Search results for: contract algebra

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: Lavinia Ciungu

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In the last decades, developing algebras related to the logical foundations of quantum mechanics became a central topic of research. Generally known as quantum structures, these algebras serve as models for the formalism of quantum mechanics. In this work, we introduce the notion of quantum-Wajsberg algebras by redefining the quantum-MV algebras starting from involutive BE algebras. We give a characterization of quantum-Wajsberg algebras, investigate their properties, and show that, in general, quantum-Wajsberg algebras are not (commutative) quantum-B algebras. We also define the ∨-commutative quantum-Wajsberg algebras and study their properties. Furthermore, we prove that any Wajsberg algebra (bounded ∨-commutative BCK algebra) is a quantum-Wajsberg algebra, and we give a condition for a quantum-Wajsberg algebra to be a Wajsberg algebra. We prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. We establish the connection between quantum-Wajsberg algebras and quantum-MV algebras, proving that the quantum-Wajsberg algebras are term equivalent to quantum-MV algebras. We show that, in general, the quantum-Wajsberg algebras are not commutative quantum-B algebras and if a quantum-Wajsberg algebra is self-distributive, then the corresponding quantum-MV algebra is an MV algebra. Our study could be a starting point for the development of other implicative counterparts of certain existing algebraic quantum structures.

Keywords: quantum-Wajsberg algebra, quantum-MV algebra, MV algebra, Wajsberg algebra, BE algebra, quantum-B algebra

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Authors: Yingxu Wang, Jianhua Lu, Jun Peng, Jiawei Zhang

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The fundamental demand in contemporary intelligent science towards Autonomous AI (AI*) is the creation of unprecedented formal means of Intelligent Mathematics (IM). It is discovered that natural intelligence is inductively created rather than exhaustively trained. Therefore, IM is a family of algebraic and denotational mathematics encompassing Inference Algebra, Real-Time Process Algebra, Concept Algebra, Semantic Algebra, Visual Frame Algebra, etc., developed in our labs. IM plays indispensable roles in training-free AI* theories and systems beyond traditional empirical data-driven technologies. A set of applications of IM-driven AI* systems will be demonstrated in contemporary intelligence science, AI*, and cognitive computers.

Keywords: intelligence mathematics, foundations of intelligent science, autonomous AI, cognitive computers, inference algebra, real-time process algebra, concept algebra, semantic algebra, applications

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Authors: Michael Lousis

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The kind of the most important and conspicuous errors the students made during the three-years of testing of their progress in Algebra are presented in this article. The way these students’ errors changed over three-years of school Algebra learning also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students, who were purposefully culled according to their participation in each occasion of testing in the development of the three-year Kassel Project in England and Greece, in both domains at once of Arithmetic and Algebra. Hence, for each of these English and Greek students, six test-scripts were available and corresponded to the three occasions of testing in both Arithmetic and Algebra respectively.

Keywords: algebra, errors, Kassel Project, progress of learning

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Alireza Gilani

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In this paper, we consider the fuzzification of implicative pseudo-ideal in a pseudo-BCK algebra, and then we investigate some of their properties. We prove that the family of fuzzy implicative pseudo-ideal is completely distributive lattice.

Keywords: BCK-algebra, pseudo-BCK algebra, pseudo-ideal, implicative pseudo-ideal

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Authors: Dchieche Amina, Aboulaich Rajae

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Profit and loss sharing suggests an equitable sharing of risks and profits between the parts involved in a financial transaction. Salam is a contract in which advance payment is made for goods to be delivered at a future date. The purpose of this work is to price a new contract for profit and loss sharing based on Salam contract, using Khiyar Al Ghabn which is an agreement of choice in case of misrepresent facts.

