Continuous extension of maps between sequential cascades

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for iterated contours of sequential cascades. A related problem of continuous extension of maps between maximal elements of sequential cascades to full subcascades is solved in full generality.     

Dimerization Constants from Acoustic Measurements: Solutions of Benzene,Cyclohexylamine and Aniline in Cyclohexane

A model assuming that the formation of dimers determines the acoustic properties of liquid mixtures, in the inert solvent cyclohexane, was applied to describe the observed dependences of sound speed on composition. The dimerization constants were estimated. The results allow one to propose that the solutes tend to form associates larger than dimers in concentrated solutions, while in dilute systems solute–solvent interactions play an important role.     

BM-Algebras and related topics

Some connections between BM-algebras and its related topics are studied. It is proved that the class of medial BH-algebras coincides with the class of BM-algebras. Moreover, the congruence lattice of a BM-algebra is investigated.     

Periodic Fluctuations of Flow and Porosity in Spouted Beds

The results of experimental investigations of bed flow hydrodynamics in spouted beds are compared with CFD simulations (Eulerian–Eulerian approach) for two different column geometries. The experimental results of bed porosity and fluctuation frequency of mass flow rate of grain in the fountain region are compared with the corresponding results of simulations. The simulation results confirmed the observations of Muir et al. (1990, Chem. Eng. Comm. 88: 153–171) and Yang and Keairns (1978, AlchE Symp. Ser. No. 176 74: 218) that fluctuations of bed flow in DTSB are caused by particle cluster formation in the loading region at the bottom of column. The solids cross into the jet and cover the column inlet and are carried upward periodically through a draft tube. Subsequent figures obtained from simulations, which show stages of particle cluster formation at the entrance of column, exactly match visual observations. The frequency of fluctuations of grain mass flow rate predicted in simulations (~5–6 Hz) is in the range of that experimentally determined. The fluctuating inflow of solids results in slug formation and explains the vertical variations of height and porosity of the fountain.     

Drying Induced Stresses in a Swelling Porous Wall

The present paper is concerned with the stresses generated in a capillary-porous wall saturated from the bottom and dried naturally on its side planes. The upper cross-section of the wall is totally isolated and no heat and moisture transfer occurs through it, while the bottom one has an a priori determined temperature and moisture content. The vertical planes of the wall are surrounded by air having different temperatures and moisture contents on the left and the right sides. The problem is solved numerically based on a mechanistic model of drying earlier developed by the authors. The distributions of temperature, moisture content, and the drying induced stresses are determined. The variation of temperature on the wall left and right surfaces is analysed dependent on the surroundings temperature. The influence of boundary conditions on the stress distribution in the wall is discussed.     

Elastic arches with large elevation. Singularly perturbed problem of nonlinear elasticity

In this paper we examine the asymptotic expansion of a three-dimensional displacement field defined over a slender, bowlike domain whose shape corresponds to a thin arch. We show that it is possible to derive from the principles of virtual work two families of arch equations whose forms vary with the scale of external forces and the curvature of the arch. The first family of models, for relatively small curvatures, is described by singularly perturbed ordinary differential equations. The second family, when the curvature of the original arch is large, is described by two-dimensional partial differential equations whose form depends on the shape of the cross-section of the solid arch.     

Effective eddy viscosities in implicit modeling of decaying high Reynolds number turbulence with and without rotation

We assess the applicability of the numerical dissipation as an implicit turbulence model. The nonoscillatory finite volume numerical scheme MPDATA developed for simulations of geophysical flows is employed as an example of a scheme with an implicit turbulence model. A series of low resolution simulations of decaying homogeneous turbulence with and without Coriolis forces in the limit of zero molecular viscosity are performed. To assess the implicit model the long-time evolution of turbulence in the simulations is investigated and the numerical velocity fields are analyzed to determine the effective spectral eddy viscosity that is attributed to the numerical discretization. The detailed qualitative and quantitative comparisons are made between the numerical eddy viscosity and the theoretical results as well as the intrinsic eddy viscosity computed exactly from the velocity fields by introducing an artificial wave number cutoff. We find that the numerical dissipation depends on the time step and exhibits contradictory dependence on rotation: it is overestimated for rapid rotation cases and is underestimated for nonrotating cases. These results indicate that the numerical dissipation may fail to represent the effects of the physical subgrid scale processes unless the parameters of a numerical scheme are carefully chosen.     

A Criterion for Compatibility of Conformal and Projective Structures

In a space-time M, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of M. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Adaptive linear combination of heuristic orderings in constructing examination timetables

In this paper, we investigate adaptive linear combinations of graph coloring heuristics with a heuristic modifier to address the examination timetabling problem. We invoke a normalisation strategy for each parameter in order to generalise the specific problem data. Two graph coloring heuristics were used in this study (largest degree and saturation degree). A score for the difficulty of assigning each examination was obtained from an adaptive linear combination of these two heuristics and examinations in the list were ordered based on this value. The examinations with the score value representing the higher difficulty were chosen for scheduling based on two strategies. We tested for single and multiple heuristics with and without a heuristic modifier with different combinations of weight values for each parameter on the Toronto and ITC2007 benchmark data sets. We observed that the combination of multiple heuristics with a heuristic modifier offers an effective way to obtain good solution quality. Experimental results demonstrate that our approach delivers promising results. We conclude that this adaptive linear combination of heuristics is a highly effective method and simple to implement.