Search results for: reciprocity theorems

Authors: A. T. Muruviwa

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To-date, the discourse on corporate social responsibility (CSR) has primarily centred on the actions and inactions of corporations; hence, the dominant focus on CSR has been on impacts and outcomes. The obscuring effect of this approach has, arguably, resulted in the emergence of what may be termed a ‘Northern’ agenda on CSR theory and practice, in contrast to an emergency ‘Southern’ discourse, which appears to highlight the crucial issues of poverty reduction, infrastructure development and the broader questions of social provisioning and community empowerment. Some scholars have explicitly called for a CSR research agenda that focuses on the 'reciprocal duties' of the stakeholders in the CSR process rather than fixate on the actions and inactions of business. It is against the backdrop of these contestations that this study assesses the reciprocal relationships amongst CSR stakeholders in a Zimbabwean platinum mining town, with a view to demonstrating how such relationships – and the expectations and obligations embedded in them – impact on the success or failure of CSR initiatives. The existence of mutual relations between the corporation and its stakeholders signifies the successes of CSR processes and hence the outcomes. The company is Zimplats Mining Company; the community is Mhondoro-Ngezi, and the stakeholders are clearly identified in the study. The study utilised a triangulated design, with data collected using a mini survey, focus groups, in-depth interview and observation. The key findings are that the CSR process in the study community is dominated by the mining company. Despite the existence of a CSR framework that recognises government, local leaders and community members as legitimate stakeholders, there is little evidence of concrete contributions made by these stakeholders towards the realisation of CSR objectives. As a result, the community development process – in so far as CSR is concerned – fails to address the developmental concerns of the various stakeholders. On the basis of these findings, the study concludes that there is a crisis of reciprocity in the CSR process in Mhondoro-Ngezi, and that a situation where the conceptualisation of local development needs and the deployment of specific development tools seems to be driven by one stakeholder almost to the exclusion of all others, can only present contradictory development outcomes. The significance of this study is that it allows for the development of a more nuanced and robust CSR discourse. Rather than focusing on the corporate and stakeholder perspectives and outcomes of CSR initiatives, this study examines the CSR- development nexus by interrogating the idea of reciprocal responsibility as a sin qua non to CSR success. This analytical strategy and focus allow the researcher to gain a clear understanding of how stakeholder relationships and duties influence CSR processes and also the overall outcome. At a more practical level, the findings of the study should help to shape the policy on corporate community relationships with a view to enhancing the role of mining in development.

Keywords: community development, processes, reciprocity, stakeholders

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: Yuanxiang Miao

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This paper aims to examine the perceptual features of couchsurfers on a new hospitality tourism platform, the free homestay website couchsurfing. As a local host, the author has accepted 61 couchsurfers in Kyoto, Japan, and attempted to figure out couchsurfers' characteristics on perception by hosting them. Moreover, the methodology of this research is mainly based on in-depth interviews, by talking with couchsurfers, observing their behaviors, doing questionnaires, etc. Five dominant perceptual features of couchsurfers were identified: (1) Trusting; (2) Meeting; (3) Sharing; (4) Reciprocity; (5) Worries. The value of this research lies in figuring out a deeper understanding of the perceptual features of couchsurfers, and the author indeed hosted and stayed with 61 couchsurfers from 30 countries and areas over one year. Lastly, the author offers practical suggestions for future research.

Keywords: couchsurfing, depth interview, hospitality tourism, perceptual features

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Authors: Elham Kiyani

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In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Atje Setiawan Abdullah, Budi Nurani Ruchjana, I. Gede Nyoman Mindra Jaya, Eddy Hermawan

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Ethnoscience is used to see the culture with a scientific perspective, which may help to understand how people develop various forms of knowledge and belief, initially focusing on the ecology and history of the contributions that have been there. One of the areas studied in ethnoscience is etno-informatics, is the application of informatics in the culture. In this study the science of informatics used is data mining, a process to automatically extract knowledge from large databases, to obtain interesting patterns in order to obtain a knowledge. While the application of culture described by naming database village on the island of Java were obtained from Geographic Indonesia Information Agency (BIG), 2014. The purpose of this study is; first, to classify the naming of the village on the island of Java based on the structure of the word naming the village, including the prefix of the word, syllable contained, and complete word. Second to classify the meaning of naming the village based on specific categories, as well as its role in the community behavioral characteristics. Third, how to visualize the naming of the village to a map location, to see the similarity of naming villages in each province. In this research we have developed two theorems, i.e theorems area as a result of research studies have collected intersection naming villages in each province on the island of Java, and the composition of the wedge theorem sets the provinces in Java is used to view the peculiarities of a location study. The methodology in this study base on the method of Knowledge Discovery in Database (KDD) on data mining, the process includes preprocessing, data mining and post processing. The results showed that the Java community prioritizes merit in running his life, always working hard to achieve a more prosperous life, and love as well as water and environmental sustainment. Naming villages in each location adjacent province has a high degree of similarity, and influence each other. Cultural similarities in the province of Central Java, East Java and West Java-Banten have a high similarity, whereas in Jakarta-Yogyakarta has a low similarity. This research resulted in the cultural character of communities within the meaning of the naming of the village on the island of Java, this character is expected to serve as a guide in the behavior of people's daily life on the island of Java.

