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The article explores geodesics on polyhedra, particularly focusing on simple closed geodesics and their properties. It discusses the classification of geodesics on regular polyhedra, the relationship between geodesics and billiards, and the uniqueness of disphenoids in having arbitrarily long geodesics. The text also addresses the existence of simple closed geodesics on tetrahedra and the properties of geodesics on nonconvex polyhedra, including the construction of long closed geodesics using seven cubes. Open questions are posed regarding geodesics on nonconvex polyhedra in different spaces and the minimal number of vertices needed for long geodesics. The author acknowledges the contributions of an anonymous referee for their feedback. [Extracted from the article]

Recent metagenomic studies have identified numerous lineages of hydrogen-dependent, obligately methyl-reducing methanogens. Yet, only a few representatives have been isolated in pure culture. Here, we describe six new species with this capability in the family Methanosarcinaceae (order Methanosarcinales), which makes up a substantial fraction of the methanogenic community in arthropod guts. Phylogenomic analysis placed the isolates from cockroach hindguts into the genus Methanimicrococcus (M. hacksteinii, M. hongohii , and M. stummii) and the isolates from millipede hindguts into a new genus, Methanolapillus (M. africanus, M. millepedarum , and M. ohkumae). Members of this intestinal clade, which includes also uncultured representatives from termites and vertebrates, have substantially smaller genomes (1.6–2.2 Mbp) than other Methanosarcinales. Genome reduction was accompanied by the loss of the upper part of the Wood–Ljungdahl pathway, several energy-converting membrane complexes (Fpo, Ech, and Rnf), and various biosynthetic pathways. However, genes involved in the protection against reactive oxygen species (catalase and superoxide reductase) were conserved in all genomes, including cytochrome bd (CydAB), a high-affinity terminal oxidase that may confer the capacity for microaerobic respiration. Since host-associated Methanosarcinales are nested within omnivorous lineages, we conclude that the specialization on methyl groups is an adaptation to the intestinal environment. [ABSTRACT FROM AUTHOR]

Current stage of proteomic research in the field of biology, medicine, development of new drugs, population screening, or personalized approaches to therapy dictates the need to analyze large sets of samples within the reasonable experimental time. Until recently, mass spectrometry measurements in proteomics were characterized as unique in identifying and quantifying cellular protein composition, but low throughput, requiring many hours to analyze a single sample. This was in conflict with the dynamics of changes in biological systems at the whole cellular proteome level upon the influence of external and internal factors. Thus, low speed of the whole proteome analysis has become the main factor limiting developments in functional proteomics, where it is necessary to annotate intracellular processes not only in a wide range of conditions, but also over a long period of time. Enormous level of heterogeneity of tissue cells or tumors, even of the same type, dictates the need to analyze biological systems at the level of individual cells. These studies involve obtaining molecular characteristics for tens, if not hundreds of thousands of individual cells, including their whole proteome profiles. Development of mass spectrometry technologies providing high resolution and mass measurement accuracy, predictive chromatography, new methods for peptide separation by ion mobility and processing of proteomic data based on artificial intelligence algorithms have opened a way for significant, if not radical, increase in the throughput of whole proteome analysis and led to implementation of the novel concept of ultrafast proteomics. Work done just in the last few years has demonstrated the proteome-wide analysis throughput of several hundred samples per day at a depth of several thousand proteins, levels unimaginable three or four years ago. The review examines background of these developments, as well as modern methods and approaches that implement ultrafast analysis of the entire proteome. [ABSTRACT FROM AUTHOR]

We offer a detailed description of our previously published new concept of the evolution of the biosphere as an integral system of its states over time, united by development trends. The structure of the biosphere is considered as a hierarchical fractal system, and the elementary unit of the biosphere is an ecosystem. The fractal structure of the biosphere corresponds to the emergent principle: each lower level is an element of a more complex system and has its own properties. The proposed concept of biosphere evolution is based on the general categories of dialectics: states and interstates, continuity and discreteness, reproducibility and uniqueness. The evolutionary history of the biosphere is a metameric picture of changing states and interstates. The most important feature of the biosphere organization in space–time is a complex system of continua. The development of an integral biospheric system occurs in a time continuum: in the biosphere, the differences between the early and subsequent states are quite significant and obvious. Moreover, these differences are associated with fundamental complications, development, which is, in fact, evolution. The states of the biosphere in certain periods are linked by trends that form an evolutionary system. Continuing states, when the system remains self-identical for a long period, are replaced by new states through interstates. Based on the principle of actualism, the problems of the biosphere's future and evolutionary trends of the biosphere under anthropogenic impact are considered. [ABSTRACT FROM AUTHOR]

