Search results for: isomorphism and homomorphism

Authors: Hussain Abdullah Al-Salamin, Elias Ogutu Azariah Tembe

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Supply chain (SC) is an operational research (OR) approach and technique which acts as catalyst within central nervous system of business today. Without SC, any type of business is at doldrums, hence entropy. SC is the lifeblood of business today because it is the pivotal hub which provides imperative competitive advantage. The paper present a conceptual framework dubbed as Homomorphic Conceptual Framework for Effective Supply Chain Strategy (HCEFSC).The term homomorphic is derived from abstract algebraic mathematical term homomorphism (same shape) which also embeds the following mathematical application sets: monomorphism, isomorphism, automorphisms, and endomorphism. The HCFESC is intertwined and integrated with wide and broad sets of elements.

Keywords: homomorphism, isomorphism, monomorphisms, automorphisms, epimorphisms, endomorphism, supply chain, operational research (OR)

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Authors: Chuluundorj Begz

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This paper presents the dynamic, psycho-cognitive approach to study of human verbal thinking on the basis of typologically different languages /as a Mongolian, English and Russian/. Topological equivalence in verbal communication serves as a basis of Universality of mental structures and therefore deep structures. Mechanism of verbal thinking consisted at the deep level of basic concepts, rules for integration and classification, neural networks of vocabulary. In neuro cognitive study of language, neural architecture and neuro psychological mechanism of verbal cognition are basis of a vector-based modeling. Verbal perception and interpretation of the infinite set of meanings and propositions in mental continuum can be modeled by applying tensor methods. Euclidean and non-Euclidean spaces are applied for a description of human semantic vocabulary and high order structures.

Keywords: Euclidean spaces, isomorphism and homomorphism, mental lexicon, mental mapping, semantic memory, verbal cognition, vector space

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Authors: Muna Tabuni

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The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

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Authors: Catalina Florentina Pricope

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The last two decades witnessed a movement towards harmonization of international financial reporting standards (IFRS) throughout the global economy. This investigation seeks to identify the factors that could explain the adoption of IFRS by poor jurisdictions. While there has been a considerable amount, of literature published on the effects and key drivers of IFRS adoption in both developed and developing countries, little attention has been paid to jurisdictions with less developed capital markets and low-income levels exclusively. Drawing upon the Institutional Isomorphism theory and analyzing a sample of 45 poor jurisdictions between 2008 and 2013, the study empirically shows that poor jurisdictions are driven by legitimacy concerns rather than by economic reasoning to adopt an international accounting perspective. This in turn has implications for the IASB, as it should seek to influence institutional pressures within a particular jurisdiction in order to promote IFRS adoption.

Keywords: IFRS adoption, isomorphism, poor jurisdictions, accounting harmonization

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Authors: Yuhong Zhang, Dan Lu, Chenyang Bu, Peipei Li, Kui Yu, Xindong Wu

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The Cross-Lingual Entity Alignment (CLEA) task aims to find the aligned entities that refer to the same identity from two knowledge graphs (KGs) in different languages. It is an effective way to enhance the performance of data mining for KGs with scarce resources. In real-world applications, the neighborhood structures of the same entities in different KGs tend to be non-isomorphic, which makes the representation of entities contain diverse semantic information and then poses a great challenge for CLEA. In this paper, we try to address this challenge from two perspectives. On the one hand, the cross-KG relation completion rules are designed with the alignment constraint of entities and relations to improve the topology isomorphism of two KGs. On the other hand, a representation method combining isomorphic weights is designed to include more isomorphic semantics for counterpart entities, which will benefit the CLEA. Experiments show that our model can improve the isomorphism of two KGs and the alignment performance, especially for two non-isomorphic KGs.