Keywords: Islamic finance, shariah compliance, profit and loss sharing, derivatives, risks, hedging, salam contract

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Authors: Xia Yang, Zheng Yang, Haiyong Sun, Yan Fang, Jingyu Liu, Jia Song

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The smart contract in Ethereum is a unique program deployed on the Ethereum Virtual Machine (EVM) to help manage cryptocurrency. The security of this smart contract is critical to Ethereum’s operation and highly sensitive. In this paper, we present a formal model for smart contract, using the separated term-obligation (STO) strategy to formalize and verify the smart contract. We use the IBM smart sponsor contract (SSC) as an example to elaborate the detail of the formalizing process. We also propose a formal smart sponsor contract model (FSSCM) and verify SSC’s security properties with an interactive theorem prover Coq. We found the 'Unchecked-Send' vulnerability in the SSC, using our formal model and verification method. Finally, we demonstrate how we can formalize and verify other smart contracts with this approach, and our work indicates that this formal verification can effectively verify the correctness and security of smart contracts.

Keywords: smart contract, formal verification, Ethereum, Coq

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Authors: Salvatore Triolo

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We discuss the possibility of extending the well-known Gelfand-Naimark-Segal representation to modules over a C*algebra. We focus our attention on the case of Hilbert modules. We consider, in particular, the problem of the existence of a faithful representation. Non-commutative Lᵖ-spaces are shown to constitute examples of a class of CQ*-algebras. Finally, we have shown that any semisimple proper CQ*-algebra (X, A#), with A# a W*-algebra can be represented as a CQ*-algebra of measurable operators in Segal’s sense.

Keywords: Gelfand-Naimark-Segal representation, CQ*-algebras, faithful representation, non-commutative Lᵖ-spaces, operator in Hilbert spaces

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Authors: Yassir I. Dinar

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We computed the weights of the adjoint action of distinguished sl2-triples in Lie algebra of type Dn using mathematical induction.

Keywords: lie algebra, root systems, representation theory, nilpotent orbits

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Authors: Dchieche Amina, Aboulaich Rajae

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In this work, we will modelize Waad Bil Mourabaha contract. This islamic contract provides the right to buy goods at a future date with a Mourabaha. Waad is a promise of sale or purchase of goods, declared in a unilateral way. In spite of the divergence between some schools of Islamic law about the Waad, this contract will allow us to study sophisticated and interesting contract: Waad Bil Mourabaha that can be used for hedging. In order to price Waad Bil Mourabaha contract, we will use an adapted Black and Scholes model using the Shariah compliant assumptions.

Keywords: Islamic finance, Black-Scholes model, call option, risks, hedging

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Authors: Fazeelat Duran, Darren Bishopp, Jessica Woodhams

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Psychological contract refers to the perceptions of an employee and their employer regarding their mutual obligations towards each other. The rationale for applying the psychological contract theory in UK policing was to investigate its impact on their wellbeing because the psychological contract is a useful tool in identifying factors having a negative effect on the wellbeing of employees. The paper will report on a study, which examined how occupational stressors and psychological contract violation may influence the wellbeing (e.g. Physical Stress and General Health) of a sample of police officers (N=127). The design of the study was cross-sectional and based on data collected through a self-report survey. The results of hierarchical regression analyses and structural equation model, suggest that occupational stressors and psychological contract violation play a critical role in both physical and psychological health. The implications of these findings and the utility of considering the psychological contract will be discussed.

Keywords: police officers, psychological contract, occupational stressors, wellbeing

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Natalia Pacheco Rego

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The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide.

Keywords: almost inner Lie-derivation, Lie-center, Lie-central derivation, Lie-derivation

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Authors: Parveen Banu Ansari, Venkatraman Chinnappan, Paramasivam Shankar

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Contract testing plays a pivotal role in the current landscape of microservices architecture. Testing microservices at the initial stages of development helps to identify and rectify issues before they escalate to higher levels, such as UI testing. By validating microservices through contract testing, you ensure the integration quality of APIs, enhancing the overall reliability and performance of the application. Contract testing, being a collaborative effort between testers and developers, ensures that the microservices adhere to the specified contracts or agreements. This proactive approach significantly reduces defects, streamlines the development process, and contributes to the overall efficiency and robustness of the application. In the dynamic and fast-paced world of digital applications, where microservices are the building blocks, embracing contract testing is indeed a strategic move for ensuring the quality and reliability of the entire system.