It is shown that when using a standard electrochemical profiling recipe that applies intensive illumination by halogen lamp with power up to 250 W of n+/n GaAs structure to generate the holes necessary for etching, the resulting electron distribution profile differs from that set during growth for an electron concentration in the n+-layer > 4 × 1018 cm–3 when using EDTA electrolyte. This difference is due to the appearance and development of etching pits caused by the increase in the degree of defectivity of GaAs layers with increasing concentration of the donor impurity—silicon. To obtain adequate electron distribution profiles in n+/n GaAs structures it is necessary to limit the illumination up to 25 W. [ABSTRACT FROM AUTHOR]

We consider a connected graph Γ as a coarse space and prove that Γ admits a 2-selector if and only if Γ is either bounded or coarsely equivalent to N or R . We apply this result to geodesic metric spaces admitting the linear orders compatible with coarse structures. [ABSTRACT FROM AUTHOR]

For a single matrix (operator) it is well-known that the spectral gap is an important quantity, as well as its estimate and computation. Here we consider, for the first time in the literature, the computation of its extension to a finite family of matrices, in other words the difference between the joint spectral radius (in short JSR, which we call here the first Lyapunov exponent) and the second Lyapunov exponent (denoted as SLE). The knowledge of joint spectral characteristics and of the spectral gap of a family of matrices is important in several applications, as in the analysis of the regularity of wavelets, multiplicative matrix semigroups and the convergence speed in consensus algorithms. As far as we know the methods we propose are the first able to compute this quantity to any given accuracy. For computation of the spectral gap one needs first to compute the JSR. A popular tool that is used to this purpose is the invariant polytope algorithm, which relies on the finiteness property of the family of matrices, when this holds true. In this paper we show that the SLE may not possess the finiteness property, although it can be efficiently approximated with an arbitrary precision. The corresponding algorithm and two effective estimates are presented. Moreover, we prove that the SLE possesses a weak finiteness property, whenever the leading eigenvalue of the dominant product is real. This allows us to find in certain situations the precise value of the SLE. Numerical results are demonstrated along with applications in the theory of multiplicative matrix semigroups and in the wavelets theory. [ABSTRACT FROM AUTHOR]

Elliptic polytopes are convex hulls of several concentric plane ellipses in R d . They arise in applications as natural generalizations of usual polytopes. In particular, they define invariant convex bodies of linear operators, optimal Lyapunov norms for linear dynamical systems, etc. To construct elliptic polytopes one needs to decide whether a given ellipse is contained in the convex hull of other ellipses. We analyse the computational complexity of this problem and show that for d = 2 , 3 , it admits an explicit solution. For larger d, two geometric methods for approximate solution are presented. Both use the convex optimization tools. The efficiency of the methods is demonstrated in two applications: the construction of extremal norms of linear operators and the computation of the joint spectral radius/Lyapunov exponent of a family of matrices. [ABSTRACT FROM AUTHOR]

A self-affine tile is a compact set G ⊂ R d that admits a partition (tiling) by parallel shifts of the set M - 1 G , where M is an expanding matrix. We find all self-affine tiles which are polyhedral sets, i.e., unions of finitely many convex polyhedra. It is shown that there exists an infinite family of such polyhedral sets, not affinely equivalent to each other. A special attention is paid to integral self-affine tiles with standard digit sets, when the matrix M and the translation vectors are integer. Applications to the approximation theory and to the functional analysis are discussed. [ABSTRACT FROM AUTHOR]

The article presents experimental study results of processes in the near-surface region of flat samples (Cu, Al, graphite, PTFE) under irradiation with powerful vacuum ultraviolet (VUV) radiation generated by pulsed high-current discharges. The typical exposure time was ≈ 3–50 μs, and the radiation energy in the vacuum-ultraviolet spectrum range was ≈ 1–2 kJ. The main characteristics of the processes were registered on Schlieren photographs and interferograms. The dynamics of vapor-plasma flows formation and development during VUV ablation were studied depending on the spectral composition and intensity of the radiation flux on the surface. The study is relevant for space and plasma technology, development of microelectronic elements, and fundamental research on the interaction of extreme radiation with matter. [ABSTRACT FROM AUTHOR]

We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded both from below (the guaranteed dwell-time) and from above (the maximal time of a single mode). The presence of upper bounds makes this problem quite different from the classical case. For instance, a stable system can now consist of unstable matrices, it may not possess Lyapunov functions, etc. We introduce the concept of a convex Lyapunov multifunction with discrete monotonicity. Its existence, as well as the existence of invariant norms, are proved. We also establish a modified Berger--Wang formula over periodizable switching laws. Those results provide a method of computation of the Lyapunov exponent with an arbitrary precision. Its efficiency is shown in numerical examples. [ABSTRACT FROM AUTHOR]