Keywords: knowledge graphs, cross-lingual entity alignment, non-isomorphic, relation completion

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Authors: Xiuzhan Guo, Arthur Berrill, Ajinkya Kulkarni, Kostya Belezko, Min Luo

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Ontology operations, e.g., aligning and merging, were studied and implemented extensively in different settings, such as categorical operations, relation algebras, and typed graph grammars, with different concerns. However, aligning and merging operations in the settings share some generic properties, e.g., idempotence, commutativity, associativity, and representativity, labeled by (I), (C), (A), and (R), respectively, which are defined on an ontology merging system (D~M), where D is a non-empty set of the ontologies concerned, ~ is a binary relation on D modeling ontology aligning and M is a partial binary operation on D modeling ontology merging. Given an ontology repository, a finite set O ⊆ D, its merging closure Ô is the smallest set of ontologies, which contains the repository and is closed with respect to merging. If (I), (C), (A), and (R) are satisfied, then both D and Ô are partially ordered naturally by merging, Ô is finite and can be computed, compared, and sorted efficiently, including sorting, selecting, and querying some specific elements, e.g., maximal ontologies and minimal ontologies. We also show that the ontology merging system, given by ontology V -alignment pairs and pushouts, satisfies the properties: (I), (C), (A), and (R) so that the merging system is partially ordered and the merging closure of a given repository with respect to pushouts can be computed efficiently.

Keywords: ontology aligning, ontology merging, merging system, poset, merging closure, ontology V-alignment pair, ontology homomorphism, ontology V-alignment pair homomorphism, pushout

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Authors: Matteo Manera, Mariateresa Torchia, Gregory Moscato

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Forensic accounting is a hot subject of research in accounting. Valuation remains one of the major topics for practitioners. Valuation standards are a powerful instrument that can contribute to a fair process: their use aims at reducing subjectivity and arbitrary decisions in courts. In most jurisdictions, valuation standards are not the law: forensic accountants are not obliged to use valuation standards when they perform valuation works for judges. To date, as far as we know, no literature work has investigated adoption and diffusion of valuation standards in the forensic accounting space. In this paper, we analyze the spread of valuation standards through the lenses of isomorphism and -as corollaries- of Agency Theory and Signaling Theory. Because of lack of research in the particular area of valuation standards adoption, the present work relies on qualitative, exploratory research, based on semi-structured interviews conducted (up to saturation) with expert forensic accountants. Our work digs into motivations behind adoption and diffusion, as well into perceptions of forensic accountants around benefits of valuation standards and into barriers to their diffusion: the result is that, while the vast majority of forensic accountants praise the great work of the standards setters in introducing valuation standards, it might be that less than 50% of forensic accountants actually use valuation standards, in courts. Our preliminary findings, to be supported or refuted by future research, lead us to address a “trilogy” of recommendations to the stakeholders involved in the process of adoption and diffusion of valuation standards in courts.

Keywords: forensic accounting, valuation standards, adoption of standards, motivations, benefits, barriers, Isomorphism

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Authors: Tomáš Bublík, Miroslav Virius

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This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and sub graph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

Keywords: AST, Java, tree matching, scripthon source code recognition

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Authors: Yousuf Alkhezi

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Since most of the literature on algebra does not make much deal with the special case of mapping cone. This paper is an alternative way to examine the special tensor product and mapping cone. Also, we show that the isomorphism that implies the mapping cone commutes with the tensor product for the ordinary tensor product no longer holds for the pinched tensor product. However, we show there is a morphism. We will introduce an alternative way of mapping cone. We are looking for more properties which is our future project. Also, we want to apply these new properties in some application. Many results and examples with classical algorithms will be provided.

Keywords: complex, tensor product, pinched tensore product, mapping cone

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Authors: Bian ChengXiang, Wang Qian

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With the deepening of the research on the connotation of cultural heritage and human geography, the cultural landscape takes landscape as a cultural product, integrates and blends cultural and natural heritage to explore the cultural value behind its material landscape. Qikou ancient town is a typical traditional settlement with a homomorphism of mountain and water veins. Its cultural accumulation and natural landscape play an important role in its development. Therefore, this paper will combine the material and cultural elements of Qikou ancient town to analyze the composition of the cultural landscape of the ancient town and explore the protection and utilization of the cultural landscape of Qikou ancient town from the four aspects of ecology, form, cultural form, and business form, so as to provide effective strategies for the development of the ancient town.

