Formal Definition Research Articles

Dynamical and thermodynamical stability of a charged thin-shell wormhole

AbstractA study of the dynamical and thermodynamical stability of a charged thin-shell wormhole built by gluing two Reissner–Nordström geometries is presented. The charge on the shell is linearly related to the matter content. For the dynamical stability, a concise inequality is obtained, valid for any barotropic equation of state that relates the pressure with the energy density at the throat. A thermodynamical description of the system is introduced, which leads to the temperature and the electric potentials. Adopting a linear equation of state for the pressure and a definite form for the entropy function, the set of equilibrium configurations that are both dynamically and thermodynamically stable is found.

Визнання Голодомору геноцидом українського народу парламентом Великої Британії: дебати 2013–2023 рр

The international recognition of the Holodomor of 1932–1933 is evidence of the establishment of historical justice in assessing the crime against humanity committed against the Ukrainian people. For the first time, the famine in Ukraine was discussed in the British Parliament in 1934: a report based on information received from Cardinal Archbishop of Vienna Theodor Innitzer and journalists William Henry Chamberlin and Malcolm Muggeridge was delivered in the House of Lords by the liberal politician Lord Charnwood. However, a number of MPs opposed the discussion of the famine in the USSR, stressing that it was an internal affair of another state, and the debate was closed. In the early 2000s, after the recognition of the Holodomor as genocide by the Verkhovna Rada of Ukraine (2006) and the intensification of the Ukrainian authorities’ efforts to raise awareness of the crimes of the Soviet regime among the world community, this issue was discussed three times (2013, 2017, 2023) in the House of Commons. P. Latham, a representative of the ruling Conservative Party, was the initiator of the debate. She presented indisputable historical facts and oral memories in her speeches, that allowed to assess the Holodomor as a deliberate act of genocide by the Soviet government, which became a deep trauma for Ukraine and had a catastrophic impact on the Ukrainian national identity. The politician also argued her thesis with the statement of the author of the concept of “genocide” R. Lemkin, who called the destruction of the Ukrainian nation a classic example of genocide, stressing that the purpose of the Holodomor was to overcome Ukrainian national resistance to the Soviet regime. In general, all the speakers emphasised the artificiality of the famine, the scale of the tragedy (from 2 to 12 million deaths), which was planned by the Stalinist totalitarian regime to achieve its main goal – the destruction of the Ukrainian nation. The MPs recognised the need to honour the memory of the millions people who were brutally murdered; condemned the Soviet regime’s confiscation of food, restrictions on the movement of the population, refusal of foreign aid, brutal suppression of protests, and Russification policy; called on the UK government to further raise awareness of the Holodomor and condemned any attempts to deny or distort this historical truth, considering it nothing less than genocide.They noted the heroism of the contemporaries of the events, in particular the British journalists Gareth Jones and M. Muggeridge, and ordinary citizens who were not afraid to speak out about the real state of affairs. In this context, the parliamentarians drew historical parallels with the present: reporters from many countries, including Ukraine itself, are endangering themselves to expose the true extent of Russian barbarism and war crimes during Russia’s illegal war against Ukraine, in which Putin aims to destroy the Ukrainian nation and the concept of Ukrainian identity. The MPs argued that the recognition of the Holodomor as genocide is not a formal definition: it is a recognition of the truth of historical events and has implications for the current war, as it sends a clear signal that the international community will not turn a blind eye to acts of cruelty and injustice. In early 2023, President of Ukraine V. Zelenskyy and Speaker of the Verkhovna Rada of Ukraine R. Stefanchuk addressed the UK Parliament, focusing on the current situation in Ukraine. However, the head of the Ukrainian parliament stressed the importance of restoring historical justice in the issue of recognising the Holodomor of 1932–1933 in Ukraine as a crime of genocide against the Ukrainian people, especially because of the unchanging policy of Russia, which commits mass war crimes and crimes against humanity. The House of Commons unanimously passed a resolution recognising the Holodomor as genocide of the Ukrainian people on 25 May 2023. The position of official London has remained unchanged: Holodomor was a horrific, man-made disaster of unimaginable scale and the government recognise the human tragedy that occurred and its importance in the history of Ukraine and Europe. Government policy is that recognition of genocides should be a matter for judicial decision and so it should be for judges, rather than Governments or non- judicial bodies, to make a designation of genocide. Such decisions should be based on a credible judicial process, and the courts are best placed to judge what are essentially criminal matters. At the same time, the government emphasises that this position in no way diminishes the gravity of the crime and the responsibility of the Soviet leadership for the deaths of millions of Ukrainians. It also assures that it will continue to support Ukraine in defending its sovereignty and territorial integrity, and international efforts to bring Russia to justice for its aggression against Ukraine. Key words: Holodomor, genocide, Great Britain, P. Latham, Ukraine.