In the paper, we describe an original 3D travel-time tomography approach. It is based on the new realization of the bending method which to some extent takes into account the band-limited nature of real seismic signals propagation. As a result, two-point ray tracing provides more reliable ray trajectories and travel times in complex media. Another original feature of the proposed tomography is that the model is represented using the Chebyshev polynomials. Such parameterization allows analytical calculation of travel times and their derivatives with respect to model parameters and significantly reduces the number of parameters to be recovered during inversion compared to more common grid tomography. In certain situations, the proposed approach provides significant computational advantages. Numerical examples prove its efficiency. [ABSTRACT FROM AUTHOR]

A mathematical model of energy metabolism in erythrocyte-bioreactors loaded with alcohol dehydrogenase and acetaldehyde dehydrogenase was constructed and analyzed. Such erythrocytes can convert ethanol to acetate using intracellular NAD and can therefore be used to treat alcohol intoxication. Analysis of the model revealed that the rate of ethanol consumption by the erythrocyte-bioreactors increases proportionally to the activity of incorporated ethanol-consuming enzymes until their activity reaches a specific threshold level. When the ethanol-consuming enzyme activity exceeds this threshold, the steady state in the model becomes unstable and the model switches to an oscillation mode caused by the competition between glyceraldehyde phosphate dehydrogenase and ethanol-consuming enzymes for NAD. The amplitude and period of metabolite oscillations first increase with the increase in the activity of the encapsulated enzymes. A further increase in these activities leads to a loss of the glycolysis steady state, and a permanent accumulation of glycolytic intermediates. The oscillation mode and the loss of the steady state can lead to the osmotic destruction of erythrocyte-bioreactors due to an accumulation of intracellular metabolites. Our results demonstrate that the interaction of enzymes encapsulated in erythrocyte-bioreactors with erythrocyte metabolism should be taken into account in order to achieve the optimal efficacy of these bioreactors. [ABSTRACT FROM AUTHOR]

The paper analyzes the state of the problem of the theoretical prediction of the retention coefficient and specific output flow for purification or concentration of industrial solutions throughout the cycle of nanofiltration separation of industrial solutions containing metal ions. To predict the nanofiltration process, a mathematical model is developed based on solving the equations of convective diffusion, the Navier–Stokes equation, and the flow continuity equation using a polar coordinate system. The theoretical results obtained as a result of solving the system of equations make it possible to evaluate the quality and productivity of nanofiltration separation by calculating the concentrations in the permeate and retentate tracts and the permeate volume. The adequacy of the developed method is assessed by comparing the data calculated using the model with the experimental data obtained on a nanofiltration unit during the separation of solutions containing Cr3+ and Zn2+ cations using semi-permeable membranes OPMN-P and AMN-P. [ABSTRACT FROM AUTHOR]

The regularity of refinable functions has been analysed in an extensive literature and is well-understood in two cases: 1) univariate 2) multivariate with an isotropic dilation matrix. The general (non-isotropic) case offered a great resistance. It was not before 2019 that the non-isotropic case was done by developing the matrix method. In this paper we make the next step and extend the Littlewood-Paley type method, which is very efficient in the aforementioned special cases, to general equations with arbitrary dilation matrices. This gives formulas for the higher order regularity in W 2 k (R n) by means of the Perron eigenvalue of a finite-dimensional linear operator on a special cone. Applying those results to recently introduced tile B-splines, we prove that they can have a higher smoothness than the classical ones of the same order. Moreover, the two-digit tile B-splines have the minimal support of the mask among all refinable functions of the same order of approximation. This proves, in particular, the lowest algorithmic complexity of the corresponding subdivision schemes. Examples and numerical results are provided. [ABSTRACT FROM AUTHOR]

If a linear switching system with frequent switches is stable, will it be stable under arbitrary switches? In general, the answer is negative. Nevertheless, this question can be answered in an explicit form for any concrete system. This is done by finding the mode-dependent critical lengths of switching intervals after which any enlargement does not influence the stability. The solution is given in terms of the exponential polynomials of least deviation from zero on a segment ("Chebyshev-like" polynomials). By proving several theoretical results on exponential polynomial approximation we derive an algorithm for finding such polynomials and for computing the critical switching time. The convergence of the algorithm is estimated and numerical results are provided. [ABSTRACT FROM AUTHOR]

