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# On iterative processes generating dense point sets

Periodica Mathematica Hungarica
Authors: G. Ambrus and A. Bezdek

## Summary

The central problem of this paper is the question of denseness of those planar point sets \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}, not a subset of a line, which have the property that for every three noncollinear points in \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}, a specific triangle center (incenter (IC), circumcenter (CC), orthocenter (OC) resp.) is also in the set \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}. The IC and CC versions were settled before. First we generalize and solve the CC problem in higher dimensions. Then we solve the OC problem in the plane essentially proving that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document} is either a dense point set of the plane or it is a subset of a rectangular hyperbola. In the latter case it is either a dense subset or it is a special discrete subset of a rectangular hyperbola.

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# Typical faces of extremal polytopes with respect to a thin three-dimensional shell

Periodica Mathematica Hungarica
Authors: Károly Böröczky, Károly Böröczky Jr., and Gergely Wintsche

## Summary

Given \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $r>1$ \end{document}, we search for the convex body of minimal volume in \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbb{E}^3$ \end{document} that contains a unit ball, and whose extreme points are of distance at least \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $r$ \end{document} from the centre of the unit ball. It is known that the extremal body is the regular octahedron and icosahedron for suitable values of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $r$ \end{document}. In this paper we prove that if \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $r$ \end{document} is close to one then the typical faces of the extremal body are asymptotically regular triangles. In addition we prove the analogous statement for the extremal bodies with respect to the surface area and the mean width.

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# Combinatorial problems in the Enomoto-Katona space

Studia Scientiarum Mathematicarum Hungarica
Author: Jörn Quistorff
Let n, k ∈ ℕ with 2 kn and X be an n -set. The Enomoto-Katona space
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{R}: = \left\{ {\{ A,B\} \subseteqq \left( {_k^X } \right)\left| {A \cap } \right.B = \not 0} \right\},$$ \end{document}
consisting of all unordered pairs of disjoint k -element subsets of X and equipped with
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$d^\mathcal{R}$$ \end{document}
({ A,B }, { S,T }) ≔ min {| A \ S |+| B \ T |,| A \ T |+| B \ S |}, is considered. The proof of the triangle inequality for
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$d^\mathcal{R}$$ \end{document}
is simplified. Upper bounds on the coding type problem, i.e. the determination of the maximum cardinality of a code consisting of unordered pairs of subsets far away from each other, are improved. The sphere packing problem, i.e. the determination of the maximum number of disjoint balls of a prescribed radius, is introduced and discussed. It is less closely connected to the first problem than it is in the most important spaces of coding theory.
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# The Historical Geography of Sophene

Author: Michaŀ Marciak

This paper deals with the historical geography of Sophene — it aims to determine its original territory and geopolitical developments from Hellenistic times to the eve of the Arab conquests. To achieve this goal, a wide range of sources have been examined with regard to geographical (and ethnographical) information on Sophene — Greek and Latin geographical and ethnographical texts, Greek and Latin historiographical accounts, Byzantine legislations, and finally Armenian writings.In the light of the available data, the heartland of Hellenistic Sophene was located in the triangle marked by the Euphrates (in the west), the Munzur Mountains (in the north), and the Tauros (in the south). This territory includes the modern Dersim (Tunceli), the lower Murat valley (on either side of the river), and the Elaziğ plain, and coincides with the center of the pre-Hellenistic — Suppani. As a political entity Sophene expanded its territory, and especially its expansion in the northeast (including Balabitene and Asthianene) and over the Tauros into the upper Tigris valley (Ingilene, Sophanene) turned out to have more lasting consequences. These territories were closely integrated into Sophene as a political and cultural entity. The first capital of Sophene was ancient Arsamosata (likely located at modern Haraba), but due to the expansion of the kingdom of Sophene over the Tauros, the capital was later moved to the bank of the Tigris as to a more central position (likely today’s Eğil — Strabo’s and Pliny’s Karkathiokerta). Sophene’s political significance resulted from its geographical location — it straddled one of the most important communication lines between West and East in ancient times (the Tomisa crossing).