On definiteness and person in Romanian vocatives

We investigate the correlations between the various morphosyntactic types of Romanian vocatives (+/- vocative-morphology, +/- definiteness) and the main types of vocative uses – addresses, evaluative, selecting calls and non-selecting calls (where ‘selecting calls’ by and large correspond to Schaden’s (2010) identificational vocatives). The Romanian data show that selecting calls and evaluative vocatives have structural properties that distinguish them from the other vocatives (used in addresses and non-selecting calls). Identificational vocatives, which are used when an addresee is selected from a larger group of potential addresees, involve a special Voc head that selects a definite DP, which may be unmarked for Person when the DP is nominal but is necessarily marked as 2nd person, via agreement, when the DP is pronominal. Morphologically-marked vocatives and [-def] vocatives obligatorily carry 2nd person. All four morphosyntactic patterns are available for addresses and non-selecting calls, the choice of one particular pattern being subject to lexical restrictions. We argue that morphological Vocative marking involves movement to the Voc-layer, as opposed to unmarked vocatives. Evaluative vocatives are obligatorily Voc-marked definites. We attribute the obligatory Voc-marking to the fact that for evaluative vocatives, the assignment of the NP property to the Addressee is new information. The specialization of the definite vocative-marked form for the evaluative use is explained as a morphological peculiarity of the nominalizing suffix that we postulate for evaluative adjectives, under the assumption that this suffix is also present with non-derived nouns used as evaluative predicates.

An Objective Classification Scheme for Solar-System Bodies Based on Surface Gravity

We introduce succinct and objective definitions of the various classes of objects in the solar system. Unlike the formal definitions adopted by the International Astronomical Union in 2006, group separation is obtained from measured physical properties of the objects. Thus, this classification scheme does not rely on orbital/environmental factors that are subject to debate—the physical parameters are intrinsic properties of the objects themselves. Surface gravity g is the property that single-handedly differentiates (a) planets from all other objects (and it leaves no room for questioning the demotion of Pluto), and (b) the six largest (g>1 m s−2) of the large satellites from dwarf planets. Large satellites are separated from small satellites by their sizes and masses/densities, which may serve as higher-order qualifiers for class membership. Size considerations are also sufficient for the classification of (i) main-belt asteroids (except possibly Ceres) as small solar-system bodies similar in physical properties to the small satellites; and (ii) a group of large Kuiper-belt objects as dwarf planets similar in physical properties to the large (but not the largest) satellites in our solar system. The selection criteria are simple and clear and reinforce the argument that body shape and environmental factors need not be considered in stipulating class membership of solar as well as extrasolar bodies.

