Under certain assumptions we show that a wavelet frame {τ(Aj , bj,k)ψ}j,k∈Z := {|detAj |−1/2ψ(A−1 j (x− bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj,k are perturbed. As a special case of our result, we obtain that if {τ(Aj , ABn)ψ}j∈Z,n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {τ(Aj , ABλn)ψ}j∈Z,n∈Zd is a ...

Rationale: Aging represents a major risk factor for coronary artery disease and aortic aneurysm formation. MicroRNAs (miRs) have emerged as key regulators of biological processes, but their role in age-associated vascular pathologies is unknown. Objective: We aim to identify miRs in the vasculature that are regulated by age and play a role in age-induced vascular pathologies. Methods and Result...

We consider the dissipative singular q-Sturm-Liouville operators acting in Hilbert space L2 w,q(R+), that extensions of a minimal symmetric operator with deficiency indices (2, 2) (in limit-circle case).We construct self-adjoint dilation and its incoming outgoing spectral representations, which make it possible to determine scattering matrix terms Weyl-Titchmarsh function operator. also functio...

Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in a...

The zero-dilation index d(A) of an n-by-n complex matrix A is the maximum size of the zero matrix which can be dilated to A. In this paper, we determine the value of this index for the KMS matrix Jn(a) =  0 a a · · · an−1 0 a . . . .. . . . . . . a . . . a 0 0  , a ∈ C and n ≥ 1, by using the Li–Sze characterization of higher-rank numerical ranges of a finite matrix. 1 Departmen...

The matricellular protein thrombospondin (TSP) 1 is induced after tissue injury and may regulate reparative responses by activating transforming growth factor-β, by suppressing angiogenesis and by modulating inflammation and matrix metabolism. We hypothesized that endogenous TSP-1 may be involved in the pathogenesis of cardiac remodeling in the pressure-overloaded heart. Myocardial TSP-1 expres...

For each r ∈ N, we construct a family of bivariate orthogonal wavelets with compact support that are nonseparable and have vanishing moments of order r or less. The starting point of the construction is a scaling function that satisfies a dilation equation with special coefficients and a special dilation matrix M : the coefficients are aligned along two adjacent rows, and |det(M)| = 2. We prove...

BACKGROUND The sequelae of aortic root dilation are the lethal consequences of Marfan syndrome. The root dilation is attributable to an imbalance between deposition of matrix elements and metalloproteinases in the aortic medial layer as a result of excessive transforming growth factor-beta signaling. This study examined the efficacy and mechanism of statins in attenuating aortic root dilation i...