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Recently, W. M. Schmidt and L. Summerer introduced a new theory that allowed them to recover the main known inequalities relating the usual exponents of Diophantine approximation to a point in ℝn and to discover new ones. They first note that these exponents can be computed in terms of the successive minima of a parametric family of convex bodies attached to the given point. Then they prove that the n-tuple of these successive minima can in turn be approximated up to bounded difference by a function from a certain class. In this paper, we show that the same is true within a smaller and simpler class of functions, which we call rigid systems. We also show that conversely, given a rigid system, there exists a point in ℝn whose associated family of convex bodies has successive minima that approximate that rigid system up to bounded difference. As a consequence, the problem of describing the joint spectrum of a family of exponents of Diophantine approximation is reduced to combinatorial analysis.

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for each of these claims drawn from the gestures that teachers and learners produce when they explain mathematical concepts and ideas. We argue that (a) pointing gestures reflect the grounding of cognition in the physical environment, (b) representational gestures manifest mental simulations of action and perception, and (c) some metaphoric gestures reflect body-based conceptual metaphors. Thus, gestures reveal that some aspects of mathematical thinking are embodied.

This study presents the design and fabrication of a physical model for the triple orthogonal projection and the draught of a line using 3D printing technology. In this paper, an educational model is presented that aims to provide a better understanding of the representation of the triple orthogonal projection of a line in space and in the draught. To create the physical model, three plates were manufactured that symbolise the three projection planes and a series of flexible cylindrical elements that embody a spatial line and its projections. The plates are articulated two by two so that they can be folded to obtain the draught.

This study presents the design and fabrication of a physical model for the triple orthogonal projection and the draught of a line using 3D printing technology. In this paper, an educational model is presented that aims to provide a better understanding of the representation of the triple orthogonal projection of a line in space and in the draught. To create the physical model, three plates were manufactured that symbolise the three projection planes and a series of flexible cylindrical elements that embody a spatial line and its projections. The plates are articulated two by two so that they can be folded to obtain the draught.

The Minimum Dominating Set (MDS) problem is one of the well-studied problems in computer science. It is well-known that this problem is NP -hard for simple geometric objects; unit disks, axis-parallel unit squares, and axis-parallel rectangles to name a few. An interesting variation of the MDS problem with rectangles is when there exists a straight line that intersects each of the given rectangles. In the recent past researchers have studied the maximum independent set, minimum hitting set problems on this setting with different geometric objects. We study the MDS problem with axis-parallel rectangles, unit-height rectangles, and unit squares in the plane. These geometric objects are constrained to be intersected by a straight line. For axis-parallel rectangles, we prove that this problem is NP -hard. When the objects are axis-parallel unit squares, we present a polynomial time algorithm using dynamic programming. We provide a polynomial time algorithm for unit-height rectangles as well. For unit squares that touch the straight line at a single point from either side of the straight line, we show that there is an O(nlogn) -time algorithm.

Language learning is an emotionally and psychologically dynamic process that is influenced by a myriad of ever-changing variables and emotional \"vibes\" that produce moment-by-moment fluctuations in learners' adaptation. This individual-level study triangulates physiological, idiodynamic, interview, and self-report survey data of three high and three low anxiety language learners to examine their language anxiety, its triggers, and the interpretations of rapidly changing affective reactions over a short period of time. Participants were videorecorded giving a presentation, while wearing heart monitors, in their Spanish as a Foreign Language class. Using the idiodynamic method, participants self-rated their moment-by-moment anxiety 42 times over three and a half minutes and later explained their reactions in an interview. The strong relationship observed among the various converging data sources demonstrates the strength of considering language learners on an individual level using triangulated quantitative and qualitative approaches. The study generated pedagogical implications for dealing with both positive and negative emotions, facilitating the reinterpretation of physiological cues, planning \"escape routes\" that allow participants to remain active in communication exchanges, and invoking the positive power of preparation, planning, and rehearsal. (Verlag).

We develop a theory of arithmetic Newton polygons of higher order that provides the factorization of a separable polynomial over a pp-adic field, together with relevant arithmetic information about the fields generated by the irreducible factors. This carries out a program suggested by Ø. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields.

A new hyper-chaotic system is presented in this paper by adding a smooth flux-controlled memristor and a cross-product item into a three-dimensional autonomous chaotic system. It is exciting that this new memristive system can show a four-wing hyper-chaotic attractor with a line equilibrium. The dynamical behaviors of the proposed system are analyzed by Lyapunov exponents, bifurcation diagram and Poincaré maps. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of hyperchaos in the system is verified theoretically. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system.

We propose here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. We establish the main properties of the system, and also derive the asymptotic speed of spreading in the direction of the line. For low diffusion, the line has no effect, whereas, past a threshold, the line enhances global diffusion in the plane and the propagation is directed by diffusion on the line. It is shown here that the global asymptotic speed of spreading in the plane, in the direction of the line, grows as the square root of the diffusion on the line. The model is much relevant to account for the effects of fast diffusion lines such as roads on spreading of invasive species.

To explore the reliability and accuracy of lung ultrasound for diagnosing neonatal pneumothorax. This study was divided into two phases. (1) In the first phase, from January 2013 to June 2015, 40 patients with confirmed pneumothorax had lung ultrasound examinations performed to identify the sonographic characteristics of neonatal pneumothorax. (2) In the second phase, from July 2015 to August 2016, lung ultrasound was undertaken on 50 newborn infants with severe lung disease who were suspected of having pneumothorax, to evaluate the sonographic accuracy and reliability to diagnose pneumothorax. (1) The main ultrasonic manifestations of pneumothorax are as follows: ① lung sliding disappearance, which was observed in all patients (100%); ② the existence of the pleural line and the A-line, which was also observed in all patients (100%); ③ the lung point, which was found in 75% of the infants with mild-moderate pneumothorax but not found to exist in 25% of the severe pneumothorax patients; ④ the absence of B-lines in the area of the pneumothorax (100% of the pneumothorax patients); and ⑤ no lung consolidation existed in the area of the pneumothorax (100% of the pneumothorax patients). (2) The accuracy and reliability of the lung sonographic signs of lung sliding disappearance as well as the existence of the pleural line and the A-line in diagnosing pneumothorax were as follows: 100% sensitivity, 100% specificity, 100% positive predictive value, and 100% negative predictive value. When the lung point exists, the diagnosis is mild-moderate pneumothorax, whereas if no lung point exists, the diagnosis is severe pneumothorax. Lung ultrasound is accurate and reliable in diagnosing and ruling out neonatal pneumothorax and, in our study, was found to be as accurate as chest X-ray.