Matrix representation of the graph model for conflict resolution based on intuitionistic preferences with applications to trans-regional water resource conflicts in the Lancang–Mekong River Basin

With the continual growth in global demand for water resources, the governance of trans-regional water resources has become an important field of cooperation between countries, and conflicts caused by competition for water resources have become a focal issue in international relations. The root causes of trans-regional water resource conflicts include unclear ownership of water resources and the limited rationality of the parties involved. The water rights trading model has proven to play a stabilizing role in resolving trans-regional water resource conflicts versus the traditional negotiation model. To demonstrate the rationality and theoretical strength of the water rights trading model in allocating trans-regional water resources in uncertain environments, this paper proposes a novel matrix representation of intuitionistic stability definitions through a graph model for conflict resolution (GMCR). First, decision-makers’ (DMs’) intuitionistic preferences, unilateral movements, and intuitionistic unilateral improvements in a GMCR with two DMs are represented in a matrix. The joint unilateral movements and joint intuitionistic unilateral improvements for a coalition in a GMCR with multiple DMs are also represented. Next, according to the logical forms of intuitionistic stability definitions, four stability definitions in a GMCR with intuitionistic preferences were redefined to enable matrix representations of graph models with either two DMs or multiple DMs. Finally, we analyzed the state transitions and strategies of all stakeholders in trans-regional water resource conflicts in the Lancang-Mekong River Basin within the intuitionistic graph model. The contributions of this paper are twofold. First, in terms of theoretical research, this article enriches and develops the GMCR and proposes a set of definitions of matrix intuitionistic stability. Second, in terms of practical application, the intuitionistic stability analysis results can provide a reference for water rights trading to solve trans-regional water resource conflicts in uncertain environments and transform trans-regional water resource governance systems.

A Privacy-Preserving Data Mining Through Comprehensive GNIPP Approach in Sensitive Data Sets

The quick growth of methods for analyzing data and the availability of easily available datasets have made it possible to build a thorough analytics model that can help with support decision-making. In the meantime, protecting personal privacy is crucial. A popular technique for medical evaluation and prediction, decision trees are easy to comprehend and interpret. However, the decision tree construction procedure may reveal personal information about an individual. By keeping the statistical properties intact and limiting the chance of privacy leaking within a reasonable bound, differential privacy offers a formal mathematical definition of privacy. To construct a boosting random forest that preserves privacy, we propose a Gaussian Noise Integrated Privacy Preservation (GNIPP) in this study. To address the issue of personal information breaches, we have designed a unique Gaussian distribution mechanism in GNIPP that enables the nodes with deeper depth to obtain more privacy during the decision tree construction process. We propose a comprehensive boosting technique based on the decision forest's prediction accuracy for assembling multiple decision trees into a forest. Furthermore, we propose an iterative technique to accelerate the assembly of decision trees. After all, we demonstrate through experimentation that the suggested GNIPP outperforms alternative algorithms on two real-world datasets.

Definite four-manifolds with exotic smooth structures

Abstract In this paper, we study smooth structures on closed, oriented four-manifolds with fundamental group Z / 2 ⁢ Z \mathbb{Z}/2\mathbb{Z} and definite intersection form. We construct infinitely many irreducible, oriented, closed, definite, smooth four-manifolds with π 1 = Z / 2 ⁢ Z \pi_{1}=\mathbb{Z}/2\mathbb{Z} and b 2 = 1 b_{2}=1 , and b 2 = 2 b_{2}=2 . As an application, we prove that, when the second Betti number b 2 b_{2} of a definite four-manifold with π 1 = Z / 2 ⁢ Z \pi_{1}=\mathbb{Z}/2\mathbb{Z} is positive and it admits a smooth structure, then it admits infinitely many smooth structures.

