User-centric energy efficiency fairness in backscatter-assisted wireless powered communication network by Yinghui YE, Liqin SHI, Guangyue LU

“…In order to address the unfair user-centric energy efficiency (EE) problem caused by channel difference in the backscatter-assisted wireless powered communication network,a resource allocation scheme was proposed.Firstly,a mixed integer nonconvex fractional programming problem was formulated to maximize the minimum user-centric EE,subject to the quality of service and energy-causality constraints.Based on the generalized fractional programming theory,the original problem was transformed into a mixed integer nonconvex subtraction problem.With the aid of the slack variable,the proof by contradiction,the auxiliary variable and the mixed integer nonconvex subtraction problem were further transformed into an equivalent convex problem.Finally,an iterative algorithm was proposed to obtain the optimal solutions.Computer simulations validated the quick convergence of the proposed iterative algorithm,and that the developed resource allocation scheme efficiently guarantees the fairness among users in terms of EE.…”
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Fractional-Order Memristor Emulator Circuits by C. Sánchez-López, V. H. Carbajal-Gómez, M. A. Carrasco-Aguilar, I. Carro-Pérez

“…To do so, a novel fractional-order integrator (FOI) topology based on current-feedback operational amplifier and integer-order capacitors is proposed. Then, the FOI is substituting the integer-order integrator inside flux- or charge-controlled memristor emulator circuits previously reported in the literature and in both versions: floating and grounded. …”
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The 3𝑥+1 Problem as a String Rewriting System by Joseph Sinyor

“…A simple system of two unary operators rewrites the length of each run, so that each new string represents the next odd integer on the 3𝑥+1 path. This approach enables the conjecture to be recast as two assertions. …”
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Dufour Effect on Transient MHD Double Convection Flow of Fractionalized Second-Grade Fluid with Caputo–Fabrizio Derivative by Imran Siddique, Sehrish Ayaz, Fahd Jarad

“…Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. …”
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New Results on the (Super) Edge-Magic Deficiency of Chain Graphs by Ngurah Anak Agung Gede, Adiwijaya

“…Similarly, the super edge-magic deficiency of a graph G, μs(G), is either the smallest nonnegative integer n such that G∪nK1 has a super edge-magic labeling or +∞ if there exists no such integer n. …”
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Powers of a product of commutators as products of squares by Alireza Abdollahi

“…We prove that for any odd integer N and any integer n>0, the Nth power of a product of n commutators in a nonabelian free group of countable infinite rank can be expressed as a product of squares of 2n+1 elements and, for all such odd N and integers n, there are commutators for which the number 2n+1 of squares is the minimum number such that the Nth power of its product can be written as a product of squares. …”
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On the Local Minima of the Order of Appearance Function by Florian Luca, Thato Mosima

“…The order of appearance z(n) of the positive integer n is the smallest positive integer k such that n divides Fk, the kth member of the Fibonacci sequence. …”
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Multiplicative Isometries on Classes Mp(X) of Holomorphic Functions by Yasuo Iida, Kazuhiro Kasuga

“…In this paper, we will generalize the result to arbitrary (not necessarily positive integer) value of the exponents 0<p<∞.…”
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Kaplansky's ternary quadratic form by James Kelley

“…This paper proves that if N is a nonnegative eligible integer, coprime to 7, which is not of the form x2+y2+7z2, then N is square-free. …”
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Some Criteria for Class Numbers to Be Non-One by Ahmad Issa, Hasan Sankari

“…Let d be a positive integer which is not a perfect square and n be any nonzero fixed integer. …”
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On Polynomial Solutions of Pell’s Equation by Hasan Sankari, Ahmad Abdo

“…Polynomial Pell’s equation is x2−Dy2=±1, where D is a quadratic polynomial with integer coefficients and the solutions X,Y must be quadratic polynomials with integer coefficients. …”
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Multi-Task Simultaneous Supervision by Afifah Rizka, Sukoyo Sukoyo, Muhammad Akbar

“…The mathematical model developed uses three techniques: Mixed-Integer Linear Programming (MILP), Mixed-Integer Quadratic Programming (MIQP), and Mixed-Integer Quadratically Constrained Programming (MIQCP). …”
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A Dual Resource Constrained Unrelated Parallel Machine Scheduling Model Considering Tardiness and Workload Balance by Karina Amanda Larasati, Sukoyo Sukoyo, Muhammad Akbar

“…This issue employs three methodologies: Mixed-Integer Linear Programming (MILP), Mixed-Integer Quadratic Problem (MIQP), and Mixed-Integer Quadratically Constrained Programming (MIQCP).  …”
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Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model by S. H. Elhag, Fatimah S. Bayones, A. A. Kilany, S. M. Abo-Dahab, Emad A.-B. Abdel-Salam, M. Elsagheer, A. M. Abd-Alla

“…These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. …”
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A Note on n-Divisible Positive Definite Functions by Saulius Norvidas

“…Let PDℝ be the family of continuous positive definite functions on ℝ. For an integer n>1, a f∈PDℝ is called n-divisible if there is g∈PDℝ such that gn=f. …”
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A construction of some ideals in affine vertex algebras by Draen AdamoviĆ

“…We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. These formulas generalize the expressions for singular vectors from Adamović (1994). …”
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Rings and groups with commuting powers by Hazar Abu-Khuzam, Adil Yaqub

“…Let n be a fixed positive integer. Let R be a ring with identity which satisfies (i) xnyn=ynxn for all x,y in R, and (ii) for x,y in R, there exists a positive integer k=k(x,y) depending on x and y such that xkyk=ykxkand (n,k)=1. …”
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Recursive formulae for the multiplicative partition function by Jun Kyo Kim, Sang Guen Hahn

“…For a positive integer n, let f(n) be the number of essentially different ways of writing n as a product of factors greater than 1, where two factorizations of a positive integer are said to be essentially the same if they differ only in the order of the factors. …”
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The Periodic Solution of Fractional Oscillation Equation with Periodic Input by Jun-Sheng Duan

“…With the input of the harmonic oscillation, the solution is derived to be a periodic function of time t with the same circular frequency as the input, and the frequency of the solution is not affected by the system frequency c as is affected in the integer-order case. These results are similar to the case of a damped oscillation with a periodic input in the integer-order case. …”
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A sustainable method for analyzing and studying the fractional-order panic spreading caused by the COVID-19 pandemic by Muhammad Farman, Evern Hincal, Parvaiz Ahmad Naik, Ali Hasan, Aceng Sambas, Kottakkaran Sooppy Nisar

“…We find a more comparable outcome when comparing non-integer orders to integer orders, which supports the non-integer order’s position. …”
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