Mitja Lakner

The one-equator property

We show the existence of points in the Mandelbrot cardioid that have the one-equator property, a property useful for the study of quaternionic dynamics. The question whether the Julia set is homeomorphic to a codimension-one sphere becomes a good deal more subtle in quaternionic dynamics.

Intramax and other objective functions: The case of Slovenia

Abstract The use of different objective functions in hierarchical aggregation procedures is examined in this paper. Specifically, we analyse the use of the original Intramax objective function, the sum-of-flows objective function, the sum-of-proportions-to-intra-regional-flows objective function, Smart’s weighted interaction index, the first and second CURDS weighted interaction indices, and Tolbert and Killian’s interaction index. The results of the functional regionalisation have been evaluated by self-containment statistics, and they show that the use of the original Intramax procedure tends to delineate operationally the most persuasive and balanced regions that, regarding the intra-regional flows, homogeneously cover the analysed territory. The other objective functions give statistically better but operationally less suitable results. Functional regions modelled using the original Intramax procedure were compared to the regions at NUTS 2 and NUTS 3 levels, as well as to administrative units in Slovenia. We conclude that there are some promising directions for further research on functional regionalisation using hierarchical aggregation procedures.

Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Abstract Background: Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past. Objectives: In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint. Methods/Approach: The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically. Results: The use of the contiguity constraint is important only at the beginning of the aggregation procedure; the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation. Conclusions: The original Intramax procedure (without the inclusion of any constraint) gives the most balanced and operative hierarchical sets of functional regions without any singletons or isolated regions.

Thermal Treatment of New Inorganic Thermal Insulation Board Based on Expanded Perlite

A new lightweight thermal insulation board, containing expanded perlite and inorganic silicate binder with corresponding industrial production procedure was developed. The industrial technology was developed in cooperation between company Trimo d.d. and Faculty of chemistry and chemical technology Ljubljana and among others includes mixing of raw materials, molding, microwave drying and high temperature treatment of the dried board. A new product has low density (130 – 160 kg/m3), good mechanical properties and durability and can be used in various fields where inorganic thermal insulation is required. The current work presents the experimental study of the final process during plate production – high temperature treatment with sintering. During thermal treatment of the board, certain shrinkage is required to obtain sufficient mechanical properties and durability. Controlling the process of high temperature thermal treatment is the key to achieve the right balance between low final density of the board and its good mechanical properties.

The Influence of the Zonation Effect on a System of Hierarchical Functional Regions

Abstract Background: Hierarchical functional regions (FRs) can be calculated using data on interactions between basic spatial units (BSUs) and a hierarchical aggregation procedure. However, the results depend on the selected system of initial BSUs. In spatial sciences, this is known as the zonation effect, which is one of the effects of the Modifiable Areal Unit Problem (MAUP). Objectives: In this paper, we analyse the influence of the zonation effect on a system of hierarchical functional regions. Methods/Approach: We compared two systems of hierarchical functional regions of Slovenia modelled by the Intramax aggregation procedure using the inter-municipal labour commuting flows for the same year, but for two different initial sets of municipalities. Besides, we have introduced a new measure to compare systems of hierarchical FRs. Results: The results show that the zonation effect has an influence on hierarchical functional regions. The clustering comparison measure suggested here is a metric measure, which is appropriate for comparing hierarchical FRs. Conclusions: The zonation effect has influence on hierarchical FRs. The clustering comparison measure suggested in this paper is easy to interpret, but it should be adjusted for the number of clusterings

Hydrogen interactions with oxidized austenitic stainless steel

An ultrahigh vacuum (UHV) chamber is generally supposed to have a constant base background outgassing rate q0 over very long periods of time. In experiments with ionized or molecular hydrogen, this level might be increased by absorption of a small fraction of hydrogen. In this work, absorption of molecular hydrogen is monitored in a small austenitic stainless steel UHV chamber during 3 h exposures at initial pressures from 0.01 to 1 mbar at room temperature. An absorbed dose of ∼1013–1014 atom H cm−2 was recorded. After gas removal, desorption period in the closed vacuum system lasted for 20 h, wherein most of the absorbed hydrogen was released. The initial desorption rate was 10–100 times higher than the previous q0. Calculations based on well accepted models for hydrogen–metal interactions confirm that the observed absorption–desorption processes are related mainly to the native oxide layer. Its reported thickness is between 1 and 3 nm and our results express its high solubility, which at 1 nm ranges fr...

The Continued Fractions Ladder of Specific Pairs of Irrationals

Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow Kuzmins probability law. Results are given for sequences of partial quotients of positive irrational numbers

An equal-area method for scalar conservation laws

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Parallel flow of immiscible liquids in a microreactor: modeling and experimental study

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Modeling of temperature distributions in canned tomato based dip during industrial pasteurization

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