The influence of the morphology of dispersed particles, sorption ability, and oxygen-containing groups of carbon black on the destabilization of the SKS-30ARK emulsion rubber latex in liquid-phase filling with nanodispersed carbon black in an ultrasonic field was studied. The latex destabilization is caused by sorption of emulsifying agents onto carbon black from the protective surface of latex globules, which is indirectly confirmed by an increase in the surface tension coefficient of the latex system. The complete coagulation of the butadiene–styrene latex is reached without using coagulants in the course of liquid-phase filling with carbon black at the component ratio carbon black : rubber 100 : 100 (wt parts) and рН ≤ 4.3 when using K354 carbon black and at the same component ratio and рН ≤ 3.6 when using P324 carbon black. Liquid-phase filling of emulsion rubbers in the step of their recovery from the latex ensures uniform distribution of nanodispersed carbon black throughout the volume of the elastomer compound due to the dispersing effect of the emulsifying components of the latex. These components migrate from the surface of latex globules to the developed active surface of carbon black under the action of ultrasonic field. [ABSTRACT FROM AUTHOR]

This study considers the full waveform inversion (FWI) method based on the asymptotic solution of the Helmholtz equation. We provide frequency-dependent ray tracing to obtain the wave field used to compute the FWI gradient and calculate the modeled data. With a comparable quality of the inverse problem solution as applied to the standard finite difference approach, the speed of the calculations in the asymptotic method is an order of magnitude higher. A series of numerical experiments demonstrate the approach's effectiveness in reconstructing the macro velocity structure of complex media for low frequencies. [ABSTRACT FROM AUTHOR]

An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from the interior of the cone. The main facts of the duality theory in convex analysis, in particular, the Fenchel-Moreau theorem, are generalized to antinorms. However, it is shown that the duality relation for antinorms is discontinuous. In every dimension, there are infinitely many self-dual antinorms on the positive orthant and, in particular, infinitely many autopolar polyhedra. For the two-dimensional case, we characterize them all. The classification in higher dimensions is left as an open problem. Applications to linear dynamical systems, to the Lyapunov exponent of random matrix products, to the lower spectral radius of nonnegative matrices, and to convex trigonometry are considered. [ABSTRACT FROM AUTHOR]

Computational material science aims to simulate substances to understand their physical properties. Bioelectronics is an interdisciplinary field that studies biological material from the conductivity point of view. In case of proteins, the folding is an important feature that directly influences physical and chemical properties. The folding modelling is a hard task. The enormous number of degrees of freedom makes modelling impossible for classical computation due to resource limits. Quantum computations aim to process multidimensional data with logarithmic growth of quantum bits. Quantum operators, gates, form quantum programs, known as circuits, which process the input data. When talking about real quantum computers, the gates are noisy and expensive to execute. Thus, it is essential to reduce the number of quantum gates both for the quality of the result and the cost of computations. This work describes an approach to decrease the number of quantum gates based on their mathematical property. [ABSTRACT FROM AUTHOR]

Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern as well. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative nature of averaging. The concept of PMA was motivated in a number of application fields, of which we consider the matrix population models and illustrate solving the PMA problem with several sets of model matrices calibrated in particular botanic case studies. The patterns of those matrices are typically nontrivial (they contain both zero and nonzero elements), the PMA problem thus having no exact solution for a fundamental reason (an overdetermined system of algebraic equations). Therefore, searching for the approximate solution reduces to a constrained minimization problem for the approximation error, the loss function in optimization terms. We consider two alternative types of the loss function and present a general algorithm of searching the optimal solution: basin-hopping global search, then local descents by the method of conjugate gradients or that of penalty functions. Theoretical disadvantages and practical limitations of both loss functions are discussed and illustrated with a number of practical examples. [ABSTRACT FROM AUTHOR]

A coarse space X endowed with a linear order compatible with the coarse structure of X is called linearly ordered. We prove that every linearly ordered coarse space X is locally convex and the asymptotic dimension of X is either 0 or 1. If X is metrizable, then the family of all right bounded subsets of X has a selector. [ABSTRACT FROM AUTHOR]

Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given k there is a minimal diameter of subsets at which there exists a covering with k subsets of any planar set of unit diameter. In order to find an upper estimate of the minimal diameter we propose an algorithm for finding sub-optimal partitions. In the cases 10 ⩽ k ⩽ 17 some upper and lower estimates of the minimal diameter are improved. Another result is that any set M ⊂ R 3 of a unit diameter can be partitioned into four subsets of a diameter not greater than 0.966. [ABSTRACT FROM AUTHOR]

