We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...

Three waveforms for transthoracic defibrillation are assessed and compared: the Pulsed Biphasic Waveform (PBW), the Rectilinear Biphasic Waveform (RBW), and the “lossless” constant current (LLCC) pulses. Two indices are introduced: 1) kf = W/W0 – the ratio between the delivered energy W and the energy W0 of a rectangular pulse with the same duration and electric charge; 2) ηC = W/WC0 – the leve...

Let H be a character Hopf algebra. Every right coideal subalgebra that contains the coradical has a PBW-basis which can be extended up to a PBW-basis of H.

in this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. also, we represent several theorems for constructing each generalized skew t-normal distribution. next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, nickel and vanadium, associated with crude oil in shadgan wetland in the south-...

In situ recovery (ISR) is the predominant method of uranium extraction in the United States. During ISR, uranium is leached from an ore body and extracted through ion exchange. The resultant production bleed water (PBW) contains contaminants such as arsenic and other heavy metals. Samples of PBW from an active ISR uranium facility were treated with cupric oxide nanoparticles (CuO-NPs). CuO-NP t...

Given a matrix over a skew field fixing the column t(1, . . . , 1), we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes.

In this paper we study the multivariate skew-normal distribution and its scale mixtures, as extensions of the similar non-skewed distributions. Different parameterizations and some properties are investigated. ∗ Subject Classification: 60E05.