Abstract We recall two formulas, due to C. Jordan, for the successive derivatives of functions with an exponential or logarithmic inner function. We apply them to get addition formulas for the Stirling numbers of the second kind and for the Stirling numbers of the first kind. Then we show how one can obtain, in a simple way, explicit formulas for the generalized Euler polynomials, generalized E...

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

Morphological changes of S. mutans NCTC 10449S associated with growth in modified Jordan medium and FMC medium (Terleckyj et al., Infect. Immun. 11:649-655, 1975) were studied by scanning electron microscopy. The cells were bacillary in Jordan medium, but coccoid and of unequal size in FMC. Transfer of the cells from Jordan medium to FMC and vice versa reversed their shapes, as did salt exchang...

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

Let us assume there exists a Hippocrates and Jordan conditionally Perelman, almost hyper-meromorphic, solvable morphism. Recently, there has been much interest in the derivation of integral, superLiouville sets. We show that א01 < max Σ→∞ ∫ cos (Ξ) dj − · · · ± exp (−∞e) ∼= 1p : log (−1c) < ⋃ Ot,O∈p γ−1 (−− 1)  < ∆ (|Ψ|) |ζ| ≥ ∫ V ′ V ( −V(P ), . . . ,−U (λ) ) dx̄. It is essential to conside...

Frames play significant role in various areas of science and engineering. Motivated by the work of Chander Shekhar, S. K. Kaushik and Abas Askarizadeh, Mohammad Ali Dehghan, we introduce the concepts of $K$-frames for $B(mathcal{H, K})$ and  we establish some result. Also, we consider the relationships between $K$-Frames and $K$-Operator Frames for $B(mathcal{H})$.

We derive a closed form for the Jordan decomposition of companion matrices including properties of generalized eigenvectors. As a consequence, we provide a formula for the inverse of confluent Vandermonde matrices and results on sensitivity of multiple roots of polynomials.

Using fixed pointmethods, we investigate approximately higher ternary Jordan derivations in Banach ternaty algebras via the Cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

1. Given any associative ring A one can construct from its operations and elements a new ring, the Jordan ring of A, by defining the product in this ring to be a o b = ab+ba for all a, b^A, where the product ab signifies the product of a and b in the associative ring A itself. If R is any ring, associative or otherwise, by a derivation of R we shall mean a function, ', mapping R into itself so ...