(k,k-1)-双正则图的平衡Judicious Partitions(英文)

Bollobás和Scott提出猜想:任意一个边数为m且最小度大于1的图存在顶点集的平衡二部划分使得每一部分点集的导出子图包含的边数不超过m/3.Bollobás和Scott证明了绝大部分正则图存在顶点集的平衡二部划分使得每一部分点集的导出子图包含的边数比m/4小.这里讨论(k,k-1)-双正则图的平衡二部划分,证明了每一个(k,k-1)-双正则图存在平衡二部划分使得每一部分点集的导出子图包含的边数是m/4左右.

最大度与最小度相差不超过2的图的平衡judicious划分

图G的顶点集V(G)的一个二部划分V_1和V_2叫做平衡二部划分,如果||V_1|-|V_2||≤1成立.Bollobas和Scott猜想:每一个有m条边且最小度不小于2的图,都存在一个平衡二部划分V_1,V_2,使得max{e(V_1),e(V_2)}≤m/3,此处e(V_i)表示两顶点都在V_i(i=1,2)中的边的条数.他们证明了这个猜想对正则图(即△(G)=δ(G))成立.颜娟和许宝刚证明了每个(k,k-1)-双正则图(即△(G)-δ(G)≤1)存在一个平衡二部划分V_1,V_2,使得每一顶点集的导出子图包含大约m/4条边.这里把该结论推广到最大度和最小度相差不超过2的图G.

Does Practice Always Make Perfect?——random notes on the need for a judicious balance between assimilative and systematic approaches in English language teaching

本文探讨外语院校英语教学中的一些问题。 英语专业有些学生基础不扎实,笔头表达能力很弱。针对这种情况,文章着重谈了三个问题: 1.语法问题:用正确的方法学习语法,辨明英语和汉语的差异有助于克服母语干扰,学好英语。 2.词典问题:在强调通过语境学习语言的同时,应当注意培养学生使用工具书的能力。查阅词典能使学生集中地研究、掌握词义和用法,可以补阅读之不足。 3.精读和泛读问题:精读和泛读各有其作用,应当二者并举,互相结合。 结论是英语教学要“两条腿走路”:一方面努力创造良好的语言环境,让学生通过自然熏陶的方式学习英语;同时也要注意引导学生有意识地研究语言和语言规律。

Biased Partitions and Judicious k-Partitions of Graphs

Let G =（V, E） be a graph with m edges. For reals p ∈ [0, 1] and q = 1-p, let m;（G） be the minimum of qe（V;） + pe（V;） over partitions V = V;∪ V;, where e（V;） denotes the number of edges spanned by V;. We show that if m;（G） = pqm-δ, then there exists a bipartition V;, V;of G such that e（V;） ≤ p;m-δ + p（m/2）;+ o（√m） and e（V;） ≤ q;m-δ + q（m/2）;+ o（√m） for δ = o(m;). This is sharp for com;lete graphs up to the error term o（√m）. For an integer k ≥ 2, let fk（G） denote the maximum number of edges in a k-partite subgraph of G. We prove that if fk（G） =（1-1/k）m + α,then G admits a k-partition such that each vertex class spans at most m/k;-Ω(m/k;) edges forα = Ω（m/k;）. Both of the above im;rove the results of Bollob′as and Scott.

图的有偏Judicious划分

Bollobás和Scott证明了每个有较大有偏割集的图存在一个judicious二部划分使得每部分的边数都较少.本文中,我们考虑一个类似的有偏划分问题.本文证明了每个图存在一个有偏二部划分使得每部分的边数不太少.同时,对有较大有偏割集的图,本文部分改进了Ballobás和Scott的结果.

Judicious Bisection of Hypergraphs

Judicious bisection of hypergraphs asks for a balanced bipartition of the vertex set that optimizes several quantities simultaneously. In this paper, we prove that if G is a hypergraph with n vertices and ni edges of size i for i = 1, 2,…, k, then G admits a bisection in which each vertex class spans at mostm1/2＋1/4m2＋…＋（1/2^k）mk＋o（m1＋…＋mk）edges, where G is dense enough or △（G） =o（n） but has no isolated vertex, which turns out to be a bisection version of a conjecture proposed by Bollobas and Scott.

Research and Analysis of Grammatical Error Correction Technology for Chinese Documents

With the widespread use of Chinese globally, the number of Chinese learners has been increasing, leading to various grammatical errors among beginners. Additionally, as domestic efforts to develop industrial information grow, electronic documents have also proliferated. When dealing with numerous electronic documents and texts written by Chinese beginners, manually written texts often contain hidden grammatical errors, posing a significant challenge to traditional manual proofreading. Correcting these grammatical errors is crucial to ensure fluency and readability. However, certain special types of text grammar or logical errors can have a huge impact, and manually proofreading a large number of texts individually is clearly impractical. Consequently, research on text error correction techniques has garnered significant attention in recent years. The advent and advancement of deep learning have paved the way for sequence-to-sequence learning methods to be extensively applied to the task of text error correction. This paper presents a comprehensive analysis of Chinese text grammar error correction technology, elaborates on its current research status, discusses existing problems, proposes preliminary solutions, and conducts experiments using judicial documents as an example. The aim is to provide a feasible research approach for Chinese text error correction technology.

