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In the present paper, we construct a cusped hyperbolic $4$-manifold with all cusp sections homeomorphic to the Hantzsche-Wendt manifold, which is a rational homology sphere. By a result of Gol\'enia and Moroianu, the Laplacian on $2$-forms on such a manifold has purely discrete spectrum. This shows that one of the main results of Mazzeo and Phillips from 1990 cannot hold without additional assumptions on the homology of the cusps. This also answers a question by Gol\'enia and Moroianu from 2012. We also correct and refine the incomplete classification of compact orientable flat $3$-manifolds arising from cube colourings provided earlier by the last two authors., Comment: 15 pages, 1 figure, 1 table; SageMath worksheets available at https://github.com/sashakolpakov/24-cell-colouring

This paper presents a Computational Fluid Dynamic computation based on Reynolds Averaged Navier-Stokes Equations (RANS) and the Shear Stress Transport (SST) turbulence model. The targeted application is the cooling process of an electronic component, which is represented by a heated wall-mounted cube exposed to an impinging jet in cross flow. In a previously published study, it was shown that adding chamfers on top of the cube, the flow structure is radically changed in favor of a significant improvement in cooling efficiency. In an attempt to determine which of the four faces has the greatest contribution to improving cooling, this study presents a detailed numerical investigation for five different cases. Namely, a base cube without chamfer, a cube with four chamfers on its upper part, a cube with a chamfer on the front face, a cube with chamfer on the back face and finally a cube with chamfers on the side faces. For the same ReH = 3410 cross-flow Reynolds number, three levels of incident jets are tested as well as a jet-free case, which will serve as a reference case for comparison. Comparing the different cases, it has been found that the case of a chamfer on the front face is the most efficient and therefore contributes effectively to the improvement of the cooling efficiency

A through transmission impact method for measuring the sound velocity in the concrete cubic samples, which are used for determination of the concrete durability, is proposed. It is shown that for elimination of the surface wave influence on the measurement accuracy of the compact cubic sample resonant frequency the impactor and the receiving transducer should be placed on the opposite sides of the cube. Besides in some cases must be used multichannel through transmission impact method.

The study described here is aimed at illuminating deformation mechanism involved in Twin-roll Thin Strip Casting Process (TRSC) with respect to high-permeability 6.5 wt.% Si electrical strip (6.5 wt.% Si strip) in terms of crystal plasticity (CP) theory, and a Visco-plastic Self-consistent model (VPSC) was utilized to explore the deformation mechanism by applying crystallographic orientation (OR) analysis. Results underscore that the activation of overall potential single slip system with regard to studied 6.5 wt.% Si strip including { 110 } 111 > , { 112 } 111 > as well as { 123 } 111 > can contribute to the OR conversion from Cube texture to Rotated-Cube texture, α-fiber texture as well as γ-fiber texture, while with different evolution rate during deformation. The potential multi-slip system of { 112 } 111 > + { 123 } 111 > with average number of activated slip system per grain ~9.1–9.4, and multi-slip system of { 110 } 111 > + { 112 } 111 > + { 123 } 111 > with average number of activated slip system per grain ~10.4–10.8 are identified to be the predominant slip systems during deformation by comparing to the actual OR features obtained from TRSC-processed 6.5 wt.% Si strip. The CP-based method proposed in present study is deemed as a reference to investigate deformation behavior involved in the other semi-solid forming process.

Fabricating green (unfired) ceramic powder compacts with complex geometry using stereolithography is well established. The advent of a low-cost professional SLA printer with a commercial ceramic resin offers designers an intriguing material choice. For engineering uses, however, it is necessary to quantitatively assess the evolution of microstructure as well as dimensional stability during post-AM densification. In pursuit of this, we designed a standard specimen based on a hollow cube, nominally 25 mm on an edge, with a wall thickness of 4 mm. The surfaces of the cubes were decorated with short cylinders, square prisms, and a square array of short pegs. The corners of the cube were chamfered. This design permits a number of independent dimensional measurements to be readily obtained. Results include: variability of dimensions, systematic deviations from average, evidence of discontinuous delamination, and some devitrification. The sensitivity of results to some geometric features, e.g., wall thickness is reported. In a separate set of experiments, the feasibility of green state joining of subcomponents using the stereolithography resin and UV lamps was tested with a simple investment casting mold that was created. Despite qualitative success with the trial mold, engineering use of the resin appears limited. Planar accuracy of green prints to model in the X and Y directions were most precise coming in at 99.7% to the nominal design, and the Z direction was 98.1%. Post-fire shrink was observed to be around 14%, and deviation from squareness was >1%. Cracking was the biggest issue with the cube prints, and several trials were conducted in efforts to understand and eliminate the cracking. Of all the variables tested, part orientation on the build platform and strategic use of fillets were the most effective in preventing cracks. An inverted cube was successfully produced without showing horizontal post-fire cracks.