[Display omitted] • The invasion of false carmine cochineal (Dactylopius opuntiae) threatens cactus pear in the Mediterranean. • Introducing Hyperaspis trifurcata reduced cochineal populations in Israel, but often too late to prevent major damage. • Accelerated establishment of H. trifurcata in new hotspots and a "predator-prey dual introduction" approach helped protect cactus pear. • Cochineal's rapid spread in the West Mediterranean vs. limited spread in the East highlights the need for similar biological control steps. • Bird phoresy likely accelerates cochineal spread; similar controls in Tunisia could prevent acclimatization in Sicily and further north along bird migration routes. The invasion of false carmine cochineal Dactylopius opuntiae (Cockerell) (Hemiptera; Dactylopiidae) in the Mediterranean region presents a serious threat to cactus pear cultivation. The cochineal was first identified in Israel in 2013, and it soon became clear that biological control is the only long-term solution to protect the cactus pear Opuntia ficus-indica. Releases of the introduced predatory beetle Hyperaspis trifurcata Schaeffer (Coleoptera; Coccinellidae) began in 2016, demonstrating high efficacy and leading to a decline in cochineal populations and plant survival. While H. trifurcata can autonomously reach new cochineal hotspots, it often arrives too late to prevent substantial damage to cactus pear. Human intervention is therefore necessary to expedite the predator's establishment in new infested sites. To facilitate the spread of the beetle, we consider two approaches: transferring beetle seeding stocks from northern locations through a volunteer network organized by the research team, and applying the 'predator – prey dual introduction' concept to preemptively mitigate new hotspots expected to emerge as the cochineal spreads southward via winds or birds. These activities have led to a major decrease in the rate of spread of the cochineal population in the East Mediterranean, and in the damage that it inflicts to cactus pear hedgerows. Implementing a similar approach in North Africa can prevent or slow the spread of the cochineal to the northern coast of the central Mediterranean and avoid the heavy damage experienced in Morocco. [ABSTRACT FROM AUTHOR]

We analyze the maximal growth of trajectories of discrete-time linear switching system, i.e., controlled linear systems with the control set being an arbitrary compact set of matrices. This is done by applying the optimal convex Lyapunov function called the Barabanov norm, which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart from special cases. In 2015 N. Guglielmi and M. Zennaro [SIAM J. Matrix Anal. Appl., 36 (2015), pp. 634-655] showed that many systems possess at least one efficiently computed Barabanov norm. In this paper we classify all possible Barabanov norms and prove that, under mild assumptions, which can be verified algorithmically, those norms are unique and are either piecewise-linear or piecewise-quadratic. For some narrow classes of systems, there are more complicated Barabanov norms, but they can still be classified and constructed. Using those results we find all trajectories of the fastest growth. Examples and numerical results are provided. [ABSTRACT FROM AUTHOR]

We address the problems of minimizing and of maximizing the spectral radius over a compact family of non-negative matrices. Those problems being hard in general can be efficiently solved for some special families. We consider the so-called product families, where each matrix is composed of rows chosen independently from given sets. A recently introduced greedy method works very fast. However, it is applicable mostly for strictly positive matrices. For sparse matrices, it often diverges and gives a wrong answer. We present the "selective greedy method" that works equally well for all non-negative product families, including sparse ones. For this method, we prove a quadratic rate of convergence and demonstrate its efficiency in numerical examples. The numerical examples are realised for two cases: finite uncertainty sets and polyhedral uncertainty sets given by systems of linear inequalities. In dimensions up to 2000, the matrices with minimal/maximal spectral radii in product families are found within a few iterations. Applications to dynamical systems and to the graph theory are considered. [ABSTRACT FROM AUTHOR]

We used MALDI-MS to study the interaction of amyloid β (Aβ) peptides with alpha-2-macroglobulin (α2M). The binding of amyloid beta (Aβ) peptides to alpha-2-macroglobulin (α2M) was found to inhibit the ability of trypsin to cleave out the peptide α2M 705–715 (Pep-α2M) from α2M. This was observed with both purified α2M and α2M in human serum. We found that Aβ 1–38, Aβ1-40, and Aβ 1–42, all inhibit the interaction of α2M with trypsin, with inhibition rate independent of the length of the Aβ peptide. Further, we show that for complete inhibition, two peptide molecules must be attached to one α2M molecule; one for each of its two subunits. A region was revealed within the Aβ sequence, in which proteolytic cleavage (Lys-28) and oxidation (Met-35) lead to a loss of their ability to inhibit the interaction of trypsin with α2M. Furthermore, we show that after the formation of a trypsin complex with α2M and cleavage of α2M to produce the α2M 705–715, Aβ peptides continue to bind to the protein in the same proportions. However, Aβ peptides treated with DMSO lost their ability to bind to α2M and thereby to inhibit the interaction of trypsin with α2M. While maintaining their primary structure, such an effect can be explained only by conformational changes in the peptides, suggesting the possibility to use our analytical approach to distinguish between conformational isomers of Aβ peptides. [Display omitted] • Amyloid beta peptides inhibit the interaction of α-2-macroglobulin with trypsin. • The inhibition can be measured directly by MALDI-MS. • Two Aβ peptide molecules bind per α2M molecule. • The interaction site appears to be located in the C-terminal region of Aβ • Binding to α2M is dependent on Aβ conformation. Summary Paragraph : We present a method for studying the interaction of amyloid β (Aβ) peptides with α-2-macroglobulin (α2M) by MALDI-MS. [ABSTRACT FROM AUTHOR]

