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In [3] we studied p-mean curvature and the associated p-minimal surfaces in the Heisenberg group from the viewpoint of PDE and differential geometry. In this paper, we look into the problem through the variational formulation. We ...
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In [3] we studied p-mean curvature and the associated p-minimal surfaces in the Heisenberg group from the viewpoint of PDE and differential geometry. In this paper, we look into the problem through the variational formulation. We study a generalized p-area and associated ( p-) minimizers in general dimensions. We prove the existence and investigate the uniqueness of minimizers. Since this is reduced to solving a degenerate elliptic equation, we need to consider the effect of the singular set and this requires a careful study. We define the notion of weak solution and prove that in a certain Sobolev space, a weak solution is a minimizer and vice versa. We also give many interesting examples in dimension 2. An intriguing point is that, in dimension 2, a C 2-smooth solution from the PDE viewpoint may not be a minimizer. However, this statement is true for higher dimensions due to the relative smallness of the size of the singular set.
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Ground penetrating radar (GPR) is considered an effective tool to detect tunnel lining voids. In this paper, an experimental study was carried out using a physical tunnel lining model to evaluate the performances of different ante...
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Ground penetrating radar (GPR) is considered an effective tool to detect tunnel lining voids. In this paper, an experimental study was carried out using a physical tunnel lining model to evaluate the performances of different antenna frequencies. We built a 4.2 m-long, 4.2 m-wide, and 2.0 m-high experimental model to simulate the secondary lining, initial lining, and surrounding rock of a tunnel structure. In the model, we created four categories of voids, which are voids in secondary and initial linings, a delamination between the secondary and initial linings, a delamination between the initial lining and sand, and a void buried in the sand, to simulate real cases in tunnel engineering. The GPR wave velocities in the sand and concrete of the model were measured using the reflection method for the calibration of void depth. We employed a commercial GPR system equipped with antennae of different centre frequencies to detect the voids. GPR data were processed using a conventional data processing flow, and the performances of different frequencies were examined. The results show that the 1000 MHz centre frequency GPR is capable of characterizing shallow buried voids in the secondary lining but is not able to penetrate into the initial lining. The 250 MHz centre frequency GPR system is not advised to detect voids in or behind tunnel linings due to its low resolving power for voids of centimetre sizes. The 500 MHz centre frequency GPR system is optimal for void detection because it demonstrated a balanced performance of resolving ability and investigation depth. The findings of this work could be useful references for antenna selection and data processing in real GPR applications.
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Secondary metabolites are often highly biologically active molecules and are widely used from antibacterial to anticancer drugs. In this issue of Chemistry and Biology, Zaehle and coworkers describe the gene cluster and biosynthes...
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Secondary metabolites are often highly biologically active molecules and are widely used from antibacterial to anticancer drugs. In this issue of Chemistry and Biology, Zaehle and coworkers describe the gene cluster and biosynthesis of the polyketide terrein, a secondary metabolite produced by the soil-borne fungus Aspergillus terreus.
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We answer a question of M. Flach by showing that there is a linear representation of a profinite group whose (unrestricted) universal deformation ring is not a complete intersection. We show that such examples arise in arithmetic ...
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We answer a question of M. Flach by showing that there is a linear representation of a profinite group whose (unrestricted) universal deformation ring is not a complete intersection. We show that such examples arise in arithmetic in the following way. There are infinitely many real quadratic fields F for which there is a mod 2 representation of the Galois group of the maximal unramified extension of F whose universal deformation ring is not a complete intersection. Finally, we discuss bounds on the singularities of universal deformation rings of representations of finite groups in terms of the nilpotency of the associated defect groups.
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We prove that the eigenvalues of the Laplacian acting on functions converge to those of the limit manifold for a special collapsing family of closed Riemannian manifolds without curvature bounds. The proof uses L 2-analysis.
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We describe all abelian groups which can appear as the fundamental groups of closed symplectically aspherical manifolds. The proofs use the theory of symplectic Lefschetz fibrations.
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The cambial activity and periodicity of secondary xylem and phloem formation have been less studied in tropical tree species than in temperate ones. This paper describes the relationship between seasonal cambial activity, xylem an...
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The cambial activity and periodicity of secondary xylem and phloem formation have been less studied in tropical tree species than in temperate ones. This paper describes the relationship between seasonal cambial activity, xylem and phloem development, and phenology in Schizolobium parahyba, a fast growing semideciduous seasonal forest tree from southeastern Brazil. From 2002 to 2003, wood samples were collected periodically and phenology and climate were recorded monthly in the same period. S. parahyba forms annual growth increments in wood, delimited by narrow initial parenchyma bands. The reduction of the cambial activity to a minimum correlates to the dry season and leaf fall. The higher cambial activity correlates to the wet season and the presence of mature leaves. In phloem, a larger conductive region was observed in the wet season, when the trees were in full foliage. The secondary phloem did not exhibit any incremental zone marker; however, we found that the axial parenchyma tends to form irregular bands.
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摘要 :The study of harmonic functions on a locally compact group G has recently been transferred to a “non-commutative” setting in two different directions: Chu and Lau replaced the algebra L ∞(G) by the group von Neumann algebra VN(...
