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The paper presents an augmented curvilinear virtual element method to determine homogenized in-plane shear material moduli of long-fibre reinforced composites in the framework of asymptotic homogenization method. The new virtual element combine an exact representation of the curvilinear computational geometry for complex fibre cross section shapes through an innovative two-dimensional cubature suite for NURBS-like polygonal domains. A selection of representative numerical tests supports the accuracy and efficiency of the proposed approach for both doubly periodic and random fibre arrangement with matrix domain. [ABSTRACT FROM AUTHOR]

Continuity and discontinuity of two-dimensional domains are thoroughly investigated for accuracy and convergence rate using two prominent discretization methods, namely smoothed and scaled boundary finite element. Because of their capability and versatility when compared to primitive elements, N-sided polygonal elements discretized from modified DistMesh and PolyMesher schemes are used. In terms of accuracy and convergence rate, NSFEM and SBFEM are found to be superior to CSFEM and ESFEM regardless of meshing alternative. The best accuracy occurs at NSFEM and SBFEM, and the obtained convergence rates are optimal. Particularly, in the smoothing domain, it is believed that DistMesh has more promising potential than PolyMesher does; yet, in the discontinuity domain, PolyMesher has been discovered to be more powerful while maintaining its efficiency. [ABSTRACT FROM AUTHOR]

The properties of polymer composites with nanofiller particles change drastically above a critical filler density known as the percolation threshold. Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not idealized disks and rods but are often modeled as such. Here we investigate the effect of the shape of the particle cross section on the geometric percolation threshold. Using connectedness percolation theory and the second-virial approximation, we analytically calculate the percolation threshold of hard convex particles in terms of three single-particle measures. We apply this method to polygonal rods and platelets and find that the universal scaling of the percolation threshold is lowered by decreasing the number of sides of the particle cross section. This is caused by the increase of the surface area to volume ratio with decreasing number of sides. [ABSTRACT FROM AUTHOR]

A crucial trend of nineteenth‐century mathematics was the search for pure foundations of specific mathematical domains by avoiding the obscure concept of magnitude. In this paper, we examine this trend by considering the "fundamental theorem" of the theory of plane area: "If a polygon is decomposed into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon." This proposition, known as De Zolt's postulate, was conceived as a strictly geometrical expression of the general principle of magnitudes "the whole is greater than the part." On the one hand, we illustrate this striving for purity in the foundations of geometry by analysing David Hilbert's classical proof of De Zolt's postulate. On the other hand, we connect this geometrical problem with the first axiomatizations of the concept of magnitude by the end of the nineteenth century. In particular, we argue that a recent result in the logical analysis of the concept of magnitude casts new light on Hilbert's proof. We also outline an alternative development of a theory of magnitude that includes a proof of De Zolt's postulate in an abstract setting. [ABSTRACT FROM AUTHOR]

We prove an analog of the Faber-Krahn inequality for the Riesz potential operator. The proof is based on Riesz's inequality under Steiner symmetrization and the continuity of the first eigenvalue of the Riesz potential operator with respect to the convergence, in the complementary Hausdorff distance, of a family of uniformly bounded non-empty convex open sets. [ABSTRACT FROM AUTHOR]

Performing isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model. The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between these centers. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when q < 1 . With increasing q, the clusters become chain-like. When q increases further, elongated clusters and regular polygonal clusters are created. In the simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l. [ABSTRACT FROM AUTHOR]

We report a new method to optically manipulate a single dielectric particle along closed-loop polygonal trajectories by crossing a suite of all-fiber Bessel-like beams within a single water droplet. Exploiting optical radiation pressure, this method demonstrates the circulation of a single polystyrene bead in both a triangular and a rectangle geometry enabling the trapped particle to undergo multiple circulations successfully. The crossing of the Bessel-like beams creates polygonal corners where the trapped particles successfully make abrupt turns with acute angles, which is a novel capability in microfluidics. This offers an optofluidic paradigm for particle transport overcoming turbulences in conventional microfluidic chips. [ABSTRACT FROM AUTHOR]

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of functions f with the property that 1 + (f ′) 2 has a primitive, including classical examples by Neile, van Heuraet and Fermat, as well as more recent ones induced by Pythagorean triples of functions. We also discuss potential benefits for our proposed definition of arc length in introductory calculus courses. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Agriculture & Nature / Kahramanmaraş Sütçü İmam Üniversitesi Tarım & Doğa Dergisi is the property of Kahramanmaras Sutcu Imam Universitesi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The shape of the needle tip that is currently used in the medical field is a "lancet point," which is a diagonally cut cylindrical pipe, further cut on both sides. The shape of the needle shank is typically cylindrical. In this paper, tip and shank shapes that differ from the standard shape are experimentally investigated for the purpose of reducing puncture resistance. Microneedles of various cross-sectional shapes, such as polygonal and star-like, were fabricated using stereo laser lithography. Before the needle penetrates the skin, sharp edges at the needle tip may be effective to generate a stress concentration on the skin, inducing a skin fracture. After the needle penetrates the skin, corners in the cross section of the needle shank may effectively reduce the frictional resistance because the contact area between the skin and needle is limited at the corners. A needle insertion experiment was conducted against an artificial skin made of polydimethylsiloxane. The puncture resistance decreased respectively for the circular needle, polygonal needle, and star-shaped needle. For the star-shaped needles, the maximum resistance decreased as the number of corners (N) decreased. For the polygonal needle, the maximum resistance increased as N increased from 3 to 5; however, there was no observable difference for N from 6 to 8. The experimental results show that a triangular star-shaped microneedle is the most effective in reducing the puncture resistance. [ABSTRACT FROM AUTHOR]

