let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

mndo semi-empirical scf mo calculations are used to study the pyramidal nitrogen atom inversion and configurational equilibria in the title compounds.

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

0

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

0

Let A be a positive (semidefinite) bounded linear operator acting on complex Hilbert space \(\big ({\mathcal {H}}, \langle \cdot , \rangle \big )\). The semi-inner product \({\langle x, y\rangle }_A := Ax, \), \(x, y\in {\mathcal {H}}\) induces seminorm \({\Vert \Vert }_A\) \({\mathcal {H}}\). T an A-bounded {H}}\), the A-numerical radius of is given by $$\begin{aligned} \omega _A(T) = \sup \Bi...

Given a discrete sample of event locations, we wish to produce a probability density that models the relative probability of events occurring in a spatial domain. Standard density estimation techniques do not incorporate priors informed by spatial data. Such methods can result in assigning significant positive probability to locations where events cannot realistically occur. In particular, when...

Golomb and Weinberger [1] described a variational approach to interpolation which reduced the problem to minimizing a norm in a reproducing kernel Hilbert space generated by means of a small number of data points. Later, Duchon [2] defined radial basis function interpolants as functions which minimize a suitable seminorm given by a weight in spaces of distributions closely related to Sobolev sp...