New proof and generalization of some results on translated sums over k-almost primes by Laib, Ilias

“…A sequence $\mathcal{A}$ of strictly positive integers is said to be primitive if none of its terms divides the others, Erdős conjectured that the sum $f(\mathcal{A},0)\le f(\mathbb{N}_{1},0),$ where $\mathbb{N}_{1}$ is the sequence of prime numbers and $f(\mathcal{A},h)=\sum _{a\,\in \,\mathcal{A}}$ $\frac{1}{a(\log a+h) }$. …”
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Computation and Calculus for Combinatorial Geometric Series and Binomial Identities and Expansions by Chinnaraji Annamalai

“…Combinatorics involves integers, factorials, binomial coefficients, discrete mathematics, and theoretical computer science for finding solutions to the problems in computing and engineering science. …”
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On the (p,q)th Relative Order Oriented Growth Properties of Entire Functions by Luis Manuel Sánchez Ruiz, Sanjib Kumar Datta, Tanmay Biswas, Golok Kumar Mondal

“…In this paper for any two positive integers p and q, we wish to introduce an alternative definition of relative (p,q)th order which improves the earlier definition of relative (p,q)th order as introduced by Lahiri and Banerjee (2005). …”
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On Complex Differential-Difference Equations of Malmquist Type by Jianjun Zhang

“…In this paper, we shall give some properties of complex differential-difference equation of the form ∑μ=1nαμz∏i=1tfz+ciai0μf′z+ciai1μ⋯fkiz+ciaikiμ/∑ν=1mβνz∏i=1tfz+cibi0νf′z+cibi1ν⋯fkiz+cibikiν=Rz,fz, where aijμ μ=1,2,…,n and bijνν=1,2,…,mi=1,2,…,t;j=0,1,…,ki are non-negative integers, cii=1,2,…,t are distinct, nonzero complex numbers, αμzμ=1,2,…,n and βνzν=1,2,…,m are small functions relative to fz, and Rz,fz is a rational function in fz with coefficients, which are small functions of fz. …”
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Evaluating vehicle trafficability on soft ground using wheel force information by Mingming Liu, Longlong Chen, Yanxi Ren

“…As parts of the proposed approach, the methods of obtaining wheel force information, identification of soil mechanical characteristics parameters and integated method of trafficability evaluation, are discussed in detail. …”
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The Multibases of Symmetric Caterpillars by Supachoke Isariyapalakul, Varanoot Khemmani, Witsarut Pho-on

“…A caterpillar cak1,k2,…,ks is called a symmetric caterpillar if ki=ks−i+1 for all integers i with 1≤i≤s. In this work, the multiresolving sets of symmetric caterpillars are studied.…”
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Nonlinear Dynamics in a Chemical Reaction under an Amplitude-Modulated Excitation: Hysteresis, Vibrational Resonance, Multistability, and Chaos by A. V. Monwanou, A. A. Koukpémèdji, C. Ainamon, P. R. Nwagoum Tuwa, C. H. Miwadinou, J. B. Chabi Orou

“…The effects of the control force on chaotic motions have been strongly analyzed, and the control efficiency is found in the cases g=0 (unmodulated case) and g≠0 with Ω=ω and Ω/w≠p/q; p and q are simple positive integers. Vibrational resonance (VR), hysteresis, and coexistence of several attractors have been studied in detail based on the relationship between the frequencies of the AM force. …”
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Super H-Antimagic Total Covering for Generalized Antiprism and Toroidal Octagonal Map by Amir Taimur, Gohar Ali, Muhammad Numan, Adnan Aslam, Kraidi Anoh Yannick

“…The graph G is said to be a,d-H antimagic total graph if there exists a bijective function f:VH∪EH⟶1,2,3,…,VH+EH such that, for all subgraphs isomorphic to H, the total H weights WH=WH=∑x∈VHfx+∑y∈EHfy forms an arithmetic sequence a,a+d,a+2d,…,a+n−1d, where a and d are positive integers and n is the number of subgraphs isomorphic to H. …”
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Induced Maps on Matrices over Fields by Li Yang, Xuezhi Ben, Ming Zhang, Chongguang Cao

