Search

In this note, we prove a family of sharp weighed inequalities which involve weighted k-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in \mathbb {R}^n. This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao's results. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness problems of fn(z)L(g) and gn(z)L(f) when they share a non-zero small function α(z) with finite weights, where L(h) represents any one of h(k)(z), h(z + c), h(z + c) - h(z) and h(k)(z + c), k ≥ 1 and c is a non-zero constant. Here f(z) and g(z) are transcendental meromorphic (or entire) functions and α(z) is a small function with respect to both f(z) and g(z). Our results improve and supplement the recent results due to Gao and Liu [Bull. Korean Math. Soc. 59 (2022), 155-166]. [ABSTRACT FROM AUTHOR]

In this paper, we focused on a one-dimensional elastic system with a double porosity structure and frictional damping acting on both porous equations. We introduce two stability numbers χ 0 {\chi_{0}} and χ 1 {\chi_{1}} and prove that the solution of the system decays exponentially provided that χ 0 = 0 {\chi_{0}=0} and χ 1 ≠ 0 {\chi_{1}\neq 0} . Otherwise, we prove the absence of exponential decay. Our results improve the results of [N. Bazarra, J. R. Fernández, M. C. Leseduarte, A. Magaña and R. Quintanilla, On the thermoelasticity with two porosities: Asymptotic behaviour, Math. Mech. Solids 24 2019, 9, 2713–2725] and [A. Nemsi and A. Fareh, Exponential decay of the solution of a double porous elastic system, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 83 2021, 1, 41–50]. [ABSTRACT FROM AUTHOR]

In [V. M. Abramov, Bull. Austral. Math. Soc., 104, 108 (2021)], the fixed-point equation was studied for an infinite nonnegative particular Toeplitz matrix. In the present work, we provide an alternative proof of the existence of a positive solution in the general case. This proof is based on the application of a version of the M. A. Krasnosel'skii fixed-point theorem. The results are then extended to the equations with infinite matrices of the general type. [ABSTRACT FROM AUTHOR]

A proper ideal I of a commutative ring R is said to be a strongly quasi-primary ideal if, whenever a , b ∈ R with a b ∈ I , then a 2 ∈ I or b ∈ I (see [S. Koc, U. Tekir and G. Ulucak, On strongly quasi primary ideals, Bull. Korean Math. Soc. 56(3) (2019) 729–743]). This paper studies the class of strongly quasi-primary ideals with a radical equal to the nil-radical of R , called the class of quasi- n -ideals. Among other results, this new class of ideals is used to characterize when the nil-radical of R is a maximal or a minimal ideal of R. Many examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

If p(z) = Xn ν=0 aνz ν is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, Jain [Bull. Math. Soc. Sci. Math. Roumania Tome, 59(2016), 339-347] proved max |z|=1 |p′ (z)| ≥ nAk max |z|=1 |p(z)|, where Ak = ( |a0| + |an|k n+1/ |ao|(1 + k n+1) + |an|(k n+1 + k 2n) ) . In this paper, we initially derive a generalized form that not only encompasses but also enhances the aforementioned inequality. Additionally, we extend this formulation to a more comprehensive result, thereby producing an improved outcome for certain established inequalities as a specific instance. [ABSTRACT FROM AUTHOR]

Leonetti and Luca ['On the iterates of the shifted Euler's function', Bull. Aust. Math. Soc. , to appear] have shown that the integer sequence $(x_n)_{n\geq 1}$ defined by $x_{n+2}=\phi (x_{n+1})+\phi (x_{n})+k$ , where $x_1,x_2\geq 1$ , $k\geq 0$ and $2 \mid k$ , is bounded by $4^{X^{3^{k+1}}}$ , where $X=(3x_1+5x_2+7k)/2$. We improve this result by showing that the sequence $(x_n)$ is bounded by $2^{2X^2+X-3}$ , where $X=x_1+x_2+2k$. [ABSTRACT FROM AUTHOR]

In this short note we show that Doyle-Grigor'yan criterion for non-parabolicity is not necessary in dimension greater than or equal to four. This gives an negative answer to Problem # 1 of Grigor'yan [Bull. Amer. Math. Soc. (N.S) 36 (1999). pp. 135–249] in this dimensional range. [ABSTRACT FROM AUTHOR]

