An Extended Quadratic Frobenius Primality Test with Average- and Worst-Case Error Estimate

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and to several other known probabilistic tests. EQFT takes time equivalent to about two or three Miller-Rabin tests, but has a much smaller error probability, namely 256/331776^t for t iterations of the test in the worst case. We also give bounds on the average-case behaviour of the test: consider the algorithm that repeatedly chooses random odd k bit numbers, subjects them to t iterations of our test and outputs the first one found that passes all tests. We obtain numeric upper bounds for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2^-155 for k = 500, t = 2. Compared with earlier similar results for the Miller-Rabin test, the results indicate that our test in the average case has the effect of nine Miller-Rabin tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point.     

Production of phosphoric acid with low content of impurities

The present work is to study the possibility for controlled distribution of the impurities when they are decomposed by sulphuric acid to wet phosphoric acid and phosphogypsum, as well as generating technological conditions for production of clean wet phosphoric acid and its derivatives - phosphoric fertilizers, food phosphates and other phosphoric products.A coefficient of distribution D_A is introduced as a general criterion for elements dispersion. The study includes relationships between the weight ratio sulphuric acid/natural phosphate and D_A; the period of decomposition and D_A; the particle's size content of the natural phosphate and D_A. The obtained experimental data and relationships about the influence of the above discussed technological parameters on dispersion of more than 23 elements allow for control of that process in wet phosphoric acid and phosphogypsum by selecting specific technological conditions. Thus, depending on the requirements of acid's consumers and procedures for secondary processing of phosphogypsum to end-products, a selective decomposition of the natural phosphates to phosphoric acid and phosphogypsum can be carried out with content of the impurities in those products varying in narrow limits.     

A Survey on the Numerics and Computations for the Landau-Lifshitz Equation of Micromagnetism

The Landau-Lifshitz (LL)equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also an interesting mathematical properties of the LL equation: nonlocal character for some quantities,nonconvex side-constraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions,are addressed. Author is supported by the Fund for Scientific Research - Flanders FWO (Belgium).     

Groundwater-surface water interactions and agricultural nutrient transport in a Great Lakes clay plain system

Nutrient export from agricultural land to surface waters is a significant environmental concern within the Great Lakes Basin (GLB). A field-based watershed-scale study was completed to investigate spatial and temporal variations of phosphorus and nitrate to assess nutrient transport pathways and groundwater-surface water interactions in an agriculturally dominated clay plain system. This was conducted in the 127 km² Upper Parkhill Watershed, near Lake Huron in southwestern Ontario, Canada. Data collection occurred from June 2018 to May 2019 via continuous sensor deployment and discrete sampling of stream water, groundwater, hyporheic zone, and tile drainage water. Samples were analyzed for various nutrient species (total, total dissolved, soluble reactive, and particulate phosphorus, and nitrate-N) to examine the hydrological dynamics of principal transport pathways of agriculturally-derived nutrients. Total phosphorus and nitrate concentrations in stream water ranged from 0.007 to 0.324 mg/L and 0.32 to 13.13 mg NO₃^?-N/L, respectively. Tile drainage water total phosphorous concentrations varied from 0.006 to 0.066 mg/L. Groundwater total dissolved phosphorus concentrations ranged from <0.003 to 0.085 mg/L. Transport of phosphorus through tile drainage was observed to be greater than through groundwater over the study period. No distinct relationship was observed between nutrient concentrations in the hyporheic zone and the vertical hydraulic gradient within this zone in the studied stream reach. Preliminary correlations were discerned between water quality observations and recognized land management practices. Given the elevated stream nutrient concentrations, these results are consequential for the continual improvement of strategies and programs devised to conserve water resources within the GLB.     

Modeling guided wave propagation with application to the long-range defect detection in railroad tracks

The aim of this work is to demonstrate the use of a commercial finite element package, ABAQUS EXPLICIT, to model ultrasonic guided waves in structural components. The particular application of interest is modeling the interaction of a broadband vertical bending mode with transverse-type defects in railroad tracks. This topic is part of a broader project on high-speed defect detection in rails by long-range ultrasonic inspections. Reflection coefficient spectra in the 20–45 kHz range are obtained for four different sizes and three different orientations of transverse head flaws. A preliminary study of Lamb waves in a free plate helps drawing modeling guidelines for the rail.     

Different Expression of Mitochondrial and Endoplasmic Reticulum Stress Genes in Epicardial Adipose Tissue Depends on Coronary Atherosclerosis

The aim of our study was to analyze mitochondrial and endoplasmic reticulum (ER) gene expression profiles in subcutaneous (SAT) and epicardial (EAT) adipose tissue, skeletal muscle, and myocardium in patients with and without CAD undergoing elective cardiac surgery. Thirty-eight patients, 27 with (CAD group) and 11 without CAD (noCAD group), undergoing coronary artery bypass grafting and/or valvular surgery were included in the study. EAT, SAT, intercostal skeletal muscle, and right atrium tissue and blood samples were collected at the start and end of surgery; mRNA expression of selected mitochondrial and ER stress genes was assessed using qRT-PCR. The presence of CAD was associated with decreased mRNA expression of most of the investigated mitochondrial respiratory chain genes in EAT, while no such changes were seen in SAT or other tissues. In contrast, the expression of ER stress genes did not differ between the CAD and noCAD groups in almost any tissue. Cardiac surgery further augmented mitochondrial dysfunction in EAT. In our study, CAD was associated with decreased expression of mitochondrial, but not endoplasmic reticulum stress genes in EAT. These changes may contribute to the acceleration of coronary atherosclerosis.     