Keywords: validation, testing, contract, agreement, microservices

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Authors: Veselin Konstantinov Hristov

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In recent years, the lease contract has become more and more applicable and occupies a key place in commercial relations and business. In Bulgaria, the legal regulation of the leasing contract is relatively new and imperfectly developed. There are many legal loopholes and it is they that determine the need for a comparative legal analysis. The purpose of the study is to analyze the various European legislations regarding the leasing contract and to find effective solutions for the legal system of Bulgaria. First of all, are examined the concept of the leasing contract, which originated in the United States of America around the 1950s and spread in Europe, and the etymology of the term "leasing". After that, the main types of lease contracts – financial and operational – are examined and analyzed in detail. Their features and characteristics were studied, as well as a comparative analysis was made between them. Next, in the research, a comparative-legal analysis of the leasing contract in different European countries was made in terms of its development and distribution, as well as its legal characteristics. The mechanism of action and functioning of the leasing contract in several European countries is analyzed. Conclusions are made regarding the legal framework under which the lease contract is most effective. Types of leasing contracts specific only to certain European countries and their advantages are examined. In conclusion, recommendations are made to improve the legal framework of the leasing contract in Bulgaria.

Keywords: alternative financing, leasing contract, financing instruments, innovation

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Authors: Wagneur Edouard

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Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra

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Authors: Yuliya Leonidovna Kiva-Khamzina

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The legal nature of the contract for educational services causes a lot of controversies. In particular, it raises the question about industry sector relationships, which require making a contract for educational services. The article describes the different types of contracts classifications for services provision from the perspective of civil law, deals with the specifics of the contract on rendering educational services; the author makes the conclusion that the contract for the provision of educational services is a complex institution that includes elements of the civil and administrative law. The following methods were used to conduct the study: dialectical method of cognition, the historical method, systemic analysis, classification.

Keywords: administrative aspect, civil aspect, educational service, industry, legal nature, services provision

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Authors: Malaw Ndiaye, Karim Konate

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Smart contracts are computer protocols that facilitate, verify, and execute the negotiation or execution of a contract, or that render a contractual term unnecessary. Blockchain and smart contracts can be used to facilitate almost any financial transaction. Thanks to these smart contracts, the settlement of dividends and coupons could be automated. Smart contracts have become lucrative and profitable targets for attackers because they can hold a great amount of money. Smart contracts, although widely used in blockchain technology, are far from perfect due to security concerns. Since there are recent studies on smart contract security, none of them systematically study the strengths and weaknesses of smart contract security. Some have focused on an analysis of program-related vulnerabilities by providing a taxonomy of vulnerabilities. Other studies are responsible for listing the series of attacks linked to smart contracts. Although a series of attacks are listed, there is a lack of discussions and proposals on improving security. This survey takes stock of smart contract security from a more comprehensive perspective by correlating the level of vulnerability and systematic review of security levels in smart contracts.

Keywords: blockchain, Bitcoin, smart contract, criminal smart contract, security

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Authors: Ranjit Biswas

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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

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Authors: Anna Rogozińska-Pawełczyk

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A psychological contract is an agreement between the employer and an employee that covers the parties’ informal and frequently non-verbalized obligations and expectations towards each other. The contract is a cognitive pattern-governing employee’s behaviour in the organization. A gap between employee’s expectations and the organizational reality may lead to difficult-to-solve conflicts or cause the employee to modify their behaviour towards organizational values and goals, if they are willing and ready to verbalize their expectations. The article discusses psychological contracts in the financial institutions in Poland. Its theoretical part outlines the types of psychological contracts in organizations (relational, transactional, and balanced) and shows the process of their verbalization. The purpose of the article is to present how the type of the psychological contract relates to employee’s readiness to verbalize it. The article ends with conclusions arising from the study.

