Tangible symmetry elements and space-group models to guide from molecular to solid-state composition

The ability to imagine symmetry and the spatial arrangement of atoms and molecules is crucial in chemistry in general. Teaching and understanding crystallography and the composition of the solid state therefore require understanding of symmetry elements and their relationships. To foster the student's spatial imagination, models representing a range of concepts from individual rotation axes to complete space groups have been designed and built. These models are robust and large enough to be presented and operated in a lecture hall, and they enable students to translate conventional 2D notations into 3D objects and vice versa. Tackling them hands-on means understanding them.

A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces

Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact controllability for a class of impulsive fractional nonlinear evolution equations with delay by using the resolvent operator theory and the theory of nonlinear functional analysis. Nonlinearity in the system is only supposed to be continuous rather than Lipschitz continuous by contrast. The results obtained in the present work are generalizations and continuations of the recent results on this issue. Further, an example is presented to show the effectiveness of the new results.

Computational optical sectioning with an incoherent multiscale scattering model for light-field microscopy

Quantitative volumetric fluorescence imaging at high speed across a long term is vital to understand various cellular and subcellular behaviors in living organisms. Light-field microscopy provides a compact computational solution by imaging the entire volume in a tomographic way, while facing severe degradation in scattering tissue or densely-labelled samples. To address this problem, we propose an incoherent multiscale scattering model in a complete space for quantitative 3D reconstruction in complicated environments, which is called computational optical sectioning. Without the requirement of any hardware modifications, our method can be generally applied to different light-field schemes with reduction in background fluorescence, reconstruction artifacts, and computational costs, facilitating more practical applications of LFM in a broad community. We validate the superior performance by imaging various biological dynamics in Drosophila embryos, zebrafish larvae, and mice.

Vibrotactile-Based Operational Guidance System for Space Science Experiments

On-orbit astronauts and scientists on the ground need to cooperate closely, to complete space science experiments efficiently. However, for the increasingly diverse space science experiments, scientists are unable to train astronauts on the ground about the details of each experiment. The traditional interaction of visual and auditory channels is not enough for scientists to directly guide astronauts to experimentalize. An intuitive and transparent interaction interface between scientists and astronauts has to be built to meet the requirements of space science experiments. Therefore, this paper proposed a vibrotactile guidance system for cooperation between scientists and astronauts. We utilized Kinect V2 sensors to track the movements of the participants of space science experiments, process data in the virtual experimental environment developed by Unity 3D, and provide astronauts with different guidance instructions using the wearable vibrotactile device. Compared with other schemes using only visual and auditory channels, our approach provides more direct and more efficient guidance information that astronauts perceive is what they need to perform different tasks. Three virtual space science experiment tasks verified the feasibility of the vibrotactile operational guidance system. Participants were able to complete the experimental task with a short period of training, and the experimental results show that the method has an application prospect.

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

The present work addresses some new controllability results for a class of fractional integrodifferential dynamical systems with a delay in Banach spaces. Under the new definition of controllability , first introduced by us, we obtain some sufficient conditions of controllability for the considered dynamic systems. To conquer the difficulties arising from time delay, we also introduce a suitable delay item in a special complete space. In this work, a nonlinear item is not assumed to have Lipschitz continuity or other growth hypotheses compared with most existing articles. Our main tools are resolvent operator theory and fixed point theory. At last, an example is presented to explain our abstract conclusions.

Space–Time Physics in Background-Independent Theories of Quantum Gravity

Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space–time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theory makes it possible to perform a complete space–time analysis in various models that have been proposed in this setting. In spite of the background-independent starting point, all these models turned out to be non-geometrical and even inconsistent to varying degrees, unless strong modifications of Riemannian geometry are taken into account. This outcome leads to several implications for potential observations as well as lessons for other background-independent approaches.

Fréchet-valued meromorphic extension along a pencil of complex lines

The aim of paper is to find the condition under which a Fréchet-valued function [Formula: see text] admitting meromorphic extension along some pencil of complex lines can be meromorphically extended to a neighborhood of [Formula: see text] Some auxiliary results concerning the domains of existence for Fréchet-valued meromorphic functions, Rothstein’s theorem, Levi extension theorem for meromorphic functions with values in a locally complete space, convergence of formal power series of Fréchet-valued homogeneous polynomials are also proved in this work.

An additive algorithm for origami design

Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.

Global glacier monitoring with TanDEM-X remote sensing – advances, challenges and requirements from the perspective of a multi-decadal approach

<p>Mountain glaciers are key indicators of the changing climate conditions worldwide. Observations in recent decades suggest that their immediate atmospheric environment is changing more rapidly than it does elsewhere. Therefore, in addition to a network for measuring climatic parameters, a continuous investigation of glacier changes is indispensable.</p><p>The Terra SAR-Add-on for Digital Elevation Measurement (TanDEM-X) mission has achieved two complete space-borne surveys of the Earth's surface and thus of all existing glaciers during its mission lifetime. This study exhibits the methodological and technical findings generated over the period 2011-2019 for multi-temporal investigations – and culminates in a recommendation map for the ongoing and follow-up bi-static SAR acquisitions.</p><p>The opportunities which TanDEM-X datasets open up for glacier monitoring are demonstrated: high spatial resolution of up to ~10 m, independence of cloud cover and daylight, smooth and homogenous elevation change fields. This enables wide spatial coverage of the observations throughout climatic and altitudinal zones. However, there are also challenges and limitations to multi-temporal glacier change monitoring. We provide initial conclusions from our repeat studies in Patagonia, the tropical Andes, the Alps and Himalaya/Karakoram. Influences such as seasonality, terrain and latitude on measurement accuracy are being investigated.</p><p>The results of this work highlight the capabilities of TanDEM-X data with our current processing strategy: We show where major uncertainties arise from, where our products complement other methods, and where they surpass them. Our analysis forms a contribution to the Regional Assessments of Glacier Mass Change (RAGMAC) initiative for a better understanding of observation disparities and collaboration potentials in glacier monitoring by remote sensing techniques. Based on our findings we will point to research needs and propose strategies for a continuous global acquisition and to partially overcome some of the deficiencies, where possible.</p>