Keywords: ethnoscience, ethno-informatics, data mining, clustering, Java island culture

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Authors: Saulius Minkevicius, Edvinas Greicius

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The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. We investigate the inequality in an open queueing network and its applications to the theorems in heavy traffic conditions (fluid approximation, functional limit theorem, and law of the iterated logarithm) for a queue of customers in an open queueing network.

Keywords: fluid approximation, heavy traffic, models of information systems, open queueing network, queue length of customers, queueing theory

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Shih-Yan Chen, Shin-Shin Kao

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In this paper, a thorough review about dual-cubes, DCn, the related studies and their variations are given. DCn was introduced to be a network which retains the pleasing properties of hypercube Qn but has a much smaller diameter. In fact, it is so constructed that the number of vertices of DCn is equal to the number of vertices of Q2n +1. However, each vertex in DCn is adjacent to n + 1 neighbors and so DCn has (n + 1) × 2^2n edges in total, which is roughly half the number of edges of Q2n+1. In addition, the diameter of any DCn is 2n +2, which is of the same order of that of Q2n+1. For selfcompleteness, basic definitions, construction rules and symbols are provided. We chronicle the results, where eleven significant theorems are presented, and include some open problems at the end.

Keywords: dual-cubes, dual-cube extensive networks, dual-cube-like networks, hypercubes, fault-tolerant hamiltonian property

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Authors: Mojtaba Hakimi-Moghaddam

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Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Qing Hui Wang, You Lin Fang, Min Chen

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In 2003 the percentage of students in Shanghai taking part in tertiary education reached 53% of the age cohort, which is at the universal level according to Trow's typology. This achievement led to a conscientious effort by the government to improve internal efficiency of local universities and colleges through a series of programs, the most important of which is the 085 Project. This paper considers the effects of the 085 Project- the 5 initiatives launched in 2008 on increasing the investment to improve institutional overall visibilities, teaching excellence, knowledge innovation, faculty development as well as internationalization. Using the approach of ERC (a theory of equality, reciprocity, and competition) model, it was found that the initiatives helped the lower tier universities and colleges make full play in the aspects of strategic planning and identifying themselves. It was also found that the rate of growth of social resources for universities as a whole increased more quickly after the implementation of the 085 Project.

Keywords: 085 Project, impact, internal efficiency, local universities and colleges

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: asymptotics, continuous spectrum, difference equations, eigenvalues, jost functions, spectral singularities

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Cheng Xu, Rui Zhong

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Utilizing a preregistered randomized experiment, this study explores the effects of anonymity and curated identity on trust within the Metaverse. Participants were randomly assigned to different conditions of anonymity and identity curation and engaged in a series of tasks designed to mirror the complexities of trust in real-world social interactions. Trust was measured using the classical trust game, allowing for a nuanced understanding of how these factors interact and influence trust. The findings reveal that higher levels of anonymity negatively impact trust, while identity curation can moderate this effect. Mechanism analysis uncovers how anonymity influences perceived reciprocity and group cohesion, and how curation can moderate these relationships. The results demonstrate a nuanced interaction between anonymity and trust, with variations across different curation levels. These insights provide a multifaceted understanding of trust within virtual environments, contributing valuable knowledge to the design, policy-making, and ethical considerations of the Metaverse

Keywords: metaverse, anonymity, curated identity, social behavior, trust

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Authors: A. Giniatoulline

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A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Lola Rosalia Saavedra Guzman, Plamen Neytchev Netchev

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In general, agnosticism is perceived as an uncertainty between a well-structured (religious) belief (in some Christian or pagan deity) and its absolute and total absence, often causing the suspicion that an agnostic is an atheist, which is "reinsured" in case if their personal belief is wrong. All of this, along with the prevailing view among the naturalists that science has already demonstrated the inexistence of God, has compelled us to seek the foundation of agnosticism and faith in the contemporary formal human logic, advanced mathematics, and the natural sciences. Along the way, we will find that no natural science can demonstrate the existence of God, nor could it discard it for rational considerations, which show that there is something beyond. After all, it seems that the human intellect is insufficient to respond surely with yes or no to the existence of higher intelligences leaving unconditional faith as the only path to God for Christians and transcendent techniques, for pagan religious beliefs.

