On almost valuation ring pairs

If [Formula: see text] are (commutative) rings, [Formula: see text] denotes the set of intermediate rings and [Formula: see text] is called an almost valuation (AV)-ring pair if each element of [Formula: see text] is an AV-ring. Many results on AV-domains and their pairs are generalized to the ring-theoretic setting. Let [Formula: see text] be rings, with [Formula: see text] denoting the integral closure of [Formula: see text] in [Formula: see text]. Then [Formula: see text] is an AV-ring pair if and only if both [Formula: see text] and [Formula: see text] are AV-ring pairs. Characterizations are given for the AV-ring pairs arising from integrally closed (respectively, integral; respectively, minimal) ring extensions [Formula: see text]. If [Formula: see text] is an AV-ring pair, then [Formula: see text] is a P-extension. The AV-ring pairs [Formula: see text] arising from root extensions are studied extensively. Transfer results for the “AV-ring” property are obtained for pullbacks of [Formula: see text] type, with applications to pseudo-valuation domains, integral minimal ring extensions, and integrally closed maximal non-AV subrings. Several sufficient conditions are given for [Formula: see text] being an AV-ring pair to entail that [Formula: see text] is an overring of [Formula: see text], but there exist domain-theoretic counter-examples to such a conclusion in general. If [Formula: see text] is an AV-ring pair and [Formula: see text] satisfies FCP, then each intermediate ring either contains or is contained in [Formula: see text]. While all AV-rings are quasi-local going-down rings, examples in positive characteristic show that an AV-domain need not be a divided domain or a universally going-down domain.

APLIKASI SISTEM PENDUKUNG KEPUTUSAN TANAMAN OBAT HERBAL UNTUK BERBAGAI PENYAKIT DENGAN METODE ROC (RANK ORDER CENTROID) DAN METODE ORESTE BERBASIS MOBILE WEB

Herbal medicinal plant is a traditional medicinal plant that is used to cure a disease. Most of modern people did not know yet the benefits that will be gotten from herbal plants for the health. This research developed a supporting decision application system of herbal medicinal plants for various diseases. ROC (Rank Order Centroid) method was used to count the total number of criteria value and Oreste method was used to rank the alternative herbal medicinal plants with criteria which influence it, namely disease, blood pressure, tall, weight, user’s condition (other diseases), age, kinds of plants, substance and efficacy of plants themselves. Final result of this system was that there were some alternative herbal medicinal plants which were appropriate to user’s disease. In this research, the researcher conducted white box testing by using path base testing to make complex logical estimates to define current action and conducted black box testing by using equivalence partitioning technique which divided domain input, decided testing case by explaining kinds of mistakes. The results of proper test for the system which were done by using questionnaire were gotten 86.75% for testing of functional system, 87% for interface and accessing testing, and 87.33% for testing of advantages system.

Domain Wall Splitting in Extra Dimension

We study the splitting of domain walls in 5-dimensional flat Minkowski spacetime. To construct a domain wall structure we utilize a potential of the form and for simplicity we assume the scalar field to be real. We also assume the coefficient a to be temperature-dependent. We find exact analytical expressions for the energy density of the domain wall and from this expression we find close analytical form for the separation of the divided domain walls. We find that near critical temperature the domain walls split. At the critical temperature, the domain walls rejoin. In the region above this critical temperature, the kink solution is nontopological. We find that the phenomena of splitting of domain walls occurs in this region as well. This effect is especially manifest near the inflection point of the potential.

Inverse limits of integral domains arising from iterated Nagata composition

By iterating the type of pullback constructions in which $P^rVD$s arise by Nagata composition, we are led to study a class of inverse limits $A=\underleftarrow{\lim}A_n$ of integral domains indexed by $\boldsymbol N$. After identifying the prime spectrum, the localizations, and the integral closure of $A$, we then characterize when, i.a., such (typically infinite-dimensional) $A$ is a Prüfer domain, Bezout domain, divided domain, or $P^rVD$.

On locally divided integral domains and CPI-overrings

It is proved that an integral domainRis locally divided if and only if each CPI-extension ofℬ(in the sense of Boisen and Sheldon) isR-flat (equivalently, if and only if each CPI-extension ofRis a localization ofR). Thus, each CPI-extension of a locally divided domain is also locally divided. Treed domains are characterized by the going-down behavior of their CPI-extensions. A new class of (not necessarily treed) domains, called CPI-closed domains, is introduced. Examples include locally divided domains, quasilocal domains of Krull dimension2, and qusilocal domains with the QQR-property. The property of being CPI-closed behaves nicely with respect to theD+Mconstruction, but is not a local property.