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The study of harmonic functions on a locally compact group G has recently been transferred to a “non-commutative” setting in two different directions: Chu and Lau replaced the algebra L ∞(G) by the group von Neumann algebra VN(G) and the convolution action of a probability measure μ on L ∞(G) by the canonical action of a positive definite function σ on VN(G); on the other hand, Jaworski and the first author replaced L ∞(G) by ${\mathcal B} (L^2(G))$ to which the convolution action by μ can be extended in a natural way. We establish a link between both approaches. The action of σ on VN(G) can be extended to $\mathcal{B} (L^2(G))$ . We study the corresponding space $\tilde{\mathcal H}_\sigma$ of “σ-harmonic operators”, i.e., fixed points in ${\mathcal B} (L^2(G))$ under the action of σ. We show, under mild conditions on either σ or G, that $\tilde{\mathcal H}_\sigma$ is in fact a von Neumann subalgebra of ${\mathcal B} (L^2(G))$ . Our investigation of $\tilde{\mathcal H}_\sigma$ relies, in particular, on a notion of support for an arbitrary operator in ${\mathcal B} (L^2(G))$ that extends Eymard’s definition for elements of VN(G). Finally, we present an approach to $\tilde{\mathcal H}_\sigma$ via ideals in ${\mathcal T} (L^2(G))$ , where ${\mathcal T}(L^2(G))$ denotes the trace class operators on L 2(G), but equipped with a product different from composition, as it was pioneered for harmonic functions by Willis.
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This replicated research project [see Hine, G. S. C. (2019). Reasons why I didn't enrol in a higher-level mathematics course: Listening to the voice of Australian senior secondary students. Research in Mathematics Education, 2 7(3...
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This replicated research project [see Hine, G. S. C. (2019). Reasons why I didn't enrol in a higher-level mathematics course: Listening to the voice of Australian senior secondary students. Research in Mathematics Education, 2 7(3), 295-313.] explored the reasons why senior secondary (i.e. Year 11 and Year 12) students elected not to enrol in a higher-level mathematics course. For this project, all senior secondary Australian Tertiary Admissions Ranking (ATAR) students within Western Australian schools (aged 17-18 years) were invited to participate in an anonymous, online survey comprised predominantly of qualitative items. The researcher analysed 1633 ATAR students' perspectives of enrolments in mathematics courses, according to a symbolic inter-actionist paradigm. Reasons included the extent to which students feel higher-level courses are too challenging, time-consuming, not required for university nor future life, and requiring more effort and stress to complete than lower-level mathematics courses. Especially outlined is the extent to which participants feel a 10% bonus is a sufficient incentive to increase higher-level course enrolments, an extension of the original project. Participants indicated a range of responses either supporting or opposing this incentive. While approximately 47% of participants agree that the incentive is sufficient, a small proportion of these supporters offer their agreement conditionally. Within the proportion asserting the incentive is insufficient, a majority of participants suggested that a higher percentage bonus should be offered to students enrolled in Mathematics Specialist.
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Introduction: Following total parathyroidectomy (PTx), transcervical thymectomy, and forearm autograft for secondary hyperparathyroidism (SHPT), recurrent SHPT can occur in the autografted forearm. However, few studies have invest...
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Introduction: Following total parathyroidectomy (PTx), transcervical thymectomy, and forearm autograft for secondary hyperparathyroidism (SHPT), recurrent SHPT can occur in the autografted forearm. However, few studies have investigated the factors contributing to re-PTx due to autograft-dependent recurrent SHPT before the completion of the initial PTx.Methods: A total of 770 patients who had autografted parathyroid fragments derived from only one of the resected parathyroid glands (PTGs) and who had undergone successful initial total PTx and transcervical thymectomy—defined by serum intact parathyroid hormone level < 60 pg/mL on postoperative day 1—between January 2001 and December 2022 were included in this retrospective cohort study. Factors contributing to re-PTx due to graft-dependent recurrent SHPT before the completion of the initial PTx were investigated using multivariate Cox regression analysis. Receiver operating characteristic (ROC) curve analysis was performed to obtain the optimal maximum diameter of PTG for autograft.Results: Univariate analysis showed that dialysis vintage and maximum diameter and weight of the PTG for autograft were significant factors contributing to graft-dependent recurrent SHPT. However, multivariate analysis revealed that dialysis vintage (P=0.010; hazard ratio [HR], 0.995; 95% confidence interval [CI], 0.992–0.999) and the maximum diameter of the PTG for autograft (P=0.046; HR, 1.107; 95% CI, 1.002–1.224) significantly contributed to graft-dependent recurrent SHPT. ROC curve analysis showed that < 14 mm was the optimal maximum diameter of PTG for autograft (area under the curve, 0.628; 95% CI, 0.551–0.705).Conclusions: The dialysis vintage and maximum diameter of PTG for autograft may contribute to re-PTx due to autograft-dependent recurrent SHPT, which can be prevented by using PTGs with a maximum diameter of < 14 mm for autograft.
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