Band 73, Heft 5

ABSTRACT In this paper, we characterize the perfect zero-divisor graphs and chordal zero-divisor graphs (its complement) of ordered sets. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graphs of rings, the annihilating ideal graphs of rings, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of groups. In fact, it is shown that these graphs associated with a commutative ring R with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from R .

A bstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q ; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q ; third, two quantales are Morita equivalent if and only if they have a joint enlargement. To prove these theorems, we use quantale matrices and modules and Morita contexts of quantales. Our main theorems and their proofs are parallel to those known for idempotent rings.

ABSTRACT The Padovan sequence { P n } n ≥0 is a ternary recurrent sequence defined recursively by the relation P n = P n –2 + P n –3 with initials P 0 = P 1 = P 2 = 1. In this note, we search all pairs of multiplicative dependent vectors whose coordinates are Padovan numbers. For this purpose, we apply Matveev’s theorem to find the lower bounds of the non-zero linear forms in logarithms. Techniques involving the LLL algorithm and the theory of continued fraction are utilized to reduce the bounds.

ABSTRACT In this paper, we provide Dirichlet series with periodic coefficients that have Riemann’s functional equation and real zeros of Dirichlet L-functions. The details are as follows. Let L ( s, χ ) be the Dirichlet L -function and G ( χ ) be the Gauss sum associated with a primitive Dirichlet character χ (mod q ). We define f(s,χ):=qsL(s,χ)+ i−κ(χ)G(χ)L(s,χ¯) , where χ¯ is the complex conjugate of χ and κ ( χ ) := (1 – χ (−1))/2. Then, we prove that f ( s , χ ) satisfies Riemann’s functional equation in Hamburger’s theorem if χ is even. In addition, we show that f ( σ , χ ) ≠ 0 for all σ ≥ 1. Moreover, we prove that f ( σ , χ ) ≠ 0 for all 1/2 ≤ σ < 1 if and only if L ( σ , χ ) ≠ 0 for all 1/2 ≤ σ < 1. When χ is real, all zeros of f ( s , χ ) with ℜ(s)>0 are on the line σ = 1/2 if and only if the generalized Riemann hypothesis for L ( s , χ ) is true. However, f ( s , χ ) has infinitely many zeros off the critical line σ = 1/2 if χ is non-real.

ABSTRACT In this paper, we exhibit a rational parametric solution for the Diophantine equations of diagonal quartic varieties. Our approach is based on utilizing the Calabi-Yau varieties including elliptic curves and diagonal quartic surfaces.

ABSTRACT We investigate the non-univalent function’s properties reminiscent of the theory of univalent starlike functions. Let the analytic function ψ(z)=∑i=1∞Aizi , A 1 ≠ 0 be univalent in the unitdisk. Non-univalent functions may be found in the class ℱ(ψ) of analytic functions f of the form f(z)=z+∑k=2∞akzk satisfying ( zf ′ ( z )/ f ( z ) – 1) ≺ ψ ( z ). Such functions, like the Ma and Minda classes k=2 of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class ℱ(ψ) . Non-analytic functions that share properties of analytic functions are known as poly-analytic functions. Moreover, we compute Bohr and Rogosinski’s radius for poly-analytic functions with analytic counterparts in the class ℱ(ψ) or classes of Ma-Minda starlike and convex functions.

ABSTRACT The purpose of this paper is to find coefficient estimates for the class of functions ℳN(γ,ϑ,λ) consisting of analytic functions f normalized by f (0) = f′ (0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a 2 , a 3 , and the Fekete-Szegő functional upper bound for f∈ℳN(γ,ϑ,λ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series.

ABSTRACT We prove a conjecture concerning the third Hankel determinant, proposed by Kumar and Kamaljeet in [A cardioid domain and starlike functions , Anal. Math. Phys. 11 (2021), Art. 54], which states that | H 3 (1)| ≤ 1/9 is sharp for the class S℘*={zf′(z)/f(z)≺φ(z):=1+zez} . In addition, we also establish bounds for sixth and seventh coefficient, and | H 4 (1)| for functions in S℘* . The general bounds for two and three folds symmteric functions related with the Ma-Minda classes S*(φ) of starlike functions are also obtained.

ABSTRACT In this paper, the sharp solutions of Fekete-Szegö problems are provided for class of quasi-convex mappings f 1 of type B and class of quasi-convex mappings f 2 of type B and order α defined on the unit ball in a complex Banach space, respectively, where x = 0 is a zero of order k + 1 of f i ( x ) − x ( i = 1, 2). Compare with some recent works, our main theorems hold without additional restrictive conditions. Also, the proof of our main theorems are more simple than those given in the previous results.

ABSTRACT In this paper, we mainly present some completely monotonic properties and new inequalities involving the k -gamma and the k -polygamma functions.

ABSTRACT This paper is concerned with the oscillation criteria of odd-order non-linear differential equations with mixed non-linear neutral terms. We provide new oscillation criteria that improve, expand, and simplify existing ones. Moreover, some examples are provided to demonstrate the theoretical findings.

ABSTRACT In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.

ABSTRACT We provide an overview of the known problem on the existence of a bi-Lipschitz equivalent metric with respect to a given quasi-ultrametric, revisiting known results and counterexamples in an unified approach based on the existence of a relaxed polygonal inequality. We present new proofs and characterizations of classical results using different techniques.

ABSTRACT In this work, a two-parameter continuous distribution, namely the Lehmann type II Teissier distribution is introduced. Some important properties including the Rényi entropy, Bonferroni curves, Lorenz curves and the exact information matrix of the proposed model are derived. Seven different techniques are being used for the estimation of parameters and a simulation is carried out to observe the maximum likelihood estimates. Interval estimates of the parameters are obtained using exact information matrix and bootstrapping techniques. Finally, to show the practical significance, three datasets related to COVID-19 and rainfall are modeled using the proposed model.

ABSTRACT In this paper, the results of El-Adll et al. [ Asymptotic prediction for future observations of a random sample of unknown continuous distribution , Complexity 2022 (2022), Art. ID 4073799], are extended to the lower negative tail index distributions. Three distinct estimators of the lower negative tail index are proposed, as well as an asymptotic confidence interval. Moreover, different asymptotic predictive intervals for future observations are constructed for distributions attracted to the lower extreme value distribution with a negative tail index. Furthermore, the asymptotic maximum likelihood estimator (AMLE) of the shape parameter, as well as an asymptotic maximum likelihood predictor (AMLP), are obtained. Finally, extensive simulation studies are conducted to demonstrate the efficiency of the proposed methods.

ABSTRACT Analytic expressions for the single and joint life annuities based on the Makeham–Beard mortality law have been derived recently in the literature, which depend on special mathematical functions such as hypergeometric functions. We verify that the arguments of the hypergeometric functions in the analytic expressions for the single and joint life annuities may assume values very close to unity (boundary of the convergence radius), and so numerical problems may arise when using them in practice. We provide, therefore, alternative analytic expressions for the single and joint life annuities where the arguments of the hypergeometric functions in the new analytic expressions do not assume values close to one.

ABSTRACT We compute the rational zero-divisor cup-length of the oriented partial flag manifold F˜(n1,…,nk)\[\widetilde{F}\left( {{n}_{1}},\ldots,{{n}_{k}} \right)\] of type ( n 1 ,…, n k ), k ≥ 2. For certain classes of oriented partial flag manifolds, we compare the rational zero-divisor cup-length and the ℤ2\[{{\mathbb{Z}}_{2}}\]-zero-divisor cup-length.