Keywords: four state, cultural landscape, ancient town, protection, development

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Authors: Inayatur Rehman

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Molodtstove developed the theory of soft sets which can be seen as an effective tool to deal with uncertainties. Since the introduction of this concept, the application of soft sets has been restricted to associative algebraic structures (groups, semi groups, associative rings, semi-rings etc.). Acceptably, though the study of soft sets, where the base set of parameters is a commutative structure, has attracted the attention of many researchers for more than one decade. But on the other hand there are many sets which are naturally endowed by two compatible binary operations forming a non-associative ring and we may dig out examples which investigate a non-associative structure in the context of soft sets. Thus it seems natural to apply the concept of soft sets to non-commutative and non-associative structures. In present paper, we make a new approach to apply Molodtsoves notion of soft sets to LA-ring (a class of non-associative ring). We extend the study of soft commutative rings from theoretical aspect.

Keywords: soft sets, LA-rings, soft LA-rings, soft ideals, soft prime ideals, idealistic soft LA-rings, LA-ring homomorphism

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Authors: Ben D. Atkins

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This study will examine the impact of September 11, 2001, terrorist attacks on the organizational development of American federal law enforcement through focusing on the Federal Bureau of Investigation. Content analysis of discourse in a federal law enforcement practitioner publication along with official FBI statements will be used to gain a better understanding of FBI organizational changes that have taken place since the events of September 11, 2001. Analysis of content trends in the FBI Law Enforcement Bulletin and public discourse of FBI officials from 1999 to 2005 indicate that, in addition to structural changes, the bureau has also undergone a variety of cultural changes. The results offer some support for the institutional theoretical perspective, suggesting that post-9/11 organizational changes such as new mission priorities and the establishment of new branches were partially initiated due to a variety external pressures, which lends support for coercive isomorphism. Furthermore, structural changes are discussed in relation to the attainment and maintenance of organizational legitimacy.

Keywords: institutional theory, organizational theory, law enforcement, public administration

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Authors: Giulia Leoni, Cristina Florio

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The paper aims to investigate the factors driving the increasing alignment of Italian earnings management (EM) research to US research on the same field. After characterizing the progressive similarity of Italian EM research with respect to US one by means of an historical comparison, the paper relies on a subsequent secondary source analysis to detect the possible causes of said alignment. Once identified that the alignment increased along three subsequent periods, the paper analyses and discusses this incremental similarity according to new institutional sociology (NIS) and highlights the presence of different combination of isomorphic pressures that help explaining this incremental similarity. The paper contributes to the institutional literature by providing evidence of isomorphism in academic research; it also contributes to accounting research by indicating the forces that are able to drive change and development in accounting research at national and international level. The paper also enlarges the explanatory value of NIS in alternative contexts, like academic accounting research.

Keywords: accounting research, earnings management, international comparison, Italy, new institutional sociology, US

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Authors: Tao Feng, Xiaomei Ma, Xian Guo, Jing Wang

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Named Data Network (NDN) is one of the future Internet architecture, all nodes (i.e., hosts, routers) are allowed to have a local cache, used to satisfy incoming requests for content. However, depending on caching allows an adversary to perform attacks that are very effective and relatively easy to implement, such as content pollution attack. In this paper, we use a method of secure network coding based on homomorphic signature system to solve this problem. Firstly ,we use a dynamic public key technique, our scheme for each generation authentication without updating the initial secret key used. Secondly, employing the homomorphism of hash function, intermediate node and destination node verify the signature of the received message. In addition, when the network topology of NDN is simple and fixed, the code coefficients in our scheme are generated in a pseudorandom number generator in each node, so the distribution of the coefficients is also avoided. In short, our scheme not only can efficiently prevent against Intra/Inter-GPAs, but also can against the content poisoning attack in NDN.

