We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains bounds for the Castelnuovo-Mumford regularity of the Rees algebra and for the Artin-Rees numbers.

We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated. Dedicated to Winfried Bruns on the occasion of his sixtieth birthday

A critical set is a partial latin square that has a unique completion to a latin square of the same order, and is minimal in this property. If P is a critical set in a latin square L, then each element of P must be contained in a latin trade Q in L such that |P ∩ Q| = 1. In the case where each element of P is contained in an intercalate (latin trade of size 4) Q such that |P∩Q| = 1 we say that ...

Recycling rare earth elements (REEs) used in advanced materials such as Nd magnets is important for the efficient use of REE resources when the supply of several REEs is limited. In this work, the feasibility of using salmon milt for REE recovery and separation was examined, along with the identification of the binding site of REEs in salmon milt. Results showed that (i) salmon milt has a suffi...

Clostridium perfringens is ubiquitous in nature and is often found as a commensal of the human and animal gastrointestinal tract. It is the primary etiological agent of clostridial myonecrosis, or gas gangrene, a serious infection that results in extensive tissue necrosis due to the action of one or more potent extracellular toxins. α-toxin and perfringolysin O are the major extracellular toxin...

We recorded the activity of midbrain dopamine neurons in an instrumental conditioning task in which monkeys made a series of behavioral decisions on the basis of distinct reward expectations. Dopamine neurons responded to the first visual cue that appeared in each trial [conditioned stimulus (CS)] through which monkeys initiated trial for decision while expecting trial-specific reward probabili...

RULE205 The 19th-Century Russian Novel The 19th-century novel is widely regarded as the supreme achievement of Russian literature. This course will trace its development from Pushkin's elegant, witty novel in verse, EUGENE ONEGIN, through the grotesque comedies of Gogol, to the realist masterpieces of Dostoevsky and Tolstoy, with their complex depiction of human psychology and the philosophical...

Although the rare earth element (REE) geochemistry of hydrothermal systems have intensively been investigated at mid-oceanic ridges, studies are relatively few at the converging plate zones like the Okinawa Trough. The “chimney” deposits obtained by using submersible “SHINKAI 2000” from the Iheya Ridge site, Okinawa Trough are largely composed of massive carbonates and silicates with minor amou...

We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...