Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turn out that Delannoy matrix, Pascal matrix, and Fibonacci matrix are all special cases of the generalized Delannoy matrices, meanwhile Schröder matrix and Catalan matrix also arise in involving inverses of the generalized Delannoy matrices. These connections are the focus of our paper. The half o...

In degenerative intervertebral discs (IVD), type X collagen (COL X) expression (associated with hypertrophic differentiation) and calcification has been demonstrated. Suppression of COL X expression and calcification during disc degeneration can be therapeutic. In the present study we investigated the potential of human parathyroid hormone 1-34 (PTH) in suppressing indicators of calcification p...

Chronic lithium (Li) therapy, used extensively in the treatment of bipolar affective disorders, is one of psychiatry's most effective treatments. The data on the effects of Li on baseline PTH and calcium (Ca) levels are conflicting. A clear resetting of the PTH set-point to the right was documented in vitro; however, the effect of Li on the Ca-PTH axis has not been rigorously studied in vivo. I...

This paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system. Given an approximate value of the average of the initial condition of the network state and some intermediate values of the network state when performing a Laplacian-based average consensus, the estimation of the Laplacian eig...

Abstract Background To investigate the causal association between serum 25-hydroxyvitamin D (25OHD), calcium (Ca), and parathyroid hormone (PTH) levels risk of coronary artery disease (CAD) in patients with diabetes using a Mendelian randomization approach. Methods Genetic signatures associated 25OHD, Ca, PTH were extracted from recently published genome-wide study (GWAS), including 79,366, 39,...

The cells of the parathyroid gland secrete parathyroid hormone (PTH), which plays a pivotal role in maintaining circulating levels of ionized calcium (Ca2þ) within a narrow physiological range. The main actions of PTH include (i) releasing calcium and phosphorus from bone, (ii) decreasing renal calcium excretion, (iii) increasing urinary phosphorus excretion and (iv) stimulating renal productio...

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

We present a method for computing pth roots using a polynomial basis over finite fields Fq of odd characteristic p, p ≥ 5, by taking advantage of a binomial reduction polynomial. For a finite field extension Fqm of Fq our method requires p− 1 scalar multiplication of elements in Fqm by elements in Fq. In addition, our method requires at most (p − 1)dm/pe additions in the extension field. In cer...