Keywords: named data networking, content polloution attack, network coding signature, internet architecture

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Authors: Eleonora Sasso

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This paper takes as its starting point the notions of cognitive linguistics and lexical blending, and uses both these theoretical concepts to advance a new reading of Margaret Atwood’s latest writings, one which sees them as paramount literary examples of norm and usage in bilingual Canadian lexicography. Atwood’s prose seems to be imbued with Canadianisms and neologisms, lexical blends of zoomorphic forms, a kind of meeting-point between two conceptual structures which follow the principles of lexical economy and asyntactic relation. Atwood’s neologisms also attest to the undeniable impact on language exerted by Canada’s aboriginal peoples. This paper aims to track through these references and with the aid of the Eskimo-English dictionary look at the linguistic issues – attitudes to contaminations and hybridisations, questions of lexical blending in literary examples, etc – which they raise. Atwood’s fiction, whose cognitive linguistic strategy employs ‘the virtues of scissors and matches’, always strives to achieve isomorphism between word form and concept.

Keywords: Atwood, Canadianisms, cognitive science, Eskimo/English dictionary

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Authors: Swati Kishor Zode, Rahul Ambekar

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Data mining is the extraction of fascinating examples on the other hand information from enormous measure of information and choice is made as indicated by the applicable information extracted. As of late, with the dangerous advancement in internet, stockpiling of information and handling procedures, privacy preservation has been one of the major (higher) concerns in data mining. Various techniques and methods have been produced for protection saving data mining. In the situation of Clinical Decision Support System, the choice is to be made on the premise of the data separated from the remote servers by means of Internet to diagnose the patient. In this paper, the fundamental thought is to build the precision of Decision Support System for multiple diseases for different maladies and in addition protect persistent information while correspondence between Clinician side (Client side) also, the Server side. A privacy preserving protocol for clinical decision support network is proposed so that patients information dependably stay scrambled amid diagnose prepare by looking after the accuracy. To enhance the precision of Decision Support System for various malady C5.0 classifiers and to save security, a Homomorphism encryption algorithm Paillier cryptosystem is being utilized.

Keywords: classification, homomorphic encryption, clinical decision support, privacy

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Authors: Ezgi Kaya, A. Dilek Maden

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A topological index is a number related to graph which is invariant under graph isomorphism. In theoretical chemistry, molecular structure descriptors (also called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds. Let G be a graph with n vertices and m edges. For a given edge uv, the quantity nu(e) denotes the number of vertices closer to u than v, the quantity nv(e) is defined analogously. The vertex PI index defined as the sum of the nu(e) and nv(e). Here the sum is taken over all edges of G. The energy of a graph is defined as the sum of the eigenvalues of adjacency matrix of G and the Laplacian energy of a graph is defined as the sum of the absolute value of difference of laplacian eigenvalues and average degree of G. In theoretical chemistry, the π-electron energy of a conjugated carbon molecule, computed using the Hückel theory, coincides with the energy. Hence results on graph energy assume special significance. The Laplacian matrix of a graph G weighted by the vertex PI weighting is the Laplacian vertex PI matrix and the Laplacian vertex PI eigenvalues of a connected graph G are the eigenvalues of its Laplacian vertex PI matrix. In this study, Laplacian vertex PI energy of a graph is defined of G. We also give some bounds for the Laplacian vertex PI energy of graphs in terms of vertex PI index, the sum of the squares of entries in the Laplacian vertex PI matrix and the absolute value of the determinant of the Laplacian vertex PI matrix.

Keywords: energy, Laplacian energy, laplacian vertex PI eigenvalues, Laplacian vertex PI energy, vertex PI index

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: M. Helen

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Chemical graph serves as a convenient model for any real or abstract chemical system. Dendrimers are novel three dimensional hyper branched globular nanopolymeric architectures. Drug delivery scientists are especially enthusiastic about possible utility of dendrimers as drug delivery tool. Dendrimers like poly L lysine (PLL), poly-propylene imine (PPI) and poly-amidoamine (PAMAM), etc., are used as gene carrier in drug delivery system because of their chemical characteristics. These characteristics of chemical compounds are analysed using topological indices (invariants under graph isomorphism) such as Wiener index, Zagreb index, etc., Prof. V. R. Kulli motivated by the application of Zagreb indices in finding the total π energy and derived Gourava indices which is an improved version over Zagreb indices. In this paper, we study the structure of PLL-Dendrimer that has the following applications: reduction in toxicity, colon delivery, and topical delivery. Also, we determine first and second Gourava indices, first and second hyper Gourava indices, product and sum connectivity Gourava indices for PLL-Dendrimer. Gourava Indices have found applications in Quantitative Structure-Property Relationship (QSPR)/ Quantitative Structure-Activity Relationship (QSAR) studies.

