On Some Properties of Tribonacci Quaternions

In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them

The prognostic value of arterial stiffness in systolic heart failure

Background: Increased arterial stiffness is an indicator of mortality. This study consists of an 18-month follow-up of the mortality in advanced heart failure patients with increased arterial stiffness.Methods: The study followed up 98 patients with a diagnosis of heart failure in NYHA class III and IV (76 males, 22 females and mean age of 60 ± 12 years) with a left ventricular ejection fraction ≤ 35% as determined by the Simpson method. Augmentation index (Aix) and pulse wave propagation velocity (PWV) parameters were used as indicators of arterial stiffness. Aix and PWV values were measured by arteriography.Results: 36 patients died. Both Aix and PWV were powerful determinants of mortality, independent of other prognostic variables (p = 0.013, OR: 0.805; p = 0.025, OR: 0.853). A cutoff value for Aix of –14.33 gave 91.2%, 80.3% sensitivity and specificity. A cutoff value for PWVof 11.06 gave 82.4%, 65.4% sensitivity and specificity mortality was predicted. Left ventricular ejection fraction (p = 0.008, OR: 0.859) and B-type natriuretic peptide (p = 0.01, OR: 0.833) was the other independent determinant of mortality. A significant difference was found inboth Aix and PWV between the compensated measurements and decompensated heart failure measurements made in 70 patients (p = 0.035, p = 0.048).Conclusions: Measurement of arterial stiffness is a convenient, inexpensive and reliable method for predicting mortality in patients with advanced heart failure

The Lehmer matrix with recursive factorial entries

WOS: 000356337000003A generalized Lehmer matrix with recursive entries from Kilic et al. (2010b) is further generalized, introducing three additional parameters and taking recursive factorials instead of a term. Certain formulae are derived for the LU and Cholesky factorizations and their inverses, as well as the determinants. Then we precisely compute the elements of the inverse of the generalized Lehmer matrix

Split Fibonacci and Lucas Octonions

WOS: 000359814200001In this paper, split Fibonacci and Lucas octonions are proposed and their some properties and relations are obtained

Some New Quaternionic Quadratics with Zeros in Terms of Second Order Quaternion Recurrences (vol 29, 14, 2019)

WOS: 000460374600001Unfortunately, the communicating editor was wrongly published as Dr. Cristina Elena Flaut instead of Prof. Rafa Abamowic

Generalization of a statistical matrix and its factorization

WOS: 000478255600001We consider a special matrix with integer coefficients and obtain an LU factorization for its member by giving explicit closed-form formulae of the entries of L and U. Our result is applied to give the closed-form formula of the inverse of the considered matrix. We give the relation between the defined matrix and Helmert matrix which has been used for proving the statistical independence of a number of statistics. Also we find the condition numbers of some matrices for some special values of q

Quaternions: Quantum calculus approach with applications

WOS: 000488617200001In this paper we introduce two types of quaternion sequences with components including quantum integers. We also introduce quantum quaternion polynomials. Moreover, we give some properties and identities for these quantum quaternions and polynomials. Finally, we give time evolution and rotation applications for some specific quaternion sequences. The applications can be converted into quantum integer forms under suitable conditions with similar considerations

Some New Quaternionic Quadratics with Zeros in Terms of Second Order Quaternion Recurrences

WOS: 000454678500001In this paper a comprehensive analysis of the Horadam quaternion zeros for some new types of bivariate quadratic quaternion polynomial equations is presented

The Fibonacci Octonions

WOS: 000350203100009In the present paper, we introduce the Fibonacci and Lucas octonions and give the generating function and Binet formulae for these octionions. In addition, we give some identities and properties of them