A way of constructing translation network operators by Bernstein operators

In the present paper,we provide a way of constructing translation network operators by Bernstein-Durrmeyer operators.     

Chemical Evolution of a Bacterial Proteome

We have changed the amino acid set of the genetic code of Escherichia coli by evolving cultures capable of growing on the synthetic noncanonical amino acid L ‐β‐(thieno[3,2‐b]pyrrolyl)alanine ([3,2]Tpa) as a sole surrogate for the canonical amino acid L ‐tryptophan (Trp). A long‐term cultivation experiment in defined synthetic media resulted in the evolution of cells capable of surviving Trp→[3,2]Tpa substitutions in their proteomes in response to the 20 899 TGG codons of the E. coli W3110 genome. These evolved bacteria with new‐to‐nature amino acid composition showed robust growth in the complete absence of Trp. Our experimental results illustrate an approach for the evolution of synthetic cells with alternative biochemical building blocks.     

Single-Molecule Photoactivation FRET: A General and Easy-To-Implement Approach To Break the Concentration Barrier

Single-molecule fluorescence resonance energy transfer (sm-FRET) has become a widely used tool to reveal dynamic processes and molecule mechanisms hidden under ensemble measurements. However, the upper limit of fluorescent species used in sm-FRET is still orders of magnitude lower than the association affinity of many biological processes under physiological conditions. Herein, we introduce single-molecule photoactivation FRET (sm-PAFRET), a general approach to break the concentration barrier by using photoactivatable fluorophores as donors. We demonstrate sm-PAFRET by capturing transient FRET states and revealing new reaction pathways during translation using μm fluorophore labeled species, which is 2–3 orders of magnitude higher than commonly used in sm-FRET measurements. sm-PAFRET serves as an easy-to-implement tool to lift the concentration barrier and discover new molecular dynamic processes and mechanisms under physiological concentrations.     

On the Auslander–Reiten conjecture for Cohen–Macaulay rings and path algebras

In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of d-th syzygy of R-modules of finite length, provided R is an isolated singularity. Based on this result, it is shown that under a mild assumption on the base ring R, satisfying the Auslander–Reiten conjecture behaves well under completion and reduction modulo regular elements. In addition, it will turn out that, if R is a commutative Noetherian ring and 𝒬 a finite acyclic quiver, then the Auslander–Reiten conjecture holds true for the path algebra R𝒬, whenever so does R. Using this result, examples of algebras satisfying the Auslander–Reiten conjecture are presented.     

激光准直检测仪的研制及其应用开发

检测仪的研制，是从工程中数量甚大的桥式起重机的安全性检测中，国家规范要求甚高而实际检测手段简陋的矛盾提出的。装置充分利用激光束的直线性和传输过程中光斑中心不变、光强较高的特性；通过集光、机、电为一体的测尺直接读出数据。应用这套装置，已进行１１台双梁桥式起重机箱形主梁的变形测定，结果表明：这套装置在现场使用方便，精度与检测要求匹配，装置价格不高，对工程单位比较实用。１９９５年获国家实用新型专利     

Auslander–Reiten Components with Sectional Bypasses

In this work, we will prove that the modules lying in a sectional bypass of an arrow in the Auslander–Reiten quiver of an artin algebra, are either all left stable or all right stable, but not τ-periodic. Moreover, if such a bypass exists, then the Auslander–Reiten quiver has an infinite left or right stable component which contains a section with a bypass.     

How useful are closed captions for learning mathematics via online video?

Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as mathematics with a reliance on the development of visual explanation while providing audio narration. In this paper, we report on a study undertaken at an Australian university, to investigate the perceived level of usefulness of captions and their automatic translations in a mathematics course. We discovered that students broadly agreed that captions are a useful learning feature: to allow flexibility of where and when a video is watched, but also to help understand speaker accents, and clarify explanations that are difficult to hear in the recording. Due to the high levels of use and perceived educational benefits of closed captions in online video but limited literature, there is a significant need for new research in this area. An urgent discussion is needed to explore how students engage with closed captions, how they may support learning, and to investigate implications on instructional design of mathematical videos.