Keywords: customer contact staff in banks, employee expectations, financial institutions, mutual expectations, psychological contract, verbalization of the psychological contract

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Authors: Quangyen Tran, YeZhuang Tian, Chengfeng Li

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Psychological contract violations may lead to damaging an organization through losing its potential employees; it is a very significant concept in understanding the employment relationships. The authors selected contents of psychological contract violation scale based on the nine areas of violation most relevant to managerial samples (High pay, training, job security, career development, pay based on performance, promotion, feedback, expertise and quality of co-workers and support with personal problems), using regression analysis, the degree of psychological contract violations was measured by an adaptation of a multiplicative scale with Cronbach’s alpha as a measure of reliability. Through the regression analysis, psychological contract violations was found have a positive impact on employees’ job satisfaction, the frequency of psychological contract violations was more intense among male employees particularly in terms of training, job security and pay based on performance. Job dissatisfaction will lead to a lowering of employee commitment in the job, enterprises in Hanoi, Vietnam should therefore offer lucrative jobs in terms of salary and other emoluments to their employees.

Keywords: psychological contract, psychological contract violation, job satisfaction, subordinate employees, employers’ obligation

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Authors: Arnab Adhikari, Arnab Bisi

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Since the inception, the fashion apparel supply chain is facing the problem of high demand uncertainty. Often the demand volatility compels the corresponding supply chain member to incur substantial holding cost and opportunity cost in case of the overproduction and the underproduction scenario, respectively. It leads to an uncoordinated fashion apparel supply chain. There exist several scholarly works to achieve coordination in the fashion apparel supply chain by employing the different contracts such as the buyback contract, the revenue sharing contract, the option contract, and so on. Specially, the application of option contract in the apparel industry becomes prevalent with the changing global scenario. Exploration of existing literature related to the option contract reveals that most of the research works concentrate on the one direction demand adjustment i.e. either to match the demand upwards or downwards. Here, we present a holistic approach to coordinate a dyadic fashion apparel supply chain comprising one manufacturer and one retailer with the help of bidirectional option contract. We show a combination of wholesale price contract and bidirectional option contract can coordinate the under expanded supply chain. We also propose a framework that captures the variation of the apparel retailer’s order quantity and the apparel manufacturer’s production quantity with the changing exercise price for the different ranges of the option price. We analytically explore that corresponding cost parameters of the supply chain members along with the nature of demand distribution play an instrumental role in the coordination as well as the retailer’s ordering decision.

Keywords: fashion apparel supply chain, supply chain coordination, wholesale price contract, bidirectional option contract

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Authors: Eunice Chiamaka Allen-Ngbale

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Cargo claims are brought by cargo interests against carriers when the goods are not delivered or delivered short or mis-delivered or delivered damaged. The objective of the cargo claimant is to seek recovery for the loss suffered through the award of damages against the carrier by a court of competent jurisdiction. Moreover, whether the vessel on which the goods were carried is or is not under charter, the bill of lading plays a central role in the cargo claim. Since the bill of lading is an important international transport document, this paper examines, by chronicling the progress of a cargo claim as governed by the English law of contract. It finds that other than by contract, there are other modes of recovery available to a consignee or endorsee of a bill of lading to obtain a remedy under the sui generis contract of carriage contained in or evidenced by a bill of lading.

Keywords: bill of lading, cargo interests, carriage contract, transfer of right of suit

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Authors: Ahmed Stifi, Sascha Gentes

