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A bilayer photothermal paper-based 3D cone flowing evaporator with high solar light absorption, low water evaporation enthalpy and excellent salt-rejecting performance is fabricated using multilayered MXene, ultralong hydroxyapatite nanowires, and hydrophilic polymers. The 3D cone flowing evaporator cooperates with a siphon effect-driven unidirectional fluid transportation unit to guide concentrated saline flows out from the evaporating surface, leading to high water evaporation rate and salt-rejecting stable seawater desalination performance. [Display omitted] • A bilayer photothermal paper-based cone flowing water evaporator is reported. • The evaporator exhibits excellent properties for solar seawater desalination. • The evaporator exhibits much higher water evaporation rate than most reported values. • The evaporator can effectively prevent salt accumulation on the evaporating surface. Solar energy-driven water evaporation technology is a promising, low-cost and sustainable approach to alleviate the global clean water shortage, but usually suffers from low water evaporation rate and severe salt deposition on the water evaporation surface. In this work, a hydrophilic bilayer photothermal paper-based three-dimensional (3D) cone flowing evaporator was designed and prepared for stable high-performance seawater desalination with excellent salt-rejecting ability. The as-prepared bilayer photothermal paper consisted of MXene (Ti 3 C 2 T x) and HAA (ultralong hydroxyapatite nanowires, poly(acrylic acid), and poly(acrylic acid-2-hydroxyethyl ester)). The accordion-like multilayered MXene acted as the efficient solar light absorber, and ultralong hydroxyapatite (HAP) nanowires served as the thermally insulating and supporting skeleton with a porous networked structure. A siphon effect-driven unidirectional fluid transportation unit in the 3D cone flowing evaporator could guide the concentrated saline flowing away from the evaporating surface to prevent salt deposition on the evaporation surface, avoiding severe deterioration of the performance in solar water evaporation. Furthermore, combining high solar light absorption and high photothermal conversion efficiencies, low water evaporation enthalpy (1838 ± 11 J g−1), and additional energy taken from the ambient environment, the as-prepared cone flowing evaporator exhibited a high water evaporation rate of 3.22 ± 0.20 kg m−2 h−1 for real seawater under one sun illumination (1 kW m−2), which was significantly higher than many values reported in the literature. This study provides an effective approach for designing high-performance solar energy-driven water evaporators for sustainable seawater desalination and wastewater purification. [ABSTRACT FROM AUTHOR]

SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership estimation and topic modeling, and the application of SCORE in real data, including two datasets on the publications of statisticians. We also review the theoretical "ideology" underlying SCORE. We show that in the spectral domain, SCORE converts a simplicial cone to a simplex and provides a simple and direct link between the simplex and network memberships. SCORE attains an exponential rate and a sharp phase transition in community detection, and achieves optimal rates in mixed membership estimation and topic modeling. [ABSTRACT FROM AUTHOR]

In 2020, Olia et al. [Olia, Z. E. D. D., Gordji, M. E. and Bagha, D. E. (2020). Banach fixed point theorem on orthogonal cone metric spaces. FACTA Universitatis (NIS) Ser. Math. Inform, 35, 1239-1250] examined orthogonal cone metric spaces. They assumed that P is a normal cone with normal constant K and that self mapping T is orthogonal continuous on the orthogonal cone metric space X in their study. This study now presentes certain required definitions on orthogonal cone metric spaces that were not previously given in [9]. The examples that show the link between existing and new definitions have also been included. The results are also generalized by eliminating the normalcy condition and utilizing point orthogonal continuity instead of general orthogonal continuity in the major results of [9]. The fundamental finding of the study is then generalized by removing the requirement of orthogonal continuity and introducing normality. In addition, certain outcomes of stated theorems are proven, and some examples are provided to demonstrate these theorems. [ABSTRACT FROM AUTHOR]

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32-49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$ . Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases. [ABSTRACT FROM AUTHOR]

In this note, we correct a mistake in the paper (López et al., J Optim Theory Appl 159(3):741-768, ). [ABSTRACT FROM AUTHOR]