Rhopalosiphum padi (L.) is one of the most economically important pests of wheat worldwide; however, the host ranges of R. padi remain unclear. Particularly, it is unknown which plants R. padi can survive and reproduce on after the harvest of crops. The results revealed that the survival, developmental times, longevity, and fecundity of the aphid varied among the 13 Gramineae weeds, with the life-history parameters significantly differing. The virginoparae could survive long-term and reproduce on 11 of the 13 weeds. Gramineae weeds can possibly play a significant role in the buildup of R. padi populations as reservoirs. The virginoparae could survive long term and reproduce on Iris lactea Pall. var. chinensis (Fisch.) Koidz (Liliflorae: Iridaceae), Iris tectorum Maxim. (Liliflorae: Iridaceae), Cyperus rotundus L. (Cyperales: Cyperaceae), and Brassica oleracea L. var. capitata (Rhoeadales: Cruciferae), but not on Fagopyrum esculentum Moench (Polygonales: Polygonaceae), F. tataricum (L.) Gaertn. (Polygonales: Polygonaceae), Chlorophytum comosum (Thunb.) Baker (Liliflorae: Liliaceae), and Ophiopogon japonicas (Thunb.) Ker-Gawl (Liliflorae: Liliaceae). Rhopalosiphum padi can survive and reproduce on non-Gramineae plants of different families. Detailed host range information would be helpful for more effective control of insect pests. The design and implementation of sustainable pest management strategies should consider the aphid population on weeds and other host plants. [ABSTRACT FROM AUTHOR]

We introduce a polygonal cylinder Cm,n, using the Cartesian product of paths Pm and Pn and using topological identification of vertices and edges of two opposite sides of Pm x Pn, and give its Hosoya polynomial, which, depending on odd and even m, is covered in seven separate cases. [ABSTRACT FROM AUTHOR]

In this article, the influence of hydrostatic stress and gravity on a clamped- free non-homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of pre-stressed and gravitated magneto electro elastic plate of polygonal cross-sections composed of non-homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the irregular surface of the polygonal plate using Fourier expansion collocation method. The complex roots of the frequency equations are obtained by secant method. The numerical computations are carried out for triangular, square, pentagon and hexagon cross sectional plates. Graphical representation is given for the various physical variables via gravity and different edge boundaries and its characteristics are discussed. This result can be applied for optimum design of concrete plates with polygonal cross sections. [ABSTRACT FROM AUTHOR]

This paper investigates the moments and stress resultants from infinite FG laminates with different polygonal cutouts subject to uniaxial tensile load. The analytical solution used for the calculation of stress resultants and moments is the basis of the complex-variable method and conformal mapping function. The impact of various factors, namely cutout orientation angle, cutout aspect ratio as well as the cutout corner curve on stress distribution and moment resultants is studied. The effect of the aforementioned parameters around triangular, square, pentagonal and hexagonal cutout is analyzed. The mechanical characteristics of the graded plates are hypothesized to vary throughout the thickness exponentially. Finite element numerical solution is employed to examine the results of the present analytical solution. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes. [ABSTRACT FROM AUTHOR]

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly captureboth shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of MeshCNN on various learning tasks applied to 3D meshes. [ABSTRACT FROM AUTHOR]

Positive density lower bound is one of the major obstacles toward large data theory for one dimensional isentropic compressible Euler equations, also known as p-system in Lagrangian coordinates. The explicit example first studied by Riemann shows that the lower bound of density can decay to zero as time goes to infinity of the order O(1/1+t), even when initial density is uniformly positive. In this paper, we establish a proof of the lower bound on density in its optimal order O(1/1+t) using a method of polygonal scheme. [ABSTRACT FROM AUTHOR]

Abstract In the present work, an ultrasonic assisted squeeze casting method is proposed for processing wrought aluminum alloys. A frame-shaped part was fabricated to verify the feasibility of ultrasonic assisted squeeze casting technology. The results show that a 2024 alloy part with a complex shape and good surface quality can be produced by the proposed ultrasonic assisted squeeze casting method. As the ultrasonic power increasing, the microstructures of the squeeze cast parts were clearly refined, and the coarse polygonal or dendritic structures evolved to fine and equiaxed grains. Mechanical properties, such as strength and plasticity, were also improved significantly as the ultrasonic power increasing. When the ultrasonic power was 1.8 kW, the UTS, YS and elongation to fracture were 372 MPa, 246 MPa and 8.5%, which were improved by 20.8%, 21.2% and 84.8%, respectively, compared to a conventional squeeze cast part. Finally, the effect of ultrasonic vibration on mold-filling and solidification was analyzed. [ABSTRACT FROM AUTHOR]

