Bulletin of The Iranian Mathematical Society最新文献

Let (({mathcal {L}}, {mathcal {A}})) be a complete duality pair. When R is a commutative ring, we prove a Quillen equivalence induced by a Sharp–Foxby adjunction on R-Mod associated to (({mathcal {L}}, {mathcal {A}})) between the Gorenstein (({mathcal {L}}, {mathcal {A}}))-projective and injective model categories, which results in a triangle equivalence between the stable category of Gorenstein (({mathcal {L}}, {mathcal {A}}))-projective modules and the stable category of Gorenstein (({mathcal {L}}, {mathcal {A}}))-injective modules. In addition, let R and (R^{prime }) be two (not necessarily commutative) rings. Under some conditions, we investigate the other Quillen equivalence between two Gorenstein (({mathcal {L}}, {mathcal {A}}))-projective model categories and prove that two stable categories consisting of all Gorenstein (({mathcal {L}}, {mathcal {A}}))-projective R-modules and all Gorenstein (({mathcal {L}}, {mathcal {A}}))-projective (R^{prime })-modules respectively are triangle equivalent by Frobenius functors.

We investigate the space-time decay rate of solution to the 3D Cauchy problem of the compressible Navier–Stokes–Korteweg system. Based on the previous temporal decay results for this system, it is shown that for any integer (Nge 3), the space-time decay rate of (kleft( in left[ 0, Nright] right) )-order spatial derivative of the solution in weighted space (H^{N-k}_{gamma }) is (t^{-frac{3}{4}-frac{k}{2}+gamma }). Our methods mainly involve delicate weighted energy estimates and interpolation trick.

In this paper, we present a Kantorovich-type Szász–Mirakjan operators. Initially, we establish the recurrence relationship for the moments of these operators and provide the central moments up to the fourth degree. Subsequently, we analyze the local approximation properties of these operators using Peetre’s K-function. We investigate the rate of convergence, by utilizing the ordinary modulus of continuity and Lipschitz-type maximal functions. Additionally, we prove weighted approximation theorems and Voronoskaja-type theorems specific to these new operators. Following this, we introduce bivariate extension of these operators and investigate some approximation properties. Lastly, we include several numerical illustrative examples.

This paper presents a theoretical exploration of local Hardy spaces associated with special para-accretive functions, denoted as (h_b^p(X)), where X is a space of homogeneous type. In pursuit of this goal, we establish inhomogeneous Plancherel–Pôlya inequality and subsequently derive the atomic and block decomposition characterizations for (h_b^p(X)). Furthermore, we culminate our study by demonstrating the boundedness of ((delta ,sigma ))-type inhomogeneous Calderón–Zygmund operators on (h_b^p(X)) with (max {frac{1}{1+delta },frac{1}{1+sigma }}<ple 1) when (T_b^*(1)in Lip_b(varepsilon )), where (varepsilon ) represents the regularity exponent of the approximation to the identity.

Let k be a commutative ring, and let (Lambda ) and (Gamma ) be two k-algebras. In this paper, we give upper and lower bounds of Gorenstein global dimension and Gorenstein weak dimension over the tensor product (Lambda otimes _k Gamma ). As its applications, the Gorenstein dimensions of several special algebras such as group algebras, matrix algebras, triangular matrix algebras and polynomial algebras can be computed. Moreover, we compare the Gorenstein global dimension of the enveloping algebra (Lambda ^e) of (Lambda ) with the Gorenstein projective dimension of (Lambda ). Some well-known results are also extended.

In this paper, all string modules of one class of basic Hopf algebras of tame type, which are denoted by (mathbb {H}_2) are studied. Firstly, the isomorphism classes of all string modules of (mathbb {H}_2) are classified. Then the projective class ring of (mathbb {H}_2) is described. Finally, the McKay matrix and the corresponding McKay quiver of (mathbb {H}_2) are discussed.

Two Riemannian manifolds are said to be isospectral if there exists a unitary operator which intertwines their Laplace-Beltrami operator. In this paper, we prove in the non-compact setting the inaudibility of the weak symmetry property and the commutative property using an isospectral pair of 23 dimensional generalized Heisenberg groups.

Denote by (mathbb {H}) the set of all quaternions. We are interested in the group (U(1,1;mathbb {H})), which is a subgroup of (2times 2) quaternionic matrix group and is sometimes called Sp(1, 1). As well known, (U(1,1;mathbb {H})) corresponds to the quaternionic Möbius transformations on the unit ball in (mathbb {H}). In this article, some similarity invariants on (U(1,1;mathbb {H})) are discussed. Our main result shows that each matrix (Tin U(1,1;mathbb {H})), which corresponds to an elliptic quaternionic Möbius transformation (g_T(z)), could be (U(1,1;mathbb {H}))-similar to a diagonal matrix. Moreover, one can see that each elliptic quaternionic Möbius transformation is quaternionic Möbius conjugate to a bi-rotation, where a bi-rotation means a map (zrightarrow pcdot z cdot q^{-1}) for some (p,qin mathbb {H}) with (|p|=|q|=1).

In this paper, we study the generalized gapped k-mer filters and derive a closed form solution for their coefficients. We consider nonnegative integers (ell ) and k, with (kle ell ), and an (ell )-tuple (B=(b_1,ldots ,b_{ell })) of integers (b_ige 2), (i=1,ldots ,ell ). We introduce and study an incidence matrix (A=A_{ell ,k;B}). We develop a Möbius-like function (nu _B) which helps us to obtain closed forms for a complete set of mutually orthogonal eigenvectors of (A^{top } A) as well as a complete set of mutually orthogonal eigenvectors of (AA^{top }) corresponding to nonzero eigenvalues. The reduced singular value decomposition of A and combinatorial interpretations for the nullity and rank of A, are among the consequences of this approach. We then combine the obtained formulas, some results from linear algebra, and combinatorial identities of elementary symmetric functions and (nu _B), to provide the entries of the Moore–Penrose pseudo-inverse matrix (A^{+}) and the Gapped k-mer filter matrix (A^{+} A).

Let ({{,textrm{Kern},}}(G)) denote the set of nonlinear irreducible character kernels of a finite group G. In this paper, we classify decomposable groups G with (|{{,textrm{Kern},}}(G)|le 3). In particular, nilpotent groups G with(|{{,textrm{Kern},}}(G)|le 3) are determined.