Michèle C. Cone (b. 1932) is perhaps best known today as a historian of French art during and after the Vichy regime and Nazi occupation, author of such books as I Artists Under Vichy: A Case of Prejudice and Persecution i (1992) and I French Modernisms: Perspectives on Art Before, During, and After Vichy i (2001). But researchers will also discover a surprising trove of material documenting Cone's previous, and intermittently parallel, life as a critic and occasional curator of contemporary art. Box of audio recordings of interviews with artists conducted by Michèle C. Cone, 1980s. [Extracted from the article]

Motivated by the art of curved crease origami we study mathematical models for folding ideal paper along curved creases. We approach the problem of finding mathematical descriptions in terms of developable surfaces of those shapes which can be folded from real paper but where its rigorous description is very often unknown. For that we investigate a particular one-parameter family of surfaces isometric to a given planar surface patch. For each such surface we parametrize the crease curves which fold those surfaces into cylinders and cones. We apply our methods to explore curved crease origami designs, such as tessellations of the plane and cylinders. • We compute explicit isometric deformations of developable surfaces that are guided by sliding on planes. • We give explicit parametrizations of crease curves between developable surfaces and cylinders and cones. • We illustrate our methods on examples such as curved crease tessellations of cylinders and planes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of radial solutions to a k-Hessian system in a general form. The existence of radial solutions is obtained under the assumptions that the nonlinearities in the given system satisfy k-superlinear, k-sublinear or k-asymptotically linear at the origin and infinity, respectively. The results presented in this paper generalize some known results. Examples are given for the illustration of the main results. [ABSTRACT FROM AUTHOR]

The Koebe-Andreev-Thurston circle packing theorem, as well as its generalization to circle patterns due to Bobenko and Springborn, holds for Euclidean and hyperbolic metrics possibly with conical singularities, but fails for spherical metrics because of the nonuniqueness coming from Möbius transformations. In this paper, we show that a unique existence result for circle pattern with spherical conical metric holds if one prescribes the total geodesic curvature of each circle instead of the cone angles. [ABSTRACT FROM AUTHOR]

This article aims to address the issues of low cultivation density and high labor intensity of manual water exchange in existing scallop seedling ponds, an upwelling recirculating water system for scallop larval cultivation is designed. EDEM-Fluent coupled modelwas used to simulate themovement of scallop larvae in the culture cone in order to guarantee the uniform distribution of larvae in the cultivation device. Design-Expert software was utilized to investigate the impact of the bottom cone angle(θ), the column height/cone height ratio(n) and the inflow velocity(v) on the variation coefficients of the axial and radial distributions of D-shaped larvae within the culture cone. The results indicated that θ = 108.97° and n = 1.8 represent the ideal structural parameters for the culture cone. The further investigation of the culture cones prototype was conducted to examine the impact of the inlet deflector angle (α), cultivation density (τ), and inflow velocity (v) on its performance. θ=108.97°, n=1.8, v=0.19m/s, α=60.94°, and τ=110pcs/ml were found to be the ideal combination of parameters, in this scenario, the D-shaped larvae's radial distributions' coefficients of variation is 22.13%, the error between the experimental and simulation results is 4.41%. Research has shown that EDEMFluent based simulation analysis methods can be used for the design and parameter optimization of upwelling recirculating water scallop larval cultivation system, this paper can provide a reference for the design of an upwelling recirculating water scallop larval cultivation system. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is composed of large quantities of inexpensive passive elements, which is able to adjust phase and amplitude shifts to reduce the system power consumption. However, the complex coupling in the RIS-aided system makes the power minimization (PowerMin) problem more difficult when compared to conventional systems. In this paper, a three-dimensional (3D) time-varying channel model is proposed for RIS-assisted networks and a downlink expression between mobile vehicles and users is derived. Additionally, a successive convex approximation (SCA) method is provided and the transmitter beamformer and RIS phase shifts are updated simultaneously at each iteration to achieve a satisfactory numerical solution. Ultimately, the simulation model in MOSEK version 10.1.28 is utilized to verify the effectiveness of analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by García-Castaño, Melguizo-Padial and Parzanese (2023, Math. Meth. Oper. Res. 97). [ABSTRACT FROM AUTHOR]