Highlights • A XPFEM is proposed for solving large deformation fracture problems. • Modeling the discontinuities is based on a coupling scheme of polygonal and quadrilateral meshes. • The presence of hanging nodes are resolved as conforming polygonal elements. • Excellent performance of the present approach is confirmed by numerical testes. Abstract The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements. [ABSTRACT FROM AUTHOR]

Abstract Terrestrial Arctic ecosystems play a key role in the global carbon (C) cycle, as they store a large amount of organic matter in permafrost. Among regions with continuous permafrost, Svalbard has one of the warmest permafrost and may provide a template of the environmental responses of Arctic regions to future climate change. We analyze the CO 2 fluxes at a polygonal tundra site in Adventdalen (Svalbard) during one full growing season across a vegetation and environmental gradient to understand how the interaction of different abiotic (thaw depth, ground surface temperature (GST), soil moisture, photosynthetic active radiation - PAR) and biotic (leaf area index (LAI), and plant phenology) factors affect the CO 2 fluxes and identify the drivers of Net Ecosystem Exchange (NEE) and Ecosystem Respiration (ER). Three distinct periods (early, peak, and late) characterized the growing season based on plant phenology and the main environmental conditions. Comparing early, peak and late season, both NEE and ER exhibited specific patterns: ER shown high values since the early season, only slightly increased at peak, and then decreased drastically in the late season, with GST being the most important driver of ER. The drivers of NEE changed during the season: thaw depth, PAR and GST during the early season, LAI at peak, and PAR during the late season. These data allow to highlight that the thawing and freezing of the upper part of the active layer during the early and late season controls ER, possibly due to the response of microbial respiration in the upper part of the soil. Especially during the late season, despite the fully developed active layer (reaching its highest thawing depth), the freezing of the uppermost 2 cm of soil induced the drastic decrease of the respiratory efflux. In addition, the seasonal C balance of our plots indicated a seasonal source at our plots, in apparent contrast with previous eddy covariance (EC) measurements from a wetter area nearby. This difference implies that drier ecosystems act as sources while wetter ecosystems are sinks, suggesting that a drying trend in polygonal tundra could switch these ecosystems from CO 2 sinks to sources in a feedback to future climate change. Highlights • We emphasize the role of the uppermost soil layer controlling CO 2 fluxes in the Arctic. • The drivers of NEE and ER change during the growing season (early, peak, late). • Thaw depth, GST, LAI and PAR in turn drive NEE; GST always drives ER. • At late season despite the maximum thawing the uppermost soil freezing controls ER. • The shift from wet to dry vegetation can switch ecosystems from CO 2 sinks to sources. [ABSTRACT FROM AUTHOR]

