Rigid-analytic varieties with projective reduction violating Hodge symmetry

We construct examples of smooth proper rigid-analytic varieties admitting formal models with projective special fibers and violating Hodge symmetry for cohomology in degrees ${\geq }3$ . This answers negatively the question raised by Hansen and Li.

FANO HYPERSURFACES WITH ARBITRARILY LARGE DEGREES OF IRRATIONALITY

We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index $e$ , then the degree of irrationality of a very general complex Fano hypersurface of index $e$ and dimension n is bounded from below by a constant times $\sqrt{n}$ . To our knowledge, this gives the first examples of rationally connected varieties with degrees of irrationality greater than 3. The proof follows a degeneration to characteristic $p$ argument, which Kollár used to prove nonrationality of Fano hypersurfaces. Along the way, we show that in a family of varieties, the invariant ‘the minimal degree of a dominant rational map to a ruled variety’ can only drop on special fibers. As a consequence, we show that for certain low-dimensional families of varieties, the degree of irrationality also behaves well under specialization.

On Some Generalized Rapoport–Zink Spaces

We enlarge the class of Rapoport–Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. Such obtained Rapoport–Zink spaces are said to be of abelian type. The class of Rapoport–Zink spaces of abelian type is strictly larger than the class of Rapoport–Zink spaces of Hodge type, but the two type spaces are closely related as having isomorphic connected components. The rigid analytic generic fibers of Rapoport–Zink spaces of abelian type can be viewed as moduli spaces of local $G$-shtukas in mixed characteristic in the sense of Scholze.We prove that Shimura varieties of abelian type can be uniformized by the associated Rapoport–Zink spaces of abelian type. We construct and study the Ekedahl–Oort stratifications for the special fibers of Rapoport–Zink spaces of abelian type. As an application, we deduce a Rapoport–Zink type uniformization for the supersingular locus of the moduli space of polarized K3 surfaces in mixed characteristic. Moreover, we show that the Artin invariants of supersingular K3 surfaces are related to some purely local invariants.

Recent Advances in Brillouin Optical Time Domain Reflectometry

In the past two decades Brillouin-based sensors have emerged as a newly-developed optical fiber sensing technology for distributed temperature and strain measurements. Among these, the Brillouin optical time domain reflectometer (BOTDR) has attracted more and more research attention, because of its exclusive advantages, including single-end access, simple system architecture, easy implementation and widespread field applications. It is realized mainly by injecting optical pulses into the fiber and detecting the Brillouin frequency shift (BFS), which is linearly related to the change of ambient temperature and axial strain of the sensing fiber. In this paper, the authors provide a review of new progress on performance improvement and applications of BOTDR in the last decade. Firstly, the recent advances in improving the performance of BOTDRs are summarized, such as spatial resolution, signal-to-noise ratio and measurement accuracy, measurement speed, cross sensitivity and other properties. Moreover, novel-type optical fibers bring new characteristics to optic fiber sensors, hence we introduce the different Brillouin sensing features of special fibers, mainly covering the plastic optical fiber, photonic crystal fiber, few-mode fiber and other special fibers. Additionally, we present a brief overview of BOTDR application scenarios in many industrial fields and intelligent perception, including structural health monitoring of large-range infrastructure, geological disaster prewarning and other applications. To conclude, we discuss several challenges and prospects in the future development of BOTDRs.

Fiber Bragg grating based displacement sensors: state of the art and trends

Purpose The purpose of this paper is to present the latest sensing structure designs and principles of information detection of fiber Bragg grating (FBG) displacement sensors. Research advance and the future work in this field have been described, with the background that displacement and deformation measurements are universal and crucial for structural health monitoring. Design/methodology/approach This paper analyzes and summarizes the existing FBG displacement sensing technologies from two aspects principle of information detection (wavelength detection, spectral bandwidth detection, light intensity detection, among others) and principle of the sensing elastomer structure design (cantilever beam type, spring type, elastic ring type and other composite structures). Findings The current research on developing FBG displacement sensors is mainly focused on the sensing method, the construction and design of the elastic structure and the design of new information detection method. The authors hypothesize that the following research trends will be strengthened in future: temperature compensation technology for FBG displacement sensors based on wavelength detection; a study of more diverse elastic structures; and fiber gratings manufactured with special fibers will greatly improve the performance of sensors. Originality/value The latest sensing structure designs and principles of information detection of FBG displacement sensors have been proposed, which could provide important reference for research group.

Properties of Asphalt Concrete with Basalt-Polymer Fibers

Asphalt mixtures are commonly used for the pavement construction for national roads with a high traffic load, as well as local roads with low traffic load. The constructions of local road pavement consisting of thinner, more flexible layers located on less stable subbase than the pavement of national roads, require reinforcement with asphalt layers characterized by increased fatigue life. Technologies that allow quick repairs and reinforcements, while improving the durability of the road pavement are being sought. Such technologies include the use of modifications of asphalt mixtures with special fibers. The paper presents the results of investigations of the properties of asphalt mixtures modified with innovative basalt-polymer fibers FRP. On the basis of the obtained test results according to the Marshall method, stiffness modulus and fatigue durability, the technical properties of asphalt mixtures with FRP fibers addition were improved. This technology significantly increases the fatigue life of asphalt concrete dedicated for repairs and reinforcements of road pavements.

Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

For a Shimura variety of Hodge type with hyperspecial level structure at a prime p, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We define and study the Ekedahl-Oort stratifications on the special fibers of those integral canonical models when p > 2. This generalizes Ekedahl-Oort stratifications defined and studied by Oort on moduli spaces of principally polarized abelian varieties and those defined and studied by Moonen, Wedhorn, and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements w in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to w is smooth of dimension l(w) (i.e., the length of w) if it is non-empty. We also determine the closure of each stratum.