Vector Arithmetic in the Triangular Grid

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Tahap Preliminary Research Pengembangan Media Pembelajaran Berbasis Komputer pada Materi Transformasi SMA/MA

The human life aspect’s is concerned with measure activities that geometry context, such as study of plane, space, size and position. Students’ faced the difficulty in understanding concept and interpreting of direction of a transformed geometry object. To solved this difficulty students’ need mathematics learning media which able to clarify transformation context. The aim of this research to know the characteristics and description of mathematics learning media of based computer on geometry transformation context which is should be preliminary research phase. This research was using Plomp model. This model consist to preliminary research phase. This research found that mathematics learning media of based computer on the geometry transformation context was preliminary research phase.

A cadaveric study of the erector spinae plane block in a neonatal sample

BackgroundThe aim of this article was to provide a detailed description of the neonatal anatomy related to the erector spinae plane block and to report the spread of the dye within the fascial planes and potential dermatomal coverage.MethodsUsing ultrasound guidance, the bony landmarks and anatomy of the erector spinae fascial plane space were identified. The erector spinae plane block was then replicated unilaterally in two fresh unembalmed neonatal cadavers. Using methylene blue dye, the block was performed at vertebral levels T5—using 0.5 mL in cadaver 1—and T8—using 0.2 mL in cadaver 2. The craniocaudal spread of dye was tracked within the space on the ultrasound screen and further confirmed on dissection.ResultsCraniocaudal spread was noted from vertebral levels T3 to T6 when the dye was introduced at vertebral level T5 and from vertebral levels T7 to T11 when the dye was introduced at vertebral level T8. Furthermore, the methylene blue spread was found anteriorly in the paravertebral and epidural spaces, staining both the dorsal and ventral rami of the spinal nerves T2 to T12. Small amounts of dye were also found in the intercostal spaces.ConclusionIn two neonatal fresh cadavers, the dye was found to spread to multiple levels and key anatomic locations.

A Basic Study on a Rectangular Plane Space Sound Absorber Using Permeable Membranes

In this communication, the sound absorption characteristics of rectangular-shaped plane space sound absorbers without any backing structure using permeable membranes (PMs) are measured by reverberation room method. First, three types of PMs, in this study woven fabrics, are selected with different flow resistances and surface densities. They are prepared in the plane rectangular-shaped space absorbers of two different sizes. The measured results are discussed through comparison with the existing theoretical and measured results for absorbers of the other shapes or configurations. The present results and discussion demonstrate that the reverberation absorption coefficients of the proposed absorbers are low at low frequencies and converge to a moderately high value at high frequencies. Especially, ones with higher flow resistance than the air impedance converge to a value greater than 0.5, which is a theoretically estimated maximum absorption coefficient of infinite single-leaf PM. This is inferred to be attributed mainly to area effect. From these results the proposed absorbers can be used effectively despite of their very simple structure. Also it is found that the proposed absorber can offer higher sound absorption than permeable membrane absorbers of other shapes or configuration. Regarding the effect of the size, the absorbers of smaller size offer higher absorption coefficients regardless of material properties of the PMs used in the experiments.

Research on the Spatial Pattern Characteristics of the Taihu Lake “Dock Village” Based on Microclimate: A Case Study of Tangli Village

“Dock Village” terrain is, as its name implies, a region that contains settlements reminiscent of docks, in terms of their elongated shape, their outward upward tilt, and their location in the center of low, wide valleys. Dock village terrain features deep, fertile soil suitable for farming. Taihu Lake contains a number of classic examples of dock villages. Dock villages are relatively independent and hidden, characteristics that not only play a role in security and defense, but also, more importantly, are associated with enhanced climate adaptability, a relative lack of cold weather, and equable levels of heat and humidity. The dock village reflects the wisdom and distillation of traditional Chinese ecological practices and is highly valued as a research topic. Based on microclimate theory and ENVI-met software, four microclimate indices, namely, air temperature, wind speed, wind direction, and relative humidity, were simulated and analyzed in this study. The correlation between spatial characteristics and microclimate was studied from four perspectives: plane space, cross-section space, vertical section space, and linear development space. This research summarizes the historical context and evolution of the dock village spatial form in the construction of contemporary human settlements. It also provides scientific suggestions for the protection and sustainable development of ancient villages.

THE STRUCTURE OF ARTISTIC SPACE IN PAVEL VEZHINOV’S NOVELLA “THE BARRIER” AND “A GENTLE CREATURE” BY FYODOR DOSTOYEVSKY

Background: The article deals with the intertextual analysis of two novellas: The Barrier by Pavel Vezhinov and A Gentle Creature by Fyodor Dostoyevsky. The methodological basis of the study is the interpretation of intertextuality as a product of reading (not the phenomenon of “writing”), according to which Vezhinov and Dostoevsky – writers belonging to different national cultures and historical eras – in some sense become contemporaries. Accordingly, A Gentle Creature, written earlier, is enriched by the meaning as a result of its comparison with The Barrier, as well as the latter by comparison with the story of Dostoevsky. Purpose: The purpose of this paper is to identify the intertextual connections of Pavel Vezhinov’s novella The Barrier and A Gentle Creature by Fyodor Dostoyevsky and to show how they deepen the content of both works in the reader’s perception. The analysis of texts is carried out within one level – the artistic space, which is “an author’s model of the world, expressed in the language of his spatial representations”. Results: Comparative analysis of the elements of spatial code and analysis of the characters’ behavior through the type of artistic space corresponding to each of them allows to understand the in-depth content of each of the two works. The storyline of both stories is based on one type of rite de passage – the transition from life “to another life”. The expected result of this transition is a radical spiritual transformation of the character and a new identity acquired by them. The events that make up the plot, in the two stories largely coincide and the last in their series is the suicide of the female character. The main character of The Barrier is a person who has gone astray and wanders within an open plane space. Meeting him with Doroteya, the character of the “vertically directed path” within the “open, voluminous space”, provokes the beginning of the “spiritual transformation” in him. However, the suicide of the female character again throw Antoni over the "barrier" of social conditioning that he managed to overcome with the help of Doroteya, and makes it impossible for him to acquire a “new identity”. The pawnbroker from A Gentle Creature is a “character of the point space” who has never been able to “expand the space” throughout the story. However, the suicide of the female character is reported as such an event, from which a real rite de passage can begin for the character, culminating in his acquisition of a way up and a radical spiritual transformation. Key words: intertextuality, artistic space, rite de passage, spiritual transformation, transfiguration.

Diagnosis of a ferroresonance type through visualisation

The paper is focused on presenting the possible enhancements in visualisation of the ferroresonance phenomenon. The investigations have been performed with the usage of overcurrent/overvoltage responses of a ferroresonance circuit. The waveforms have been measured and recorded in a ferroresonant test circuit. Phase–plane/–space graphs analysed in this paper are a visual display of certain type characteristics for the time dependent system of nonlinear differential equations. The application of Poincare maps is also mentioned in the paper.