“…Suppose that 𝔽 is a field and m,n≥3 are integers. Denote by Mmn(𝔽) the set of all m×n matrices over 𝔽 and by Mn(𝔽) the set Mnn(𝔽). …”
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Quantitative functional calculus in Sobolev spaces by Carlo Morosi, Livio Pizzocchero

“…Assuming sufficient smoothness for G, we give a “tame” bound on the Hn norm of this composite function in terms of a linear function of the Hn norm of f, with a coefficient depending on G and on the Ha norm of f, for all integers n,a,d with a>d/2. In comparison with previous results on this subject, our bound is fully explicit, allowing to estimate quantitatively the Hn norm of the function x↦G(f(x),x). …”
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Completing a 2×2 Block Matrix of Real Quaternions with a Partial Specified Inverse by Yong Lin, Qing-Wen Wang

“…This paper considers a completion problem of a nonsingular 2×2 block matrix over the real quaternion algebra ℍ: Let m1,  m2,  n1,  n2 be nonnegative integers, m1+m2=n1+n2=n>0, and A12∈ℍm1×n2, A21∈ℍm2×n1, A22∈ℍm2×n2, B11∈ℍn1×m1 be given. …”
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Group-Valued Multisets by Andrei Alexandru, Gabriel Ciobanu

“…Hybrid sets are defined as multisets having also negative multiplicities, i.e. as functions from a crisp set to the group of all integers. In this article, we introduce a significant advancement in hybrid sets through the concept of <i>group-valued multisets</i>. …”
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On incidence algebras and directed graphs by Ancykutty Joseph

“…So in this paper, we define an incidence algebra I(G,ℤ) for (G,≤) over ℤ, the ring of integers, by I(G,ℤ)={fi,fi*:V×V→ℤ} where fi(u,v) denotes the number of directed paths of length i from u to v and fi*(u,v)=−fi(u,v). …”
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Ramp from replica trick by Xuchen Cao, Thomas Faulkner

“…Our method involves an application of the replica trick, where we first calculate the correlator tr ρ A n tr ρ A m $$ \left\langle \textrm{tr}{\rho}_A^n tr{\rho}_A^m\right\rangle $$ at large bond dimension and then analytically continue the indices n, m from integers to arbitrary complex numbers. We use steepest descent methods at large modular times to extract the ramp. …”
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Two-Party Quantum Private Comparison Protocol for Direct Secret Comparison by Min Hou, Yue Wu

“…Our protocol encodes participants’ secret integers directly into the amplitudes of single-photon states and introduces a novel method for secret-to-secret comparison rather than the traditional bit-to-bit comparison, resulting in improved scalability. …”
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Efficient Time-Frequency Localization of a Signal by Satish Chand

“…In our proposed work, we use cosine and sine signals defined over the time intervals, each of length 2πm/(2nω), m≤2n, m and n are nonnegative integers, to develop cosine- and sine-type wavelets. …”
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General encoding of canonical k-mers by Wittler, Roland

“…For efficient indexing or storage, k-mers are often encoded as integers, e.g., applying some bijective mapping between all possible σk k-mers and the interval [0, σk −1], where σ is the alphabet size. …”
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Homogeneous-Like Generalized Cubic Systems by G. R. Nicklason

“…We consider properties and center conditions for plane polynomial systems of the forms x˙=-y-p1(x,y)-p2(x,y), y˙=x+q1(x,y)+q2(x,y) where p1, q1 and p2, q2 are polynomials of degrees n and 2n-1, respectively, for integers n≥2. We restrict our attention to those systems for which yp2(x,y)+xq2(x,y)=0. …”
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Hybrid didactic design in mathematics learning on fraction: A hermeneutic phenomenology by Ahmad Muzaki, Ita Chairun Nissa, Sri Yuliyanti, Masjudin, Muhamad Galang Isnawan

“…The study's findings revealed that students' low ability to operate integers, especially multiplication and division, was a primary factor in learning difficulty. …”
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The evolution of binary system from predynastic Egypt to Leibniz era by Z. Pourfereidouni, M. Radjabalipour

“…The novelty of the present paper is the study of the evolution of the binary number system from the predynastic Egypt down to the Leibniz era who, by the benefit of  Khwarazmi's  "Indian Arithmetics,"  completed this evolution by representing integers in $0-1$ forms and performing the hybrid decimal/binary Egyptian arithmetic operations purely inside the $0-1$ system. …”
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