Calibration Method for Line-Structured Light Three-Dimensional Measurements Based on a Single Circular Target

Single circular targets are widely used as calibration objects during line-structured light three-dimensional (3D) measurements because they are versatile and easy to manufacture. This paper proposes a new calibration method for line-structured light 3D measurements based on a single circular target. First, the target is placed in several positions and illuminated by a light beam emitted from a laser projector. A camera captures the resulting images and extracts an elliptic fitting profile of the target and the laser stripe. Second, an elliptical cone equation defined by the elliptic fitting profile and optical center of the camera is established based on the projective geometry. By combining the obtained elliptical cone and the known diameter of the circular target, two possible positions and orientations of the circular target are determined and two groups of 3D intersection points between the light plane and the circular target are identified. Finally, the correct group of 3D intersection points is filtered and the light plane is progressively fitted. The accuracy and effectiveness of the proposed method are verified both theoretically and experimentally. The obtained results indicate that a calibration accuracy of 0.05 mm can be achieved for an 80 mm × 80 mm planar target.

Computational approach to solving problems of spatial processing of point sets on two-dimensional regular grids

The paper presents an approach to solving problems of spatial processing on sets of points on a plane. The presented method consists in plotting regions of an arbitrary geometric shape near given points of the set on a regular grid and determining the intersection points of the regions using spatial hash tables to improve the efficiency of operations. The proposed approach is implemented in the form of software for determining the spatial relationships between points as a sequence of operations with discretized sets and allows visualization of research results. Figs.: 2. Refs.: 13. Keywords: spatial processing task; point set; plane; regular grid; spatial hash table.

Mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration

ABSTRACTEnzyme behaviour is typically characterised in the laboratory using very diluted solutions of enzyme. However, in vivo processes usually occur at [ST] ≈ [ET] ≈ Km. Furthermore, the study of enzyme action usually involves analysis and characterisation of inhibitors and their mechanisms. However, to date, there have been no reports proposing mathematical expressions that can be used to describe enzyme activity at high enzyme concentration apart from the simplest single substrate, irreversible case. Using a continued fraction approach, equations can be easily derived to apply to the most common cases in monosubstrate reactions, such as irreversible or reversible reactions and small molecule (inhibitor or activator) kinetic interactions. These expressions are simple and can be understood as an extension of the classical Michaelis-Menten equations. A first analysis of these expressions permits to deduce some differences at high vs low enzyme concentration, such as the greater effectiveness of allosteric inhibitors compared to catalytic ones. Also, they can be used to understand catalyst saturation in a reaction. Although they can be linearised following classical approaches, these equations also show some differences that need to be taken into account. The most important one may be the different meaning of line intersection points in Dixon plots. All in all, these expressions may be useful tools for the translation in vivo of in vitro experimental data or for modelling in vivo and biotechnological processes.

In Situ Transmission Electron Microscopy Investigation of Melting/Evaporation Kinetics in Anisotropic Gold Nanoparticles

We report on thermal stability and phase transition behaviors of triangular Au nanoprisms through in situ heating transmission electron microscopy. With rising temperature, Au nanoprisms exhibit fluctuating surface reconstructions at the corner regions. When a quasi-melting state is reached at the temperature below bulk melting points, the evaporation is initiated commonly at a corner with low curvature and containing sharp intersection points. The subsequent annealing process leads to the gradual evaporation, which, in the absence of thick carbon coverages, is accompanied by marked shape reconstructions. The thermal stability and evaporation behaviors are not evidently regulated by nanoprism aggregations.

On point processes defined by angular conditions on Delaunay neighbors in the Poisson–Voronoi Tessellation

Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$ . The first is the set of points that belong to some one-dimensional facet of the Voronoi tessellation and such that the angle with which they see the two nuclei defining the facet is $\theta$ . The main question of interest on this first point process is its intensity. The second point process is that of the intersections of the said tessellation with a straight line having a random orientation. Its intensity is well known. The intersection points almost surely belong to one-dimensional facets. The main question here concerns the Palm distribution of the angle with which the points of this second point process see the two nuclei associated with the facet. We will give answers to these two questions and briefly discuss their practical motivations. We also discuss natural extensions to three dimensions.

