The Fibonomial coe¢ cients are known as interesting generalization of binomial coe¢ cients. In this paper, we derive a (k + 1)th recurrence relation and generating matrix for the Fibonomial coe¢ cients, which we call generalized Fibonomial matrix. We …nd a nice relationship between the eigenvalues of the Fibonomial matrix and the generalized right-adjusted Pascal matrix that they have the same ...

We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formulæ are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm.

β-lactamases are bacterial enzymes that confer resistance to β-lactam antibiotics, such as penicillins and cephalosporins. There are four classes of β-lactamase enzymes, each with characteristic sequence and structure properties. Enzymes from class A are the most common and have been well characterized across the family; however, less is known about how physicochemical properties vary across th...

we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

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In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...

An iterative algorithm is constructed to solve the linear matrix equation pair AXB E, CXD F over generalized reflexive matrix X. When the matrix equation pair AXB E, CXD F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the ...

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH M,N , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair X1, Y1 , the generalized reflexive solutions can be obtained b...

A hybrid method is proposed for the frequency analysis of rounded metallic objects inductively loaded in rectangular waveguides. The combines efficiency generalized scattering matrix (GSM) and flexibility moments (MoM) fact that fields cannot exist inside perfect electric conductors. Metallic discontinuities are modelled as a dielectric medium with extreme conductivity volume emptied except sur...

the purpose of this review article is to characterize all of the parameters regarding the types, polymers used, and release kinetics of matrix tablets. matrix system was the earliest oral extended release platform for medicinal use. matrix tablets are most commonly used methods to modulate the release profile of drugs. they are much desirable and preferred for such therapy because they offer be...