in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

Explicit expressions for the second order statistics of cepstral components representing clean and noisy signal waveforms are derived. The noise is assumed additive to the signal, and the spectral components of each process are assumed statistically independent complex Gaussian random variables. The key result developed here is an explicit expression for the cross-covariance between the log-per...

Every virtually cyclic group Γ that surjects onto the infinite dihedral group D∞ contains an index two subgroup Π of the form H ⋊α Z. We show that the Waldhausen Nil-group of Γ vanishes if and only if the Farrell Nil-group of Π vanishes. 1. Statement of results. The Bass Nil-groups, Farrell Nil-groups, and Waldhausen Nil-groups appear respectively as pieces in the computation of the algebraicK-...

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...

The producing cells of the negative regulator of interleukin-3 (NIL-3) were investigated. The 5-fluorouracil-treated bone marrow cells did not produce NIL-3. The bone marrow cells of stem cell-depleted W/WV mouse did not produce the NIL-3, either. The production of NIL-3 was different among mouse strains. Mice of C3H/HeN, A/J and ICR strains produced NIL-3, but the C57BL/6 mice did not produce ...

We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol’skĭi. We then give examples of important groups (namely lattices in Nil and Sol) which have deep pockets.

We construct new explicit proper biharmonic functions on the 3-dimensional Thurston geometries Sol, Nil, S̃L2(R), H 2 × R and

All gold and silver coins legally current in the UK Certain French, Spanish and American gold coins 5-franc pieces of the Latin Union All bronze coins legally current in the UK nil nil 3. Gold Coast and Dependencies ditto nil nil ditto Nickel-bronze 1/10 of a penny, halfpenny and 1-penny pieces nil 4. Southern Nigeria (Western Province) ditto Certain French, spanish and american gold coins nil ...