Keywords: connectivity Gourava indices, dendrimer, Gourava indices, hyper GouravaG indices

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Authors: Asraful Islam

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Extended dependency graph (EDG) is a state-of-the-art isomorphic graph to represent normal logic programs (NLPs) that can characterize the consistency of NLPs by graph analysis. To construct the vertices and arcs of an EDG, additional renaming atoms and rules besides those the given program provides are used, resulting in higher space complexity compared to the corresponding traditional dependency graph (TDG). In this article, we propose an extended labeled dependency graph (ELDG) to represent an NLP that shares an equal number of nodes and arcs with TDG and prove that it is isomorphic to the domain program. The number of nodes and arcs used in the underlying dependency graphs are formulated to compare the space complexity. Results show that ELDG uses less memory to store nodes, arcs, and cycles compared to EDG. To exhibit the desirability of ELDG, firstly, the stable models of the kernel form of NLP are characterized by the admissible coloring of ELDG; secondly, a relation of the stable models of a kernel program with the handles of the minimal, odd cycles appearing in the corresponding ELDG has been established; thirdly, to our best knowledge, for the first time an inverse transformation from a dependency graph to the representing NLP w.r.t. ELDG has been defined that enables transferring analytical results from the graph to the program straightforwardly.

Keywords: normal logic program, isomorphism of graph, extended labelled dependency graph, inverse graph transforma-tion, graph colouring

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Authors: Rabiaal Adawiyah Shazali, Corina Joseph

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The disclosure of Intellectual Capital (IC) information is getting more vital in today’s era of a knowledge-based economy. Companies are advised by accounting bodies to enhance IC disclosure which complements the conventional financial disclosures. There are no accounting standards for Intellectual Capital Disclosure (ICD), therefore the disclosure is entirely voluntary. Hence, this study aims to investigate the extent of ICD and to examine the relationship between corporate governance and ICD in Malaysia. This study employed content analysis of 100 annual reports by the top 100 public listed companies in Malaysia during 2012. The uniqueness of this study lies on its underpinning theory used where it applies the institutional isomorphism theory to support the effect of the attributes of corporate governance towards ICD. In order to achieve the stated objective, multiple regression analysis were employed to conduct this study. From the descriptive statistics, it was concluded that public listed companies in Malaysia have increased their awareness towards the importance of ICD. Furthermore, results from the multiple regression analysis confirmed that corporate governance affects the company’s ICD where the frequency of audit committee meetings and the board size has positively influenced the level of ICD in companies. Findings from this study would provide an incentive for companies in Malaysia to enhance the disclosure of IC. In addition, this study would assist Bursa Malaysia and other regulatory bodies to come up with a proper guideline for the disclosure of IC.

Keywords: annual report, content analysis, corporate governance, intellectual capital disclosure

