Czech project in history of mathematics

The paper describes the Czech project in the history of mathematics which was initiated at the Faculty of Mathematics and Physics of Charles University in Prague at the end of the eighties of the 20th century. Its main aim is to map the development of mathematical research in the Czech lands in the second half of the nineteenth and the first half of the twentieth century. The main result of this project is the production of monographs. These chart out the life and work of some prominent Czech personalities-mathematicians who have had substantial influence on the development of Czech mathematics. The aim of the project, the structure of the monographs and the general method are discussed in the paper.     

Hygrothermal properties of glass fiber reinforced cements subjected to elevated temperature

The effect of elevated temperatures on basic hygric and thermal properties of three types of glass fiber reinforced cement composites (GFRC) is analyzed in the paper. The main difference in the composition of particular GFRC is the use of wollastonite and vermiculite in two of them instead of usual sand aggregates. The composites containing wollastonite and vermiculite are found to have about four times lower thermal conductivity and two to three times lower thermal diffusivity in room temperature conditions. After heating the samples to 800°C and subsequent cooling, a decrease in room-temperature thermal conductivity as high as 50% and an increase in moisture diffusivity in the range of one to two orders of magnitude are observed for all types of studied materials. The application of wollastonite and vermiculite exhibits a positive effect on the high temperature linear thermal expansion coefficient. On the other hand, for temperatures higher than 450°C the thermal diffusivity of materials with wollastonite and vermiculite is higher than of common GFRC with sand aggregates.

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Résumé L'effet des températures élevées sur les principales propriétés hygriques et thermiques de trois types de matériaux composites à base de ciment renforcés par des fibres de verre (GFRC) est analysé dans cet article. La différence majeure de composition de ces matériaux est l'utilisation de wollastonite et de vermiculite dans deux d'entre eux au lieu des granulats de sable habituels. Les matériaux composites contenant de la wollastonite et de la vermiculie s'avèrent posséder une conductivité thermique environ quatre fois inférieure et une diffusivité thermique deux à trois fois inférieure en conditions de température ambiante. Après avoir chauffé les échantillons à 800°C puis les avoir refroidis, on observe pour tous les types de matériaux étudiés une diminution de la conductivité thermique à température ambiante, à hauteur de 50%, et une augmentation de la diffusivité d'humidité, d'environ un à deux ordres de grandeur. L'application de la wollastonite et de la vermiculite montre un effet positif sur le coefficient linéaire à haute température de dilatation thermique. D'autre part, pour les températures supérieures à 450°C, la diffusivité thermique des matériaux contenant de la wollastonite et de la vermiculite est plus élevée que celle des GFRC communs avec des granulats de sable.

     

Inverted surface hysteresis loops in heterogeneous (nanocrystalline/amorphous) Fe<Subscript>81</Subscript>Nb<Subscript>7</Subscript>B<Subscript>12</Subscript> alloys

Inverted hysteresis loops were observed for the first time in the near-surface layers of heterogeneous (nanocrystalline/amorphous) Fe₈₁Nb₇B₁₂ alloys. In particular, a negative residual magnetization is retained when a positive magnetic field applied in the sample plane is decreased to zero. The inverted hysteresis is qualitatively explained within the framework of a two-phase model, according to which the heterogeneous alloys contain two dissimilar phases exhibiting uniaxial magnetic anisotropy and featuring antiferromagnetic exchange interaction.     

Anomalous Excess Heat Capacities of Ethanol + Alkane Mixtures

A thermodynamic study at atmospheric pressure on the ethanol + n-dodecane and ethanol + n-tridecane binary systems near their liquid-liquid critical points has been carried out. To this end, densities and speeds of sound were determined in the temperature range from 288.15 to 308.15 K, whereas differential scanning calorimetry was used to obtain isobaric heat capacities per unit volume from 288.15 to 303.15 K as well as liquid-liquid equilibrium curves. All these results for the mentioned properties were obtained over the complete composition range. They were used to obtain molar volumes, isentropic compressibilities, isobaric thermal expansivities, isothermal compressibilities, isochoric heat capacities, and the excess quantities of all these properties. An untypical behavior of the excess heat capacities at the lowest measuring temperatures resulting from the critical behavior of the isobaric heat capacity is observed. No clear anomalies for the excess volumetric properties are detected.     