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵ 2 u = f (u , ▵ u) on an annular domain Ω in R N with the Navier boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : R + × R − → R + is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f (ξ , η) to have superlinear or sublinear growth on ξ , η as | (ξ , η) | → 0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones. [ABSTRACT FROM AUTHOR]

The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric space, which is not a cone metric space, are given. We establish some results of fixed point precisely about Hardy–Rogers type contraction on C2CMS and provide examples. Finally, we present an application of our results and how our results solve the Fredholm integral equation of generalizing several existing and unique fixed point theorems. [ABSTRACT FROM AUTHOR]

One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse—i.e., the difficult part—can be neglected because only the shadow ellipse needs to be determined. [ABSTRACT FROM AUTHOR]

In this paper, we introduced the concept of C-star bodies in a fixed pointed closed convex cone C and studied the dual mixed volume for C-star bodies. For C-star bodies, we established the corresponding dual Brunn-Minkowski inequality, dual Minkowski inequality, and dual Aleksandrov-Fenchel inequality. Moveover, we found that the dual Brunn-Minkowski inequality for C-star bodies can strengthen the Brunn-Minkowski inequality for C-coconvex sets. [ABSTRACT FROM AUTHOR]

In this paper, we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flow, where the deformation speed is given by a homogeneous smooth symmetric positive function γ$\gamma$ defined in a symmetric open cone. The main result of this paper is about the uniqueness of γ$\gamma$‐translators in the class of complete graphs defined on a ball. [ABSTRACT FROM AUTHOR]

In this paper we revisit the double cone wormhole introduced by Saad, Shenker and Stanford (SSS), which was shown to reproduce the ramp in the spectral form factor. As a first approximation we can say that this solution computes Tr[e−iKT], a trace of the "evolution" operator that generates Schwarzschild time translations on the two sided wormhole geometry. This point of view leads to a simple way to compute the normalization factor of the wormhole. When we have bulk matter fields, SSS suggested using a modified evolution which involves a slightly complex geometry, so that we are really computing . We argue that, for general black holes, the spectrum of is given by quasinormal mode frequencies. We explain that this reproduces various features that were previously predicted from the spectral form factor on hydrodynamics grounds. We also give a general algebraic construction of the modified boost in terms of operators constructed from half sided modular inclusions. For the special case of JT gravity, we work out the backreaction of matter on the geometry of the double cone and find that it deforms the geometry in an undesirable direction. We finally give some comments on the possible physical interpretation of . [ABSTRACT FROM AUTHOR]

This paper investigates pseudo-polymorphism in 2-pyridylmethoxy derivatives of p-tert-butylcalix[4]arene (PyC4), p-tert-butyldihomooxa-calix[4]arenes (PyHOC4), and p-tert-butylhexahomotrioxacalix[3]arenes (PyHO3C3), presenting 11 crystal structures with 15 crystallographically independent molecules. The macrocycle of PyC4 is smaller and less flexible with respect to those of PyHOC4 and PyHO3C3, and in solution, the cone conformation of these three molecules exhibits different point symmetries: C4, Cs, and C3, respectively. A correlation is observed between the macrocycle's structural rigidity and the number of pseudo-polymorphs formed. The more rigid PyC4 displays a higher number (six) of pseudo-polymorphs compared to PyHOC4 and PyHO3C3, which exhibit a smaller number of crystalline forms (three and two, respectively). The X-ray structures obtained show that the conformation of the macrorings is primarily influenced by the presence of an acetonitrile guest molecule within the cavity, with limited impact from crystal packing and intermolecular co-crystallized solvent molecules. Notably, both calix[4]arene derivatives produce a host–guest complex with acetonitrile, while the most flexible and less aromatic PyHO3C3 does not give crystals with acetonitrile as the guest. Intertwined 1D and 2D solvent channel networks were observed in the PyHOC4-hexane and in the PyHO3C3-H2O-MeOH crystal structures, respectively, while the other pseudopolymorphs of PyHOC4 and PyHO3C3 and all PyC4 crystal forms exhibit closely packed crystal structures without open channels. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integrodifferential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results. [ABSTRACT FROM AUTHOR]