We show that group actions on irreducible ${\rm CAT(0)}$ cube complexes with no free faces are uniquely determined by their $\ell^1$ length function. Actions are allowed to be non-proper and non-cocompact, as long as they are minimal and have no finite orbit in the visual boundary. This is, to our knowledge, the first length-spectrum rigidity result in a setting of non-positive curvature (with the exception of some particular cases in dimension 2 and symmetric spaces). As our main tool, we develop a notion of cross ratio on Roller boundaries of ${\rm CAT(0)}$ cube complexes. Inspired by results in negative curvature, we give a general framework reducing length-spectrum rigidity questions to the problem of extending cross-ratio preserving maps between (subsets of) Roller boundaries. The core of our work is then to show that, when there are no free faces, these cross-ratio preserving maps always extend to cubical isomorphisms. All our results equally apply to cube complexes with variable edge lengths. As a special case of our work, we construct a compactification of the Charney-Stambaugh-Vogtmann Outer Space for the group of untwisted outer automorphisms of an (irreducible) right-angled Artin group. This generalises the length function compactification of the classical Culler-Vogtmann Outer Space., Comment: 51 pages, 1 figure; minor changes to the exposition, to appear on J. Lond. Math. Soc

It is a 300-year-old counterintuitive observation of Prince Rupert of the Rhine that in the cube a straight tunnel can be cut through which a second congruent cube can be passed. A hundred years la...

Amorphous materials have no long-range order, but there are ordered structures at short range (2–5 A), medium range (5–20 A) and even longer length scales1–5. While regular6,7 and semiregular polyhedra8–10 are often found as short-range ordering in amorphous materials, the nature of medium-range order has remained elusive11–14. Consequently, it is difficult to determine whether there exists any structural link at medium range or longer length scales between the amorphous material and its crystalline counterparts. Moreover, an amorphous material often crystallizes into a phase of different composition15, with very different underlying structural building blocks, further compounding the issue. Here, we capture an intermediate crystalline cubic phase in a Pd-Ni-P amorphous alloy and reveal the structure of the medium-range order, a six-membered tricapped trigonal prism cluster (6M-TTP) with a length scale of 12.5 A. We find that the 6M-TTP can pack periodically to several tens of nanometres to form the cube phase. Our experimental observations provide evidence of a structural link between the amorphous and crystalline phases in a Pd-Ni-P alloy at the medium-range length scale and suggest that it is the connectivity of the 6M-TTP clusters that distinguishes the crystalline and amorphous phases. These findings will shed light on the structure of amorphous materials at extended length scales beyond that of short-range order. An intermediate cube phase with a medium-range order structure is identified in Pd-Ni-P metallic glass, which links the amorphous and crystalline phases.

Let $$p\equiv 2,5\ \mathrm {mod}\ 9$$ be a prime. In this paper, we prove that at least one of 3p and $$3p^2$$ is a cube sum by constructing certain nontrivial Heegner points. We also establish the explicit Gross–Zagier formulae for these Heegner points and give variants of the Birch and Swinnerton–Dyer conjecture of the related elliptic curves.

The registration of a 3D model over an image can be seen as the alignment of visual correspondences extracted from these two data. This is a challenging task and it is even more complex when the two images have a different modality. This paper introduces an approach that allows matching features detected in two different modalities: photographs and 3D models, by using a common 2D representation. Our approach is based on a modification of the Marching Cubes algorithm aiming to remove ambiguous cases without adding further calculations in each cube. We share the idea about the crucial importance of splitting the equivalence cases into two classes. Considering all the possible states inside/outside in the four corners of a cube side, indeed, there are only four non-trivial cases after eliminating those equivalences through the rotation. The obtained results allow us to validate the feasibility of the proposed methodology.

Connectivity and diagnosability of a multiprocessor system or an interconnection network are two important study topics. A measure for fault diagnosis of the system G is called the g -good-neighbor diagnosability of G that restrains every fault-free node containing at least g fault-free neighbors. Another measure for fault diagnosis of the system G is called the g -extra diagnosability of G that requires every component of G − S has at least ( g + 1 ) vertices. The center k -ary n -cube C Q n k is an interconnection network. In this paper, we prove that (1) the g -good-neighbor ( g -extra) connectivity of C Q n k is 2 n ( 2 n ) for 0 ≤ g ≤ 2 n − 1 ; (2) the g -good-neighbor ( g -extra) diagnosability of C Q n k under the PMC model is 2 n + g ( 2 n + g ) for n ≥ 2 and 0 ≤ g ≤ 2 n − 1 ; (3) the g -good-neighbor ( g -extra) diagnosability of C Q n k under the MM ∗ model is 2 n + g ( 2 n + g ) for n ≥ 2 and 0 ≤ g ≤ 2 n − 2 .

Electrical conductivity measurements show that the {100} faces of a perfect SrTiO3 cube are insulating, but the {110} faces of a SrTiO3 truncated rhombic dodecahedron are considerably more conducti...

The Roller boundary is a well-known compactification of a CAT(0) cube complex X. When X is locally finite, essential, irreducible, non-Euclidean and admits a cocompact action by a group G, Nevo-Sageev show that a subset, B(X), of the Roller boundary is the realization of the Poisson boundary and that the action of G on B(X) is minimal and strongly proximal. Additionally, these authors show B(X) satisfies many other desirable dynamical and topological properties. In this article we give several equivalent characterizations for when B(X) is equal to the entire Roller boundary. As an application we show, under mild hypotheses, that if X is also 2-dimensional then X is G-equivariantly quasi-isometric to a CAT(0) cube complex X' whose Roller boundary is equal to B(X'). Additionally, we use our characterization to show that the usual CAT(0) cube complex for which an infinite right-angled Coxeter/Artin group acts on geometrically has Roller boundary equal to B(X), as long as the corresponding group does not decompose as a direct product., Incorporates referee's comments. This is the final pre-publication version; to appear in Israel Journal of Mathematics

To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor, a unified framework of burning surface regression simulation has been developed based on minimum distance function. In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface, a fast distance querying method based on the equal size cube voxel structure was employed. An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements, achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously. The cases of star grain, finocyl grain, and non-uniform tube grain were studied to verify the proposed method. The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.

