Note on covering monotone orthogonal polygons with star-shaped polygons

In 1986, Keil provided an O(n²) time algorithm for the problem of covering monotone orthogonal polygons with the minimum number of r-star-shaped orthogonal polygons. This was later improved to O(n) time and space by Gewali et al. in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63]. In this paper we simplify the latter algorithm—we show that with a little modification, the first step Sweep1 of the discussed algorithm—which computes the top ceilings of horizontal grid segments—can be omitted.In addition, for the minimum orthogonal guard problem in the considered class of polygons, our approach provides a linear time algorithm which uses O(k) additional space, where k is the size of the optimal solution—the algorithm in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63] uses both O(n) time and O(n) additional space.     

Cathodic reduction of acids in dimethylformamide on platinum

A linear correlation was shown to exist between the acidity and the cyclic voltammetric half-potential of the reduction of acids in DMF for carboxylic and N-acids in the pK_a range of 6-16. Chlorophenols are reduced at slightly lower potentials giving a separate parallel line. Applying the obtained equation and employing the same method to literature data in DMSO, the pK_a values for conjugate aids of DMF and DMSO can be calculated, showing DMSO·H⁺ to be more acidic (pK_a = 2.9) than DMF·H⁺ (pK_a = 5.7). The analysis of cyclovoltammetric data demonstrated that a CE mechanism operates in the reduction of strong acids, including the conjugate acid of DMF. Weaker acids are reduced by direct discharge or a mixed mechanism.     

Recursion from iteration

In a simply-typed, call-by-value (CBV) language with first-class continuations, the usual CBV fixpoint operator can be defined in terms of a simple, infinitely-looping iteration primitive. We first consider a natural but flawed definition, based on exceptions and “iterative deepening” of finite unfoldings, and point out some of its shortcomings. Then we present the proper construction using full first-class continuations, with both an informal derivation and a proof that the behavior of the defined operator faithfully mimics a “built-in” recursion primitive. In fact, given an additional uniformity assumption, the construction is a two-sided inverse of the usual definition of iteration from recursion. Continuing, we show that the CBV looping primitive is in fact the direct-style equivalent of a continuation-passing-style fixpoint, and that this correspondence extends all the way to traditional definitions of these operators in terms of reflexive types.     

Ein Beitrag zur Bestimmung der mittleren Zeitkonstante von Diffusionsprozessen

In the paper the general Galerkin method has been applied for the determination of the equivalent time constant of diffusion processes. After establishing the step function response the general formulas have been obtained, which allow for the consideration of boundary conditions of various kinds. The method has been illustrated with some numerical examples.     

Dielectric integrity of thin thermal oxides on silicon

The role of silicon dioxide layers in microelectronics and the importance of their integrity are undisputable. From passivating coatings and masking layers for diffusion to ultra-thin tunneling films — all the silicon technology could not exist without silicon dioxide. This review deals with some aspects of the integrity of thin silicon dioxide films for VLSI applications. The problems of dielectric strength and wear-out are considered from the point of view of their mechanisms, models, oxide processing dependence, testing, and measuring. A brief presentation of statistical approaches commonly applied to reliability topics is also included.     

Determination of porous glass surface free energy components from contact angles

The contact angles of water drops and diiodomethane drops on pellets made of controlled porosity glasses have been measured. The surface of the glasses was modified by thermal treatment at 873 K which led to an increase in the surface concentration of boron atoms. Glass modified with Carbowax 20M (polyethylene glycol) and fully hydroxylated glass have also been studied. Using the measured contact angles and modified Young equation, the dispersion and nondispersion components of the glass surface free energy have been calculated. The values show that with increasing heating time (increasing surface density of boron atoms) an increase in the surface polarity takes place. However, the polarity of the same samples decreases after treatment with Carbowax, increasingly so with higher boron atom concentrations.     

Morse set classification and hierarchical refinement using Conley index

Morse decomposition provides a numerically stable topological representation of vector fields that is crucial for their rigorous interpretation. However, Morse decomposition is not unique, and its granularity directly impacts its computational cost. In this paper, we propose an automatic refinement scheme to construct the Morse Connection Graph (MCG) of a given vector field in a hierarchical fashion. Our framework allows a Morse set to be refined through a local update of the flow combinatorialization graph, as well as the connection regions between Morse sets. The computation is fast because the most expensive computation is concentrated on a small portion of the domain. Furthermore, the present work allows the generation of a topologically consistent hierarchy of MCGs, which cannot be obtained using a global method. The classification of the extracted Morse sets is a crucial step for the construction of the MCG, for which the Poincare′ index is inadequate. We make use of an upper bound for the Conley index, provided by the Betti numbers of an index pair for a translation along the flow, to classify the Morse sets. This upper bound is sufficiently accurate for Morse set classification and provides supportive information for the automatic refinement process. An improved visualization technique for MCG is developed to incorporate the Conley indices. Finally, we apply the proposed techniques to a number of synthetic and realworld simulation data to demonstrate their utility.     

An optimization of allocation of information granularity in the interpretation of data structures: toward granular fuzzy clustering

Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules-clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure. By invoking the granulation-degranulation scheme, we design granular prototypes being reflective of the structure of data to a higher extent than the representation that is provided by their numeric counterparts (prototypes). The design is formulated as an optimization problem, which is guided by the coverage criterion, meaning that we maximize the number of data for which their granular realization includes the original data. The granularity of the prototypes themselves is treated as an important design asset; hence, its allocation to the individual prototypes is optimized so that the coverage criterion becomes maximized. With this regard, several schemes of optimal allocation of information granularity are investigated, where interval-valued prototypes are formed around the already produced numeric representatives. Experimental studies are provided in which the design of granular prototypes of interval format is discussed and characterized.     

Modified calcium silicates as active rubber fillers

The physicochemical characteristics of calcium silicates obtained from the reaction of sodium metasilicate solution with calcium nitrate are given. Further, studies of the modification of the silicate surface with silane and titanate coupling agents are presented. By wettability measurements and an analysis of the chemically adsorbed carbon arising from the coupling agents, the degree of modification of these surfaces was estimated. The modification of the surface of the silicates with the same agents, but in the presence of acid protons, was also performed with a positive effect. The usefulness of modifications is justified by the results of strength studies of vulcanizates filled with the modified silicates.     

The Co-Culture of Staphylococcal Biofilm and Fibroblast Cell Line: The Correlation of Biological Phenomena with Metabolic NMR1 Footprint

Staphylococcus aureus is one of the most prevalent pathogens associated with several types of biofilm-based infections, including infections of chronic wounds. Mature staphylococcal biofilm is extremely hard to eradicate from a wound and displays a high tendency to induce recurring infections. Therefore, in the present study, we aimed to investigate in vitro the interaction between S. aureus biofilm and fibroblast cells searching for metabolites that could be considered as potential biomarkers of critical colonization and infection. Utilizing advanced microscopy and microbiological methods to examine biofilm formation and the staphylococcal infection process, we were able to distinguish 4 phases of biofilm development. The analysis of staphylococcal biofilm influence on the viability of fibroblasts allowed us to pinpoint the moment of critical colonization—12 h post contamination. Based on the obtained model we performed a metabolomics analysis by ¹H NMR spectroscopy to provide new insights into the pathophysiology of infection. We identified a set of metabolites related to the switch to anaerobic metabolism that was characteristic for staphylococcal biofilm co-cultured with fibroblast cells. The data presented in this study may be thus considered a noteworthy but preliminary step in the direction of developing a new, NMR-based tool for rapid diagnosing of infection in a chronic wound.