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The contract in its simplest definition is an agreement involving parties with a number of documents which may be as little as a marriage contract involving two parties or as big as a contract of construction and operation of a nuclear power plant involving companies and stakeholders with hundreds or even thousands of documents. All parties in the construction industry, not only the contract experts, agree that the success of a project is linked primarily to the form of contract regulating the relationship between stakeholders of the project. Therefore it is essential for the construction industry to study, analyze and improve its contracts forms continuously. However, it should be mentioned that different contract forms are developed to suit the construction evolution in term of its machinery, materials and construction process. There exist some similarities in some clauses and variations in many of these forms depending upon the type of project, the kind of clients and more importantly the laws and regulations governing the transaction in the country where the project is carried out. This paper will discuss the most important forms of construction contracts starting from national level, intended to the contract form in Germany and moving on to the international level introducing FIDIC contracts and its different forms, some newly developed contracts forms namely the integrated form of agreement, the new engineering contract and the project alliance agreement. The result of the study shows that many of the contract’s paragraphs are similar and the main difference comes in the approach of the relationship between the parties. Is it based on co-operation and mutual trust, or in some cases a load of responsibility for a particular party which increases the problems and disputes that affects the success of the project negatively. Thus we can say that the form of the contract, that plays an essential role in the approach of the project management, which is ultimately the key factor for the success of the project. So we advise to use a form of contract, which enhance the mutual trust between the project parties, contribute to support the cooperation between them, distribute responsibility and risks on an equitable basis and build on the principle “win-win". In additional to the conventional role of the contract it should integrate all parties into one team to achieve the target value of the project.

Keywords: contract, FIDIC, integrated form of agreement, new engineering contract, project alliance agreemen

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Authors: Afsheen Masood, Sumaira Rashid, Nadia Ijaz, Shama Mazahir

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The current study examined the relationship between moral disengagement, psychological contract, organizational citizenship behavior and counterproductive work behavior. It is hypothesized that there is likely to be a significant relationship between moral disengagement, psychological contract, organizational citizenship behavior and counterproductive work behavior. It is hypothesized that moral disengagement is likely to significantly predict counterproductive work behavior. It is hypothesized that psychological contract is likely to moderate the relationship between moral disengagement, and counterproductive work behavior. Cross-sectional survey research design was used for the study. The sample consisted of 500 middle managers, age ranging between 30-45 years working in private and public sector. The measures used were Moral Disengagement Scale, Psychological Contract Scale, and Counterproductive Work Behavior. Series of Correlation analyses, Regression analysis, moderation analysis and t-test was run in order to execute descriptive and inferential analyses. The findings revealed that there was a significant positive relationship between moral disengagement and counterproductive work behaviors. Psychological contract significantly mediated the relationship between moral disengagement and counterproductive work behaviors. There were significant gender differences reported in psychological contract and counterproductive work behaviors. The insightful findings carry significant implication for organizational psychologists and organizational stakeholders.

Keywords: psychological contract, moral disengagement, counterproductive work behaviors, mediation analysis

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: Fazeelat Duran, Darren Bishopp, Jessica Woodhams

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Negative emotions resulting from the breach of perceived obligations by an employer is called the psychological contract violation. Employees perceiving breach and feelings of negative emotions result in adverse outcomes for both the employee and employer. This paper aims to identify the relationships between contract breach, violation, stress and wellbeing and investigate whether fairness and self-efficacy mediate the relationships. A mixed method approach was used to analyze the online-surveys and semi-structured interviews with the police officers. It was identified that the psychological contract violation predicts stress and job-related well-being. Fairness and self-efficacy were identified as significant mediators to understand the underlying mechanisms of association. Whilst, in the interviews social support was identified as a popular mediator. Practical implications for employers are discussed.

Keywords: psychological contract violation and breach, stressors, depression, anxiety

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Authors: Arkady Kitover

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We obtain a complete description of semi-Fredholm spectra of operators of the form (T f)(z) = w(z)f(B(z) acting on the disk algebra in the case when B is either elliptic or double parabolic finite Blaschke product and w has no zeros on the unit circle. Actually, in this case the lower semi-Fredholm spectrum is a disk, and the upper semi-Fredholm spectrum is a circle. We consider some examples and discuss some unsolved problems Our results hint on the possibility of interesting connections between the spectral properties of weighted composition operators and complex dynamics.

Keywords: weighted composition operators, essential spectra, Blaschke products, Julia set

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