By a combination of the nanoindentation and electron probe microanalysis (EPMA) techniques, the traditional diffusion couple technique is extended to map the mechanical property of β-type Ti alloys over a wide composition range, which can be utilized to develop very versatile novel bio-Ti alloys for hard tissue replacements in artificial bones, joints, and dental implants. To create complete single-phase composition ranges of Ti-based bcc solid solution, 12 types of bcc Ti–Nb–Zr–Mo/Ti–Nb–Zr–Ta quaternary diffusion couples were fabricated and annealed at 1273 K for 25 h. In this way, the composition-mechanical property relationships in the vast composition space of Ti-based alloys were established using EPMA and nanoindentation probes. Notably, the measured composition-dependent Young's moduli, hardness, and elastic recovery as well as the derived ratio of hardness to Young's modulus, and the ratio of the cube of hardness to the square of Young's modulus, in the developed compositional mechanical property database, were visualized in a five-dimensional scatter plot. This enables an effective tool to screen the Ti–Nb–Zr-based alloys for orthopedic and dental applications according to different clinical requirements, and to rationalize the fundamental mechanical relationships in the rapid development of β-Ti alloys.

Facies cube is a required part of a static model, especially concerning fields characterized by complicated geological structure. The important quantitative limitations for modeling are facies proportions in the formation volume. Nowadays these proportions are calculated using standard geostatistical methods without considering particular properties of facies data. These properties are specific geometrical characteristics of sedimentological units. The consequences are significant differences between calculated and actual data and unreliable hydrocarbon reserves estimation.In order to enhance reliability of reserves estimation on the basis of 3D static models, this article is devoted to special methods of geostatistical analysis for facies data: object geometrization and object clustering. These methods allow taking into account specific geometrical parameters of formations deposited in different environments, therefore, allow reducing differences between calculated and actual facies data and enhancing reliability of reserves estimation.

Nanoparticle motion and self-assembly have been regarded as a promising pathway for forming ordered nanostructures. However, the detailed dynamics processes induced by ligand involvement remained poorly understood. Here, we used in situ liquid-cell electron microscopy technology to image the formation of face-to-face Pt cube ordered structures: pairs, linear chains, and squares. The van der Waals interaction between the two neighboring cubes was quantified in real time. Interestingly, the two different formation processes of the square phase were achieved via a rotational and translational method. It is found that the space between two neighboring cubes was the same as the ex-TEM results. The density functional theory calculation demonstrated that it was attributed to the DMF ligand interactions of the cubes that promoted their face-to-face attachment.

A correction is needed to minimize errors in contact area caused by surface tilt in nanoindentation. Surface tilt decreases the contact area calculated using standard analyses that assume the tested surface is not tilted and thus results in overestimation of hardness and elastic modulus. Both the direction of tilt with respect to the pyramid face and the angle of the pyramidal probe are important when characterizing error caused by surface tilt. Here, a geometric model was used to create contour plots from which the area correction factor can be directly determined using only the ratios of side lengths measured from an image of the triangular nanoindentation impression. Contour plots for Berkovich, cube corner, and two nonstandard pyramidal probe geometries are given. The efficacy of the method was demonstrated in the correction of Berkovich nanoindentation on facets in freshly prepared poly(methyl methacrylate) with surface tilts as high as 6°.

Control and insight into the abundance of inter-shelled channel active sites and charge transport mechanism are the long-term challenges for enhancing photocatalytic activity. Herein, the Ni2P quantum dots (QDs) are decorated in the multi-shelled CaTiO3 cube for creating the abundance of inter-shelled channel active sites, which greatly improve the photocatalytic performances for generating H2 and degrading tetracycline (TC) relative to pure CaTiO3 and Ni2P. Moreover, the Z-scheme mechanism and the quantum effect of the Ni2P in multi-shelled CaTiO3 cube play a crucial role for enhancing photocatalytic performance. Furthermore, the photoelectric researches demonstrate that the Ni2P/CaTiO3 heterostructure possesses more abundant active sites, smaller interface transmission resistance and faster photo-generated charge transfer efficiency. This work provides a meaningful model to research other materials with creating the abundance of inter-shelled channel active sites for the photo-electrocatalytic field.

In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper., 9 pages. arXiv admin note: text overlap with arXiv:1711.06533

A three-dimensional multitransmitting formula is developed in ADINA to simulate the input of seismic waves and the scattering of infinite domains at the same time, consistent with the progress of the explicit finite element method of lumped mass. A three-dimensional cube model is built, and a delta pulse wave is input to compare the simulation results with the analytical solutions. The simulation results show that the peak error is 0.2% of the input wave, which meets the requirements of the usual numerical simulation. This method has a certain efficiency advantage in site effect analyses of fine models for localized fields. A velocity structure model of the Yuxi Basin is built, and the associated basin effect is studied by numerical simulation. The distribution of the focusing effect is related to the structure of the narrow east-west and wide north-south features in the Yuxi Basin, and the edge effect is related to the slope of the basin base. A distribution map is given of the amplification effect of ground motion in the basin.