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Authors: P. G. Romeo

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A Lie group is a highly sophisticated structure which is a smooth manifold whose underlying set of elements is equipped with the structure of a group such that the group multiplication and inverse-assigning functions are smooth. This structure was introduced by the Norwegian mathematician So- phus Lie who founded the theory of continuous groups. The Lie groups are well developed and have wide applications in areas including Mathematical Physics. There are several advances and generalizations for Lie groups and Lie groupoids is one such which is termed as a "many-object generalization" of Lie groups. A groupoid is a category whose morphisms are all invertible, obviously, every group is a groupoid but not conversely. Definition 1. A Lie groupoid G ⇒ M is a groupoid G on a base M together with smooth structures on G and M such that the maps α, β: G → M are surjective submertions, the object inclusion map x '→ 1x, M → G is smooth, and the partial multiplication G ∗ G → G is smooth. A bundle is a triple (E, p, B) where E, B are topological spaces p: E → B is a map. Space B is called the base space and space E is called total space and map p is the projection of the bundle. For each b ∈ B, the space p−1(b) is called the fibre of the bundle over b ∈ B. Intuitively a bundle is regarded as a union of fibres p−1(b) for b ∈ B parametrized by B and ’glued together’ by the topology of the space E. A cross-section of a bundle (E, p, B) is a map s: B → E such that ps = 1B. Example 1. Given any space B, a product bundle over B with fibre F is (B × F, p, B) where p is the projection on the first factor. Definition 2. A principal bundle P (M, G, π) consists of a manifold P, a Lie group G, and a free right action of G on P denoted (u, g) '→ ug, such that the orbits of the action coincide with the fibres of the surjective submersion π : P → M, and such that M is covered by the domains of local sections σ: U → P, U ⊆ M, of π. Definition 3. A Lie group bundle, or LGB, is a smooth fibre bundle (K, q, M ) in which each fibre (Km = q−1(m), and the fibre type G, has a Lie group structure, and for which there is an atlas {ψi: Ui × G → KUi } such that each {ψi,m : G → Km}, is an isomorphism of Lie groups. A morphism of LGB from (K, q, M ) to (K′, q′, M′) is a morphism (F, f ) of fibre bundles such that each Fm: Km → K′ is a morphism of Lie groups. In this paper, we will be discussing the Lie groupoid bundles. Here it is seen that to a Lie groupoid Ω on base B there is associated a collection of principal bundles Ωx(B, Ωx), all of which are mutually isomorphic and conversely, associated to any principal bundle P (B, G, p) there is a groupoid called the Ehresmann groupoid which is easily seen to be Lie. Further, some interesting properties of the category of Lie groupoids and bundles will be explored.

Keywords: groupoid, lie group, lie groupoid, bundle

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Authors: V. Yu. Volgutov, A. I. Orlova, S. A. Khainakov

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NaZr2(PO4)3 (NZP) and their structural analogues are characterized by a peculiar behaviors on heating – they have different expansion and contraction along different crystallographic directions due to specific arrangements of crystal structure in these compounds. An important feature of such structures is the ability to incorporate into their structural analogues wide variety of metal cations having different size and oxidation states, with different combinations and concentrations. These cations are located in different crystallographic non-equivalent positions of octahedral tetrahedral crystal framework as well as in inter-framework cavities. Through, due to iso- and hetero-valent isomorphism of the cations (and the anions) in NZP, it becomes possible to tuning the compositions and to obtain the compounds with ‘on a plan’ properties. For the design of compounds with low and ultra-low thermal expansion including those with tailored thermal expansion properties, the following crystallochemical principles it seems are promising: 1) Insertion into crystal M1 position the cations having different sizes and, 2) the variation in the composition of compounds, providing different occupation of crystal M1 position. Following these principles we have designed and synthesized the next NZP-type phosphates series: a) where radii of the cations in the M1 crystal position was varied: Zr1/4Zr2(PO4)3 - Th1/4Zr2(PO4)3 (series I); R1/3Zr2(PO4)3 where R= Nd, Eu, Er (series II), b) where the occupation of M1 crystal position was varied: Zr1/4Zr2(PO4)3-Er1/3Zr2(PO4)3 (series III) and Zr1/4Zr2(PO4)3-Sr1/2Zr2(PO4)3 (series IV). The thermal expansion parameters were determined over the range of 25-800ºC. For each series the minimum axial coefficient of thermal expansion αa = αb, αc and their anisotropy Δα = Iαa - αcI, 10-6 K-1 was found as next: -1.51, 1.07, 2.58 for Th1/4Zr2(PO4)3 (series I); -0.72, 0.10, 0.81 for Nd1/3Zr2(PO4)3 (series II); -2.78, 1.35, 4.12 for Er1/6Zr1/8Zr2(PO4)3 (series III); 2.23, 1.32, 0.91 for Sr1/2Zr2(PO4)3 (series IV). The measured tendencies of the thermal expansion of crystals were in good agreement with predicted ones. For one of the members from the studied phosphates namely Th1/16Zr3/16Zr2(PO4)3 structural refinement have been carried out at 25, 200, 600, and 800°C. The dependencies of the structural parameters with the temperature have been determined.