NJEGOŠOLOGIJA – NEPROLAZNI IZAZOVI NOVIH TUMAČENJA NJEGOSHOLOGY - AN IMPERISHABLE CHALLENGE OF NEW INTERPRETATIONS

Science has not yet written the last word when it comes to the complexity of the work and personality of Peter II Petrovic Njegos. His existence marked a short segment of Montenegrin history (1813-1851), but he established himself as an inviolable beacon of Montenegrin and South Slavic cultural heritage. The cultural-memorial reflection of Njegoš's oeuvre must include considerations at various levels. It embraces the role that his texts and political activity play in the formation of the national tradition, the relation of fictional discourse to the national past, the relation of the literary text to the cultural constructions of national identity, consideration of the representational role of the literary text as a constitutive part of the culture as a whole, problems of critical and historical literary canonization, etc. On the one hand, interpretation of Njegoš's legacy allows us to get a complete picture of the peculiarities of his poetic code. On the other hand, it enables us to see his work as a cultural-memory matrix without which it is impossible to imagine the coordinates of Montenegrin cultural identity. Within such research, the uniqueness of what was said gains its entire meaning through a network of attitudes towards language, tradition, ideology. On the intersections of these networks are projected many symbols fused into a matrix of timeless paradigms, i.e., all ethical, aesthetic, poetic categories and identity patterns contained in the whole of Njegoš's legacy. Although each of Njegoš's texts represents an ideologically and thematically independent semantic whole, by carefully reading his entire legacy, we come across intersection points, which opens the possibility of chaining the meaning and expanding the reference planes of the semantic constituents of the text.

Classification of the Real Roots of the Quartic Equation and their Pythagorean Tunes

Presented is a very detailed two-tier analysis of the location of the real roots of the general quartic equation $$x^4 + a x^3 + b x^2 + c x + d = 0$$ x 4 + a x 3 + b x 2 + c x + d = 0 with real coefficients and the classification of the roots in terms of a, b, c, and d, without using any numerical approximations. Associated with the general quartic, there is a number of subsidiary quadratic equations (resolvent quadratic equations) whose roots allow this systematization as well as the determination of the bounds of the individual roots of the quartic. In many cases the root isolation intervals are found. The second tier of the analysis uses two subsidiary cubic equations (auxiliary cubic equations) and solving these, together with some of the resolvent quadratic equations, allows the full classification of the roots of the general quartic and also the determination of the isolation interval of each root. These isolation intervals involve the stationary points of the quartic (among others) and, by solving some of the resolvent quadratic equations, the isolation intervals of the stationary points of the quartic are also determined. The presented classification of the roots of the quartic equation is particularly useful in situations in which the equation stems from a model the coefficients of which are (functions of) the model parameters and solving cubic equations, let alone using the explicit quartic formulæ , is a daunting task. The only benefit in such cases would be to gain insight into the location of the roots and the proposed method provides this. Each possible case has been carefully studied and illustrated with a detailed figure containing a description of its specific characteristics, analysis based on solving cubic equations and analysis based on solving quadratic equations only. As the analysis of the roots of the quartic equation is done by studying the intersection points of the “sub-quartic” $$x^4 + ax^3 + bx^2$$ x 4 + a x 3 + b x 2 with a set of suitable parallel lines, a beautiful Pythagorean analogy can be found between these intersection points and the set of parallel lines on one hand and the musical notes and the staves representing different musical pitches on the other: each particular case of the quartic equation has its own short tune.

Christian Theological Grounds of Jurisprudence: Historical and Contemporary Aspects

The purpose of this study is to reveal historical and contemporary aspects of the similarity, difference and interaction of Christian and legal spheres of the social reality. In particular, the interdisciplinary approach provided the combination of exegesis and hermeneutics, dialectics, dogmatic and historical methodological tools, and was used to retrace the evolution of the law and to disclose various connections between legal and religious prescriptions and the content. The main intersection points of the law and religion, particularly Christianity, such as sacredness, values, morality and axiomatic assertions are disclosed as well as the religious basis of the historical and contemporary law is proved in the article.