Highlights • HiRISE/CRISM data are analyzed to assess irregular polygonal ridge formation. • Ridge geometry suggests they are mineralized fractures or clastic intrusions. • Ridges and host rock share all diagnostic spectral features of Mg-bearing clays. • However, ridges express weaker absorptions compared to their host rock. • Weaker absorptions are likely due to textural effects or VNIR inactive mineralogy. Abstract Roughly 16,000, ∼20–50 m wide, morphologically diverse, erosionally resistant ridges have been exhumed and mapped in Noachian-aged terrain across a large region in Nili Fossae and the Nilosyrtis Highlands. However, the formation of these landforms has been widely debated. Their morphology and geologic context suggest surface processes such as aeolian, fluvial, and glacial sedimentary deposition are unlikely candidates for their formation. Possible subsurface ridge formation mechanisms include: 1) volcanic dike intrusions along pre-existing fractures, 2) breccia dikes from impact cratering, 3) clastic dikes or deformation bands, and 4) chemical alteration or precipitation of minerals in or along pre-existing fractures or faults. The ridges are being exhumed from a phyllosilicate-bearing host rock, but whether the ridges themselves have an aqueous origin remains unknown. Although, previous studies used comparative morphology to assess their formation, each hypothesized formation mechanism implies different mineralogical suites possibly detectable in remotely sensed spectral data. Here we combine spectral and morphological analyses to assess the origin of a subset of ridges (n = 797) that have irregular polygonal ridge network morphology. We use observations from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) and High Resolution Imaging Science Experiment (HiRISE), supplemented with Context Camera (CTX) imagery, to analyze the spectral signatures and geometry in order to 1) measure ridge morphology (orientation and intersection angles) and 2) isolate the spectral signatures of the ridges from their host unit to evaluate hypothesized ridge formation mechanisms. The irregular polygonal nature, near-orthogonal intersections, and lack of dominant orientation are characteristics consistent with fracture propagation under horizontal near-isotropic extensional stress in a physically heterogeneous host rock (inconsistent with impact- or volcanic-related features). Alternatively, very shallow clastic intrusion could produce similar ridge geometry. Our key findings are: 1) ridge orientation-frequency and distribution suggest mineralization or cementation of subsurface fractures or shallow clastic intrusions as favored formation mechanisms and 2) ridges share all the diagnostic spectral features of Mg-smectite (saponite) and/or mixed-layered talc-saponite clays of the host materials; however, ridges express weaker absorptions. If the CRISM spatial and/or spectral resolution has not limited our ability to detect a spectrally unique cementing agent, then both grain size or texture and visible to near-infrared inactive mineralogy could be responsible for the ridge's weaker spectral absorptions (such as quartz and silica, some oxide group minerals, and amorphous materials). Our results imply that shallow subsurface groundwater and hydrothermal activity was likely extensive prior to and during the opening of the Nili Fossae and played an integral role in the formation of the ridges observed throughout the region. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A thin layer of gold was coated on an aluminum dimple array and then heated. • The gold layer was transformed into numerous gold particles by the thermal treatment. • The transformation rate increases with the temperature of the thermal treatment. • Multiply-twinned particles were distributed on the surface. • The gold particle array exhibited excellent adhesion properties. Abstract Gold nanoparticles were fabricated on an ordered aluminum dimple array via aluminum anodizing, sputter coating, and thermal treatment, and the transformation behavior and nanostructural characterization were investigated in detail. Electropolished aluminum specimens were anodized in an oxalic acid solution under self-ordering conditions at 40 V, and then the porous alumina was selectively dissolved to expose an ordered aluminum dimple array with each dimple measuring 100 nm. A thin layer of gold was coated onto the dimple array, and a thermal treatment was subsequently performed. The gold layer was transformed into numerous particles by the thermal treatment due to dewetting. When the values of gold layer thickness, thermal treatment temperature, and thermal treatment duration were optimized, the gold particles were located at the bottom of each aluminum dimple. Consequently, multiply-twinned particles with polygonal and elliptical shapes were regularly distributed on the aluminum dimple array treated at 473 K. Although the rate of the transformation induced by dewetting increased with the temperature of the thermal treatment, non-uniform gold nanostructures were formed by extended thermal treatment at 873 K. The gold particles formed on the aluminum surface exhibited excellent adhesion upon ultrasonication. [ABSTRACT FROM AUTHOR]

Abstract Given a set X of points inside a polygonal region P , two distinguished points s , t ∈ X , we study the problem of finding a simple polygonal path that uses only the points of X as vertices and lies in P , from s to t. We present an O (n 2 + n log n log (m n) + m log m) time and O (n 2 + m) space algorithm for computing a simple path from s to t or reporting no simple paths exist, where n is the number of points of X and m is the number of vertices of P. This gives a significant improvement upon the previously known O (m 2 n 2) time and space algorithm, and O (n 3 log m + m n) time and O (n 3 + m) space algorithm. Our result is mainly obtained by showing that the visibility graph of X inside P , together with an implicit representation of the shortest paths from s to all other points of X , is sufficient to give a solution to the considered problem. [ABSTRACT FROM AUTHOR]

We present a new algorithm for finding minimum-link rectilinear paths among rectilinear obstacles in the plane. Given a triangulated rectilinear domain of h pairwise-disjoint rectilinear obstacles with a total of n vertices, our algorithm can find a minimum-link rectilinear path between any two points in O(n+hlogh) time. Further, within the same time our algorithm can build an O(n)-size data structure for any source point s, such that given any query point t, the number of edges of a minimum-link rectilinear path from s to t can be computed in O(logn) time and the actual path can be output in additional time linear in the number of the edges of the path. The previously best algorithms for the problems run in O(nlogn) time. [ABSTRACT FROM AUTHOR]

Generally bivariate probability density function defined in a rectangular area is used to calculate the cumulative distribution function from the bivariate probability density function. However, definition limits of the probability density functions being non-rectangular are in existence in practice. In this paper, primarily arbitrary non-rectangular areas are defined by applying a polygonal approach. The polygonal area obtained as a result of this approach constitutes boundaries of the probability density function. Thus, the bivariate piecewise probability density function can be defined in an arbitrary area. Then the cumulative distribution function is calculated in the obtained area. Two types of approaches are used for these calculations. The first approach is applied to take integral analytically of bivariate continuous probability density function in the polygonal area. The second approach is developed a numerical method since the explicit integral of the selected probability density function cannot be found. [ABSTRACT FROM AUTHOR]