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# Hydrodeoxygenation of benzofuran over activated carbon supported Pt, Pd, and Pt–Pd catalysts

Reaction Kinetics, Mechanisms and Catalysis
Authors: Chunyan Liu, Zhengfeng Shao, Zihui Xiao, and Changhai Liang

contact time under 340 °C and 3.0 MPa with a H 2 /oil ratio of 1000 in volume ( filled square MCH, filled circle ECH, filled up-pointing triangle ECHE, filled down-pointing triangle OHBF, filled diamond ECHO, open up-pointing triangle DHBF

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# Planar sets with few empty convex polygons

Studia Scientiarum Mathematicarum Hungarica
Author: A. Dumitrescu

. 33 116 118 KATCHALSKI, M. and MEIR, A., On empty triangles determined by points in the plane, Acta. Math. Hungar . 51 (1988), 323-328. MR 89f

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# Johann Ignaz Cimbal „védjegye”, a VSG-monogram

Művészettörténeti Értesítő
Author: Gaylhoffer-Kovács Gábor

Next to his signature, Viennese painter Johann Ignaz Cimbal often added a peculiar sign in his frescoes and oils. It is a combination of letters, appearing in a different form in each of the studied cases (Zalaegerszeg, Oberlaa, Zwettl, Peremarton, Tornyiszentmiklós, Nagykároly [ Carei]), which – and the poor state of the works – make the identification of the letters difficult. In most cases the sign reads VSG, so it is not the initials of the painter.

In some Cimbal works the three letters also appear with iconographic meaning. On the picture of the King Saint Stephen side altar in the parish church of Tornyiszentmiklós the letters shining in the halo around the Holy Cross were identified as VSG earlier and decoded as “Vera Sacra Crux”. However, it is more likely that this abbreviation hides the same meaning as the monograms next to Cimbal’s signatures.

Guidance to the elucidation of the monogram was provided by the ceiling fresco in the southern vestry-room of Székesfehérvár cathedral. The clearly readable VSG abbreviation appears in the corners of the triangle symbolizing the Holy Trinity, which leaves no doubt that it is in connection of the Holy Trinity. The most obvious explanation is the letters being the initials of the German words for the three divine entities, Vater, Sohn and [Heiliger] Geist.

The attribution of the picture (Maria Immaculata) on the high altar of the parish church of Sárospatak to Cimbal was suggested on the basis of this motif, here in three corners of a triangular aureole around the Ark of Covenant. The attribution is also confirmed by style critical analyses. (Analogous are Cimbal’s Immaculata figures in Zalaeregszeg, Tornyiszentmiklós and Székesfehérvár.)

The abbreviation alluding to the Holy Trinity, which is perfectly embedded in the iconographic fabric of some paintings, was also used by Cimbal independently of the theme, attached to his name. Inserting a sign referring to the Holy Trinity above his name must have been a religious gesture. Having completed a picture, the painter crossed himself, as it were, offering his work to God. He sealed his offering with the mysterious sign of God “in the name of the Father, the Son and the Holy Ghost”. (A similar religious gesture must underlie the signature 70 of an early Cimbal work, the Saint Anne altar picture in Vienna’s Barmherzigenkirche. The abbreviation “Zimbal i. VR” is traditionally interpreted as “In veneratione” with the explanation that the painter made the picture as a votive offering.) Cimbal always created a new composition out of the three letters, so it cannot have been his aim to make a recognizable constant “trade-mark”. (For this purpose he used his name with the customary addition “invenit et pinxit”.) The linking of the three letters is not just a customary formal solution as in monograms, but it has a meaning: it symbolizes the unity of the three divine persons, just as the circle in the triangle in Székesfehérvár.

An extremely expressive iconographic solution needs special mention, applied almost to each of his depictions of the Holy Trinity in Hungary. It is the sceptre held by the three coeternal persons (hence it has extreme length). As it occurs so frequently, it cannot be part of an occasional client’s wish but much rather it is the painter’s invention. Perhaps a comprehensive examination of the entire oeuvre will discover further examples in support of the author’s hypothesis that the Holy Trinity was a particularly favourite theme of Cimbal. It was again his personal devotion that led him to use the Holy Trinity monogram.

