Ore algebras are an algebraic structure used to model many different kinds of functional equations like differential and recurrence equations. The elements of an Ore algebra are polynomials for which the multiplication is defined to be usually non-commutative. As a consequence, Gauß’ lemma does not hold in many Ore polynomial rings and hence the product of two primitive Ore polynomials is not n...

Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüfer (i.e, its integral closure is a Prüfer domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content cD(g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with cD(g) v = D. Using these facts, the...

In this paper, we summarize our progress on two interaction techniques (point-based and ray-based) for haptic rendering. First, we describe a new point-based rendering technique that is computationally less expensive than previously proposed methods. We use a localized search procedure to reduce the number of computations and make it independent of the number polygons of the polyhedron. Second,...

this is the report of a mandibular neuroectodermal/ewing sarcoma in an 8-year-old male cross breed dogthat is unique because of tumor origin location. pedunculated, ulcerative, firm 6.0 × 4.0 × 5.5 cm tumor masseffaced the bone at the rostral part of the mandible and had a white-sanguineous color at cross sectionappearance. histopathologically, small round blue cell tumor was diagnosed. immunoh...

Vdra-ba society in western Sichuan, China, has been represented by evolutionist Chinese scholars as a primitive matrilineal that was transition to patrilineal system, and it likened of the Na/Moso. This is misleading characterization. no tribal organizations critically shaped overarching Tú-s? system for many centuries. The kinship centered on “house,” better described undifferentiated. gá-yì (...

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of ...

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in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

Coding theory plays an important role in efficient transmission of data over noisy communication channels. It consists of two steps; the first step is to encode the data to reduce its sensitivity to noise during transmission, and the second step is to decode the received data by detecting and correcting the noise induced errors. In this thesis an algebraic approach is used to develop efficient ...