Abstract Polygonal-shaped about 75 nm sized and highly crystallized Eu3+-doped β-NaYF 4 particles were directly prepared under mild conditions using the polyol process. A set of operating parameters were optimized for such a purpose. A conventional heating under reflux for 30 min of a mixture of Y(III) and Eu(III) acetate, ammonium fluoride, sodium hydroxide and oleic acid (OA) dissolved in ethyleneglycol offered a pertinent material processing route if a large excess of NH 4 F and an enough amount of OA were used. Typically, the former parameter provides an exclusive stabilization of the desired β allotropic form, while the latter allows a significant size decrease of the particles. Thanks to their coating by a double OA layer, the produced particles exhibited a hydrophilic surface feature when dispersed in water and when excited under UV light they emitted a very intense red photoluminescence. Additionally, they did not evidence any accurate cytotoxicity when incubated with healthy human foreskin fibroblast (BJH) cells for doses as high as 50 μg·mL−1 and contact time as long as 48 h, highlighting the ability of the prepared particles to be used as efficient down-converter light sources for cell labelling. Graphical abstract Unlabelled Image Highlights • Water-soluble down-conversion β-NaYF 4 :Eu nanoparticles were produced by the ployol process. • The particles they did not evidence any accurate cytotoxicity when incubated with healthy human foreskin fibroblast (BJH) cells. • They were successfully employed as red emitting dyes when incubated with BJH cells. [ABSTRACT FROM AUTHOR]

Binocalix dichotomus gen. et sp. nov. is the first British Ordovician aristocystitid diploporite to be named. It is known from a single holotype that is partly disarticulated and incomplete. Nevertheless, it differs from all previously described aristocystitids in having a pair of relatively large ambulacral facets developed above a smooth ambulacral platform and on a single circum‐oral plate. When densely developed, the diplopores become polygonal and have a central tubercle. They closely resemble those of the sphaeronitid subgenus Sphaeronites (Peritaphros), but all species of Sphaeronites s.l. have narrow ambulacral grooves ending in small facets. The similarities in the diplopores are thought to be convergent. Among aristocystitids, only "Calix" inornatus and Triamara are known to have paired ambulacral facets developed on single circum‐oral plates. The former differs from Binocalix in having a smooth thecal surface and flush ambulacral facets. Triamara has raised ambulacral facets but lacks the distinctive ambulacral platforms found in Binocalix. Its diplopores always lack central tubercles, and currently it is only known from the Silurian. [ABSTRACT FROM AUTHOR]

Abstract Lots of bananas were wasted before commercialization. It is necessary to search potential industrial applications of banana. In the present study, starches from seven banana cultivars (labeled as A–G) were isolated and then characterized. These starches presented different and irregular shapes, such as sphere, long spheroid and polygonal granules. The distribution of size and analyses of average molecular weight showed more small granules in samples B, D, F and G than other samples. The amylose content varied from 22.59% to 38.40%. The crystal types of these starches were a mixture of B-type and C-type, and the relative crystallinity varied greatly. The differential scanning calorimetry (DSC) results showed that the onset temperature of gelatinization increased as follows: A < B < E < C ≈ D < F. The maximum viscosity of banana starch decreased as follows: G > C > D > F > E = B > A. The in vitro digestibility test showed that the content of resistant starch was very high in banana starches. These results would be useful to the application of those starches in food and nonfood industries. [ABSTRACT FROM AUTHOR]

Abstract The surface topography, chemical composition, and pore size distributions of low-rank coal treated with RF (Radio Frequency) plasmas using various periods were investigated by the means of SEM-EDS, XPS, and BET to realize the potential of plasma technology for the surface modification of low-rank coal in the selective flotation. Moreover, the wettability and floatability of coal sample were studied after plasma pretreatment. The results showed that a large sum of stripes and polygonal pits were generated, which significantly increased surface roughness, gradually decreased the contents of C C and C H, and increased COO content through the plasma pretreatment. The contact angle of coal sample decreased from 75° to 0° with the increase of treatment time. The flotation tests indicated that the floatability of the low-rank coal sample sharply decreased through the plasma pretreatment. The remarkable differences in the contact angle and the flotation yields between the untreated coal and the treated coal under various treatment periods suggested that the reverse flotation performance of low-rank coal can be efficiently improved through modifying the surface properties of coal by plasma pretreatment. Graphical abstract Unlabelled Image Highlights • Low-temperature air plasma was used to modify the surface properties of coal. • Surface compositions and changes of coal were analyzed using various methods. • Plasma pretreatment of low-rank coal improved the reverse-flotation efficiency. [ABSTRACT FROM AUTHOR]

Abstract Electrochemical hydrogen permeation tests were utilized to investigate the diffusion and trapping of hydrogen in API X70 pipeline steel. Thermomechanical processing was used in order to produce 4 samples with different microstructural features. Detailed characterization was performed to measure the size and fraction of microstructural constituents of the samples and their effects on hydrogen diffusion were studied. After thermomechanical treatment the samples contained pearlite, polygonal ferrite, acicular ferrite, and martensite/austenite islands, the size and amount of which depends on the processing parameters. Hydrogen trapping density and hydrogen diffusion coefficient were measured for each sample and it is showed that depending on the properties of the microstructural constituents the diffusion coefficient can vary in the range of 0.33 × 10−6 cm2/s to 1.61 × 10−6 cm2/s. Highlights • Fourier and Laplace methods give similar results for studying hydrogen diffusivity. • Hydrogen diffusion in API X70 steel is controlled by traps. • Trapping behavior depends on size and amount of microstructural features. [ABSTRACT FROM AUTHOR]