The utilization of multibeam sonar systems has significantly facilitated the acquisition of underwater bathymetric data. However, efficiently processing vast amounts of multibeam point cloud data remains a challenge, particularly in terms of rejecting massive outliers. This paper proposes a novel solution by implementing a cone model filtering method for multibeam bathymetric point cloud data filtering. Initially, statistical analysis is employed to remove large-scale outliers from the raw point cloud data in order to enhance its resistance to variance for subsequent processing. Subsequently, virtual grids and voxel down-sampling are introduced to determine the angles and vertices of the model within each grid. Finally, the point cloud data was inverted, and the custom parameters were redefined to facilitate bi-directional data filtering. Experimental results demonstrate that compared to the commonly used filtering method the proposed method in this paper effectively removes outliers while minimizing excessive filtering, with minimal differences in standard deviations from human-computer interactive filtering. Furthermore, it yields a 3.57% improvement in accuracy compared to the Combined Uncertainty and Bathymetry Estimator method. These findings suggest that the newly proposed method is comparatively more effective and stable, exhibiting great potential for mitigating excessive filtering in areas with complex terrain. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of three-dimensional smooth humps with varying deflection angles (φ) on the linear stability of streamwise vortices over a yawed cone with a 7° half-angle at a 6° angle-of-attack, free-stream Mach number of 6, and unit Reynolds number of 1.0 × 10 7 /m. The steady laminar flow is obtained using direct numerical simulations. The eN method based on global stability theory is used to predict the transition location of the streamwise vortices along the centerline on the leeward side of the cone. The results reveal that φ plays a significant role in the outward vortex generation location, with smaller values of φ effectively delaying the outward vortex generation. Moreover, there is a qualitative relationship between the instability of the streamwise vortices and the inward/outward vortex structure characteristics of the base flow over a yawed cone. Namely, the transition delay effect of the streamwise vortices is proportional to the delay in the generation location of the outward vortex, which provides insights into the control of the transition induced by streamwise vortices. In particular, the configuration based on a hump with φ = 9 ° and a height of 0.57 times the local boundary layer thickness delays the transition by approximately 38.2% at the critical N-factor ( N t r = 12.5) without significantly increasing the instability of the inner mode. [ABSTRACT FROM AUTHOR]

The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated cone creates the open-ended cavity. In this paper the certain physical aspects of diffraction which are known to cause mathematical difficulties are considered. It includes an accurate analysis of the wave-mode transformation phenomena at the open end of the cavity, as well as a study of wave radiation from the cavity into the biconical waveguide. The primary outcome of this paper is a precise treatment of the wave diffraction problem mentioned above using new techniques and establishing new properties of resonance modes' penetration into the biconical waveguide region. [ABSTRACT FROM AUTHOR]

Cones are among the significant and controversial landforms on Mars. Martian cones exhibit various morphological characteristics owing to their complex origin, and their precise origin remains an active research topic. A limited number of cones have been manually mapped from high-resolution images in local areas, and existing detection methods are only applicable to a single type of cone that has a similar morphology and spatial distribution, leading to the vast majority remaining unidentified. In this paper, a novel cone identification approach is proposed that is specially designed for adequately recognizing cones from different regions in high-resolution planetary images. First, due to the lack of a publicly available cone database for reference, we annotated 3681 cones according to the literature on manual interpretation and the cone information provided by the Lunar and Planetary Laboratory (IRL) in HiRISE images. Then, the cone identification problem was converted into an instance segmentation task, i.e., a cone identification approach was designed based on deep neural networks. The Feature Pyramid Network-equipped Mask R-CNN was utilized as the detection and segmentation model. Extensive experiments were conducted for fine recognition of Martian cones with HiRISE. The results show that the proposed approach achieves high performance; it especially efficiently detects multiple types of cones while generating accurate segmentation to describe the geometry contour of cones. Finally, a Martian cone dataset with deep learning-based instance segmentation (DL-MCD) was built, containing 3861 cones for exploring geological processes on the surface of Mars. [ABSTRACT FROM AUTHOR]

