SCHEMES OF SOLID-PHASE SPECTROPHOTOMETRIC ANALYSIS OF FOOD OBJECTS

The aim of research is development of approaches to the development of schemes for microelement analysis of food objects. This will make it possible to monitor food quality by simple and affordable methods in factory laboratories. Based on data on the immobilization of dyes on ion exchangers and on the interaction of metal ions or their complexes with immobilized dyes, solid-phase spectrophotometric (SPS) and photometric methods for determining metal ions in food technology, biotechnology and the environment have been developed. Techniques are sensitive. High distribution coefficients (D³104 cm3/g) of metal ions help to reduce the detection limit when using immobilized dye as compared to the reaction in solution. Based on the detection limit values (DLV), the proposed sorption-spectrophotometric methods for determining metal ions are second only to the atomic absorption (AAS) determination of Cd (II) and Hg (II) ions and the polarographic determination of Cd (II) ions. However, the proposed methods for the determination of these metal ions are sufficient for the determination of Cd (II) and Hg (II) ions in food products at the MPC level. In the case of determination of Pb (II), Zn (II), Cu (II), Fe (III) ions, the developed methods have advantages over standard methods for determination of metal ions in food products, since they make it possible to determine these ions at a level ≤0.1…0.5 MPC; Ion exchangers with immobilized dyes and solid-phase spectrophotometric determination methods with their participation are environmentally safe, since they do not require the use of toxic organic reagents; are simple in execution and economically advantageous because of the low cost of used materials and reagents. The correctness of the results of the determination by the developed methods is proved: by comparison with the results of determinations on standard methods at various analysis objects using the method of additives, standard samples. The relative standard deviation of the developed SPS determination procedures does not exceed 0.10, which indicates satisfactory reproducibility of the results. The developed methods exceed the majority of standard and best analogs, known from the literature, for sensitivity and selectivity. The used methods of analysis are characterized by the simplicity of the experiment, ecological safety, do not require special expensive equipment, highly qualified personnel and a stationary laboratory

Adjacency Graphs of Polyhedral Surfaces

We study whether a given graph can be realized as an adjacency graph of the polygonal cells of a polyhedral surface in $\mathbb{R}^3$. We show that every graph is realizable as a polyhedral surface with arbitrary polygonal cells, and that this is not true if we require the cells to be convex. In particular, if the given graph contains $K_5$, $K_{5,81}$, or any nonplanar $3$-tree as a subgraph, no such realization exists. On the other hand, all planar graphs, $K_{4,4}$, and $K_{3,5}$ can be realized with convex cells. The same holds for any subdivision of any graph where each edge is subdivided at least once, and, by a result from McMullen et al. (1983), for any hypercube. Our results have implications on the maximum density of graphs describing polyhedral surfaces with convex cells: The realizability of hypercubes shows that the maximum number of edges over all realizable $n$-vertex graphs is in $\Omega(n \log n)$. From the non-realizability of $K_{5,81}$, we obtain that any realizable $n$-vertex graph has $O(n^{9/5})$ edges. As such, these graphs can be considerably denser than planar graphs, but not arbitrarily dense.Comment: To appear in Proc. SoCG 202

Sublinear Explicit Incremental Planar Voronoi Diagrams

A data structure is presented that explicitly maintains the graph of a Voronoi diagram of $N$ point sites in the plane or the dual graph of a convex hull of points in three dimensions while allowing insertions of new sites/points. Our structure supports insertions in $\tilde O (N^{3/4})$ expected amortized time, where $\tilde O$ suppresses polylogarithmic terms. This is the first result to achieve sublinear time insertions; previously it was shown by Allen et al. that $\Theta(\sqrt{N})$ amortized combinatorial changes per insertion could occur in the Voronoi diagram but a sublinear-time algorithm was only presented for the special case of points in convex position.Comment: 14 pages, 10 figures. Presented ant JCDCGGG 201

Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of $n$ vertices and $h$ holes. We introduce a \emph{graph of oriented distances} to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in $\min \{\,O(n^\omega), O(n^2 + nh \log h + \chi^2)\,\}$ time, where $\omega<2.373$ denotes the matrix multiplication exponent and $\chi\in \Omega(n)\cap O(n^2)$ is the number of edges of the graph of oriented distances. We also provide a faster algorithm for computing the diameter that runs in $O(n^2 \log n)$ time

Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in O(min(n^omega, n^2 + nh log h + chi^2)) time, where omega<2.373 denotes the matrix multiplication exponent and chi in Omega(n) cap O(n^2) is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in O(n^2 log n) time

Compatible Paths on Labelled Point Sets

Let P and Q be finite point sets of the same cardinality in R 2 , each labelled from 1 to n. Two noncrossing geometric graphs GP and GQ spanning P and Q, respectively, are called compatible if for every face f in GP , there exists a corresponding face in GQ with the same clockwise ordering of the vertices on its boundary as in f. In particular, GP and GQ must be straightline embeddings of the same connected n-vertex graph G. No polynomial-time algorithm is known for deciding whether two labelled point sets admit compatible geometric graphs. The complexity of the problem is open, even when the graphs are constrained to be triangulations, trees, or simple paths. We give polynomial-time algorithms to find compatible paths or report that none exist in three scenarios: O(n) time for points in convex position; O(n 2 ) time for two simple polygons, where the paths are restricted to remain inside the closed polygons; and O(n 2 log n) time for points in general position if the paths are restricted to be monotonePeer ReviewedPostprint (published version

Levinas et le jeu des langues. La Russie à Auteuil

E. Lévinas was not only a great philosopher, but also an exceptional writer. His publications bear witness to his prodigious work on language and to the unique style which he creates page by page. This work applies to the French language, but it is from Russian, his mother-tongue, as fertilised by the great classics, that Levinas essentially draws his creative inspiration. Furthermore, the fact that he belonged to a truly unique social category, namely Russian intelligentsia, nourishes his prose — and, if one may say so, his poetry — just as does the richness and suppleness of the Russian language. (Transl.by J. Dudley).E. Lévinas ne fut pas seulement un grand philosophe mais également un écrivain hors pair. Son œuvre témoigne de son prodigieux travail sur le langage, ainsi que du style unique qu'il crée au fil des pages. Ce travail s'applique à la langue française, mais c'est dans le russe, sa langue maternelle, telle qu'elle fut fécondée par les grands classiques, que Lévinas écrivain puise essentiellement son inspiration créatrice. Par ailleurs, son appartenance à une catégorie sociale réellement unique, l'intelligentsia russe, nourrit sa prose — et, oserons-nous dire, sa poésie — au même titre que la richesse et la souplesse de la langue russe.Arseneva Elena. Levinas et le jeu des langues. La Russie à Auteuil. In: Revue Philosophique de Louvain. Quatrième série, tome 100, n°1-2, 2002. pp. 65-79

Levinas et le jeu des langues. La Russie à Auteuil

E. Lévinas was not only a great philosopher, but also an exceptional writer. His publications bear witness to his prodigious work on language and to the unique style which he creates page by page. This work applies to the French language, but it is from Russian, his mother-tongue, as fertilised by the great classics, that Levinas essentially draws his creative inspiration. Furthermore, the fact that he belonged to a truly unique social category, namely Russian intelligentsia, nourishes his prose — and, if one may say so, his poetry — just as does the richness and suppleness of the Russian language. (Transl.by J. Dudley).E. Lévinas ne fut pas seulement un grand philosophe mais également un écrivain hors pair. Son œuvre témoigne de son prodigieux travail sur le langage, ainsi que du style unique qu'il crée au fil des pages. Ce travail s'applique à la langue française, mais c'est dans le russe, sa langue maternelle, telle qu'elle fut fécondée par les grands classiques, que Lévinas écrivain puise essentiellement son inspiration créatrice. Par ailleurs, son appartenance à une catégorie sociale réellement unique, l'intelligentsia russe, nourrit sa prose — et, oserons-nous dire, sa poésie — au même titre que la richesse et la souplesse de la langue russe.Arseneva Elena. Levinas et le jeu des langues. La Russie à Auteuil. In: Revue Philosophique de Louvain. Quatrième série, tome 100, n°1-2, 2002. pp. 65-79