Cube texture ({001}) is a desired final texture in non-oriented electrical steel sheets used as magnetic cores because it contains two easy axes in the sheet plane, which is beneficial to the magnetic properties. However, the cube texture is very difficult to form in non-oriented electrical steels through conventional rolling and annealing. It has been shown that after conventional rolling, the deformed //ND (normal direction) grains provided nucleation sites for the unfavourable //ND texture during recrystallization, leading to a final //ND texture. To eliminate the //ND texture and promote the {001} texture, an uncommon rolling process, i.e. inclined rolling, was adopted in this study. By rotating the hot rolling direction by 60° around the ND, an uncommon initial texture, the rotated Goss ({110}), was intentionally generated. This was intended to change the orientation flow during plastic deformation, and suppress the formation of the conventional //ND texture in the deformed microstructure. Plane-strain compression (rolling) of the rotated Goss grains produced shear bands within these grains due to their large Taylor factor. Electron backscatter diffraction (EBSD) characterization of the shear bands illustrated that, crystallites with the cube orientation were formed within these shear bands. During recrystallization, the shear bands provided preferential nucleation sites, and the cube crystallites preferentially nucleate within the shear bands. These cube crystals can then grow into the deformed matrix, and lead to the formation of a strong cube texture in the final annealed steel sheets.

Deep Learning frameworks are gaining increased popularity in image processing tasks such as computational hyperspectral imaging. While these frameworks achieve state-of-the-art results in terms of reconstruction quality and run time, they often require massive databases of hyperspectral cubes for training the reconstruction algorithms. Unfortunately, such databases are usually hard to acquire due to complexity and cost considerations. To mitigate these challenges, we propose a method for generating a synthetic database of hyperspectral cubes in the visible range using a limited number of natural hyperspectral cubes, an unlimited number of RGB images, and a Generative Adversarial Network model. The suggested algorithm, dubbed SHS-GAN, is trained to get a query RGB image and to output a synthetic hyperspectral cube. While the spectral domain of the synthetic hyperspectral cube shares similar statistical properties as the natural hyperspectral cubes used in the training process, the SHS-GAN is trained to preserve the spatial characteristics of the query RGB image, whereas the R, G, B values provide an additional constraint along with the spectral domain. Our suggested framework was utilized for performing Snapshot Spectral Imaging (SSI) from a single monochromatic dispersed and diffused snapshot using the DD-Net reconstruction neural network. We demonstrate, by simulations and lab experiments, that enhancing the training database with synthetic data from the SHS-GAN improves the reconstruction quality of the hyperspectral cube. In addition, we share a new original database of more than 10,000 hyperspectral cubes of real objects of size 256x256x29 in the 420-700 nm visible range.

A core test is practiced to determine in-situ cube strength, but most codes give different results depending on the factors used. The general problems of core testing are well known. The factors including core diameter, length-to-diameter ratio (L/d), concrete age, aggregate characteristics, the direction of coring, and the moisture condition at the time of testing are known, which affect the relationship between core strength and the corresponding standard cube or cylinder strength. Another potential factor influencing the testing of cores is the presence of reinforcing bars within the core. Only a few researchers have investigated the effects of steel bars on the strength of cores. Along with these existing factors, the inclination of rebar is believed to influence the core strength, but which has not been taken into consideration so far. In this paper, the finite element simulation studies carried out on concrete cores embedded with reinforcing bars at various inclination is described in detail. The wave propagation through the concrete core is studied, and regression analysis is carried out considering the multiple factors.

Multi-beam echo sounders (MBESs) are characterized by the high resolution and high density of the sounding data. The processing of MBES bathymetry data is of special interest currently in marine surveying. The Combined Uncertainty and Bathymetry Estimator (CUBE) and surface filtering are the main MBES-processing algorithms for outliers. These algorithms involve five adjustable parameters; however, few studies have looked at parameter optimization. In this paper, a Parameter Group Optimization (PGO) method that determines the optimal parameters of CUBE and surface filtering based on the seafloor topographic characteristics of the survey area is presented. The method includes typical area selection, optimal grid resolution analysis, parameter group testing and batch processing, sounding and grid analysis. Raw MBES datasets from shallow- and deep-water survey areas (between 10 and 11000 m deep) are used to validate the proposed method. The results show that when the optimized parameters are used in the CUBE and filtering algorithm, the outliers are automatically eliminated; the processed bathymetry data is in good agreement with the bathymetry derived by a traditional manual processing method, while the processing efficiency can be improved by more than 8 times.

These days, applications of nanotechnology in the field of construction are looking for a resolution to decrease the practice of cement and accordingly to decrease the discharge of pollutants in the environment. In this concern, the outcome of different proportions of the functionalized Multi - Walled Carbon Nanotubes (MWCNTs) on the alteration of mechanical properties of hardened cement paste and cubes was inspected. The addition percentages of Ordinary Portland Cement (OPC) & Portland Pozzolana Cement (PPC) with % replacement of MWCNT were 0%, 0.01%, 0.025% and 0.05%. Additionally, the Mechanical Property of the hardened Cement Concrete was inspected by the use of different tests on cement, aggregates, on fresh and hardened concrete. The concrete cube is tested in different temperatures (Room Temperature, High Temperature and Low Temperature) in this work. The results show that replacement of Ordinary Portland Cement (OPC) & Portland Pozzolana Cement (PPC) with up to 0.05% of the functionalized Carbon Nanotubes, as the optimum amount, can be considered both for enlightening mechanical properties with increase in strength up to 22% for OPC and 26% for PPC in different Temperatures (Room Temperature, High Temperature and Low Temperature).