Positively identifying serpentine mineral types is important for a wide range of disciplines in the Earth sciences and health sciences. Although Raman spectroscopy has been widely applied as a tool to distinguish four of the main serpentine minerals (i.e., antigorite, lizardite, chrysotile, and polygonal serpentine), some uncertainty remains as to whether all four varieties have unique Raman spectra. In this paper, submicron Raman spectroscopy mapping was performed directly on electron‐transparent regions of serpentine samples that were unambiguously identified by transmission electron microscopy (TEM). The increased spatial resolution of the Raman mapping technique (~370 nm), combined with the detailed characterization provided by TEM, indicates that polygonal serpentine has the same Raman spectrum as lizardite and therefore cannot be spectrally distinguished from lizardite. Furthermore, the Raman spectral profile that has previously been reported as unique to polygonal serpentine is likely to represent a mixture of chrysotile and polygonal serpentine/lizardite. To positively discriminate between lizardite and polygonal serpentine requires TEM investigation. Submicron Raman spectroscopy mapping was performed directly on electron‐transparent regions of serpentinite samples that were characterised by transmission electron microscopy (TEM). The unambiguous identification of serpentine mineral types provided by TEM, combined with the spatial resolution of the Raman mapping technique (approximately 370‐nm resolution), indicates that polygonal serpentine has the same Raman spectrum as lizardite and therefore they cannot be spectrally distinguished. [ABSTRACT FROM AUTHOR]

Mathematical tools underlie a method that has strong potential to lower the cost of fixture-setup when finishing large castings that have machined surfaces where other components are attached. One math tool, the kinematic transformation, is used for the first time to construct Tolerance-Map® (T-Map)® models of geometric and size tolerances that are applied to planar faces and to the axes of round shapes, such as pins or holes. For any polygonal planar shape, a generic T-Map primitive is constructed at each vertex of its convex hull, and each is sheared uniquely with the kinematic transformation. All are then intersected to form the T-Map of the given shape in a single frame of reference. For an axis, the generic T-Map primitive represents each circular limit to its tolerance-zone. Both are transformed to a central frame of reference and are intersected to form the T-Map. The paper also contains the construction for the first five-dimensional (5D) T-Map for controlling the minimum wall thickness between two concentric cylinders with a least-material-condition (LMC) tolerance specification on position. It is formed by adding the dimension of size to the T-Map for an axis. The T-Maps described are consistent with geometric dimensioning and tolerancing standards and industry practice. Finally, transformations are presented to translate between small displacement torsor (SDT) coordinates and the classical coordinates for lines and planes used in T-Maps. [ABSTRACT FROM AUTHOR]

In a low-alloyed multi-phase transformation-induced plasticity steel, solute carbon content in polygonal ferrite, bainitic ferrite, and martensite was characterized using site-specific atom probe tomography. Selected area diffraction patterns were obtained using transmission electron microscopy, and the geometric distortion thereof was determined. The results showed that the lattice distortion increased in a sequence of polygonal ferrite, lath-like bainitic ferrite, and martensite. This increasing distortion corresponded to an increase in carbon content of the phase. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Two three-dimensional interconnected Mg scaffolds were evaluated by immersion. • The interconnectivity of both scaffolds was gradually inhibited by the deposition. • The internal pores struts degraded slower compared with the external pore struts. • The cambered pore struts degraded faster than the polygonal pore struts. Abstract The degradation behavior in consideration of the pore strut and the interconnectivity of two Mg scaffolds with different three-dimensional interconnected porous structures were evaluated. The interconnectivity of the two scaffolds gradually decreased along with the clogged interconnected pores due to the deposition formation on the pore wall. Mg scaffold with spherical pores and cambered pore strut degraded faster but exhibited better resistance to the deterioration of the interconnectivity compared with Mg scaffold with irregular pores and polygonal pore struts. Direct cell culture of MC3T3-E1 osteoblasts on the two scaffolds indicated a promising potential for bone tissue engineering. [ABSTRACT FROM AUTHOR]

Polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. We demonstrate that the densities of polygonal distributions are dense in the class of continuous and concave densities with bounded second derivatives. Furthermore, we prove that polygonal density functions provide O(g− 2) approximations (where g is the number of triangular distribution components), in the supremum distance, to any density function from the hypothesized class. Parametric consistency and Hellinger consistency results for the maximum likelihood (ML) estimator are obtained. A result regarding model selection via penalized ML estimation is proved. [ABSTRACT FROM AUTHOR]