Public Authentic-Replica Sampling Mechanism in Distributed Storage Environments

With the rapid development of wireless communication and big data analysis technologies, the storage of massive amounts of data relies on third-party trusted storage, such as cloud storage. However, once data are stored on third-party servers, data owners lose physical control over their data, making it challenging to ensure data integrity and security. To address this issue, researchers have proposed integrity auditing mechanisms that allow for the auditing of data integrity on cloud servers without retrieving all the data. To further enhance the availability of data stored on cloud servers, multiple replicas of the original data are stored on the server. However, in existing multi-replica auditing schemes, there is a problem of server fraud, where the server does not actually store the corresponding data replicas. To tackle this issue, this paper presents a formal definition of authentic replicas along with a security model for the authentic-replica sampling mechanism. Based on time-lock puzzles, identity-based encryption (IBE) mechanisms, and succinct proof techniques, we design an authentic replica auditing mechanism. This mechanism ensures the authenticity of replicas and can resist outsourcing attacks and generation attacks. Additionally, our schemes replace the combination of random numbers and replica correspondence tables with Linear Feedback Shift Registers (LFSRs), optimizing the original client-side generation and uploading of replica parameters from being linearly related to the number of replicas to a constant level. Furthermore, our schemes allow for the public recovery of replica parameters, enabling any third party to verify the replicas through these parameters. As a result, the schemes achieve public verifiability and meet the efficiency requirements for authentic-replica sampling in multi-cloud environments. This makes our scheme more suitable for distributed storage environments. The experiments show that our scheme makes the time for generating copy parameters negligible while also greatly optimizing the time required for replica generation. As the amount of replica data increases, the time spent does not grow linearly. Due to the multi-party aggregation design, the verification time is also optimal. Compared to the latest schemes, the verification time is reduced by approximately 30%.

Teaching practice aimed at promoting student engagement with metarules of defining

By viewing students’ learning to define as learning about meta-discursive rules about defining and how to engage with them in their activity of defining, we investigated teaching practices that aim to promote such learning by analyzing a teaching experiment in which Calculus II students reinvented a formal definition of a limit. The teaching practices we identified addressed how students view defining tasks by providing a method to check whether their narratives satisfied the metarules that they aimed to follow and also provided guidance about how to revise their definitions to satisfy those metarules. Our results provide an example for the teaching practice that promotes student learning about and engagement with new meta-discursive rules that existing literature called for in general, especially in their reinvention of a formal definition of a mathematical object.

Critical Mass and Mature Equilibria for Two-Sided Platforms, and the Strength of the Externalities Between the Sides

Abstract Critical mass is central to the development of two-sided platforms. It is the level of participation on both sides that is required to have the platform grow on its own force to a mature equilibrium. Despite this commonly understood dynamic, a formal definition of critical mass is missing in the literature on two-sided platforms, except for a proposal by Evans and Schmalensee (2010. “Failure to Launch: Critical Mass in Platform Businesses.” Review of Network Economics 9 (4)) who defined critical mass not as a single combination of platform sizes, but as a frontier in the two-dimensional space of those levels. We set out a demand model for two-sided platforms, propose a measure for the strength of the externalities between the sides and define critical mass in terms of this externality parameter. Our definition is more in line with the way critical mass is defined for one-sided networks. We also set out the conditions that must be met for the occurrence of critical mass.

A distributed end-to-end fair bandwidth allocation algorithm for multi-path networks

Multi-path transmission significantly improves network performance, yet it complicates the problem of fair resource allocation. While traditional fair bandwidth allocation schemes thrive in single-path settings, they often falter when applied to multi-path environments, highlighting the challenge of achieving fair bandwidth sharing in such networks. To tackle this issue, the concept of "max-min similarity" of queuing delays has been introduced based on insight into the intrinsic interactions between queuing packets, delays, and bandwidth allocation, which leads to a formal definition of max-min fair bandwidth allocation for multi-path environments. Theoretical analysis shows that the max-min similarity of queuing delays is a sufficient condition for max-min fair bandwidth allocation in single bottleneck environments. A novel distributed end-to-end fair bandwidth allocation algorithm, named DMFBA, is then proposed, which separates the control into flow-level and transmission path-level. In achieving max-min similarity in queuing delays by dynamically adjusting the distribution of flows’ queuing packet quotas across paths it achieves the goal of max-min fair bandwidth allocation. Two sets of numerical simulation experiments were conducted and the results show that DMFBA has less overhead and faster convergence than the traditional utility fair algorithms.

Concluding remarks.

