Entropy viscosity method for nonlinear conservation laws

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method.     

Thermodynamics of Micellization from Heat‐Capacity Measurements

Differential scanning calorimetry (DSC), the most important technique for studying the thermodynamics of structural transitions of biological macromolecules, is seldom used in quantitative thermodynamic studies of surfactant micellization/demicellization. The reason for this could be ascribed to an insufficient understanding of the temperature dependence of the heat capacity of surfactant solutions (DSC data) in terms of thermodynamics, which leads to problems with the design of experiments and interpretation of the output signals. We address these issues by careful design of DSC experiments performed with solutions of ionic and nonionic surfactants at various surfactant concentrations, and individual and global mass‐action model analysis of the obtained DSC data. Our approach leads to reliable thermodynamic parameters of micellization for all types of surfactants, comparable with those obtained by using isothermal titration calorimetry (ITC). In summary, we demonstrate that DSC can be successfully used as an independent method to obtain temperature‐dependent thermodynamic parameters for micellization.     

Non-isothermal reduction of silica-supported nickel catalyst precursors in hydrogen atmosphere: a kinetic study and statistical interpretation

A series of silica-supported nickel catalyst precursors was synthesized with different SiO₂/Ni mole ratios (0.20, 0.80 and 1.15). Non-isothermal reduction of Ni catalyst precursors was investigated by temperature-programmed reduction at four different heating rates (2, 5, 10 and 20 °C min^?1), in a hydrogen atmosphere. Kinetic parameters (E _a, A) were determined using Friedman isoconversional method. It was found that for all mole ratios, apparent activation energy is practically constant in conversion range of α = 30–70 %. In considered conversion range, the following values of apparent activation energy were found: E _a = 129.5 kJ mol^?1 (SiO₂/Ni = 0.20), E _a = 133.8 kJ mol^?1 (SiO₂/Ni = 0.80) and E _a = 125.0 kJ mol^?1 (SiO₂/Ni = 1.15). Using two special functions (y(α) and z(α)), the kinetic model was determined. It was established that reduction of Ni catalyst precursors with different SiO₂/Ni mole ratios is a complex process and can be described by two-parameter ?esták–Berggren (SB) autocatalytic model. Based on established values of SB parameters for each mole ratio, the possible mechanism was discussed. It was found that for all investigated ratios, the Weibull distribution function fits very well the experimental data, in the wide range of conversions (α = 5–95 %). Based on obtained values of Weibull shape parameter (θ), it was found that experimentally evaluated density distribution functions of the apparent activation energies can be approximated by the unbalanced peaked normal distribution.     

Veber on knowledge and factuality

The article deals with the development of the philosophy of France Veber (1890–1975), the pupil of Meinong and a main Slovene philosopher. One of the most important threads of Veber’s philosophy is the consideration of knowledge and factuality, which may be seen as a driving force of its development. Veber’s philosophical development is usually divided into three phases: the object theory phase, the phase when he created his philosophy of a person as a creature at the crossing of the natural and the spiritual world, who as an active, not merely passive subject possesses her own causal powers, and the third phase, when he supplemented his earlier philosophy with the theory of a special side of our experience which he called hitting-upon-reality. It is a direct experience of reality, a special kind of intentionality, which is however fundamentally different from presentational intentionality, which alone is taken into account by object theory or phenomenology. The questions of knowledge and factuality are closely connected in Veber’s philosophy since, pace Veber, knowledge is a kind of, we may say, justified experience the object of which is a factual entity. Hence, if we want to understand what knowledge is, we must face the challenge of comprehending factuality. There are five stages to be noted in the development of his epistemology. The first two belong to his object theory phase, the third to his person phase, the fourth is characterised by his distinguishing and exploring truth and validity with regard to the thought about God, and the basis of the fifth phase lies in his theory of hitting-upon-reality. In Introduction to Philosophy and The System of Philosophy, that is in the year 1921, Veber believed that factuality (“truth,”) was a property of the object, which we do present, but we do not present the factuality of this factuality (that is why he distinguishes between the merely objective truths and truths that are in addition transcendental truths). In 1923, in The Problems of Contemporary Philosophy and in the work Science and Religion, he already rejected such a view. There is something that makes things factual, but that is a complete unknown X. Therefore we cannot even say what kind of an entity this factuality is. Some people would probably demand the following formulation: if X is an ultimate mystery, we should not claim even that it is an entity. In The Problems of Presentation Production (1928) Veber claimed that factuality is not a property since this would lead to a regressum ad infinitum. Philosophy (1930) related internally correct experience to personal will. In The Book about God (1934) he developed the thesis that factuality depends on the act of God. In The Question of Reality (1939) he importantly modified, developed and enriched the thesis that we do not present reality with his theory of immediate experience of (hitting upon) factuality.     