Compressive and tensile strength are important parameters to know the quality of concrete. This study represents a method predicting the split tensile strength through the compressive strength (0 up to 65 MPa) of cube and cylinder specimens of concrete by polynomial regression analysis. The polynomial equation for both 7 and 28 days have been developed and cube compressive strength are adjusted by multiplying a factor 0.8. To formulate the model, experimental data have been gathered from various literatures. It is noticed that the geopolymer concrete split tensile and compressive strength ratio showed more nonlinearity than existing prediction models and the split tensile strength gaining rate is not so high in 7 days. It is also noticed that existing geopolymer concrete prediction models are good fit in 7 days than the 28 days and traditional prediction models are not also suitable for geopolymer concrete tensile strength prediction. The suggested equations are evaluated based on R2, RMSE, MAPE, and IAE parameters and compared with other models.

Compressive and tensile strength are important parameters to know the quality of concrete. In some circumstances, tensile strength is also required to analyze and design a structure. This study represents a method predicting the split tensile strength through the compressive strength (0 to 120 MPa) of cube and cylinder specimens of concrete by polynomial regression analysis. The polynomial equation for 7 and 28 days have been developed for the following two cases: one is for a cylinder and adjusted cylinder any compressive strength (f‘c) with w/b ratio ≥ 0.51 or a cylinder and adjusted cylinder compressive strength (f‘c) ≤ 20 MPa with any w/b ratio and other is for a cylinder and adjusted cylinder compressive strength (f‘c) > 20 MPa with w/b ratio

The effect of quality of original concrete, from which coarse recycled concrete aggregate particles were derived, on mechanical properties of three grades of recycled aggregate concrete (RAC) has been investigated for the following two weight replacement levels of natural coarse aggregates (NCA) with the recycled aggregates: 50% and 100%. The original concrete samples made with natural coarse aggregates were designed for 28-day nominal cube crushing strengths of 20 MPa, 40 MPa and 60 MPa. The results indicated that the grade of original concrete did not have a significant effect on the mechanical properties viz. compressive strength, splitting tensile strength and flexural strength of the three grades of RCA concretes of this investigation. All the aforesaid properties were inferior to those of the control concrete made only with NCA. However, in case of the high-strength parent concrete, the mechanical properties of the resultant RAC were superior as compared to RAC made with normal and medium strength parent concrete.

El modelado de onda elástico presenta un reto de implementación debido a que es un procedimiento computacionalmente costoso. En la actualidad, debido al incremento en la potencia en GPU junto con el desarrollo de la computación HPC, es posible ejecutar modelado elástico con mejores tiempos de ejecución y uso de memoria. Este estudio evalúa el desempeño de 2 estrategias para implementar modelado elástico usando diferentes diseños para ejecución de kernel, estrategias de asignación de memoria para el cálculo de CPML y administración del almacenamiento del campo de onda. Las mediciones de desempeño muestran que el algoritmo que incluye diseño de ejecución de kernel 2D, la estrategia de memoria reducida CPML y el almacenamiento en memoria global de GPU del campo de onda alcanza un máximo de 88.4% mejor tiempo de ejecución y utiliza un 13.3 veces menos memoria para obtener los mismos resultados de modelado elástico. Existe también una creciente tendencia de mejora de tiempo de ejecución y ahorro de memoria cuando se trabaja con modelos de tamaños más grandes con esta estrategia.

Foreground detection is one of the key steps in computer vision applications. Many foreground and background models have been proposed and achieved promising performance in static scenes. However, due to challenges such as dynamic background, irregular movement, and noise, most algorithms degrade sharply in complex scenes. To address the problem, we propose a motion-aware structured matrix factorization approach (MSMF), which integrates the structural and spatiotemporal motion information into a unified sparse-low-rank matrix factorization framework. Technologically, it has three main contributions: First, a variant of structured sparsity-inducing norm is proposed to constrain both structure and sparsity of foreground. The model is robust to the statistical variability of the underlying foreground pixels in complex scenes. Second, to capture the ambiguous pixels, a spatiotemporal cube-based motion trajectory is extracted for assisting matrix factorization. Finally, to solve the optimization problem of structured matrix factorization, we develop an augmented Lagrange multiplier method with the alternating direction strategy and Douglas-Rachford monotone operator splitting algorithm. Experiments demonstrate that the proposed approach achieves impressive performance in separating irregular moving foreground while suppressing the dynamic background and the noise, and outperforms some state-of-the-art algorithms.

In this paper, we consider the sine-Gordon equation with a high-frequency parametric pumping and a weak dissipative force. We examine the class of π-kink-type solutions that are soliton solutions of the nonperturbed sine-Gordon equation. In contrast to stable 2π-kinks, these solutions are unstable. We prove that the time of decaying of π-kinks due to small perturbations is proportional to the cube of the inverse period of fast oscillations of the parametric pumping. We derive a two-time asymptotic expansion of a solution of the boundary-value problem and analyze evolution of a wave packet whose leading term has the form of a π-kink. Numerical simulations of solutions confirm the good qualitative agreement with asymptotic expansions.

