Cleaning Schedule Optimization of Heat Exchangers with Fouling on Tube and Shell Sides: A Metaheuristic Approach by João P. V. de Cesaro, Mauro A. S. S. Ravagnani, Fernando D. Mele, Caliane B. B. Costa

“…This paper addresses these issues by adding shell-side fouling to the model and by transforming cleaning time variables into integers, reducing the problem of optimizing cleaning schedules to an integer nonlinear programming (INLP) problem. …”
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Subharmonics with Minimal Periods for Convex Discrete Hamiltonian Systems by Honghua Bin

“…By using variational methods and dual functional, we obtain that the system has a -periodic solution for each positive integer , and solution of system has minimal period as subquadratic growth both at 0 and infinity.…”
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Universality of Dirichlet L-functions with shifted characters by Ramūnas Garunkštis

“… We study Dirichlet L-functions with shifted characters L(s, χ, H) = ⅀∞n=1 χ(n+H) ∕ ns, where H is an integer. Here we obtain a joint universality theorem for such functions. …”
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On the Diophantine equation x3=dy2±q6 by Fadwa S. Abu Muriefah

“…Let q>3 denote an odd prime and d a positive integer without any prime factor p≡1(mod3). In this paper, we have proved that if (x,q)=1, then x3=dy2±q6 has exactly two solutions provided q≢±1(mod24).…”
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Divisibility Criteria for Class Numbers of Imaginary Quadratic Fields Whose Discriminant Has Only Two Prime Factors by A. Pekin

“…We will prove a theorem providing sufficient condition for the divisibility of class numbers of certain imaginary quadratic fields by 2g, where g>1 is an integer and the discriminant of such fields has only two prime divisors.…”
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Polynomial Roots and Calabi-Yau Geometries by Yang-Hui He

“…We study the space of roots to certain integer polynomials arising naturally in the context of Calabi-Yau spaces, notably Poincaré and Newton polynomials, and observe various salient features and geometrical patterns.…”
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Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation by Naglaa M. El-Shazly

“…In this paper necessary and sufficient conditions for the matrix equation to have a positive definite solution are derived, where , is an identity matrix, are nonsingular real matrices, and is an odd positive integer. These conditions are used to propose some properties on the matrices , . …”
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Recursive determination of the enumerator for sums of three squares by John A. Ewell

“…For each nonnegative integer n, r3(n) denotes the number of representations of n by sums of three squares. …”
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A note on an extension of Lindelöf's theorem to meromorphic functions by Mohammad Salmassi

“…He also obtained an expression for the characteristic function of a meromorphic function of integer order. In this note we give estimates for log|f(reiθ)| of such functions.…”
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Machine Learning-Based Offloading Strategy for Lightweight User Mobile Edge Computing Tasks by Shuchen Zhou, Waqas Jadoon, Junaid Shuja

“…Firstly, a scheme for multiuser frequency division multiplexing approach in mobile edge computing offloading is proposed, and a mixed-integer nonlinear optimization model for energy consumption minimization is developed. …”
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A novel approach to Lyapunov stability of Caputo fractional dynamic equations on time scale using a new generalized derivative by Michael Precious Ineh, Edet Peter Akpan, Hossam A. Nabwey

“…These examples highlighted the advantage of our definition of fractional-order derivative over integer-order approaches in capturing the intricacies of dynamic behavior.…”
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A Reliable Approach for Solving Transmission Network Expansion Planning with Objective of Planning Cost Reduction by Yongqiu Liu

“…The optimization problem represented in this paper is a large-scale non-convex mixed integer nonlinear programming problem with multiple local minima. …”
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A note on derivations in semiprime rings by Joso Vukman, Irena Kosi-Ulbl

“…We prove in this note the following result. Let n>1 be an integer and let R be an n!-torsion-free semiprime ring with identity element. …”
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An Inconsistency in the Spectrum of Bosonic Open 2-Brane by M. Abdul Wasay, Ding-fang Zeng

“…Moreover, the spectrum of this open 2-brane only contains half integer mass squared values.…”
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Powersum formula for differential resolvents by John Michael Nahay

“…We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the α-resolvent. …”
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Nonplanarity of Iterated Line Graphs by Jing Wang

“…The 1-crossing index of a graph G is the smallest integer k such that the kth iterated line graph of G has crossing number greater than 1. …”
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Fractional Derivative Regularization in QFT by Vasily E. Tarasov

“…We propose in this paper a new regularization, where integer-order differential operators are replaced by fractional-order operators. …”
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Trace theorems for Sobolev-Slobodeckij spaces with or without weights by Doyoon Kim

“…Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev-Slobodeckij spaces Wps(Ω) when s-1/p is an integer.…”
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A combinatorial commutativity property for rings by Howard E. Bell, Abraham A. Klein

“…We study commutativity in rings R with the property that for a fixed positive integer n, xS=Sx for all x∈R and all n-subsets S of R.…”
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On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz by Yuanyuan Deng, Wenpeng Zhang

“…Using the elementary method and some properties of the least solution of Pell’s equation, we prove that the equation xy+yx=zz has no positive integer solutions (x,y,z) with x and y being odd primes.…”
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