Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model

We study and exactly solve the two-photon and k-photon Jaynes-Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the $SU(2)$ group and let us diagonalize the Hamiltonian of these models by properly choosing the coherent state parameters of the transformation. Finally, we explicitly obtain the energy spectrum and eigenfunctions for each model.Comment: 12 page

Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates

We consider mean-reverting stochastic processes and build self-consistent models for forward price dynamics and some applications in power industries. These models are built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward prices and their volatility. Some analytical solutions are presented in the one factor case and for specific regular forward price/interest rates volatility. Those models will also play a role of initial conditions for a stochastic process describing forward price and interest rates volatility. Subsequently, the curved manifold of the internal space i.e. a discrete version of the bond term space (the space of bond maturing) is constructed. The dynamics of the point of this internal space that correspond to a portfolio of different bonds is studied. The analysis of the discount bond forward rate dynamics, for which we employed the Stratonovich approach, permitted us to calculate analytically the regular and the stochastic volatilities. We compare our results with those known from the literature.: Stochastic Differential Geometry, Mean-Reverting Stochastic Processes and Term Structure of Specific (Some) Economic/Finance Instruments

Quantifying Flexibility Real Options Calculus

We expose a real options theory as a tool for quantifying the value of the operating flexibility of real assets. Additionally, we have pointed out that this theory is an appropriated methodology for determining optimal operating policies, and provide an example of successful application of our approach to power industries, specifically to valuate the power plant of electricity. In particular by increasing the volatility of prices will eventually lead to higher assets values.real options, Black-Scholes Approach, Wiener processes, stochastic processes, Quantifying Flexibility, volatility

Knowledge management activities in social enterprises: lessons for small and non-profit firms

Purpose: This paper explores what Social Enterprises (SEs) in the UK know and how they acquire, convert, apply and protect this knowledge. This will enable them to manage their knowledge effectively, hence improve their practices and maximize the creation of social, environmental and economic value. Design/methodology/approach: This study follows a qualitative approach, comprising of 21 interviews with founders and senior members of SEs in UK. Findings: The results show that the investigated SEs have KM practices similar to the already identified in SMEs, associated with informality, reliance on external sources and focus on socialisation activities, but they have unique challenges on managing their knowledge related to their hybrid mission, to include social and economic objectives, and their closed relationship with stakeholders. Research limitations/implications: As there is limited research on Knowledge Management (KM) practices in SEs; they were defined based on previous studies in large, private and public companies. Therefore, not all practices may be included. This research is a starting point in the study of KM in SEs. Practical implications: This study identifies knowledge activities that enable the creation of social, environmental and economic value in SEs. This allows SEs, small firms and non-profit organisations to review their current practices and develop plans for their further improvement. Social implications: Originality/value: This paper is one of the first empirical studies exploring KM practices in SEs, highlighting their informal nature as well as their impact in and on the enterprise