We propose matrix decomposition algorithms for the efficient solution of the linear systems arising from Kansa radial basis function discretizations of elliptic boundary value problems in regular polygonal domains. These algorithms exploit the symmetry of the domains of the problems under consideration which lead to coefficient matrices possessing block circulant structures. In particular, we consider the Poisson equation, the inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. Numerical examples demonstrating the applicability of the proposed algorithms are presented. [ABSTRACT FROM AUTHOR]

In a separable Hilbert space, a stochastic differential inclusion with coefficients whose values are closed not necessarily convex sets is considered. Two existence theorems for strong solutions are proved. In the first theorem, the proof is based on the use of Euler polygonal lines; in the second, on the successive approximation method. Instead of the assumption that the coefficients of the inclusion are globally Lipschitz, which is traditional in such cases, some conditions that are less restrictive for the problems in question are used. [ABSTRACT FROM AUTHOR]

We report here on design and computer simulation of computer-generated holograms for three dimensional (3D) imaging and display. Angular spectrum of general polygon patches was calculated in closed analytical form that includes angular dependence of the intensity and linear gradient of phase at each polygon. Special attention was paid to reduction of the dynamic range in the amplitude transmittance of the hologram by proper random choices of slopes and initial phases of each polygon. Numerical computer simulation results proved that our polygon-patched design demonstrates halftones of object shades and shows expected sharp focusing of different parts of the reconstructed 3D images in their different cross-sections. [ABSTRACT FROM AUTHOR]

Inside a two-dimensional region ("cake"), there are m nonoverlapping tiles of a certain kind ("toppings"). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same "certain kind," such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks. [ABSTRACT FROM AUTHOR]

Designing of noble-metal free and morphologically controlled advanced photocatalysts for photocatalytic water splitting using solar light is of huge interest today. In the present work, novel polygonal Zn 2 TiO 4 (ZTO) nanostructures have been synthesized by citricacid assisted solid state method for the first time and synthesized nanostructures were characterized by using various techniques like PXRD, UV-Vis-DRS, PL, FT-IR, BET, FE-SEM and TEM for their structural, optical, chemical, surface and morphological properties. The PXRD and UV-Vis-DRS analysis show the existence of cubic and tetragonal phases. FE-SEM and TEM results confirm the formation of polygonal ZTO nanostructures. Synthesised ZTO nanostructures have been potentially applied for solar light-driven photocatalytic hydrogen evaluation from water splitting and compare the photocatalytic activity with synthesized conventional Zn 2 TiO 4 and commercially available TiO 2 , ZnO photocatalysts. A high rate of 529 μmolh −1 g −1 solar light-driven photocatalytic H 2 evolution has been achieved by using a small amount (5 mg) of polygonal Zn 2 TiO 4 nanostructures from glycerol-water solution. The enhanced photocatalytic performance of the polygonal Zn 2 TiO 4 nanostructures compare to conventional Zn 2 TiO 4 under solar light irradiation is due to the large surface area and low recombination rate. However having the same bandgap, the polygonal Zn 2 TiO 4 nanostructures have shown enhanced photocatalytic performance than that of commercially available TiO 2 , ZnO photocatalysts. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a two-grid finite element method for a class of quasilinear elliptic problems under minimal regularity of data in a bounded convex polygonal Ω ⊂ R 2 , which can be thought of as a type of linearization of the nonlinear system using a solution from a coarse finite element space. With this technique, solving a quasilinear elliptic problem on the fine finite element space is reduced into solving a linear problem on the fine finite element space and solving the quasilinear elliptic problem on a coarse space. Convergence estimates in the H 1 -norm are derived to justify the efficiency of the proposed two-grid algorithm. Moreover, we propose a natural and computationally efficient residual-based a posteriori error estimator of the two-grid finite element method for this nonmonotone quasilinear elliptic problem and derive the global upper and lower bounds on the error in the H 1 -norm. Numerical experiments are provided to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract: CO2 methanation catalysts were prepared by co-sputtering with Ru and metal oxides such as TiO2 and ZrO2 using the polygonal barrel-sputtering method. The co-sputtering technique not only resulted in the decrease in the reaction temperature but also maintained the deposition of smaller Ru particles during the reaction at higher temperature.Graphical Abstract: [ABSTRACT FROM AUTHOR]

Aims To investigate histological, immunohistochemical, and molecular features, especially uncommon morphology of hyalinizing clear cell carcinoma (HCCC) to expand the morphological spectrum of HCCC. Methods and results We examined 5 cases of HCCC by histological, immunohistochemical, and molecular analysis. Generally, 5 HCCC cases shared similar characteristics, exhibiting clear to slightly eosinophilic cells arranged in cords, nests, islands, or trabeculae with a hyalinized stroma, while myxoid stroma, perineural invasion, and polygonal cells with high-grade nuclei were observed in 3 cases. Immunohistochemically, 5 cases were entirely immunoreactive for CKpan, whereas 80% HCCC cases were positive for P63, and CK14. None expressed immunoreactivity for S-100, Calponin, or GFAP. The positive rate of Ki-67 staining was about 5% in the classic area of case 3, but 40% in the high-grade area. As for the result of FISH findings, EWSR1 gene break was detected in all 5 HCCC cases. Conclusions Our study has expanded the morphological spectrum of HCCC, and proposed the diagnosis of HCCC should be confirmed by fully analyzing histological, immunohistochemical, and molecular features practically. [ABSTRACT FROM AUTHOR]