The motivation behind commissions for religious art works in the period was first of all the client’s personal religiosity. The religious motifs of the artists can usually only be inferred from indirect data and in connection with few works. One such sign is that for the duration of painting the frescoes Franz Anton Maulbertsch joined the Scapular Confraternity of Székesfehérvár, while the group portrait on the organ loft of Sümeg permits the assumption that he took part in the devotions of the Angelic Society founded by bishop Márton Padányi Biró. His pupil Johannes Pöckel who settled in Sümeg was a member of the local Confraternity of the Cord. Unfortunately, no information to this effect is known about Cimbal.

His signature and Holy Trinity monogram testify that not only the client but also the painter offered his work to God.

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# Proviregi

## Dimensional Aspects of the Conflicts between Institutional and Aesthetic Value-Systems

Neohelicon
Author: Endre Szkárosi

Summary The new avant-garde, experimental and interdisciplinary subculture, which later became a sort of parallel culture, presented its perspective potential already in the early 1970s. It went beyond the canonized and largely conformed literary and artistic languages and worked out the practice of a systematic compenetrability of literary and artistic languages in general. In the late 1970s and in the 80s this artistic productivity became stronger and more coherent in quality. Because of the radical reinterpretation of language and, consequently, thinking and radical speaking about society and art this new current came into conflict with political power yet standing on an ideological basis. On the other hand and because of the same reason, it arrived at an opposition with cultural institutions and informal power groups and persons inside them. These institutions and power groups had developed a kind of modus vivendi with political power, so they could secure the limits of canonized languages and ways of communication in the cultural sphere. Thus, the new avant-garde and experimental trends came into conflict with the settled value-systems after all. The common denominator of those who were interested in preserving existing political power and the aesthetic status quo against the new avant-garde experimentalism, was the “protection' of the national and linguistic identity. This possibility was severely denied to the other part. This typically Hungarian and typically East-Central-European triangle (which, in reality, meant one aesthetic opposition) formed a characteristically Hungarian and characteristically East-Central-European mutant of the new avant-garde experimentalism, which proved to be highly productive. By reason of several linguistic and poetical characteristics this mutant can be distinguished from “western' avant-garde and experimental waves and trends, which, at the same time, often meant a starting point and a background of creative energies for it. For lack of minimal recognition and perspective canonicity at least, the intellectual survival and development, furthermore the aesthetically credible canonization of this parallel culture were made possible by two factors. One of these factors was the not overwhelmingly numerous, but coherent public of this scene. The other one appeared in its more and more organic work-contacts developed with western new-avant-garde-experimental trends. Simplifying a little: the characteristically Hungarian new-avant-garde, after having been cut off from national cultural canon, could function being embedded in the international avant-garde scene. This process, even if in a different way, ran its course at the same time in the Central-East-European countries. Back to back, knowing little about each other, they kept their eyes on the “West'. That's how they formed their own supranational and, at the same time, specifically regional artistic practice, poetics and languages. Even their meeting points took shape within the various institutions of West-European avant-garde culture. Some stable points of regional organization appeared only in the 90s. All these, at times contradictory processes and events of the afore characterized part of cultural history should be analysed in the dimensions of the provincial, the regional and the universal.

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# The effect of an aminoalcohol on the polymerization of acrylates with type II initiators

Journal of Thermal Analysis and Calorimetry
Authors: Feyza Karasu and Nergis Arsu

Fig. 1 . Fig. 1 UV-absorption spectra of ITX ( filled square ), TX ( filled circle ), TX-Np ( triangle ) and BP ( diamond ) in CH 2 Cl 2 .([ITX], [TX] and [TX-Np] = 0.15 mM; [BP] = 0.6 mM

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# Feszített ponyvaszerkezetek szabásmintáinak összehasonlító elemzése

Építés - Építészettudomány
Authors: Krisztián Hincz and Gyula Galaskó

Acad. Sci. Hung. 107 27 36 Galaskó Gy., Trompette, P.: Calculation of cutting patterns using triangles. In

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