We consider a function-analytic approach to study synchronizing automata, primitive and ergodic matrix families. This gives a new way to establish some criteria for primitivity and for ergodicity of families of nonnegative matrices. We introduce a concept of canonical partition and use it to construct a polynomial-time algorithm for finding a positive matrix product and an ergodic matrix product whenever they exist. This also provides a generalization of some results of the Perron-Frobenius theory from one nonnegative matrix to families of matrices. Then we define the h -synchronizing automata and prove that the existence of a reset tuple is polynomially decidable. The question whether the functional-analytic approach can be extended to the h -primitivity is addressed and several open problems are formulated. [ABSTRACT FROM AUTHOR]

We obtain a complete classification of polyhedral sets (unions of finitely many convex polyhedra) that admit self-affine tilings, i.e., partitions into parallel shifts of one set that is affinely similar to the initial one. In every dimension, there exist infinitely many nonequivalent polyhedral sets possessing this property. Under an additional assumption that the affine similarity is defined by an integer matrix and by integer shifts ("digits") from different quotient classes with respect to this matrix, the only polyhedral set of this kind is a parallelepiped. Applications to multivariate wavelets and to Haar systems are discussed. [ABSTRACT FROM AUTHOR]

Given a coarse space (X; 𝜀), we consider linear orders on X compatible with the coarse structure 𝜀 and explore interplays between these orders and macro-uniform selectors of (X; 𝜀). [ABSTRACT FROM AUTHOR]

The procedure of 3D seismic diffraction imaging for the depth structure followed by calculation of the diffraction attributes is considered. The algorithm is based on asymmetric summation of seismic data and makes it possible to identify three characteristics of the medium: the structural diffraction attribute, the point diffraction attribute, and the structural diffraction azimuth. These attributes allow one to distinguish between the fracture and cavernous zones and to determine the orientation of fractures. The practical evaluation of the approach is presented on real seismic data. [ABSTRACT FROM AUTHOR]

Methods for improving upper and lower bounds for various coverings of planar sets are proposed. New bounds for various numbers of partition constituents are presented, and suggestions for the generalization of the presented methods are offered. [ABSTRACT FROM AUTHOR]

Given a coarse space (X, Ɛ), we endow X with the discrete topology and denote X# = {p 2 G: each member P 2 p is unbounded }. For p, q 2 X#, p||q means that there exists an entourage E 2 E such that E[P] 2 q for each P 2 p. We say that (X, Ɛ) is orbitally discrete if, for every p 2 X#, the orbit p = {q 2 X#: p||q} is discrete in G. We prove that every orbitally discrete space is almost finitary and scattered. [ABSTRACT FROM AUTHOR]

Modeling the propagation of hydraulic fractures is a complex problem that involves solving the equations that describe the intimate coupling between the cracked and porous solid phase and the fracturing fluid that drives the process according to established crack extension criteria. Most of the existing computational techniques become prohibitively expensive if applied to three-dimensional configurations, especially those involving multiple fractures because their accuracy relies on extremely fine discretizations of the geometry. These include the standard finite element method and standard displacement discontinuity method, which require substantial mesh densities in the vicinity of the crack front to capture the complex nature of the singular fields associated with fluid-driven cracks. Models have recently been proposed that offer sufficient accuracy and a significant increase in computational efficiency. These include the enhanced pseudo-3D model that explicitly incorporates a non-local elasticity relation and known crack-front asymptotic solutions that capture the multiscale near-front behavior. Here, we present an enhanced pseudo-3D model for simulating the propagation of multiple planar and nonplanar hydraulic fractures in a linear elastic medium. The algorithm is built on a fixed mesh with an adaptive tip element, and it incorporates leak-off, as well as stress interaction between the fractures. The model is validated against reference solutions of plane strain, radial, and multi-planar fracture geometries, for various sets of parameters that cover the majority of the problem parametric space. [ABSTRACT FROM AUTHOR]

The structure and magnetic hysteresis properties of nanocrystallized melt-spun ribbons with composition (Sm0.8Zr0.2)(Fe0.72Co0.24Ti0.04)z (z = 10 – 12) are studied. It is shown that substitution of a part of iron in the composition of the alloy by cobalt raises substantially the Curie temperature but almost halves the coercivity. The decrease is connected with growth in the volume fraction of the α-(Fe, Co) soft magnetic phase and incompleteness of the process of ordering of the ThMn12-type phase during annealing at 875 – 900°C. In contrast to the rapidly hardened alloys not containing Co, hydrogenation of the of (Sm0.8Zr0.2)(Fe0.72Co0.24Ti0.04) RHA powders is not accompanied by absorption of hydrogen and growth of the magnetic hysteresis properties. [ABSTRACT FROM AUTHOR]