Circular colorings of edge‐weighted graphs

The notion of (circular) colorings of edge‐weighted graphs is introduced. This notion generalizes the notion of (circular) colorings of graphs, the channel assignment problem, and several other optimization problems. For instance, its restriction to colorings of weighted complete graphs corresponds to the traveling salesman problem (metric case). It also gives rise to a new definition of the chromatic number of directed graphs. Several basic results about the circular chromatic number of edge‐weighted graphs are derived. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 107–116, 2003     

Duality and operator algebras: automatic weak* continuity and applications

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras, and give several applications of the surprising fact that certain maps are always weak^*-continuous on dual spaces. In particular, if X is a subspace of a C^*-algebra A, and if a∈A satisfies aX⊂X, then we show that the function x?ax on X is automatically weak^* continuous if either (a) X is a dual operator space, or (b) a^*X⊂X and X is a dual Banach space. These results hinge on a generalization to Banach modules of Tomiyama's famous theorem on contractive projections onto a C^*-subalgebra. Applications include a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and a generalization of the theory of W^*-modules to the framework of modules over such algebras. We also give a Banach module characterization of σ-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra.     

Composition of the essential oil of Geocaryum cynapioides (Guss.) L. Engstrand

Volatile constituents from two fresh samples of the subendemic Geocaryum cynapioides (Guss.) L. Engstrand (Apiaceae) obtained by hydrodistillation were analyzed by GC and GC-MS. Forty four and one hundred-twenty three constituents identified in the oils accounted for 98.7 % and 98.4 % of the total oils, respectively. The major component of both oils was (E)-β-farnesene (73.3 % and 57.7 %) while the other major contributors were: (E,E)-α-farnesene (4.8 % and 14.6 %) and trans-sesquisabinene hydrate (12.2 % and 3.0 %). The constituents endo-fenchyl acetate, and three sesquiterpene lactones belonging to the selinane (callitrisin) and guaiane (grilactone and jalcaguaianolide) series, with a rather restricted natural occurrence, were present in only one of the samples (4.7 %, trace amount, 0.1 %, 0.5 %, respectively) and completely absent from the other distinguishing so the two samples. A chemotaxonomic discussion of the results is presented.     

Sessile droplet spread into porous substrates--determination of capillary pressure using a continuum approach

The problem of primary and secondary spread of sessile droplets into a porous substrate was formulated and solved numerically. A continuum approach for liquid- and gas-phases was utilized. The governing equations were discretized by finite difference method and solutions for both phases are obtained by marching in time using the fourth-order Runge-Kutta integration algorithm. This type of spread is a purely momentum-driven process that is caused by gradients both in capillary pressure and in saturation. A methodology was developed for finding the capillary pressure function for sessile droplets, which has not been described before. This approach was based on experimental data for a liquid/porous medium pair, and using universal, non-dimensional curves. Similar solutions were generated by the continuum approach and validated using experimental results. The model shows qualitative and quantitative agreement with experimental data. Although the focus of this work was to understand the interaction of chemical warfare agents with porous media, the approaches are universal and can be applied to determining the spread of any liquid into a porous material.     

Interval Minors of Complete Bipartite Graphs

Interval minors of bipartite graphs were recently introduced by Jacob Fox in the study of Stanley–Wilf limits. We investigate the maximum number of edges in ‐interval minor‐free bipartite graphs. We determine exact values when and describe the extremal graphs. For , lower and upper bounds are given and the structure of ‐interval minor‐free graphs is studied.