3,709 research outputs found
n-absorbing ideal factorization of commutative rings
In this article, we show that Mori domains, pseudo-valuation domains, and
-absorbing ideals, the three seemingly unrelated notions in commutative ring
theory, are interconnected. In particular, we prove that an integral domain
is a Mori locally pseudo-valuation domain if and only if each proper ideal of
is a finite product of 2-absorbing ideals of . Moreover, every ideal of
a Mori locally almost pseudo-valuation domain can be written as a finite
product of 3-absorbing ideals. To provide concrete examples of such rings, we
study rings of the form where is a subring of a commutative ring
and is indeterminate, which is of independent interest, and along with
several characterization theorems, we prove that in such a ring, each proper
ideal is a finite product of -absorbing ideals for some if and only
if and are both Artinian reduced rings and the contraction map
is a bijection. A complete description of
when an order of a quadratic number field is a locally pseudo valuation domain,
a locally almost pseudo valuation domain or a locally conducive domain is
given
BOgen: Generating Part-Level 3D Designs Based on User Intention Inference through Bayesian Optimization and Variational Autoencoder
Advancements in generative artificial intelligence (AI) have introduced
various AI models capable of producing impressive visual design outputs.
However, when it comes to AI models in the design process, prioritizing outputs
that align with designers' needs over mere visual craftsmanship becomes even
more crucial. Furthermore, designers often intricately combine parts of various
designs to create novel designs. The ability to generate designs that align
with the designers' intentions at the part level is pivotal for assisting
designers. Hence, we introduced BOgen, which empowers designers to proactively
generate and explore part-level designs through Bayesian optimization and
variational autoencoders, thereby enhancing their overall user experience. We
assessed BOgen's performance using a study involving 30 designers. The results
revealed that, compared to the baseline, BOgen fulfilled the designer
requirements for part recommendations and design exploration space guidance.
BOgen assists designers in navigation and development, offering valuable design
suggestions and fosters proactive design exploration and creation.Comment: 17 pages, 13 figure
On --absorbing ideals
Let be a commutative ring with identity, a multiplicative subset of
and an ideal of disjoint from . In this paper, we introduce the
notion of an --absorbing ideal which is a generalization of both the
-prime ideals and -absorbing ideals. Moreover, we investigate the basic
properties, quotient extension, existence and amalgamation of --absorbing
ideals.Comment: 18page
Stability of hydrogenation states of graphene and conditions for hydrogen spillover
The hydrogen spillover mechanism has been discussed in the field of hydrogen storage and is believed to have particular advantage over the storage as metal or chemical hydrides. We investigate conditions for practicality realizing the hydrogen spillover mechanism onto carbon surfaces, using first-principles methods. Our results show that contrary to common belief, types of hydrogenation configurations of graphene (the aggregated all-paired configurations) can satisfy the thermodynamic requirement for room-temperature hydrogen storage. However, the peculiarity of the paired adsorption modes gives rise to a large kinetic barrier against hydrogen migration and desorption. It means that an extremely high pressure is required to induce the migration-derived hydrogenation. However, if mobile catalytic particles are present inside the graphitic interstitials, hydrogen migration channels can open and the spillover phenomena can be realized. We suggest a molecular model for such a mobile catalyst which can exchange hydrogen atoms with the wall of graphene.open151
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