Keywords: high-temperature crystallography, NaZr2(PO4)3, (NZP) analogs, structural-chemical principles, tuning thermal expansion

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Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

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Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. In particular, the usual rules of associativity, commutativity and distributivity hold. Fields also appear in many other areas of mathematics; see the examples below. When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a commutative field or a rational domain. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a division ring ordivision algebra or sometimes a skew field. Also non-commutative field is still widely used. In French, fields are called corps (literally, body), generally regardless of their commutativity. When necessary, a (commutative) field is called corps commutative and a skew field-corps gauche. The German word for body is Körper and this word is used to denote fields; hence the use of the blackboard bold to denote a field. The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher. An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental. The aim of Galois Theory is the study of algebraic extensions of a field. Given a field k, various kinds of closures of k may be introduced. For example, the algebraic closure, the separable closure, the cyclic closure et cetera. The idea is always the same: If P is a property of fields, then a P-closure of k is a field K containing k, having property, and which is minimal in the sense that no proper subfield of K that contains k has property P. For example if we take P (K) to be the property ‘every non-constant polynomial f in K[t] has a root in K’, then a P-closure of k is just an algebraic closure of k. In general, if P-closures exist for some property P and field k, they are all isomorphic. However, there is in general no preferable isomorphism between two closures.

Keywords: field theory, mechanic maths, supertech, rolltech

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Authors: Giorgi Chichinadze, David Shengelia, Tamara Tsutsunava, Nikoloz Maisuradze, Giorgi Beridze

Abstract:

The Jalovchat gabbro intrusive is exposed on the northern and southern slopes of Main Range zone of the Greater Caucasus, on an area about 25km2. It is intruded in Precambrian crystalline schists and amphibolites intensively metamorphose them along the contact zone. The intrusive is represented by hornblende-bearing gabbro, gabbro-norites and norites including thin vein bodies of gabbro-pegmatites, anorthosites and micro-gabbros. Especially should be noted the veins of gabbro-pegmatites with the gigantic (up to 0.5m) hornblende crystals. From this point of view, the Jalovchat gabbroid intrusive is particularly interesting and by its unusual composition has no analog in the Caucasus overall. The comprehensive petrologic and geochemical study of the intrusive was carried out by the authors. The results of investigations are following. Amphiboles correspond to magnesiohastingsite and magnesiohornblende. In hastingsite and hornblende as a result of isovalent isomorphism of Fe2+ by Mg, content of the latter has been increased. By AMF and Na20+K diagrams the intrusive rocks correspond to tholeiitic basalts or to basalts close to it by composition. According to ACM-AMF double diagram the samples distributed in the fields of MORB and alkali cumulates. In TiO2/FeO+Fe2O3, Zr/Y-Zr and Ti-Cr/Ni diagrams and Ti-Cr-Y triangular diagram samples are arranged in the fields of island-arc and mid-oceanic basalts or along the trends reflecting mid-oceanic ridges or island arcs. K2O/TiO2 diagram shows that these rocks belong to normal and enriched MORB type. According to Th/Nb/Y ratio, the Jalovchat intrusive composition corresponds to depleted mantle, but by Sm/Y-Ce/Sm - to the MORB area. Th/Y and Nb/Y ratios coincide with the MORB composition, Th/Yb-Ta/Yb and La/Nb-Ti ratios correspond to N MORB, and Rb/Y and N/Y - to the lower crust formations. Exceptional are Ce/Pb-Ce and Nb/Th-Nb diagrams, showing the area of primitive mantle. Spidergrams are characterized by almost horizontal trend, weakly expressed Eu minimums and by a slight depletion of light REE. Similar are characteristic of typical tholeiit basalts. In comparison to MORB spidergrams, they are characterized by depletion of light REE. Their correlation to the spidergrams of Jalovchat intrusive proves that they are more depleted. The above cited points to the gradual depletion of mantle with the light REE in geological time. The RE and REE diagrams reveal unexpected regularity. In particular, petro-geochemical characteristics of Jalovchat gabbroid intrusive predominantly correspond to MORB, that usually is an anomalous phenomenon, since in ‘ophiolitic’ section magmatic formations represented mainly by gigantic prismatic hornblende-bearing gabbro and gabbro-pegmatite are not indicated. On the basis of petro-mineralogical and petro-geochemical data analysis, the authors consider that the Jalovchat intrusive belongs to the subduction geodynamic type. In the depleted mantle rich in water the MORB rock system has subducted, where the favorable conditions for crystallization of hornblende and especially for its gigantic crystals occurred. It is considered that the Jalovchat intrusive was formed in deep horizons of the Earth’s crust as a result of crystallization of water-bearing Bajocian basalt magma.

