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The aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles.

Using the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles.

Findings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles.

To the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.

To run a job guarantee public policy scheme, it is important to know the aspiration level or the reference point of labor, and accordingly, the labor hour and the wage sequence are to be prepared. The existing job guarantee schemes consider the same wage rates for all types of jobs. As a result, it is to identify the reference point. The present work aims to propose a job guarantee scheme where different types of jobs have different wage rates. The paper explains the choice problem between labor and leisure at different wage rates and proposes complete computational tools to be incorporated into the job guarantee schemes. The paper also gives a mechanism to prepare the list of jobs and corresponding wage rates by maintaining a balance between labor and leisure, where productive activities measure labor hours and labor welfare measures leisure hours. Lastly, the paper provides the analytical tools to interpret the ex-post data of the job guarantee public policy schemes.

The paper has been written based on the Coordination Game and its Welfare Implications in the job guarantee public policy schemes.

The present paper gives an initial work to measure the choice between labor and leisure for the different wage rates practically. This will help in getting the equilibrium strategies, namely, the combination of the labor hour and the wage rate between the policymaker and the labor. This method will help to implement the job guarantee schemes. For example, to run successfully the Basic Income policy, the basic income calculation should give due care; otherwise, there will be a downward trend in the basic income and the welfare of labor will be reduced, because the labor would have to supply excess labor to meet the target income.

This paper derives theories and explains how the equilibrium in this coordination game can be achieved. The paper explains how the policy of the job guarantee schemes can be practiced practically. In the MGNREGA scheme, the public institution declares different categories of jobs with different wage rates. The categories have been classified with respect to the hours required to complete the job. Therefore, the public institution declares different lists or a sequence of pairs of labor hours and wage rates. Moreover, the list is stochastic, because the list can be changed by the inclusion of an offer from the market as well. The labor has to select from the list. The challenge on the part of the public institution is to prepare the list in such a way so that the inclusion of the market offers will not distort the equilibrium of the coordination game. An important method has been proposed here to analyze the ex-post data of job offers so that the preparation of the future sequence of the job offers can be prepared with due care. One objective of the policymaker here is to make a list of job offers in such a way so that the labor supply will be converging to a point and that will not deviate if the wage rate increases further. This objective will make a balance of the distribution of funds between the existing registered labor and the new entrants into the job guarantee schemes.

The author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1.

The author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7.

The author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4).

To the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.

The purpose of this paper is to investigate whether and how bundling services may achieve leverage of market power from the telco's home to a secondary service market (e.g. video broadcasting). Despite digital convergence, in many countries the former telco monopolist remains to hold significant market power in its home market for telecommunication services.

To this extent the author considers a formal game‐theoretic model where the telco firm holds a monopoly in the market for telecommunications services, while competing with a cable firm in the market for video broadcasting services. Services may differ in quality. For the firms, the provision of high‐quality services is more costly than the provision of low‐quality services. Conversely, consumers have a greater reservation price for higher service qualities. Therefore firms face a trade off between revenues and cost when selecting the optimal service quality.

The model shows that the telco firm can achieve market power leverage by bundling its services, which therefore is more profitable than offering each service separately. In particular, the quality leverage mechanism is highlighted, which reveals that bundling alters the optimal service quality choice of the competitors favorably.

Like every game‐theoretic model, the present model rests on formal assumptions representing stylized facts. Future research should determine these by empirical evidence.

The paper reveals how bundling may be employed as a strategic weapon in order to increase profits in the converging communications market.

The paper shows that bundling communications services can not only have significant ramifications for the quality of these services, but also for the competition in industry.

The paper analyzes how the goal-setting of two individuals or social units A and B determines the utilities, which the two parties can gain in a dyadic interaction.

The analysis is based on a dyadic utility space representing the utilities of A and B along the x and y axis, respectively. In this space the goal-orientation of an individual action is mapped with a vector, where its angle shows the combination of utilities of A and B aimed at, and the length corresponds to the strength of an action.

Analyzing actions of A and responses of B in the dyadic utility space allows (a) calculating single and joint utilities, (b) identifying the narrow range of equal utility for both and (c) identifying four vectors for maximizing different combinations of utility. Studying combinations of these four vectors in a 4 × 4 ‘Interaction - Utility Matrix’ shows how the goal-setting of A for a prime action widely predetermines, before a response of B, the realizable dyadic utility for both.

The dyadic utility space allows illustrating any dyadic interaction: It shows all possible dyadic “payoffs” investigated in game theory; it allows studying repeated exchange and resulting accumulation of utility; it allows mapping power relations.

The paper shows the interrelation between cybernetic principles of control, goal-orientated human behavior and the utility concept of social sciences. And it allows rejecting Adam Smith’s 18th myth of an “invisible hand”.

The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics.

This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively.

This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups.

The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric.

The purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.

The paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.

The geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.

All results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

General shell equations of motion applicable to the structures of arbitrary topology are derived. The formulation is co‐ordinate‐free and local equations suitable for computation are easily written down for arbitrary choices of co‐ordinate systems.

Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

This chapter examines the impact of recent airline consolidations in the United States on the technical efficiencies of the airlines involved. Data envelopment analysis (DEA) is used to assess the efficiencies, and the consolidations examined are those that occurred among major network carriers between 2005 and 2013. The airline production process is conceptualized as the transformation of labor, fuel, and fleet-wide seating capacity into available seat-miles, or, under an alternative model specification, into user value, as measured by the airline’s operating revenue. Efficiency is conceptualized in terms of minimizing the airline’s usage of the three inputs, given its output level. The analysis seeks to determine whether the airlines that consolidated were more efficient, post-consolidation, than they were prior to consolidation, compared to airlines that did not enter into consolidations. Although there are limitations owing to the small number of airlines in the dataset, the chapter finds no evidence that the consolidations enhanced the efficiencies of the airlines involved, relative to the efficiencies of the airlines that did not enter into consolidations.