Peptides with a sequence of Nap-Ix-GPLGLAG-R4-NH2 (x = 2, 4, and 6, shorted as I2R4, I4R4, and I6R4) were used as capping agents for the synthesis of zeolitic imidazolate framework-8 (ZIF-8) in water. Peptide addition can significantly inhibit the growth of ZIF-8 crystals. The shape and size of ZIF-8 crystals was related closely to the number of isoleucine (Ile, I) residues as well as concentration of the peptide. The shape of ZIF-8 crystals changes from rhomboid dodecahedron to truncated rhombic dodecahedron to cube with the decreasing number of isoleucine residues from six to two. At a peptide concentration of 1.0 mM, the morphology of ZIF-8 crystals was cubic, truncated rhombic dodecahedron, and typical rhombic dodecahedron in the cases of I2R4, I4R4, and I6R4, respectively. Also, the particle size can be regulated from ca. 1.7 μm to

Introduction. To solve the problem of accelerating the construction of roads, improving their quality, it is advisable to use a continuous action unit to form a underlying layer. The main working elements of this unit are buckets, which cut off the soil layer from below and side. At the same time, the bottom knife cuts off the ground layer from below, the right knife - on the side, and the console knife partially cuts the top layer of soil from below for the next bucket. In particular, the analysis of interaction with the ground of the bottom knife of the continuous action unit is of theoretical and practical interest. To do this, the lower knife is divided into elements and the interaction of these elements with the soil is analyzed. The consistent impact on the soil of many bottom knives, within the width of the grip of the unit, is replaced by the impact on the ground of one conventional bottom knife at a distance necessary for the development of one cubic meter of soil. The forces of interaction of the conventional bottom knife with the soil are called conditional forces.The method of research. The method of calculating energy costs when introducing the bottom knife into the ground is presented. In general, when introducing the bottom knife in the ground, there are energy costs: to separate the soil, to overcome the friction of the ground on the edge of the blade, to overcome the pressure of the ground on the face, to the rise of the ground, to the vertical acceleration of the ground by the phase, to overcome the friction of the ground on the face, to overcome the friction of the ground on the surface, to overcome the friction of the ground on the lower plane. The total energy costs of interacting with a one cubic metre soil are derived from the addition of private energy costs. The method of calculating the horizontal longitudinal force needed to move the bottom knife is given.Results. On the basis of the developed method, energy costs are calculated in the introduction of the lower knife: on the separation of the soil, on overcoming the friction of the ground on the edge of the blade, on overcoming the pressure of the ground on the face, on the rise of the ground, on the vertical acceleration of the ground face, on overcoming the friction of the ground on the fascia, to overcome the friction of the ground on the lower plane. Energy costs to overcome the friction of the ground on the surface of the bottom knife are zero, as the soil flies over it. The total energy costs of the bottom knife interact with the soil of one cubic meter. The horizontal long-lived force needed to move the bottom knife has been determined.Conclusion. As a result of the calculations: the energy needed to cut the ground with the bottom knives, about 5 kJ/cube m., horizontal longitudinal force needed to move the lower knife - 16 N. To determine the total energy costs of moving the boiler unit to remove the top layer of soil from the underlying layer of the road, you need to analyze the interaction with the soil of other elements of the bucket.

Line of Sight (LoS) networks provide a model of wireless communication which incorporates visibility constraints. Vertices of such networks can be embedded onto the cube { ( x 1 , x 2 , … , x d ) : x i ∈ { 1 , … , n } , 1 ≤ i ≤ d } so that two vertices are adjacent if and only if their images lay on a line parallel to one of the cube edges and their distance is less than a given range parameter ω . In this paper we study large independent sets in LoS networks. We prove that the computational problem of finding a maximum independent set can be solved optimally in polynomial time for one dimensional LoS networks. However, for d ≥ 2 , the (decision version of) the problem becomes NP-complete for any fixed ω ≥ 3 . In addition, we show that the problem is APX-hard when ω = n for d ≥ 3 . On the positive side, we show that LoS networks generalize chordal graphs. This implies that there exists a simple d -approximation algorithm for the maximum independent set problem in LoS networks. Finally, we describe a polynomial time approximation scheme for the maximum independent set problem in LoS networks for the case when ω is a constant and present an improved heuristic algorithm for the problem in the case ω = n .

We present a new method to realize a vector magnetometer that has been optically referenced to an external coordinate system. The vector magnetometer is made up of three Hall sensors attached to the orthogonal faces of a glass cube. When placed in a homogeneous magnetic field, rotating the vector magnetometer around two axes allows the orientation of each sensor to be determined with respect to the glass cube. The orientation of the glass cube is detected by an autocollimator and optically referenced to an external coordinate system. A direction uncertainty below $130~\mu $ rad (which is traceable to angle standards) is achieved.

In this work, we describe the discovery of synthesizing γ-AlOOH particles via direct reaction of Al(OH)3 and H2O under a green, facile and cost-effective hydrothermal treatment, in which no addition of other additives is required. The as-synthesized γ-AlOOH is in cube-like morphology with micrometres size, which is subsequently used as a precursor to fabricate Mg stabilized Na-β″-Al2O3 powder with high β″-Al2O3 phase content through solid-state reaction. Time-dependent experiments are carried out to investigate the microstructure and phase evolutions of the γ-AlOOH precursor during the hydrothermal treatment process, and the sintering temperature on the β″-Al2O3 phase content and microstructure of the terminal Na-β″-Al2O3 powder are also studied. The present approach inspires a new and facile way in the fabrication of γ-AlOOH and Na-β″-Al2O3 on a large scale.

