ABSTRACT: In this paper we improve the known bound for the X-rank RX(P ) of an element P ∈ PN in the case in which X ⊂ Pn is a projective variety obtained as a linear projection from a general v-dimensional subspace V ⊂ Pn+v . Then, if X ⊂ Pn is a curve obtained from a projection of a rational normal curve C ⊂ Pn+1 from a point O ⊂ Pn+1, we are able to describe the precise value of the X-rank f...

Bone remodeling requires a precise balance between resorption and formation. It is a complex process that involves numerous factors: hormones, growth factors, vitamins, and cytokines, and notably osteoprotegerin (OPG) and receptor activator for nuclear factor-κB (RANK) ligand. The signaling pathway OPG/RANK/RANKL is key to regulation for maintaining the balance between the activity of osteoblas...

Abstract We study ensembles of sparse block-structured random matrices generated from the adjacency matrix a Erdös–Renyi graph with N vertices average degree Z , inserting real symmetric d × block at each non-vanishing entry. consider several rank r &lt; and maximal rank, = . The spectral moments are evaluated for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"...

Bone biology and the molecular basis of normal bone remodeling are important for understanding bone health, particularly for medical professionals who are treating patients with skeletal complications. Key factors in bone remodeling include RANK ligand, which stimulates bone resorption, and osteoprotegerin (OPG), which inhibits bone resorption. The ratio between these two factors regulates oste...

In this paper we consider a problem of the similarity complex symmetric operators to perturbations restrictions normal operators. For subclass cyclic in finite-dimensional Hilbert space prove rank-one The main tools are truncated moment $\mathbb{C}$, and some objects similar from theory spectral problems for Jacobi matrices.