In this paper, for d ≥ 1 and s ∈ (0 , d 2) , we study the Bianchi–Egnell quotient Q (f) = inf f ∈ H ˙ s (R d) \ B ‖ (- Δ) s / 2 f ‖ L 2 (R d) 2 - S d , s ‖ f ‖ L 2 d d - 2 s (R d) 2 dist H ˙ s (R d) (f , B) 2 , f ∈ H ˙ s (R d) \ B , where S d , s is the best Sobolev constant and B is the manifold of Sobolev optimizers. By a fine asymptotic analysis, we prove that when d = 1 , there is a neighborhood of B on which the quotient Q (f) is larger than the lowest value attainable by sequences converging to B . This behavior is surprising because it is contrary to the situation in dimension d ≥ 2 described recently in König (Bull Lond Math Soc 55(4):2070–2075, 2023). This leads us to conjecture that for d = 1 , Q (f) has no minimizer on H ˙ s (R d) \ B , which again would be contrary to the situation in d ≥ 2 . As a complement of the above, we study a family of test functions which interpolates between one and two Talenti bubbles, for every d ≥ 1 . For d ≥ 2 , this family yields an alternative proof of the main result of König (Bull Lond Math Soc 55(4):2070–2075, 2023). For d = 1 we make some numerical observations which support the conjecture stated above. [ABSTRACT FROM AUTHOR]

The set of degrees of maps D(M,N), where M,N are closed oriented n-manifolds, always contains 0 and the set of degrees of self-maps D(M) always contains 0 and 1. Also, if a,b\in D(M), then ab\in D(M); a set A\subseteq \mathbb {Z} so that ab\in A for each a,b\in A is called multiplicative. On the one hand, not every infinite set of integers (containing 0) is a mapping degree set (Neofytidis, Wang, and Wang [Bull. Lond. Math. Soc. 55 (2023), pp. 1700–1717]) and, on the other hand, every finite set of integers (containing 0) is the mapping degree set of some 3-manifolds (Costoya, Muñoz and Viruel [ Finite sets containing zero are mapping degree sets , arXiv: 2301.13719 ]). We show the following: Not every multiplicative set A containing 0,1 is a self-mapping degree set. For each n\in \mathbb {N} and k\geq 3, every D(M,N) for n-manifolds M and N is D(P,Q) for some (n+k)-manifolds P and Q. As a consequence of (ii) and Costoya, Muñoz and Viruel, every finite set of integers (containing 0) is the mapping degree set of some n-manifolds for all n\neq 1,2,4,5. [ABSTRACT FROM AUTHOR]

This paper presents a series of results about the fuzzy degree of a hypergoup. It is considered a sequence of membership functions and of join spaces, obtained by starting with a hypergroupoid (H, ⊗), see Corsini's paper [Southeast Asian Bull. Math. 27 (2003) 221-229]. The fuzzy grade is the minumum natural number i such that two consecutive associated join spaces, of the above mentioned sequence, Hi and Hi+1 are isomorphic. [ABSTRACT FROM AUTHOR]

Inspired by a determinantal inequality for partial traces given by Lin [Can Math Bull 59 (2016)], we present some inequalities related to the partial determinants of positive semidefinite block matrices. Some interesting inequalities involving determinants are included. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of at least three weak solutions for the fourth-order problem with indefinite weights involving the Leray–Lions operator with nonstandard growth conditions. We generalize the result obtained by Kefi et al. [On the fourth-order Leray–Lions problem with indefinite weight and nonstandard growth conditions. Bull Math Sci. 2021;DOI:10.1142/S1664360721500089]. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano [On the structure of the critical set of nondifferentiable functions with a weak compactness condition. Appl Anal. 2010;89:1–10]. [ABSTRACT FROM AUTHOR]

We correct mistakes in Lemma 8 and in the proof of Lemma 10 from (Bull. Lond. Math. Soc. 49 (2017), no. 6, 965–978). [ABSTRACT FROM AUTHOR]

If is a polynomial of degree n having all its zeros in |z| 6 k, k > 1, V.K. Jain [Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 59 (2016), 339-347] proved We first obtain a generalization as well as improvement of the above inequality. Further, we extend our first result to a more generalized result which yields improved results of some known inequalities as particular case. [ABSTRACT FROM AUTHOR]

This note is a corrigendum to the author's paper "On a Problem of Lang for Matrix Polynomials, Bull. London Math. Soc. 54 (2022), 1552–1567". [ABSTRACT FROM AUTHOR]