Search Results (5)

To enhance the aerodynamic performance of organic Rankine cycle (ORC) turbines under increasing energy demands, surrogate-based optimization was applied to a 100 kW ORC turbine rotor. Four representative surrogate models—a radial basis neural network (RBNN), Kriging, response surface approximation (RSA), and a PRESS-based weighted (PBW) ensemble—were comparatively evaluated under identical numerical conditions. Independent optimizations of the first- and second-stage rotors enabled an examination of how different design variable space characteristics influenced surrogate predictive behavior. A fractional factorial sampling strategy was used to construct the training dataset, and learning curve analysis was conducted to assess sample size adequacy. Sensitivity estimation revealed distinct response surface characteristics between stages, allowing the interpretation of variations in surrogate stability. In both stages, geometric modifications were primarily concentrated near the outlet blade angle, identified as a dominant variable influencing efficiency. CFD validation confirmed that surrogate-based exploration successfully identified improved rotor geometries. Flow-field analysis indicated reduced entropy generation near the trailing edge region, suggesting the mitigation of aerodynamic losses. The results demonstrate that surrogate-based optimization can reliably improve turbine performance within a bounded design space, while the relative effectiveness of surrogate models depends on the sensitivity structure of the underlying problem. Full article

The q-Heisenberg algebra ${\mathfrak{h}}_n\left(q\right)$ is a significant class of solvable polynomial algebras, and it unifies the canonical commutation relations of Heisenberg algebras and the deformation theory of quantum groups. In this paper, we employ Gröbner-Shirshov basis theory and PBW (Poincar$\acute{e}$-Birkhoff-Witt) basis techniques to systematically investigate ${\mathfrak{h}}_n\left(q\right)$. Our main results establish that: ${\mathfrak{h}}_n\left(q\right)$ possesses an iterated skew-polynomial algebra structure, and it satisfies the important homological regularity properties of being Auslander regular, Artin-Schelter regular, and Cohen-Macaulay. These findings provide deep insights into the algebraic structure of ${\mathfrak{h}}_n\left(q\right)$, while simultaneously bridging the gap between noncommutative algebra and quantum representation theory. Furthermore, our constructive approach yields computable methods for studying modules over ${\mathfrak{h}}_n\left(q\right)$, opening new avenues for further research in deformation quantization and quantum algebra. Full article

The Clifford–Weyl algebra ${𝒜}_q^{\pm }$, as a class of solvable polynomial algebras, combines the anti-commutation relations of Clifford algebras ${𝒜}_q^{+}$ with the differential operator structure of Weyl algebras ${𝒜}_q^{-}$. It exhibits rich algebraic and geometric properties. This paper employs Gröbner–Shirshov basis principles in concert with Poincaré–Birkhoff–Witt (PBW) basis methodology to delineate the iterated skew polynomial structures within ${𝒜}_q^{+}\mathrm{and}{𝒜}_q^{-}$. By constructing explicit PBW generators, we analyze the structural properties of both algebras and their modules using constructive methods. Furthermore, we prove that ${𝒜}_q^{+}\mathrm{and}{𝒜}_q^{-}$ are Auslander regular, Cohen–Macaulay, and Artin–Schelter regular. These results provide new tools for the representation theory in noncommutative geometry. Full article

Silicon (Si) has been shown to promote peanut growth and yield, but whether Si can enhance the resistance against peanut bacterial wilt (PBW) caused by Ralstonia solanacearum, identified as a soil-borne pathogen, is still unclear. A question regarding whether Si enhances the resistance of PBW is still unclear. Here, an in vitro R. solanacearum inoculation experiment was conducted to study the effects of Si application on the disease severity and phenotype of peanuts, as well as the microbial ecology of the rhizosphere. Results revealed that Si treatment significantly reduced the disease rate, with a decrement PBW severity of 37.50% as compared to non-Si treatment. The soil available Si (ASi) significantly increased by 13.62–44.87%, and catalase activity improved by 3.01–3.10%, which displayed obvious discrimination between non-Si and Si treatments. Furthermore, the rhizosphere soil bacterial community structures and metabolite profiles dramatically changed under Si treatment. Three significantly changed bacterial taxa were observed, which showed significant abundance under Si treatment, whereas the genus Ralstonia genus was significantly suppressed by Si. Similarly, nine differential metabolites were identified to involve into unsaturated fatty acids via a biosynthesis pathway. Significant correlations were also displayed between soil physiochemical properties and enzymes, the bacterial community, and the differential metabolites by pairwise comparisons. Overall, this study reports that Si application mediated the evolution of soil physicochemical properties, the bacterial community, and metabolite profiles in the soil rhizosphere, which significantly affects the colonization of the Ralstonia genus and provides a new theoretical basis for Si application in PBW prevention. Full article

A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of the existence of a root system and a Poincare-Birkhoff-Witt (PBW) basis basis, but, for nondiagonal examples (e.g., Fomin–Kirillov algebras), this is an ongoing surprise. In this article, we discuss this phenomenon and observe that it continues to hold for the graded character of the involved group and for automorphisms. First, we discuss thoroughly the diagonal case. Then, we prove factorization for a large class of nondiagonal Nichols algebras obtained by the folding construction. We conclude empirically by listing all remaining examples, which were in size accessible to the computer algebra system GAP and find that again all graded characters factorize. Full article