Judicious partitions of weighted hypergraphs

Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/3？ We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes.In particular, it is shown that any graph G with m edges has a partition V_1,..., V_k such that each vertex set meets at least（1-（1-1/k）~2）m ＋ o（m） edges, which answers a related question of Bollobás and Scott.

Foundations and Applications of Information Systems Dynamics

Although numerous advances have been made in information technology in the past decades,there is still a lack of progress in information systems dynamics(ISD),owing to the lack of a mathematical foundation needed to describe information and the lack of an analytical framework to evaluate information systems.The value of ISD lies in its ability to guide the design,development,application,and evaluation of largescale information system-of-systems(So Ss),just as mechanical dynamics theories guide mechanical systems engineering.This paper reports on a breakthrough in these fundamental challenges by proposing a framework for information space,improving a mathematical theory for information measurement,and proposing a dynamic configuration model for information systems.In this way,it establishes a basic theoretical framework for ISD.The proposed theoretical methodologies have been successfully applied and verified in the Smart Court So Ss Engineering Project of China and have achieved significant improvements in the quality and efficiency of Chinese court informatization.The proposed ISD provides an innovative paradigm for the analysis,design,development,and evaluation of large-scale complex information systems,such as electronic government and smart cities.

An Empirical Assessment and Analysis of the United Nations Convention on Contracts Judicial Applicability in China

Chinese domestic legislation on the judicial applicability of international treaties has been unsettled,especially under the Civil Code,which is silent on this issue.However,previous studies have depicted an image of a“pro-CISG”attitude in Chinese legal practice,which is distinguished from the tendency to circumvent the CISG in other jurisdictions such as the U.S.This contradictory phenomenon,namely the absence of guiding norms versus the embracement of the CISG in judicial practice,is rarely discussed,especially within the context of civil codification and recent external economic challenges.To verify this paradox,a manually collected dataset of 223 court decisions from 2013 to 2023 identifies some basic characteristics of the CISG judicial applicability in China,including the application rate,legal reasoning paths,citation frequencies of specific provisions,and some qualitative observations about the judicial behaviors in the international sales dispute resolution.The main finding is that Chinese courts have been applying the CISG at an obviously higher rate,compared with both their foreign counterparts and the general rate of applying foreign law in the international civil and commercial litigations in China.To explain this gap between“law in book”and“law in action,”the context of Chinese judicial practice should be considered.Despite the vagueness of domestic legislation,the judicial policy promotion,the innovative guiding cases system,the legal transplantation,and other factors may contribute to the“pro-CISG”attitude.As for the future promotion of CISG in the Chinese style of international commercial dispute resolution,these factors may coordinate with the legislative improvements.

Human Rights in Civil Judicial Documents:Conception and Function

Traditional human rights theory tends to hold that human rights should be aimed at defending public authority and that the legal issue of human rights is a matter of public law.However,the development of human rights concepts and practices is not just confined to this.A textual search shows that the term“human rights”exists widely in China’s civil judicial documents.Among the 3,412 civil judicial documents we researched,the concept of“human rights”penetrates all kinds of disputes in lawsuits,ranging from property rights,contracts,labor,and torts to marital property,which is embedded in both the claims of the parties concerned and the reasoning of judges.Human rights have become the discourse and yardstick for understanding and evaluating social behavior.The widespread use of the term“human rights”in civil judicial documents reflects at least three concepts related to human rights:first,the rights to subsistence and development are the primary basic human rights;second,the judicial protection of human rights is a bottom-line guarantee;third,the protection of human rights aims to achieve equal rights.Today,judges quote the theory of human rights in judicial judgments from time to time,evidencing that human rights have a practical function in judicial adjudication activities,and in practice this is mainly manifested in declaring righteous values and strengthening arguments with the values and ideas related to human rights,using the provisions concerning human rights in the Constitution to interpret the constitutionality,and using the principles of human rights to interpret blurred rules and rank the importance of different rights.

Challenges and Countermeasures for Integrating the Protection of Environmental Rights into Actions for Addressing Climate Change

Climate change,which is the result of human activities,has wide-ranging impact.It poses a serious threat to human rights.Environmental rights are where the protection of the ecological environment and the development of human rights intersect.In view of the close relationship between the actions for addressing climate change and environmental rights,China should integrate the protection of environmental rights into the actions for addressing climate change,so as to achieve simultaneous development of both.In the process of coping with climate change,the right to climate stability that mainly pursues a“harmless”environment and the right to a more livable climate that pursues a“beautiful eco-environment”are specific manifestations of environmental rights and should be the priority of protection efforts.However,there are still some obstacles to achieving the coordinated development of the efforts to address climate change and the protection of environmental rights because traditional rights protection methods mainly give individuals subjective rights with the power to claim and are thus difficult to meet the needs of environmental rights protection in the context of climate change,and there are inherent value differences between responding to climate change and the realization of other human rights.Building a multi-level national obligation system to address climate change,giving full play to the role of courts in responding to climate change through moderate judicial activism,and coordinating the efforts to cope with climate change and the development of human rights under the guidance of a holistic system view are effective ways to overcome the aforementioned difficulties.

