FP-GR-INJECTIVE MODULES

In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers. We also prove that (1) (⊥gr-FI, gr-FI) is a hereditary cotorsion theory if and only if R is a left gr-coherent ring, (2) If R is right gr-coherent with FP-gr-id(RR) ≤ n, then (gr-FIn, gr-F n⊥) is a perfect cotorsion theory, (3) (⊥gr-FIn, gr-FIn) is a cotorsion theory, where gr-FI denotes the class of all FP-gr-injective left R-modules, gr-FIn is the class of all graded right R-modules of FP-gr-injective dimension at most n. Some applications are given

TRIANGULAR MATRIX REPRESENTATIONS OF SKEW MONOID RINGS

Let R be a ring and S a u.p.-monoid. Assume that there is a monoid homomorphism &#945; : S &#8594; Aut (R). Suppose that &#945; is weakly&#12288;rigid and lR(Ra) is pure as a left ideal of R for every element a &#8712; R. Then the skew monoid ring R*S induced by &#945; has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is R*S.</p

Radial Spokes-A Snapshot of the Motility Regulation, Assembly, and Evolution of Cilia and Flagella

Propulsive forces generated by cilia and flagella are used in events that are critical for the thriving of diverse eukaryotic organisms in their environments. Despite distinctive strokes and regulations, the majority of them adopt the 9+2 axoneme that is believed to exist in the last eukaryotic common ancestor. Only a few outliers have opted for a simpler format that forsakes the signature radial spokes and the central pair apparatus, although both are unnecessary for force generation or rhythmicity. Extensive evidence has shown that they operate as an integral system for motility control. Recent studies have made remarkable progress on the radial spoke. This review will trace how the new structural, compositional, and evolutional insights pose significant implications on flagella biology and, conversely, ciliopathy

Imaging Ferroelectric Domains via Charge Gradient Microscopy Enhanced by Principal Component Analysis

Local domain structures of ferroelectrics have been studied extensively using various modes of scanning probes at the nanoscale, including piezoresponse force microscopy (PFM) and Kelvin probe force microscopy (KPFM), though none of these techniques measure the polarization directly, and the fast formation kinetics of domains and screening charges cannot be captured by these quasi-static measurements. In this study, we used charge gradient microscopy (CGM) to image ferroelectric domains of lithium niobate based on current measured during fast scanning, and applied principal component analysis (PCA) to enhance the signal-to-noise ratio of noisy raw data. We found that the CGM signal increases linearly with the scan speed while decreases with the temperature under power-law, consistent with proposed imaging mechanisms of scraping and refilling of surface charges within domains, and polarization change across domain wall. We then, based on CGM mappings, estimated the spontaneous polarization and the density of surface charges with order of magnitude agreement with literature data. The study demonstrates that PCA is a powerful method in imaging analysis of scanning probe microscopy (SPM), with which quantitative analysis of noisy raw data becomes possible

Share Ownership Distribution, Non-renewable Resources Extraction Rate and Pollution Intensity

There is increasing concern for scarcity of natural resources and deterioration of the environment due to economic activity. Although theoretically the Hotelling rule not only provides an optimal extraction for the resource owner's profit maximization problem but also provides the optimal solution for society as a whole, the rule fails to fit the facts and only applies to the idealised world for which it was constructed. In particularly, when the resource firm realises it can affect its price depending on extraction, shareholders will disagree on the extraction rate. Thus, how to deal with the shareholders' interests and make decisions for resource firms is of central importance. Endogenizing firms' objectives through shareholder voting via majority rule is considered as the solution. This thesis analyzes the behaviour of resources firms in shareholder voting equilibrium when the firms' decisions are taken through shareholder voting. Firstly, theoretical models are formulated for the extraction rate and pollution intensity of resources firms respectively. We show that the share ownership owned by the largest shareholder is an important determinant of extraction rate and pollution intensity. Moreover empirical studies using panel data are conducted to test the hypothesis. We find strong evidence supporting our theoretical implications. As for the extraction rate in resource firms, the results indicate a significant and negative relation between extraction rate and the share owned by the largest shareholder. However, a significantly positive relation is found using oil fields level data. As for the pollution emissions in firms, we find the firm where the largest shareholder holds a larger share will have lower pollution intensity