This paper studies spaces of distributions on a dyadic half-line, which is the positive half-line equipped with bitwise binary addition and Lebesgue measure. We prove the nonexistence of a space of dyadic distributions which satisfies a number of natural requirements (for instance, the property of being invariant with respect to the Walsh–Fourier transform) and, in addition, is invariant with respect to multiplication by linear functions. This, in particular, is evidence that the space of dyadic distributions suggested by S. Volosivets in 2009 is optimal. We also show applications of dyadic distributions to the theory of refinement equations and wavelets on the dyadic half-line. [ABSTRACT FROM AUTHOR]

We study the surface regularity of compact sets G ⊂ ℝn which is equal to the supremum of numbers s ≥ 0 such that the measure of the set Gε\G does not exceed C εs, ε > 0, where Gs denotes the ε-neighborhood of G. The surface dimension is by definition the difference between n and the surface regularity. Those values provide a natural characterization of regularity for sets of positive measure. We show that for self-affine attractors and tiles those characteristics are explicitly computable. We find them for some popular tiles. This, in particular, gives a refined regularity scale for the multivariate Haar wavelets. The classification of attractors of the highest possible regularity is addressed. The relation between the surface regularity and the Holder regularity of multivariate refinable functions and wavelets is found. Finally, the surface regularity is applied to the theory of synchronizing automata, where it corresponds to the concept of parameter of synchronization. [ABSTRACT FROM AUTHOR]

We develop a matrix approach to the maximal acyclic subgraph (MAS) problem by reducing it to find the closest nilpotent matrix to the matrix of the graph. Using recent results on the closest Schur stable systems and on minimizing the spectral radius over special sets of nonnegative matrices, we obtain an algorithm for finding an approximate solution of the MAS problem. Numerical results for graphs from 50 to 1500 vertices demonstrate its fast convergence and give a rate of approximation larger than 0.6 in most cases. This method also gives the precise solution for the following weakened version of MAS: find the minimal r such that the graph can be made acyclic by cutting at most r incoming edges from each vertex. We also consider several modifications in the case when each vertex is assigned its own maximal number ri of cut edges, and some of the edges are untouchable."" Some applications are discussed. [ABSTRACT FROM AUTHOR]

A bornology ℬ on a set X is called minmax, if the smallest and largest coarse structures on X compatible with ℬ coincide. We prove that ℬ is minmax, if and only if the family ℬ# = {p ∈ βX : {X\B : B ∈ ℬ} ⊂ p} consists of ultrafilters which are pairwise non-isomorphic via ℬ-preserving bijections of X. In addition, we construct a minmax bornology ℬ on 𝜔 such that the set ℬ# is infinite. We deduce this result from the existence of a closed infinite subset in 𝛽𝜔 that consists of pairwise non-isomorphic ultrafilters. [ABSTRACT FROM AUTHOR]

The problem of finding the closest stable matrix for a dynamical system has many applications. It is studied for both continuous and discrete-time systems and the corresponding optimization problems are formulated for various matrix norms. As a rule, nonconvexity of these formulations does not allow finding their global solutions. In this paper, we analyze positive discrete-time systems. They also suffer from nonconvexity of the stability region, and the problem in the Frobenius norm or in the Euclidean norm remains hard for them. However, it turns out that for certain polyhedral norms, the situation is much better. We show that for the distances measured in the max-norm, we can find an exact solution of the corresponding nonconvex projection problems in polynomial time. For the distance measured in the operator ℓ∞-norm or ℓ1-norm, the exact solution is also efficiently found. To this end, we develop a modification of the recently introduced spectral simplex method. On the other hand, for all these three norms, we obtain exact descriptions of the region of stability around a given stable matrix. In the case of the max-norm, this can be seen as an extension onto the class of nonnegative matrices, the Kharitonov theorem, providing a stability criterion for polynomials with interval coefficients [V. L Kharitonov, Differ. Uravn., 14 (1978), pp. 2086--2088; K. Panneerselvam and R. Ayyagari, Internat. J. Control Sci. Engrg., 3 (2013), pp. 81--85]. For practical implementation of our technique, we developed a new method for approximating the maximal eigenvalue of a nonnegative matrix. It combines the local quadratic rate of convergence with polynomial-time global performance guarantees. [ABSTRACT FROM AUTHOR]