Keywords: The Greater Caucasus, gabbro-pegmatite, hornblende-bearing gabbro, petrogenesis

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Authors: Noury Bakrim

Abstract:

When dealing with motivation/arbitrariness, forming form (Forma Formans) and morphodynamics are to be grasped as relevant implications of enunciation/enactment, schematization within the specificity of language as sound/meaning articulation. Thus, the fact that a language is a form does not contradict stasis/dynamic enunciation (reflexivity vs double articulation). Moreover, some languages exemplify the role of the forming form, uttering, and schematization (roots in Semitic languages, the Chinese case). Beyond the evolutionary biosemiotic process (form/substance bifurcation, the split between realization/representation), non-isomorphism/asymmetry between linguistic form/norm and linguistic realization (phonetics for instance) opens up a new horizon problematizing the role of Brain – sensorimotor contribution in the continuous forming form. Therefore, we hypothesize biotization as both process/trace co-constructing motivation/forming form. Henceforth, referring to our findings concerning distribution and motivation patterns within Berber written texts (pulse based obstruents and nasal-lateral levels in poetry) and oral storytelling (consonant intensity clustering in quantitative and semantic/prosodic motivation), we understand consonant clustering, motivation and schematization as a complex phenomenon partaking in patterns of oral/written iconic prosody and reflexive metalinguistic representation opening the stable form. We focus our inquiry on both Amazigh and English clusters (/spl/, /spr/) and iconic consonant iteration in [gnunnuy] (to roll/tumble), [smummuy] (to moan sadly or crankily). For instance, the syllabic structures of /splaeʃ/ and /splaet/ imply an anamorphic representation of the state of the world: splash, impact on aquatic surfaces/splat impact on the ground. The pair has stridency and distribution as distinctive features which specify its phonetic realization (and a part of its meaning) /ʃ/ is [+ strident] and /t/ is [+ distributed] on the vocal tract. Schematization is then a process relating both physiology/code as an arthron vocal/bodily, vocal/practical shaping of the motor-articulatory system, leading to syntactic/semantic thematization (agent/patient roles in /spl/, /sm/ and other clusters or the tense uvular /qq/ at the initial position in Berber). Furthermore, the productivity of serial syllable sequencing in Berber points out different expressivity forms. We postulate two Components of motivated formalization: i) the process of memory paradigmatization relating to sequence modeling under sensorimotor/verbal specific categories (production/perception), ii) the process of phonotactic selection - prosodic unconscious/subconscious distribution by virtue of iconicity. Basing on multiple tests including a questionnaire, phonotactic/visual recognition and oral/written reproduction, we aim at patterning/conceptualizing consonant schematization and motivation among EFL and Amazigh (Berber) learners and speakers integrating biolinguistic hypotheses.

Keywords: consonant motivation and prosody, language and order of life, anamorphic representation, represented representation, biotization, sensori-motor and brain representation, form, formalization and schematization

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