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An important role in the roads design is played by plane curves, if the road lies on a plane surface and by space curves, if the road can not be embeded in a plane. This article presents some work done in the two and three dimensional roads design, by using the differential geometry methods. A study of a general case for plane roads is given.

Both notions, of an infinitesimal bending of a curve and of a rectifying curve, play important roles in the theory of curves. In this short note, we begin the study of the infinitesimal bending of a rectifying curve. [ABSTRACT FROM AUTHOR]

B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no proper pointwise semi-slant warped product submanifold other than contact CRwarped products in Sasakian manifolds. We give non-trivial examples of such submanifolds in cosymplectic manifolds and obtain several fundamental results, including a characterization for warped product pointwise semi-slant submanifolds. [ABSTRACT FROM AUTHOR]

We establish an inequality for an intrinsic invariant of Chen-type defined on quaternionic CR-submanifolds in quaternionic space forms, in terms of the squared mean curvature, the main extrinsic invariant, by using the method of constrained extrema.

The ligand field theory is an early and yet perennial class of quantum models accounting for the optical and magnetic properties of metal ions as a function of their environment in compounds. In the context of modern quantum chemistry, in order to predict properties from first principles, the ligand field paradigm can serve to illuminate the black box of heavy calculations, extracting heuristic meaning and causal roots. The genuine ligand field models are tacitly affected by an artificial feature, so-called holohedrization. It induces an inversion symmetry, even in cases where the local geometry does not show this element. This aspect received little attention over decades of using the ligand field Hamiltonians. In this work, we systematically investigate, assisted by state-of-the-art ab initio computer experiments, whether holohedrization is a hidden drawback of early models or if it also appears in realistic modeling. We found that the holohedrization trend also appears when using data from modern ab initio calculations. [ABSTRACT FROM AUTHOR]

Aim: This review aims to summarize published evidence on the real-world (RW) outcomes of abiraterone or enzalutamide in first-line metastatic castration-resistant prostate cancer. Materials & methods: Studies reporting on RW effectiveness, safety, economic and/or health-related quality of life outcomes were identified by systematic literature review (2011–2021, incl. Embase®, MEDLINE®) and presented in a qualitative synthesis. Risk of bias was assessed using ROBINS-I or the Molinier checklist. Results: 88 studies (n = 83,427 patients) were included. Median progression-free (40 studies) and overall survival (38 studies) ranged from 3.7 to 20.9 months and 9.8 to 45 months, respectively. Survival, safety and economic outcomes were similar across individual treatments, while limited health-related quality of life evidence suggested improvements with abiraterone. Risk of bias was moderate to high. Conclusion: RW outcomes in first-line metastatic castration-resistant prostate cancer remain poor despite treatment, highlighting an unmet need for new regimens. This review was supported by AstraZeneca and Merck Sharp & Dohme. A #systematicreview of #realworld outcomes for first-line #abiraterone or #enzalutamide in #mCRPC including 88 studies reports that, despite treatment, PFS and OS remain poor highlighting an unmet need for new regimens: www.futuremedicine.com/doi/10.2217/FON-2023-0377 [ABSTRACT FROM AUTHOR]