The Faraday Discussion on Correlated electronic structure took place from the 17th to the 19th of July 2024 in London, UK. The Discussion encompassed various facets of electron correlation, ranging from its formal definition and quantification to emerging frontiers in electronic structure theory, with applications in the solid state, integration with machine learning, and quantum computing.

Fuzzy Double S – Hausdorff Spaces

This study introduces and explores the concept of fuzzy double s-Hausdorff spaces within the field of fuzzy topology. Fuzzy double s-Hausdorff spaces extend the classical Hausdorff condition by incorporating two distinct fuzzy topologies on a single set, allowing for a more nuanced approach to separation where uncertainty and gradation are involved. The research develops formal definitions and characterizations of these spaces, establishing key theorems that outline their properties and behavior. In this article, a meaning of FDS -T2 remains presented through covering the description of S- T2 introduce by Srivastava [3] and obtain result analogues towards the result of S- T2.

Smart-KG: Partition-Based Linked Data Fragments for querying knowledge graphs

RDF and SPARQL provide a uniform way to publish and query billions of triples in open knowledge graphs (KGs) on the Web. Yet, provisioning of a fast, reliable, and responsive live querying solution for open KGs is still hardly possible through SPARQL endpoints alone: while such endpoints provide a remarkable performance for single queries, they typically can not cope with highly concurrent query workloads by multiple clients. To mitigate this, the Linked Data Fragments (LDF) framework sparked the design of different alternative low-cost interfaces such as Triple Pattern Fragments (TPF), that partially offload the query processing workload to the client side. On the downside, such interfaces still come with the expense of unnecessarily high network load due to the necessary transfer of intermediate results to the client, leading to query performance degradation compared with endpoints. To address this problem, in the present work, we investigate alternative interfaces, refining and extending the original TPF idea, which also aims at reducing server-resource consumption, by shipping query-relevant partitions of KGs from the server to the client. To this end, first, we align formal definitions and notations of the original LDF framework to uniformly present existing LDF implements and such “partition-based” LDF approaches. These novel LDF interfaces retrieve, instead of the exact triples matching a particular query pattern, a subset of pre-materialized, compressed, partitions of the original graph, containing all answers to a query pattern, to be further evaluated on the client side. As a concrete representative of partition-based LDF, we present smart-KG+, extending and refining our prior work (In WWW ’20: The Web Conference 2020 (2020) 984–994 ACM / IW3C2) in several respects. Our proposed approach is a step forward towards a better-balanced share of the query processing load between clients and servers by shipping graph partitions driven by the structure of RDF graphs to group entities described with the same sets of properties and classes, resulting in significant data transfer reduction. Our experiments demonstrate that the smart-KG+ significantly outperforms existing Web SPARQL interfaces on both pre-existing benchmarks for highly concurrent query execution as well as an accustomed query workload inspired by query logs of existing SPARQL endpoints.

Towards autonomous supply chains: Definition, characteristics, conceptual framework, and autonomy levels

Recent global disruptions, such as the COVID-19 pandemic and the ongoing geopolitical conflicts, have profoundly exposed vulnerabilities in traditional supply chains, requiring exploration of more resilient alternatives. Among various solution offerings, Autonomous supply chains (ASCs) have emerged as key enablers of increased integration and visibility, enhancing flexibility and resilience in turbulent trade environments through the widespread automation of low level decision making. Although ASC solutions have been discussed and trialled over several years, they still lack well-established theoretical foundations. This paper addresses this research gap by presenting a formal definition of ASC along with its defining characteristics and auxiliary concepts. We propose a layered conceptual framework, called the MIISI model. An illustrative case study focusing on the meat supply chain demonstrates an initial ASC implementation based on this conceptual model. Furthermore, we introduce a seven-level supply chain autonomy reference model, delineating a trajectory towards achieving full supply chain autonomy. Recognising that this work represents an initial endeavour, we emphasise the need for continued exploration in this emerging domain. This work is designed to stimulate further research, both theoretical and technical, and contribute to the continual evolution of ASCs.