Keywords: agnosticism, formal logic, axioms and postulates, Gödel theorems, and logical faults

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Authors: Yongsheng Guo, Mengyu Lu

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This study investigates how Chinese SMEs manage financial risks in customer financing. 32 interviews were conducted, and grounded theory models were developed to link the causal conditions, actions, and consequences. This study found that Chinese ethical principles, including integrity, friendship, reciprocity, and cultural traits, including collectivism, acquaintance society, and long-term orientation, provide conditions for customer financing. The SMEs establish trust-based relationships with customers and build a social network. The SMEs reduce financial risk through diversification, frequent operations and enterprise reputations. Both customers and SMEs can get benefits, including customer experience and financial rewards for customers and financial resources and customer base for SMEs. But there are some problems, like default for customers and financial cost for enterprises. This study develops a resource and process capability theory of SMEs and a customer capital and customer value theory to connect finance, accounting, and management concepts.

Keywords: CRM, culture, ethics, financing from customer, SME

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Authors: František Včelař, Zuzana Pátíková

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Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Keywords: fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity

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Authors: Fariba Ebrahimi, Mehdi Ghorbani

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Achieving to integrated Water management fundamentally needs to effective relation, coordination, collaboration and synergy among various actors who have common but different responsibilities. In this sense, the foundation of comprehensive and integrated management is not compatible with centralization and top-down strategies. The aim of this paper is analysis institutional network of water relevant stakeholders and water policy monitoring in Shemiranat. In this study collaboration networks between informal and formal institutions co-management process have been investigated. Stakeholder network analysis as a quantitative method has been implicated in this research. The results of this study indicate that institutional cohesion is medium; sustainability of institutional network is about 40 percent (medium). Additionally the core-periphery index has measured in this study according to reciprocity index. Institutional capacities for integrated natural resource management in regional level are measured in this study. Furthermore, the necessity of centrality reduction and promote stakeholders relations and cohesion are emphasized to establish a collaborative natural resource governance.

Keywords: policy monitoring, water management, social network, stakeholder, shemiranat

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: C. Caudwell, R. Syed, C. Lacey

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While the development and advancement of information communication technologies (ICTs) offers powerful opportunities for meaningful connections and relationships, shame is a significant barrier to social and cultural acceptance. In particular, artificial intelligence and socially oriented robots are increasingly becoming partners in romantic relationships with people, offering bonding, support, comfort, growth, and reciprocity. However, these relationships suffer hierarchical, anthropocentric shame that is a significant barrier to their success and longevity. This paper will present case studies of human and artificially intelligent agent relationships, in the context of internal and external shame, as cultivated, propagated, and communicated through ICT. Using an interdisciplinary methodology we aim to present a framework for technological shame, building on the experimental and emergent psychoanalytical theories of emotions. Our study finds principally that socialization is a powerful factor in the vectors of shame as experienced by humans. On a wider scale, we contribute understanding of social emotion and the phenomenon of shame proliferated through ICTs, which is at present under-explored, but vital, as society and culture is increasingly mediated through this medium.

Keywords: shame, artificial intelligence, romance, society

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Authors: Ren Guangchun

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The village in the city is surrounded by formal cities but retains distinct social and morphological characteristics of the countryside, and has the ability of self-growth. County is the basic unit of urban-rural integration development, and urban village is the key focus of integration. At present, the flow of urban and rural factors in Chongqing does not match the development needs of urban villages. Based on the multi-case study of Chongqing 's districts and counties, this paper studies the characteristics of its geospatial advantages, composite functions, open spatial structure, pluralistic social structure, and reciprocity. From the aspects of community governance, social relations and space construction, this paper analyzes the dilemma of lack of subjectivity and social atomization faced by the interaction between urban villages and cities, and explores the strategies of community opening and social integration in urban villages, so as to present diversified landscapes and value spaces.

Keywords: gated community, open community, city update, Urban village

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Authors: Paola Cattabriga

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According to Gödel’s first incompleteness argument it is possible to construct a formally undecidable proposition in Principia mathematica, a statement that, although true, turns out to be neither provable nor refutable for the system, making therefore incomplete any formal system suitable for the arithmetic of integers. Its features and limitation effects are today widespread basics throughout whole scientific thought. This article brings Gödel’s achievement into question by the definition of the refutability predicate as a number-theoretical statement. We develop proof of invalidity of Theorem VI in Gödel’s 1931, the so-called Gödel’s first incompleteness theorem, in two steps: defining refutability within the same recursive status as provability and showing that as a consequence propositions (15) and (16), derived from definition 8.1 in Gödel’s 1931, are false and unacceptable for the system. The achievement of their falsity blocks the derivation of Theorem VI, which turns out to be therefore invalid, together with all the depending theorems. This article opens up thus new perspectives for mathematical research and for the overall scientific reasoning.