A green synthesis of gold and silver nanoparticles is described in the present report using platycodon saponins from Platycodi Radix ( Platycodon grandiflorum) as reducing agents. Platycodin D (PD), a major triterpenoidal platycodon saponin, was enriched by an enzymatic transformation of an aqueous extract of Platycodi Radix. This PD-enriched fraction was utilized for processing reduction reactions of gold and silver salts to synthesize gold nanoparticles (PD-AuNPs) and silver nanoparticles (PD-AgNPs), respectively. No other chemicals were introduced during the reduction reactions, providing an entirely green, eco-friendly, and sustainable method. UV-visible spectra showed the surface plasmon resonance bands of PD-AuNPs at 536 nm and PD-AgNPs at 427 nm. Spherically shaped nanoparticles were observed from high-resolution transmission electron microscopy with average diameters of 14.94 ± 2.14 nm for PD-AuNPs and 18.40 ± 3.20 nm for PD-AgNPs. Minor triangular and other polygonal shapes were also observed for PD-AuNPs along with spherical ones. Atomic force microscopy (AFM) images also demonstrated that both nanoparticles were mostly spherical in shape. Curvature-dependent evolution was employed to enhance the AFM images and precisely measure the sizes of the nanoparticles. The sizes were measured as 19.14 nm for PD-AuNPs and 29.93 nm for PD-AgNPs from the enhanced AFM images. Face-centered cubic structures for both nanoparticles were confirmed by strong diffraction patterns from high-resolution X-ray diffraction analyses. Fourier transform infrared spectra revealed the contribution of -OH, aromatic C=C, C-O, and C-H functional groups to the synthesis. Furthermore, the catalytic activity of PD-AuNPs was assessed with a reduction reaction of 4-nitrophenol to 4-aminophenol in the presence of sodium borohydride. The catalytic activity results suggest the potential application of these gold nanoparticles as catalysts in the future. The green strategy reported in this study using saponins as reducing agents will pave new roads to develop novel nanomaterials with versatile applications. [ABSTRACT FROM AUTHOR]

An obstacle representation of a graph G is a set of points in the plane representing the vertices of G, together with a set of polygonal obstacles such that two vertices of G are connected by an edge in G if and only if the line segment between the corresponding points avoids all the obstacles. The obstacle number $${{\mathrm{obs}}}(G)$$ of G is the minimum number of obstacles in an obstacle representation of G. We provide the first non-trivial general upper bound on the obstacle number of graphs by showing that every n-vertex graph G satisfies $${{\mathrm{obs}}}(G) \le n\lceil \log {n}\rceil -n+1$$ . This refutes a conjecture of Mukkamala, Pach, and Pálvölgyi. For n-vertex graphs with bounded chromatic number, we improve this bound to O( n). Both bounds apply even when the obstacles are required to be convex. We also prove a lower bound $$2^{\Omega (hn)}$$ on the number of n-vertex graphs with obstacle number at most h for $$h

The author introduces and analyzes a model that allows organizing visualization of primary linear constructs such as interval, simplex and polygonal lines in multidimensional space. [ABSTRACT FROM AUTHOR]

In order to consider corner configurations with straight corner fronts in three-dimensional (3D) solids, a super polygonal prismatic element containing a straight corner front is established by using the numerical eigensolutions of singular stress fields and the Hellinger-Reissner variational principle. Singular stresses near the corner front subject to far-field boundary conditions can be obtained by incorporating the super singular element with conventional 3D brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of 3D corner configurations and cracks. The usage of the super singular element can avoid mesh refinement near the corner front domain that is necessary for conventional and enriched finite element methods, and lead to high accuracy and fast convergence. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated problems of stress singularity in elasticity including multiple defects. [ABSTRACT FROM AUTHOR]

Consider the Poisson equation with the Dirichlet boundary condition on a bounded convex polygonal domain Ω ⊂ R 2 . We investigate the finite element approximation of singular solutions that are due to the non-smoothness of the domain in the W p 1 norm ( 1 < p ≤ ∞ ). In particular, with analysis in weighted Sobolev spaces and weighted Hölder spaces, we provide regularity requirements on the given data and specific parameter-selection criteria for graded meshes, such that the resulting numerical approximation achieves the optimal convergence rate in W p 1 . Sample results from various numerical tests are provided to confirm the theory. [ABSTRACT FROM AUTHOR]