“Fundamental Rights and Private Law” in China

The Qi Yuling case is a crucial juncture in the study of “fundamental rights and private law” in China, yet relevant research is underpinned on two clues. The first is that the increasing interest in the “constitutionalization of private law” worldwide provides knowledge resources and reference materials for scholars in China;the second is the understanding and exploration of the judicial application of the Constitution since the 1980s. Among them, such concepts as “the Constitution has direct legal effect” and “the Constitution needs to be implemented by the people” could have directly affected the Qi Yuling case. Focusing on such topics as the case of Qi Yuling, judicial enforcement of the Constitution, and the compilation of the Civil Code, scholars discussed the ways and scope for inclu ding fundamental rights in private law based on their experience abroad. They also looked into specific issues, covering how fundamental rights affect civil acts and the private law effects fundamental rights like personality rights, equali ty rights, freedom of speech, and protection of personal information. In the context of promoting the full implementation of the Constitution in the new era, “fundamental rights and private law” is still a field with great potential in both practice and theory.

Impact of Global Climatic and Environmental Changes on Agricultural Research Challenges and Wheat Productivity in Pakistan

Food security is a human right,within a global context by aligning the opportunities to eliminate poverty,to attain the peace,the rational and implications of sustainable use and judicious management of natural resources,are the road map,to combat the disasters.The prevailing International tension with respect to climate change suggests that the food security can be achieved by penetrating,in depth,the agricultural research.Pakistan is under threat to

Administrative Patent Enforcement in China

China is one of the major markets for patent filing and patent exploitation.A powerful enforcement environment may boost both of patent filing and exploitation.A two-track system for the patent enforcement is available in China:the administrative system via local intellectual property offices,and the judicial system via courts.

Differences of language learning beliefs of postg raduates and undergraduates

The Company Law of 1993 is important in protecting the interests of both companies and shareholders.But on stock right,it always arouses heated debate among scholars.Before the promulgation of New Company Law of 2006,varieties of theories of this issue have been formed.Through analyzing and refuting those theories,I try to clear the ambiguous definition by explaining the essence of right and comparing related right,so as to reach the conclusion that the stock right is only the changeable form of the ownership of shareholders.

Judicial Application of International Human Rights Treaties in China

Since the Chinese Constitution does not stipulate the status of international treaties in the domestic legal system,the question of whether the domestic court can apply international human rights treaties keeps obscure all the time.China’s official statement and academic opinions generally believe that the domestic court couldn’t resort to the human rights treaties.In recent years,however,several cases have come out involving direct reference to human rights treaties by the court.The following factors contribute together to the direct reference:the inward-looking nature of international human rights treaties,specific requirements of human rights treaties,and the possible institutional room in Chinas’s current legal system.Take the view off ulfilling international human rights obligations,the practice of judicial application should be fully affirmed.Nevertheless,it should also be noted that relevant practice is still in its infancy,there are some problems such as inconsistent understanding and non-standard application.From the perspective of top-level design,it is necessary to provide a normative basis for the practice of the court,so as to make the international human rights treaties play their due role.

Word Segmentation for Chinese Judicial Documents

Word segmentation is an integral step in many knowledge discovery applications. However, existing word segmentation methods have problems when applying to Chinese judicial documents:(1) existing methods rely on large-scale labeled data which is typically unavailable in judicial documents, and (2) judicial document has its own language features and writing formats. In this paper, a word segmentation method is proposed for Chinese judicial documents. The proposed method consists of two steps:(1) automatically generating some labeled data as legal dictionaries, and (2) applying a hybrid multilayer neural networks to do word segmentation incorporating legal dictionaries. Experiments are conducted on a dataset of Chinese judicial documents showing that the proposed model can achieve better results than the existing methods.

On Stock Right

The Company Law of 1993 is important in protecting the interests of both companies and shareholders.But on stock right,it always arouses heated debate among scholars.Before the promulgation of New Company Law of 2006,varieties of theories of this issue have been formed.Through analyzing and refuting those theories,I try to clear the ambiguous definition by explaining the essence of right and comparing related right,so as to reach the conclusion that the stock right is only the changeable form of the ownership of shareholders.

The Socialist Rule of Law with Chinese Characteristics and Human Rights Protection

Law is the fundamental method of governance and the rule of law symbolizes modern civilization. The socialist rule of law is the rule of law rooted in the Chinese tradition, and designed and led by the Communist Party of China(CPC). It is not only a tool for government, but also a driver of social progress. Meanwhile, the Chinese human rights system is also designed by the CPC. Both concepts—the socialist rule of law and the human rights system——are different from the West in terms of theory, path and systems. Human rights are the fundamental values of and the ultimate goal pursued by the rule of law; and the rule of law is the recognition of and guarantee for human rights. Efforts must be made to advance legislative, administrative and judicial protection of human rights.