Bulletin of The Iranian Mathematical Society最新文献

Following closely the analysis performed by Andrew C. Fowler to derive the first canonical equation for nonlinear dune dynamics, but considering some appropriate changes of variables, suitable scalings, and by neglecting higher-order terms, we obtain an adaptation of the aforementioned equation, which contains an additional term, to describe dune morphodynamics.

The first part of this paper introduces and studies the class of strongly nonnil-coherent rings, a subclass of the already defined and studied class of nonnil-coherent rings. Contrary to the classical result that every Noetherian ring is coherent, a nonnil-Noetherian ring need not be nonnil-coherent. To remedy this, the second part introduces and studies the class of strongly nonnil-Noetherian rings, a subclass of the class of nonnil-Noetherian rings. Some examples are also given to illustrate the results.

Abstract

In this study, we demonstrate that any solution to the Finslerian Ricci flow encountering a singularity on a compact manifold is invariably associated with an unbounded hh-curvature tensor. Furthermore, we establish the extended temporal viability of the Finslerian Ricci flow under the constraint of bounded curvature. To achieve this, we derive the evolution equation for the hh-curvature tensor and establish precise estimates for the covariant derivatives of the Cartan curvature tensor.

Let K/F be a finite extension of number fields and S be a finite set of primes of F, including all the Archimedean ones. In this paper, using some results of González-Avilés (J Reine Angew Math 613:75–97, 2007), we generalize the notions of the relative Pólya group ({{,textrm{Po},}}(K/F)) (Chabert in J Number Theory 203:360–375, 2019; Maarefparvar and Rajaei in J Number Theory 207:367-384, 2020) and the Ostrowski quotient ({{,textrm{Ost},}}(K/F)) (Shahoseini et al. in Pac J Math 321(2):415–429, 2022) to their S-versions. Using this approach, we obtain generalizations of some well-known results on the S-capitulation map, including an S-version of Hilbert’s Theorem 94.

A. Huber and B. Kahn construct a relative slice filtration on the motive M(X) associated to a principal T-bundle (Xrightarrow Y) for a smooth scheme Y. As a consequence of their result, one can observe that the mixed Tateness of the motive M(Y) implies that the motive M(X) is mixed Tate. In this note we prove the inverse implication for a principal G-bundle, for a split reductive group G.

In this paper, we prove the non-existence of non-trivial statistical structures of constant holomorphic sectional curvature based on complex space forms with dimension greater than 2. For 2-dimensional complex space forms we show an example to illustrate there do exist non-trivial statistical structures of constant holomorphic sectional curvature, and we also obtain a rigidity theorem in this case. Finally, in contrast to complex space forms, we construct some new examples of non-trivial statistical structures of constant sectional curvature based on real space forms.

In this paper, we shall consider a new constant (DW_B(X)) which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant (DW^p_B(X)) that is a generalization of (DW_B(X)). Interestingly, the upper bounds of (DW_B(X)) and the Dunkl–Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere and calculate the value of (DW^p_B(l_infty -l_1)).

Partially balanced incomplete block (PBIB)-designs are well known to be the generalization of combinatorial 2-designs. In this paper, we first construct PBIB-designs from diametral paths of distance-regular graphs, which generalizes the result for strongly regular graphs. Furthermore, for Q-polynomial distance-regular graphs associated with regular semilattices, we obtain the construction of PBIB-designs through descendents with fixed dual width.

Abstract

In this paper, we consider the biharmonic Choquard equation with the nonlocal term on the weighted lattice graph ({mathbb {Z}}^N) , namely for any (p>1) and (alpha in (0,,N)) $$begin{aligned} Delta ^2u-Delta u+V(x)u=left( sum _{yin {mathbb {Z}}^N,,ynot =x}frac{|u(y)|^p}{d(x,,y)^{N-alpha }}right) |u|^{p-2}u, end{aligned}$$ where (Delta ^2) is the biharmonic operator, (Delta ) is the (mu ) -Laplacian, (V:{mathbb {Z}}^Nrightarrow {mathbb {R}}) is a function, and (d(x,,y)) is the distance between x and y. If the potential V satisfies certain assumptions, using the method of Nehari manifold, we prove that for any (p>(N+alpha )/N) , there exists a ground state solution of the above-mentioned equation. Compared with the previous results, we adopt a new method to finding the ground state solution from mountain-pass solutions.

Suppose that x is a sufficiently large number and (jge 2) is any integer. Let (L(s, textrm{sym}^j f)) be the j-th symmetric power L-function associated with the primitive holomorphic cusp form f of weight k for the full modular group SL(_{2}(mathbb {Z})). Also, let (lambda _{textrm{sym}^j f}(n)) be the n-th normalized Dirichlet coefficient of (L(s, textrm{sym}^j f)). In this paper, we establish asymptotic formulas for sums of Dirichlet coefficients (lambda _{textrm{sym}^j f}(n)) over two sparse sequences of positive integers, which improves previous results.