Hydrolysis of fish oils containing polymers of triacylglycerols by pancreatic lipasein vitro

Fish oils containing different levels of polymers of triacylglycerols formed during autoxidation were incubated with pancreatic lipase to establish whether these polymers are substrates for lipase hydrolysis. With oils containing low amounts (less than 4%) of triacylglycerol polymers as substrates, both triacylglycerols and polymers of triacylglycerols were almost completely hydrolyzed, and fatty acid monomers and monoacylglycerols were the major lipid products. Under the same incubation conditions, some triacylglycerols remained intact when highly oxidized oils containing 20 or 30% triacylglycerol polymers were the substrate. The fatty acid composition of these residual triacylglycerols was almost identical to that of triacylglycerols present at the start of the assay. When fish oil containing 30% triacylglycerol polymers was incubated with the lipase, the component triacylglycerols and polymers of triacylglycerols were hydrolyzed at similar rates, and fatty acid dimers were detected as a product. It is concluded that the high molecular weight polymers of triacylglycerols present in oxidized fish oils can be hydrolyzed by pancreatic lipasein vitro.     

Physical crosslinking effects in α,ω-dihydroxy terminated polybutadienes

Structure and molecular dynamics of α,ω-dihydroxy terminated polybutadienes of varying number averaged molecular weight (1320-10?500 g/mol) have been investigated by Fourier-transformed infrared (FTIR) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, dielectric relaxation spectroscopy (DRS), differential scanning calorimetry (DSC) and wide-angle X-ray scattering (WAXS). DSC and DRS revealed an increase in the glass transition temperature upon decrease of the molecular weight, accompanied by an increasing dynamic fragility m (or steepness index) of the dielectric α-process. This correlation between T_g and m for different molecular weights indicates the presence of a physical network, where H-bonded end-group clusters act as temporary crosslinks. From the dielectric relaxation strength Δ?_α(M_n), the fraction of associated hydroxy groups (f_bond) was estimated showing a peak value for the two but shortest polymers, a behaviour that strongly resembles the molecular weight dependence of the fragility. By considering the quantity f_bond(M_n) in a modified Fox-Flory approach, the measured T_g(M_n) behaviour could be reproduced in a satisfying way. FTIR results support this general picture and show a considerable dependence of the extent of hydrogen bonding and formation of hydroxy groups associates on the molecular weight. Further, WAXS and DSC results disprove the idea of formation of pseudo-crystalline hydrophobic microdomains in these compounds as suggested by other authors.     

Continuous Levels‐of‐Detail and Visual Abstraction for Seamless Molecular Visualization

Molecular visualization is often challenged with rendering of large molecular structures in real time. We introduce a novel approach that enables us to show even large protein complexes. Our method is based on the level‐of‐detail concept, where we exploit three different abstractions combined in one visualization. Firstly, molecular surface abstraction exploits three different surfaces, solvent‐excluded surface (SES), Gaussian kernels and van der Waals spheres, combined as one surface by linear interpolation. Secondly, we introduce three shading abstraction levels and a method for creating seamless transitions between these representations. The SES representation with full shading and added contours stands in focus while on the other side a sphere representation of a cluster of atoms with constant shading and without contours provide the context. Thirdly, we propose a hierarchical abstraction based on a set of clusters formed on molecular atoms. All three abstraction models are driven by one importance function classifying the scene into the near‐, mid‐ and far‐field. Moreover, we introduce a methodology to render the entire molecule directly using the A‐buffer technique, which further improves the performance. The rendering performance is evaluated on series of molecules of varying atom counts.     

Approximate Symmetry Detection in Partial 3D Meshes

Symmetry is a common characteristic in natural and man‐made objects. Its ubiquitous nature can be exploited to facilitate the analysis and processing of computational representations of real objects. In particular, in computer graphics, the detection of symmetries in 3D geometry has enabled a number of applications in modeling and reconstruction. However, the problem of symmetry detection in incomplete geometry remains a challenging task. In this paper, we propose a vote‐based approach to detect symmetry in 3D shapes, with special interest in models with large missing parts. Our algorithm generates a set of candidate symmetries by matching local maxima of a surface function based on the heat diffusion in local domains, which guarantee robustness to missing data. In order to deal with local perturbations, we propose a multi‐scale surface function that is useful to select a set of distinctive points over which the approximate symmetries are defined. In addition, we introduce a vote‐based scheme that is aware of the partiality, and therefore reduces the number of false positive votes for the candidate symmetries. We show the effectiveness of our method in a varied set of 3D shapes and different levels of partiality. Furthermore, we show the applicability of our algorithm in the repair and completion of challenging reassembled objects in the context of cultural heritage.