Applications of degree estimate for subalgebras

Let $K$ be a field of positive characteristic and $K$ be the free algebra of rank two over $K$. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S.J. Gong and J.T. Yu's results: (1) An element $p(x,y)\in K$ is a test element if and only if $p(x,y)$ does not belong to any proper retract of $K$; (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of $K$ is an automorphism; (3) If there exists some injective endomorphism $\phi$ of $K$ such that $\phi(p(x,y))=x$ where $p(x,y)\in K$, then $p(x,y)$ is a coordinate. And we reprove that all the automorphisms of $K$ are tame. Moreover, we also give counterexamples for two conjectures established by Leonid Makar-Limanov, V. Drensky and J.-T. Yu in the positive characteristic case.Comment: 12 page

A New Range Finding Method Using a Varifocal Mirror

A new range finding method is proposed in this paper which makes use of a varifocal mirror. The three-dimensional object space is first discretized into a sequence of spherical shells with a specially designed nonlinear vibrating varifocal mirror. These discrete spherical shell images are then recorded by a video camera. A deblurring algorithm is introduced in this paper which is used to remove the blurred components in the images. Different depth ranges can be obtained by controlling the vibration amplitude and the direct current component of the driving wave for the varifocal mirror. The depth accuracy is adjusted by varying the vibration period of the varifocal mirror. This range finding technique can be made real time by increasing the frame frequency of the camera

A Compositional Analysis of Unbalanced Usages of Multiple Left-turn Lanes

Lane usage measures distribution of a specific traffic movement across multiple available lanes in a given time. Unbalanced lane usages decrease the capacity of subject segment. This paper took multiple left-turn lanes at signalized intersections as case study, and explored the influences of some factors on the lane usage balance. Lane usages were calculated from field collected lane volumes and the constant-sum constraint among them was explicitly considered in the statistical analysis. Classical and compositional analysis of variance was respectively conducted to identify significant influential factors. By comparing the results of compositional analysis and those of the classical one, the former ones have better interpretability. It was found that left-turn lane usages could be affected by parameter variance of geometric design or traffic control, such as length of turning curve, length of upstream segment, length of signal phase or cycle. These factors could make the lane usages achieve relative balance at different factor levels.</p

VISUAL ORTHOGRAPHIC VARIATION AND LEARNING TO READ ACROSS WRITING SYSTEMS

This research examined the extent to which visual characteristics of orthographies affect learning to read within and across writing systems, with an eye toward the role of mapping principles – the manner in which graphemes map to linguistic units (e.g., phonemes, syllables, and morphemes) in this process. Study 1 explained visual orthographic variation by developing a measurement system to quantify complexity of graphemes in 131 orthographies. The results show that grapheme complexity varies across writing systems and that this variation is driven by grapheme inventory, a consequence of mapping principles. Next, we questioned how visual orthographic variation impacts individuals’ perceptual learning of graphemes – one of the initial stages of learning to read. Study 2 tested the degree to which mastering first-language (L1) graphemes with different complexities affects visual perceptual discrimination for individuals using different mapping principles (Online cross-writing-system experiment; eight participant groups: Hebrew, English, Russian, Arabic, Hindi, Telugu, Japanese, and Chinese, n = 60, respectively) and individuals using the same mapping principle (Lab within-writing-system experiment: simplified vs. traditional Chinese, n = 60, respectively). Consistent results from both experiments show that discrimination difficulty is a function of grapheme stimulus complexity itself as well as its relationship to the complexity of participants’ L1, regardless of mapping principles. These results were confirmed in Study 3, in which we developed a universal orthographic neural network encoder focus on statistical properties of visual patterns to simulate human behaviors. We trained each of 131 identical encoders to learn the structure of a different orthography; a strong, positive association was found between grapheme complexity and network learning difficulty. Taken together, our results suggest that visual orthographic variation, encompassing both grapheme complexity and grapheme inventory required for orthographic mastery, affects visual discrimination processing of graphemes; these complexity effects are driven significantly, but not absolutely, by mapping principles across writing systems