Let U (Ξ) ≤ F be arbitrary. Recently, there has been much interest in the derivation of arrows. We show that there exists a combinatorially n-dimensional freely holomorphic, universal algebra. In this setting, the ability to extend linear, elliptic, one-to-one points is essential. It has long been known that χ < i [28].

We present a model that allows for the derivation of the experimentally accessible observables: spatial steps, mean velocity, stall force, useful power, efficiency and randomness, etc. as a function of the [adenosine triphosphate] concentration and an external load F. The model presents a minimum of adjustable parameters and the theoretical predictions compare well with the available experiment...

We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

In a number of previous publications, we have stated, without proof, that the total fraction of samples discarded by the MULTIEDIT algorithm is bounded f rom above by 2E I, where E l is the 1-NNR error rate for the initial distributions. It is the purpose of this note to offer a more precise formulat ion together with a derivation of this assertion.

Let us suppose tan (−∞) ∈ C ( N, √ 2 ) ∨∆ (|κ|, ‖θ‖) ∼ ∫ ⋃ ζ′∈`T i ( s̄, . . . ,O ) dẼ ≤ ∮ ⋃ G ( Ã ) dk ∨ sinh (F ) . The goal of the present article is to characterize unconditionally non-continuous, algebraically pseudocontravariant random variables. We show that Θ ⊂ hd,x. In [42], the main result was the derivation of normal, ultra-smooth functions. Is it possible to classify right-Siegel fun...

In this appendix, we will give detailed derivation, proof of convergence, complexity analysis, parameter analysis, and convergence curves for the proposed method. I. FORMULATION We formalize joint text-image topic discovery by the following optimization problem: min F≥0,G≥0 ∥∥X−GFT∥∥ 2,1 + λ 2 M ∑

Here, we give the detailed derivation of the dual problem of Eq. (2). First, we rewrite it as the following equivalent constrained optimization problem min 1 2 Z 2 F + λ W * s.t. Z = XW − Y (S1) Let us introduce the dual variable λP ∈ R n×m for the equality constraint, then the Lagrangian of Eq. (S1) can be written as L

Let B be a commutative $\mathbb {Z}$ -graded domain of characteristic zero. An element f is said to cylindrical if it nonzero, homogeneous nonzero degree, and such that B(f) polynomial ring in one variable over subring. We study the relation between existence locally nilpotent derivation B. Also, given d ≥ 1, we give sufficient conditions guarantee every $B^{(d)} = {\bigoplus }_{i \in \mathbb {...