null,"abstract":"We discuss special types of the factorization method for the so-called β-difference hypergeometric equation, and then illustrate them by solving or transforming difference and q-difference hypergeometric equations, including the Askey-Wilson second order q-difference equation.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127065858","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}
Linear algebra is undoubtedly one of the most powerful structures of pure and applied mathematics. It combines extreme generality with deeply held spatial intuitions. In economics and data science, one would dare to say, lies at the basis of most of the other mathematical techniques used. Yet, standard presentations of the subject tend to refrain from displaying the full extent of the deeply intuitive nature of the underlying structures, despite the fact that such intuitions are so useful when applying linear algebra, and when extending techniques to tackle nonlinear problems. In the context of the “Intuitive Mathematical Economics Series”, this is the first paper of a series dedicated to presenting linear algebra emphasizing both, its intuitive, and its general nature. In this case we present linear manifolds and vector spaces.
{"title":"Intuitive Mathematical Economics Series. Linear Structures I. Linear Manifolds, Vector Spaces and Scalar Products","authors":"S. Pernice","doi":"10.2139/ssrn.3357144","DOIUrl":"https://doi.org/10.2139/ssrn.3357144","url":null,"abstract":"Linear algebra is undoubtedly one of the most powerful structures of pure and applied mathematics. It combines extreme generality with deeply held spatial intuitions. In economics and data science, one would dare to say, lies at the basis of most of the other mathematical techniques used. Yet, standard presentations of the subject tend to refrain from displaying the full extent of the deeply intuitive nature of the underlying structures, despite the fact that such intuitions are so useful when applying linear algebra, and when extending techniques to tackle nonlinear problems. In the context of the “Intuitive Mathematical Economics Series”, this is the first paper of a series dedicated to presenting linear algebra emphasizing both, its intuitive, and its general nature. In this case we present linear manifolds and vector spaces.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130470084","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}
D. Bertulfo, Elisabetta Gentile, Gaaitzen J. de Vries
Global value chains (GVCs) have been a vehicle for job creation in developing Asia, but there is mounting concern that more sophisticated and cost-effective technology could displace workers through automation or reshoring of production. We use the demand-based input–output approach in Reijnders and de Vries (2018) to examine how employment responded to consumption, trade, and technological advances in 12 economies that accounted for 90% of employment in developing Asia during the period 2005–2015. Structural decomposition analysis based on the Asian Development Bank Multiregional Input–Output Tables combined with harmonized cross-country occupation data indicates that, other things being equal, technological change within GVCs was associated with a decrease in labor demand across all sectors, and an increase in the share of nonroutine cognitive occupations. We also find that increased domestic consumption expenditures of goods and services generated an increase in labor demand large enough to offset the negative employment impact of technological change. Finally, we do not find evidence of major shifts in occupational labor demand due to reshoring.
{"title":"The Employment Effects of Technological Innovation, Consumption, and Participation in Global Value Chains: Evidence from Developing Asia","authors":"D. Bertulfo, Elisabetta Gentile, Gaaitzen J. de Vries","doi":"10.2139/ssrn.3343998","DOIUrl":"https://doi.org/10.2139/ssrn.3343998","url":null,"abstract":"Global value chains (GVCs) have been a vehicle for job creation in developing Asia, but there is mounting concern that more sophisticated and cost-effective technology could displace workers through automation or reshoring of production. We use the demand-based input–output approach in Reijnders and de Vries (2018) to examine how employment responded to consumption, trade, and technological advances in 12 economies that accounted for 90% of employment in developing Asia during the period 2005–2015. Structural decomposition analysis based on the Asian Development Bank Multiregional Input–Output Tables combined with harmonized cross-country occupation data indicates that, other things being equal, technological change within GVCs was associated with a decrease in labor demand across all sectors, and an increase in the share of nonroutine cognitive occupations. We also find that increased domestic consumption expenditures of goods and services generated an increase in labor demand large enough to offset the negative employment impact of technological change. Finally, we do not find evidence of major shifts in occupational labor demand due to reshoring.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129967043","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 introduce a purely mathematical measure, Γ, of the accumulation of asset value over time that robustly measures cumulative return against market movement under whatever investment strategy is employed in buying into any given market over any period of time. Requiring no underlying assumptions about price behavior, the purely mathematical factor Γ captures the qualitative and quantitative structural elements of wealth accumulation. In direct application Γ accurately reveals the computational role and influence of volatility and mean price movement in the popular strategy of Dollar Cost Averaging. At the last Γ suggests a proportional Buy&Hold strategy that is generally more successful.