On the set of values of a positive ternary quadratic form

It is shown that the set of values of an integer positive definite quadratic form in three variables contains an infinite arithmetic progression.

Curvature in plants

Curvatures are ubiquitous in the animal kingdom - the spiral shell of the nautilus and the corkscrew horns of the blackbuck being iconic examples. Dynamic changes in curvature (i.e., curving) are most striking in the locomotion of some animal species - swimming in fishes and mollusks, looping in leeches, undulatory locomotion in snakes and lampreys, and also sperm motility through flagellum beating. When it comes to plants, which are sessile organisms with a rigid body, the terms 'curvature' and 'curving' evoke very different images - leaves of grass swaying in the breeze, a trunk dangerously bent by a powerful gust of wind, a branch sagging under the weight of its own fruits, as well as the frail arabesques of twining plants like the morning glory and the ivy, which were so influential in the Art Nouveau movement and many other artistic traditions. These various vegetal curves not only prompt creative inspiration in the mind of the beholder, they also initiate signaling cascades leading to developmental responses of the plant. Conversely, curvature can result from a biologically active process in response to an internal or external stimulus. Active curving or decurving are indeed important aspects of the plastic interplay of the developmental program of plants and their environment. Although easily accessible to observation, curvature and curving have only recently become the focus of active research in plant development. Lying at the nexus of biology, physics and mathematics, they require an interdisciplinary approach. The aim of this primer is to give readers an intuitive but accurate understanding of what curvature and curving are, as observed in the plant kingdom, then a more formal definition. We will discuss their role in plant development, both as a signal and as a response, and finally the practical issues and solutions involved in measuring plant curvatures.

Além da costa: o papel da Seenemar na economia azul do Rio de Janeiro

This study analyzes the strategy of the State Secretary of Energy and Sea Economy (SEENEMAR) in promoting the blue economy in the State of Rio de Janeiro (ERJ), focusing on environmental and social sustainability. The analysis of projects, such as the Fishery Naval Hub and offshore wind energy, reveals significant contributions to economic growth, environmental sustainability, and social inclusion. SEENEMAR has shown effectiveness in job creation, attracting investments, and decarbonization, as well as promoting social inclusion through training programs and valuing sea gastronomy. However, the lack of a formal blue economy definition at the federal level may limit the expansion of these initiatives. This study suggests that the continuity and success of SEENEMAR’s policies depend on constant monitoring and adjustments based on empirical data.

Attribute-Based Designated Combiner Transitive Signature Scheme

Transitive signatures allow any entity to obtain a valid signature of (i,k) by combining signatures of (i,j) and (j,k). However, the traditional transitive signature scheme does not offer fine-grained control over the combiner. To address this issue, we propose a formal definition of the attribute-based designated combiner transitive signature (ABDCTS) and its security model, where only entities whose inherent attributes meet the access policy can combine signatures. By introducing the fine-grained access control structure, control over the combiner is achieved. To demonstrate the feasibility of our primitive, this paper presents the first attribute-based designated combiner transitive signature scheme. Under an adaptive chosen-message attack, we prove its security based on the one-more CDH problem and the co-CDH problem, and that its algorithms have robustness.

Text VS Discourse: Reformulating the Definition, Integrating Different Perceptions

There have long been different perceptions on what text and discourse are. Some experts in linguistics view these two objects as the same thing whereas others see them as two different forms. Occasionally, text and discourse are parallel to each other but often the former is seen as the subordinate of the latter and vice versa. This paper aimed at formulating new definitions of text and discourse in order to clarify the nature of each as well as the relations that may exist between them. The method applied in this study was by collecting as many as definitions of text and discourse as stated by linguistic experts and quoted in references. These data were then compared and contrasted to find out the similarities and the differences between the objects for drawing a conclusion in the form of definitions and descriptions that precisely represent the characteristics of each. The result shows that, text and discourse share both similarities and differences. At certain level, they can be seen as the same entity but in other conditions one may take position as part of the other.