Lake Baikal's ecosystem is among the oldest lacustrine ecosystems on the planet with a diverse and unique flora and fauna. Amphipods (Amphipoda, Crustacea) are one of the most diverse groups among the lake's invertebrate animals. The lake contains more than 350 species and subspecies of amphipods, and each of these species play a significant role in the lake's food webs. However, their relationships with microorganisms are poorly investigated, which leaves gaps in understanding the relations between aquatic crustaceans and bacteria. We studied the diversity of a specific group of culturable microorganisms (Actinobacteria), and their possible relations with deepwater endemic amphipods present in Lake Baikal. We found that while 73% of the isolated strains belong to the widely distributed genus of Streptomyces, 27% of the isolates belong to rare genera such as Amycolatopsis, Micromonospora, and Pseudonocardia. Fifty-three percent of the studied strains expressed antibiotic activity against Gram-positive bacteria and possess polyketide synthase (PKS) genes. Thus, Actinobacteria associated with Baikal's endemic deepwater amphipods might both protect amphipods against pathogenic microorganisms and be an untapped source of new natural products with biosynthetic potential. [ABSTRACT FROM AUTHOR]

The first successful Eucalyptus stands were planted in Israel in 1884. This tree genus, particularly E. camaldulensis, now covers approximately 11,000 ha and constitutes nearly 4% of all planted ornamental trees. Here we review and discuss the information available about indigenous and invasive species of insects that develop on Eucalyptus trees in Israel and the natural enemies of specific exotic insects of this tree. Sixty-two phytophagous species are recorded on this tree of which approximately 60% are indigenous. The largest group are the sap feeders, including both indigenous and invasive species, which are mostly found on irrigated trees, or in wetlands. The second largest group are wood feeders, polyphagous Coleoptera that form the dominant native group, developing in dying or dead wood. Most of the seventeen parasitoids associated with the ten invasive Eucalyptus-specific species were introduced as biocontrol agents in classical biological control projects. None of the polyphagous species recorded on Eucalyptus pose any threat to this tree. The most noxious invasive specific pests, the gall wasps (Eulophidae) and bronze bug (Thaumastocoris peregrinus), are well controlled by introduced parasitoids. Potential entomological hazards of Eucalyptus in Israel are most likely to originate from the Australian insect fauna. [ABSTRACT FROM AUTHOR]

Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every nonnegative function. In particular, this composition is an identity transform in the class of nonnegative concave functions. Applications of this result in Hilbert space operator theory and the theory of quantum systems are indicated. Several open problems are formulated. [ABSTRACT FROM AUTHOR]

This paper presents a detailed regularity analysis of multivariate refinable functions with general dilation matrices, with emphasis on the anisotropic case. In the univariate setting, the smoothness of refinable functions is well understood by means of the matrix approach. In the multivariate setting, this approach has been extended only to the special case of isotropic refinement with the dilation matrix all of whose eigenvalues are equal in the absolute value. The general anisotropic case has resisted to be fully understood: the matrix approach can determine whether a refinable function belongs to C (R s) or L p (R s) , 1 ≤ p < ∞ , but its Hölder regularity remained mysteriously unattainable. We show how to compute the Hölder regularity in C (R s) or L p (R s) , 1 ≤ p < ∞. In the anisotropic case, our expression for the exact Hölder exponent of a refinable function reflects the impact of the variable moduli of the eigenvalues of the corresponding dilation matrix. In the isotropic case, our results reduce to the well-known facts from the literature. We also analyze the higher regularity of anisotropic refinable functions. We illustrate our results with several examples. [ABSTRACT FROM AUTHOR]

A ballean is a set endowed with a coarse structure. We introduce and explore three constructions of balleans from a pregiven family of balleans: bornological products, bouquets, and combs. We analyze also the smallest and largest coarse structures on a set X compatible with a given bornology on X. [ABSTRACT FROM AUTHOR]

In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If G is a group, we denote by L (G) the family of all subgroups of G. For two groups G and H , we relate their algebraic structure via the ballean structure of L (G) and L (H). [ABSTRACT FROM AUTHOR]

A scheme for construction of a magnetometer based on periodic spatial modulation of magnetic flux density by a multielement HTS structure is proposed and physically substantiated. The magnetic flux density is measured using a planar magnetooptical device with a sensitivity of no worse than 10–12 T. [ABSTRACT FROM AUTHOR]

A ballean B (or a coarse structure) on a set X is a family of subsets of X called balls (or entourages of the diagonal in X × X) defined in such a way that B can be considered as the asymptotic counterpart of a uniform topological space. The aim of this paper is to study two con- crete balleans defined by the ideals in the Boolean algebra of all subsets of X and their hyperballeans, with particular emphasis on their con- nectedness structure, more specifically the number of their connected components. [ABSTRACT FROM AUTHOR]