The paper aims to estimate the error of a cubature formula acting on an arbitrary function from the Sobolev space on a multidimensional cube. The norm of the error in the dual space of the Sobolev ...

Two-dimensional (2D) layer of water molecules has been observed in crystalline hydrate (C10H18N)3Fe(CN)6·17H2O (1). The layer is generated by interconnection of cube-like clusters by two oxygen ato...

Introduction.Tosolve the problem of accelerating the construction of roads, improving their quality, it is advisable to use a continuous action unit to form a underlying layer. The main working bodies of this unit are buckets, which cut off the soil layer from below and on the side. At the same time, the bottom knife cuts off the ground layer from below, the right knife on the side, and the console knife partially cuts the top layer of soil from below for the next bucket. In particular, the analysis of interaction with the soil of the right knife of the continuous action unit is of theoretical and practical interest. To do this, the right knife is divided into elements and analyzed the interaction of these elements with the ground. The consistent impact on the soil of many right knives, within the width of the grip of the unit, is replaced by the impact on the ground of one conventional right knife at a distance necessary for the development of one cubic meter of soil. The forces of interaction of the conventional right knife with the ground are called conditional forces.The method of research.The method for calculating the energy costs during punching the right knife into the ground is shown: on separating the formation of the ground from its body, on overcoming the ground friction on the edge of the blade, on overcoming the ground pressure on the edge of the blade, on accelerating the ground of the blade by means of the axle, on overcoming the ground friction on the shelf, to overcome the ground friction against the outside surface.The total energy costs of interacting with a soil of one cubic meter are derived from the addition of private energy costs. The method of calculating the horizontal longitudinal force needed to move the right knife is given.Results.On the basis of the methodology developed, energy costs are calculated when introducing the right knife into the ground: on separating the soil from its body, on overcoming the friction of the ground on the edge of the blade, on overcoming the pressure of the ground on the face of the blade, on the acceleration of the ground with a fascia blade, on overcoming the ground friction on the face. The total energy costs of the right knife interact with the soil of one cubic meter. The horizontal long-lived force needed to move the right knife has been determined.Conclusion.As a result of the calculations: the energy needed to cut the ground with the right knives, more than 71 J/cube. The horizontal longitudinal force needed to move the right knife is 730 N. To determine the total energy spent on cutting the ground by buckets of the unit to remove the top layer of soil from the underlying layer of the road, it is necessary to analyze the interaction with the soil of other elements of the bucket.

As a widely used measurement technique in rock mechanics, spatial correlation modeling of acoustic emission (AE) scattering signals is attracting increasing focus for describing mechanical behavior quantitatively. Unlike the statistical description of the spatial distribution of randomly generated AE signals, spatial correlation modeling is based mainly on short-range correlation considering the interrelationship of adjacent signals. As a new idea from percolation models, the covering strategy is used to build the most representative cube cluster, which corresponds to the critical scale at peak stress. Its modeling process of critical cube cluster depends strongly on the full connection of the main fracture network, and the corresponding cube for coverage is termed the critical cube. The criticality pertains to not only the transition of local-to-whole connection of the fracture network but also the increasing-to-decreasing transition of the deviatoric stress with an obvious stress drop in the brittle failure of granite. Determining a reasonable critical cube guarantees the best observation scale for investigating the failure process. Besides, the topological connection induces the geometric criticality of three descriptors, namely anisotropy, pore fraction, and specific surface area, which are evaluated separately and effectively. The results show that cluster modeling based on the critical cube is effective and has criticality in both topology and geometry, as well as the triaxial behavior. Furthermore, the critical cube length presents a high confidence probability of being correlated to the mineral particle size. Besides, its pore fraction of cube cluster is influenced strongly by the critical cube length and confining pressure.

Photodynamic therapy (PDT) has greatly been hindered by its extreme dependence on oxygen, undesired local photodamage, and a shallow tissue penetration depth. Chemotherapy always encounters obstacl...

To clarify the influence of the deformation texture on the mechanical properties, pure Mo plates were processed by various cross rolling procedures, and the relation among texture, microstructure and mechanical properties was discussed. The results show that cross rolling of the Mo plates is beneficial for the formation of the rotated cube component, i.e., {001}〈110〉. The corresponding orientation density exhibits a positive correlation with the total rolling deformation and the current-pass deformation. When the total deformation is 96% or greater, the Mo plates form a texture orientation dominated by {001}〈110〉, whereas the γ-fibre texture becomes weaker and the cube texture {100}〈100〉 disappears completely. The presence of {001}〈110〉 has great effects on the properties of cross-rolled Mo plates, which is beneficial for strength enhancement and plasticity reduction in both the rolling direction (RD) and the transverse direction (TD).

Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra -- shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural 2D fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In 3D the Platonic attractor is dominant: remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation., main: 6 pages, 6 figures, supplementary: 18 pages, 12 figures

This paper presents a ZnO-CuO p-n heterojunction chemiresistive sensor that comprises CuO hollow nanocubes attached to ZnO spherical cores as active materials. These ZnO-CuO core-hollow cube nanostructures exhibit a remarkable response of 11.14 at 1 ppm acetone and 200 °C, which is a superior result to those reported by other metal-oxide-based sensors. The response can be measured up to 40 ppb, and the limit of detection is estimated as 9 ppb. ZnO-CuO core-hollow cube nanostructures also present high selectivity toward acetone against other volatile organic compounds and demonstrate excellent stability for up to 40 days. The outstanding gas-sensing performance of the developed nanocubes is attributed to their uniform and unique morphology. Their core-shell-like structures allow the main charge transfer pathways to pass the interparticle p-p junctions, and the p-n junctions in each particle increase the sensitivity of the reactions to gas molecules. The small grain size and high surface area of each domain also enhance the surface gas adsorption.

Hypothesis The shape of colloidal particles affects the structure of colloidal dispersions. The effect of the cube shape on the thermodynamics of colloidal cube dispersions has not yet been studied experimentally. Static light scattering measurements on colloidal cubic silica shells at finite concentrations allows us to measure the structure factor of colloidal cube fluids and to test theoretical predictions for the equation of state of hard convex superballs. Experiments Hollow silica nanocubes of varying concentrations in N,N,-dimethylformamide were studied with static light scattering. The structure factor was extracted from the scattering curves using experimental form factors. From this experimental structure factor, the specific density of the particles, and the osmotic compressibility were obtained. This osmotic compressibility was then compared to a theoretical equation of state of hard superballs. Findings The first experimental structure factors of a stable cube fluid are presented. The osmotic compressibility of the cube fluid can be described by the equation of state of a hard superball fluid, showing that silica cubes in N,N,-dimethylformamide with LiCl effectively interact as hard particles.

Interconnection network is usually represented by a simple graph G. The structure connectivity κ ( G ; H ) and substructure connectivity κ s ( G ; H ) are the new proposed indicators to measure network fault tolerance and reliability when the network fails with different structures. As a variant of the popular network hypercube, the crossed cube is also a famous interconnection network in parallel and distributed systems. In this paper, we establish the H-structure connectivity of the n-dimensional crossed cube when H ∈ { K 1 , 1 , K 1 , 3 , P k , C 4 } and 3 ≤ k ≤ n and H-substructure connectivity of the n-dimensional crossed cube when H ∈ { K 1 , 1 , K 1 , 3 , P k , C m } , 3 ≤ k ≤ n and 4 ≤ m ≤ n .

The article presents theresults of research on the influence of modes of the volume electric arc surfacing on the geometric accuracy of objects of the “cube” type made of 09G2S and 06Kh19N9T steel fillers. It was found, that when surfacing thesamples made of 09G2S steel, the actual dimensions in length and width, generally exceed, and in height are smallerthan the specified dimensions of the model. Itmay be due to melt spreading on the substrate during formation of the first layers. The optimal surfacing mode for objects of the “cube” type made of 09G2S steel was defined. When surfacing the samples of 06Kh19N9T steel, spreading does not occur, but all the actual dimensions are smaller in relation to the specified. Itmight bedue to the influence of shrinkage processes occurring in the surfaced layers during their solidification. The most optimal mode for the samples made of 06Kh19N9T steel is the mode in which the size reduction in length and width was no more than 2.5 %, and in height – 13.5 %. Studies on the influence of welding arc voltage and the grade of filler material on width of the surfaced track confirmed the tendency of 09G2S steel to spread over the substrate in the entire studied voltage range (11 – 19 V). The structure of the surfacedsamples was investigated. Mechanical tests on the tensile strength of the surfaced samples at room temperature have shown that they have an acceptable set of mechanical properties that exceed the reference values.

We show that the quantum automorphism group of the Clebsch graph is $SO_5^{-1}$. This answers a question by Banica, Bichon and Collins from 2007. More general for odd $n$, the quantum automorphism group of the folded $n$-cube graph is $SO_n^{-1}$. Furthermore, we show that if the automorphism group of a graph contains a pair of disjoint automorphisms this graph has quantum symmetry., 19 pages, corrected a mistake in the proof of Theorem 2.2 + minor changes

Background filtering for roadside Light Detecting and Ranging (LiDAR) data could benefit detection of road users with high frequency and accuracy. But existing methods are unsatisfactory under traffic congestions and neglect noises of LiDAR sensors. This paper attempts to develop background identification and filtering methods for heavy traffics and LiDAR noises. In particular, a 3-D space-time diagram of the LiDAR's detection space over frames is divided into plenty of subspace-frames, where one subspace-frame refers to one subspace from the isometric division of detection space in one frame. For subspace-frames at the same position, an unsupervised clustering method with unknown number of clusters is applied for classifying subspace-frames into different groups and the background group is identified based on background characteristics. The proposed clustering method is a t-distribution mixture model with constraints, where weights follow a Dirichlet distribution so that some weights have the possibility to be 0. A Bayesian estimation framework is developed to carry out the clustering. Then each background subspace-frame is divided into cubes with equal lengths. By aggregating points over frames in the same cube, the cube with aggregated points is regarded as background cube. For background filtering, points in background cubes are background points and excluded. Finally, examined by data from a Velodyne VLP-32 LiDAR sensor, the proposed approach has better filtering results no matter under free-flow conditions or congestions. Using background filtering results for road users' detection is introduced as well.