Keywords: Gödel numbering, incompleteness, provability predicate, refutability predicate

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Authors: Tabrej Khan, Tamer A. Sebaey, Balbir Singh, M. A. Umarfarooq

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Spread-tow thin-ply-based technology has resulted in the progress of optimized reinforced composite plies with ultra-low thicknesses. There is wide use of composite bolted joints in the aircraft industry for load-bearing structures, and they are regarded as the primary source of stress concentration. The purpose of this study is to look into the bearing strength and structural performance of single shear bolt joint configurations in composite laminates, which are basically a combination of conventional thin-plies and thick-plies in some specific stacking sequence. The placement effect of thin-ply within the configured stack on bearing strength, as well as the potential damages, were investigated. Mechanical tests were used to understand the disfigurement mechanisms of the plies and their reciprocity, as well as to reflect on the single shear bolt joint properties and its load-bearing capacity. The results showed that changing the configuration of laminates by inserting the thin plies inside improved the bearing strength by up to 19%.

Keywords: hybrid composites, delamination, stress concentrations, mechanical testing, single bolt joint, thin-plies

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Authors: Manita Ale, Ganesh P. Shivakoti, Ram C. Bastakoti

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Irrigation system, a system for enhancing agricultural productivity, requires regular maintenance in order to avoid irregular allocation of water. For maintenance of the system in long run, farmers’ participation plays a key role increasing the performance of system. The performance of any irrigation system mainly relies on various factors which affect collective action plus decision making, as well as their shared impacts. The paper consists of system level information that were collected from 12 Irrigation Systems (IS) from three-sampled districts of Nepal and the household information that were collected from 160 irrigation water users. The results reveal that, out of 12 sampled irrigation systems, only 4 systems shows high performance levels. The high performance level of those systems was characterized on the basis of adequate availability of water, good maintenance of system infrastructure, and conformance to existing rules followed. In addition, the paper compares different irrigation systems based on trust, reciprocity, cropping intensity, command area and yield as tools to indicate the importance of collective action in performance of irrigation system.

Keywords: collective action, decision-making, farmers’ participation, performance

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Manuel Urueña Palomo

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In this paper, we introduce the study of a new solution to gravitational singularities by violating the energy conditions of the Penrose Hawking singularity theorems. We consider that a shift to negative energies, and thus, to negative masses, takes place at the event horizon of a black hole, justified by the original, singular and exact Schwarzschild solution. These negative energies are supported by relativistic particle physics considering the negative energy solutions of the Dirac equation, which states that a time transformation shifts to a negative energy particle. In either general relativity or full Newtonian mechanics, these negative masses are predicted to be repulsive. It is demonstrated that the model fits actual observations, and could possibly clarify the size of observed and unexplained supermassive black holes, when considering the inflation that would take place inside the event horizon where massive particles interact antigravitationally. An approximated solution of the model proposed could be simulated in order to compare it with these observations.

Keywords: black holes, CPT symmetry, negative mass, time transformation

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: engineering education, errors, limits, mathematics competences, problem solving

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Authors: Ahmed Tarek, Ahmed Alveed

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In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

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Authors: Po-Yuan Tung, Jen-Chueh Kuo, Chia-Ray Chen, Chien-Hsing Li, Kuo-Liang Pan

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The main-body structure of satellite is mainly constructed by lightweight material, it should be able to withstand certain vibration load during launches. Since various kinds of change possibility in the space, it is an extremely important work to study the random vibration response of satellite structure. This paper based on the reciprocity relationship between sound and structure response and it will try to evaluate the dynamic response of satellite main body under random acoustic load excitation. This paper will study the technical process and verify the feasibility of sonic-borne vibration analysis. One simple plate exposed to the uniform acoustic field is utilized to take some important parameters and to validate the acoustics field model of the reverberation chamber. Then import both structure and acoustic field chamber models into the vibro-acoustic coupling analysis software to predict the structure response. During the modeling process, experiment verification is performed to make sure the quality of numerical models. Finally, the surface vibration level can be calculated through the modal participation factor, and the analysis results are presented in PSD spectrum.

Keywords: vibration, acoustic, modal, honeycomb panel

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