Behavior of a Competitive System of Second-Order Difference Equations by Q. Din, T. F. Ibrahim, K. A. Khan

“…We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: xn+1=(α1+β1xn-1)/(a1+b1yn), yn+1=(α2+β2yn-1)/(a2+b2xn), where the parameters αi, βi, ai, and bi for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. Some numerical examples are given to verify our theoretical results.…”
Get full text

The Interconnection Between Calculus of Variations, Partial Differential Equations and Differential Geometry by Delphin Mwinken

“…Calculus of variations is a fundamental mathematical discipline focused on optimizing functionals, which map sets of functions to real numbers. This field is essential for numerous applications, including the formulation and solution of partial differential equations (PDEs) and the study of differential geometry. …”
Get full text

Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero by R. N. Rath, J. G. Dix, B. L. S. Barik, B. Dihudi

“…We find necessary conditions for every solution of the neutral delay difference equation Δ(rnΔ(yn−pnyn−m))+qnG(yn−k)=fn to oscillate or to tend to zero as n→∞, where Δ is the forward difference operator Δxn=xn+1−xn, and pn, qn, rn are sequences of real numbers with qn≥0, rn>0. Different ranges of {pn}, including pn=±1, are considered in this paper. …”
Get full text

Holderian functional central limit theorem for linear processes by Mindaugas Juodis

“… Let (Xt)t ≥ 1 be a linear process defined by Xt =  ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of  real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. …”
Get full text

Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals by Aneta Sikorska-Nowak

“…We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. …”
Get full text

Function smoothing regularization for precision factorization machine annealing in continuous variable optimization problems by Katsuhiro Endo, Kazuaki Z. Takahashi

“…This study shows that in the widely used case where real numbers are represented by a combination of binary variables, the function surface of the Hamiltonian obtained by FM can be very noisy. …”
Get full text

Some Generalizations of Ulam-Hyers Stability Functional Equations to Riesz Algebras by Faruk Polat

“…Let 𝜀 and 𝛿 be nonnegative real numbers, then for every mapping 𝑓 of a ring ℛ onto a Banach algebra ℬ satisfying ||𝑓(𝑥+𝑦)−𝑓(𝑥)−𝑓(𝑦)||≤𝜀 and ||𝑓(𝑥⋅𝑦)−𝑓(𝑥)𝑓(𝑦)||≤𝛿 for all 𝑥,𝑦∈ℛ, there exists a unique ring homomorphism ℎ∶ℛ→ℬ such that ||𝑓(𝑥)−ℎ(𝑥)||≤𝜀,𝑥∈ℛ. …”
Get full text

Real Root Polynomials and Real Root Preserving Transformations by Suchada Pongprasert, Kanyarat Chaengsisai, Wuttichai Kaewleamthong, Puttarawadee Sriphrom

“…Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial p with complex coefficients has a complex root. …”
Get full text

Ulam-Hyers Stability of Trigonometric Functional Equation with Involution by Jaeyoung Chung, Chang-Kwon Choi, Jongjin Kim

“…Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. …”
Get full text

Efficient discrimination between real and complex quantum theories by Josep Batle, Tomasz Białecki, Tomasz Rybotycki, Jakub Tworzydło, Adam Bednorz

“…We improve the test to show the impossibility of a quantum theory based on real numbers by a larger ratio of complex-to-real bound on a Bell-type parameter. …”
Get full text

Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables by Dug Hun Hong, Seok Yoon Hwang

“…If P{|Xmn|≥t}≤P{|X|≥t} for all nonnegative real numbers t and E|X|p(log+|X|)3<∞, for 1<p<2, then we prove that ∑i=1m∑j=1n(Xij−EXij)(mn)1/p→0    a.s.   …”
Get full text

Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 by Stevo Stević, Bratislav Iričanin

“…The following difference equation xn=xn−lxn−k−1, n∈ℕ0, where k,l∈ℕ, k<l, gcd(k,l)=1, and the initial values x-l,…,x-2,x-1 are real numbers, has been investigated so far only for some particular values of k and l. …”
Get full text

Generalized Fuzzy Bonferroni Harmonic Mean Operators and Their Applications in Group Decision Making by Jin Han Park, Eun Jin Park

“…In particular, all these operators can be reduced to aggregate interval or real numbers. Then based on the GFWBHM and GFOWBHM operators, we present an approach to multiple attribute group decision making and illustrate it with a practical example.…”
Get full text

Bounds of Degree-Based Molecular Descriptors for Generalized F-sum Graphs by Jia Bao Liu, Sana Akram, Muhammad Javaid, Abdul Raheem, Roslan Hasni

“…A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. …”
Get full text

Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…It is also proved that construction of extended real hypernumbers is defined by a definite invariance principle: the space of all extended real hypernumbers is the biggest Hausdorff factorization of the sequential extension of the space of all real numbers with the topology of conical neighborhoods. …”
Get full text

Dynamics of the rational difference equations by Burak Oğul

“…The method presented may be simply applied to other rational recursive issues. nIn this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial valueb 𝑥𝑛+1 = 𝑥𝑛𝑥𝑛−8 ±𝑥𝑛−7 ± 𝑥𝑛𝑥𝑛−7𝑥𝑛−8 , 𝑛 ∈ N0.…”
Get full text

Univalent functions maximizing Re[f(ζ1)+f(ζ2)] by Intisar Qumsiyeh Hibschweiler

“…The situation where the extremal value is equal to zero can occur and it is proved, in this case, that the Koebe function is a solution if and only if z1 and z2 are both real numbers and z1z2<0.…”
Get full text

Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense by Ferenc Móricz, U. Stadtmüller

“…In the case of double sequences of real numbers, we present necessary and sufficient Tauberian conditions, which are so-called one-sided conditions. …”
Get full text

Eventually Periodic Solutions of a Max-Type Difference Equation by Taixiang Sun, Jing Liu, Qiuli He, Xin-He Liu, Chunyan Tao

“…We study the following max-type difference equation xn=max⁡{An/xn-r,xn-k}, n=1,2,…, where {An}n=1+∞ is a periodic sequence with period p and k,r∈{1,2,…} with gcd(k,r)=1 and k≠r, and the initial conditions x1-d,x2-d,…,x0 are real numbers with d=max⁡{r,k}. We show that if p=1 (or p≥2 and k is odd), then every well-defined solution of this equation is eventually periodic with period k, which generalizes the results of (Elsayed and Stevic´ (2009), Iričanin and Elsayed (2010), Qin et al. (2012), and Xiao and Shi (2013)) to the general case. …”
Get full text

Novel Development to the Theory of Dombi Exponential Aggregation Operators in Neutrosophic Cubic Hesitant Fuzzy Sets: Applications to Solid Waste Disposal Site Selection by Ateeq Ur Rehman, Muhammad Gulistan, Nasreen Kausar, Sajida Kousar, Mohammed M. Al-Shamiri, Rashad Ismail

“…Then, we proposed Dombi exponential operational laws in which the exponents are neutrosophic cubic hesitant fuzzy values and bases are positive real numbers. To use neutrosophic cubic hesitant fuzzy sets in decision-making, we are developing Dombi exponential aggregation operators in the current study. …”
Get full text