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SVN-Ostrowski Type Inequalities for (α, β, γ, δ) -Convex Functions
Maria Khan,Asif Raza Khan,Ali Hassan International Journal of Computer ScienceNetwork S 2024 International journal of computer science and netw Vol.24 No.1
In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1<sup>st</sup> and 2<sup>nd</sup> kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1<sup>st</sup> and 2<sup>nd</sup> kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.
RPSMDSM: Residential Power Scheduling and Modelling for Demand Side Management
( Sheeraz Ahmed ),( Ali Raza ),( Shahryar Shafique ),( Mukhtar Ahmad ),( M. Yousaf Ali Khan ),( Asif Nawaz ),( Rohi Tariq ) 한국인터넷정보학회 2020 KSII Transactions on Internet and Information Syst Vol.14 No.6
In third world countries like Pakistan, the production of electricity has been quickly reduced in past years due to rely on the fossil fuel. According to a survey conducted in 2017, the overall electrical energy capacity was 22,797MW, since the electrical grids have gone too old, therefore the efficiency of grids, goes down to nearly 17000MW. Significant addition of fossil fuel, hydro and nuclear is 64.2%, 29% and 5.8% respectively in the total electricity production in Pakistan. In 2018, the demand crossed 20,223MW, compared to peak generation of 15,400 to 15,700MW as by the Ministry of Water and Power. Country faces a deficit of almost 4000MW to 5000MW for the duration of 2019 hot summer term. Focus on one aspect considering Demand Side Management (DSM) cannot oversea the reduction of gap between power demand and customer supply, which eventually leads to the issue of load shedding. Hence, a scheduling scheme is proposed in this paper called RPSMDSM that is based on selection of those appliances that need to be only Turned-On, on priority during peak hours consuming minimum energy. The Home Energy Management (HEM) system is integrated between consumer and utility and bidirectional flow is presented in the scheme. During peak hours of electricity, the RPSMDSM is capable to persuade less power consumption and accomplish productivity in load management. Simulations show that RPSMDSM scheme helps in scheduling the electricity loads from peak price to off-peak price hours. As a result, minimization in electricity cost as well as (Peak-to-Average Ratio) PAR are accomplished with sensible waiting time.