Large Deflection Stability of Slender Beam-Columns with Semirigid Connections: Elastica Approach

The large-deflection elastic analysis of slender beam-columns of symmetrical cross sections with semirigid connections under end loads (forces and moments) including the effects of out-of-plumbness is developed in a classical manner. The classical theory of the “Elastica” and the corresponding elliptical functions are utilized in the proposed method which can be used in the large-deflection stability analysis of slender beam-columns with rigid, semirigid, and simple connections under any combination of end loads (conservative and nonconservative). The proposed method consisting of a closed-form solution of the Elastica can also be utilized in the large deflection analysis of beam-columns whose connections suffer from flexural degradation or, on the contrary, flexural stiffening. The main limitation of the Elastica is that only flexural strains are considered (the effects of axial and shear strains are neglected). Therefore results from the proposed method are theoretically exact from small to very large curvatures and transverse and longitudinal displacements for plane beam-columns under bending actions. The large-deflection analysis of a beam-column with flexible connections at both ends becomes a complex problem requiring the simultaneous solution of at least two highly nonlinear equations with elliptical integrals. The solution of this problem becomes even more complex when the end connections are nonlinear or the direction of the applied end load changes (like “follower” loads). The validity and effectiveness of the proposed method and equations are verified against available solutions of very large deflection elastic analysis of beam-columns. Four comprehensive examples are included for verification and easy reference.     

Assessing Reference Evapotranspiration by the Hargreaves Method in Southern Spain

The Hargreaves method enables reference crop evapotranspiration (ET0) estimation in areas where meteorological information is scarce, as, for example, southern Spain. However, this method is known to produce considerable bias in this region, especially during the dry, hot summer months. An evaluation of the method is made by comparing daily estimates with those made by the more commonly recommended Penman–Monteith method at 16 meteorological stations. Computed ET0 values at the coastal stations are, on average, 0.69 mm?d?1 smaller than the Penman–Monteith estimates whereas at inland stations a small average overestimation of 0.13 mm?d?1 is shown. The adjusted Hargreaves coefficient (AHC), obtained through regression analysis, increases at the coastal stations, on average, to 0.0029, and decreases at the inland stations to 0.0022. Adjustment with the Samani method does generally not produce more accurate estimates in this region. Finally a linear relationship between the AHC and the rate of the average temperature to the average daily temperature range is proposed for the regional adjustment of the Hargreaves coefficient.     

Energy Partitions and Image Segmentation

We address the issue of low-level segmentation for real-valued images. The proposed approach relies on the formulation of the problem in terms of an energy partition of the image domain. In this framework, an energy is defined by measuring a pseudo-metric distance to a source point. Thus, the choice of an energy and a set of sources determines a tessellation of the domain. Each energy acts on the image at a different level of analysis; through the study of two types of energies, two stages of the segmentation process are addressed. The first energy considered, the path variation, belongs to the class of energies determined by minimal paths. Its application as a pre-segmentation method is proposed. In the second part, where the energy is induced by a ultrametric, the construction of hierarchical representations of the image is discussed.     

Application of Kernel-Based Feature Space Transformations and Learning Methods to Phoneme Classification

This paper examines the applicability of some learning techniques to the classification of phonemes. The methods tested were artificial neural nets (ANN), support vector machines (SVM) and Gaussian mixture modeling (GMM). We compare these methods with a traditional hidden Markov phoneme model (HMM), working with the linear prediction-based cepstral coefficient features (LPCC). We also tried to combine the learners with linear/nonlinear and unsupervised/supervised feature space transformation methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA), springy discriminant analysis (SDA) and their nonlinear kernel-based counterparts. We found that the discriminative learners can attain the efficiency of HMM, and that after the transformations they can retain the same performance in spite of the severe dimension reduction. The kernel-based transformations brought only marginal improvements compared to their linear counterparts.