{"title":"The Accumulation of Value Over Time","authors":"Dennis Sentilles","doi":"10.2139/ssrn.3347937","DOIUrl":"https://doi.org/10.2139/ssrn.3347937","url":null,"abstract":"We introduce a purely mathematical measure, Γ, of the accumulation of asset value over time that robustly measures cumulative return against market movement under whatever investment strategy is employed in buying into any given market over any period of time. Requiring no underlying assumptions about price behavior, the purely mathematical factor Γ captures the qualitative and quantitative structural elements of wealth accumulation. In direct application Γ accurately reveals the computational role and influence of volatility and mean price movement in the popular strategy of Dollar Cost Averaging. At the last Γ suggests a proportional Buy&Hold strategy that is generally more successful.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127019368","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. Aouad, Jacob B. Feldman, D. Segev, Dennis J. Zhang
In this paper, we introduce the click-based MNL choice model, a novel framework for capturing customer purchasing decisions in e-commerce settings. Our main modeling idea is to assume that the click behavior within product recommendation or search results pages provides an exact signal regarding the alternatives considered by each customer. We study the resulting assortment optimization problem, where the objective is to select a subset of products, made available for purchase, to maximize the expected revenue. Our main algorithmic contribution comes in the form of a polynomial-time approximation scheme (PTAS) for this problem, showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. In the course of establishing this result, we develop novel technical ideas, including enumeration schemes and stochastic inequalities, which may be of broader interest. In order to quantify the benefits of incorporating click behavior within choice models, we present a case study based on data acquired in collaboration with the retail giant Alibaba. We fit click-based MNL and standard MNL models to historical sales and click data in a setting where the online platform must present customized six-product displays to users. We demonstrate that utilizing the click-based MNL model leads to substantial improvements over the standard MNL model in terms of prediction accuracy. Furthermore, we generate realistic assortment optimization instances that mirror Alibaba's customization problem, and implement practical variants of our approximation scheme to compute assortment recommendations in these settings. We find that the recommended assortments have the potential to be at least 9% more profitable than those resulting from a standard MNL model. We identify a simple greedy heuristic, which can be implemented at large scale, while also achieving near-optimal revenue performance in our experiments.
{"title":"Click-Based MNL: Algorithmic Frameworks for Modeling Click Data in Assortment Optimization","authors":"A. Aouad, Jacob B. Feldman, D. Segev, Dennis J. Zhang","doi":"10.2139/ssrn.3340620","DOIUrl":"https://doi.org/10.2139/ssrn.3340620","url":null,"abstract":"In this paper, we introduce the click-based MNL choice model, a novel framework for capturing customer purchasing decisions in e-commerce settings. Our main modeling idea is to assume that the click behavior within product recommendation or search results pages provides an exact signal regarding the alternatives considered by each customer. We study the resulting assortment optimization problem, where the objective is to select a subset of products, made available for purchase, to maximize the expected revenue. Our main algorithmic contribution comes in the form of a polynomial-time approximation scheme (PTAS) for this problem, showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. In the course of establishing this result, we develop novel technical ideas, including enumeration schemes and stochastic inequalities, which may be of broader interest. \u0000 \u0000In order to quantify the benefits of incorporating click behavior within choice models, we present a case study based on data acquired in collaboration with the retail giant Alibaba. We fit click-based MNL and standard MNL models to historical sales and click data in a setting where the online platform must present customized six-product displays to users. We demonstrate that utilizing the click-based MNL model leads to substantial improvements over the standard MNL model in terms of prediction accuracy. Furthermore, we generate realistic assortment optimization instances that mirror Alibaba's customization problem, and implement practical variants of our approximation scheme to compute assortment recommendations in these settings. We find that the recommended assortments have the potential to be at least 9% more profitable than those resulting from a standard MNL model. We identify a simple greedy heuristic, which can be implemented at large scale, while also achieving near-optimal revenue performance in our experiments.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123085467","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}
This paper proposes the Knightian Uncertainty Hypothesis (KUH), a new approach to macroeconomics and finance theory. KUH rests on a novel mathematical framework that characterizes both measurable and Knightian uncertainty about economic outcomes. Relying on this framework and Muthi?½s pathbreaking hypothesis, KUH represents participantsi?½ forecasts to be consistent with both uncertainties. KUH thus enables models of aggregate outcomes that 1) are premised on market participantsi?½ rationality, and 2) accord a role to both fundamental and psychological (and other non-fundamental) factors in driving outcomes. The paper also suggests how a KUH modeli?½s quantitative predictions can be confronted with time-series data.
{"title":"The Knightian Uncertainty Hypothesis: Unforeseeable Change and Muth’s Consistency Constraint in Modeling Aggregate Outcomes","authors":"R. Frydman, S. Johansen, Anders Rahbek, M. Tabor","doi":"10.2139/ssrn.3341203","DOIUrl":"https://doi.org/10.2139/ssrn.3341203","url":null,"abstract":"This paper proposes the Knightian Uncertainty Hypothesis (KUH), a new approach to macroeconomics and finance theory. KUH rests on a novel mathematical framework that characterizes both measurable and Knightian uncertainty about economic outcomes. Relying on this framework and Muthi?½s pathbreaking hypothesis, KUH represents participantsi?½ forecasts to be consistent with both uncertainties. KUH thus enables models of aggregate outcomes that 1) are premised on market participantsi?½ rationality, and 2) accord a role to both fundamental and psychological (and other non-fundamental) factors in driving outcomes. The paper also suggests how a KUH modeli?½s quantitative predictions can be confronted with time-series data.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132399494","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：