Intuitionistic fuzzy subgroups with respect to norms (\(T,S\))
EASL-Vol. 3 (2020), Issue 2, pp. 40 – 53 Open Access Full-Text PDF
Rasul Rasuli
Abstract: The purpose of this paper is introduce the notion of intuitionistic fuzzy subgroups with respect to norms (\(t\)-norm \(T\) and \(s\)-norm \(S\)). Also we introduce intersection and normality of them and investigate some properties of them. Finally, we provide some results of them under group homomorphisms.
On Caputo fractional derivatives via exponential \((s,m)\)-convex functions
EASL-Vol. 3 (2020), Issue 2, pp. 32 – 39 Open Access Full-Text PDF
Saad Ihsan Butt, Mehroz Nadeem, Ghulam Farid
Abstract: In this paper, we establish several integral inequalities including Caputo fractional derivatives for exponential \((s,m)\)-convex functions. By using convexity for exponential \((s,m)\)-convex functions of any positive integer order differentiable function some novel results are obtained.
New perspectives on internet electricity use in 2030
EASL-Vol. 3 (2020), Issue 2, pp. 19 – 31 Open Access Full-Text PDF
Anders S.G. Andrae
Abstract: The main problems with several existing Information and Communication Technology (ICT) power footprint investigations are: too limited (geographical and temporal) system boundary, overestimation of power saving potential in the next decade, assume that historical power use can predict future global power use in the next decade despite unprecedented data traffic growth, assume that Moore´s law relation to digital circuitry can continue “forever” and that no problems with extra cooling power will occur for several decades. The highly variable outlooks for the future power consumptions depend on “starting values”, disruptions, regional differences and perceptual estimations of electricity intensity reductions and data traffic increase. A hugely optimistic scenario – which takes into account 20% annual improvement of the J/bit in data centers and networks until 2030 is presented. However, the electric power consumption of the present ICT scope will be significant unless great efforts are put into power saving features enabling such improvements of J/bit. Despite evident risks, it seems though that planned power saving measures and innovation will be able to keep the electricity consumption of ICT and the World under some kind of control. The major conclusion is based on several simulations in the present study – that future consumer ICT infrastructure cannot slow its overall electricity use until 2030 and it will use more than today. Data traffic may not be the best proxy metric for estimating computing electricity. Operations and J/operation seem more promising for forecasting and scaling of bottom-up models.
New fractional Hadamard and Fejér-Hadamard inequalities associated with exponentially \((h,m)\)-convex functions
EASL-Vol. 3 (2020), Issue 2, pp. 9 – 18 Open Access Full-Text PDF
Sajid Mehmood, Ghulam Farid,, Khuram Ali Khan, Muhammad Yussouf
Abstract: The aim of this paper is to establish some new fractional Hadamard and Fejér-Hadamard inequalities for exponentially \((h,m)\)-convex functions. These inequalities are produced by using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold for various kinds of convexities and well known fractional integral operators.
Leap Zagreb and leap hyper-Zagreb indices of Jahangir and Jahangir derived graphs
EASL-Vol. 3 (2020), Issue 2, pp. 1 – 8 Open Access Full-Text PDF
Fatima Asif, Zohaib Zahid, Sohail Zafar
Abstract: Topological indices are numerical parameters of a graph which characterize its topology. The second degree of a vertex in a graph is equal to the number of its second neighbors. In this paper, we will compute leap Zagreb indices and leap hyper-Zagreb indices of Jahangir graph and its line graph based on the 2-distance degree of the vertices. Moreover we will compute the same indices for the subdivision graph and the line graph of the subdivision of Jahangir graph.