The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, and optimization. In the paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone/conical surface in real (topological) linear spaces. Basically, we follow the separation approach by Kasimbeyli [SIAM J. Optim., 20 (2010), pp. 1591-1619] based on augmented dual cones and Bishop--Phelps type (normlinear) separating functions. Classical separation theorems for convex sets are the key tool for proving our main nonlinear cone separation theorems. [ABSTRACT FROM AUTHOR]

Aiming at the unclear reorganization of a water cone shape, its sweep range, and water saturation distribution of horizontal well in heavy oil reservoirs with bottom water, a mathematical method was proposed in this paper to establish a microtube model and physical model with the starting pressure gradient (SPG) to study the water cone behavior. The results showed that the different water-cut stage, mobility, depth from oil-water interface (DOWI), and liquid production strength have an obvious impact on water cone behavior. Moreover, we found an interesting phenomenon on an extreme point in water saturation derivation among water cone, which could be a reason for further adjustment. Finally, we confirmed the calculation results with physical simulation, which is highly consistent. The new method proposed in this paper was significant in the water cone behavior study and has a broad application in heavy oil reservoir development in the future. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces based on cone asperity. Design/methodology/approach: A detailed numerical study is conducted to examine the effects of contact load, fractal dimensional, fractal roughness and material properties on the TCC of rough surfaces. Findings: The results indicate that when the fractal dimension D is less than 2.5, the TCC of rough surfaces increases nonlinearly with the increase of the contact load. However, when the fractal dimension D is greater than or equal to 2.5, the TCC of rough surfaces increases linearly with the increase of the contact load; the TCC of the rough surfaces increases with the increase of the fractal dimension D and the decrease of the fractal roughness G; the material parameters also have an influence on the TCC of the rough surfaces, and the extent of the effect on the TCC is related to the fractal dimension D. Originality/value: A fractal model of TCC of rough surfaces based on cone asperity is established in this paper. Some new results and conclusions are obtained from this work, which provides important theoretical guidance for further study of TCC of rough surfaces. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a converse duality theorem for higher order Wolfe type multiobjective programming with cone constraints under appropriate assumptions. This fills some gaps in the work of Kim et al. [Kim, D.S., Kang, H.S., Lee, Y.J., Seo, Y.Y., Higher order duality in multiobjective programming with cone constraints, Optimization, 59(1), 29-43, (2010)]. [ABSTRACT FROM AUTHOR]

Wall temperature is a crucial factor for the transition of hypersonic boundary layers. This paper investigates the wall temperature effects on the hypersonic boundary-layer transition over an inclined blunt cone with two wall temperatures by direct numerical simulations and instability analysis. The breakdown processes of leeward streamwise vortices and crossflow vortices are both studied. Inner modes with lower phase velocities and outer modes with higher phase velocities are responsible for the breakdown of leeward streamwise vortices, respectively, in cooled- and heated-wall cases. A higher wall temperature will promote the boundary layer transition in the vicinity of the leeward centerline due to the collision of nearby crossflow vortices with the leeward mushroom structure, instead of by destabilizing inner and outer modes. In the crossflow-dominated region, the transition is triggered by the interaction between second modes and crossflow vortices for the cooled-wall case. Increasing the wall temperature will promote the transition in this region even though second modes are suppressed. [ABSTRACT FROM AUTHOR]

This paper successfully describes the analysis between 3D image location in air and arc-shaped scratches on cone-shaped arc 3D display. The arc 3D display is typically flat and its analysis has already appeared. However, when we would like to extend it to cone shape, the dimensional extension of analysis should be necessary, since the lack of adequate analysis increases the approximation error of the 3D image location. In this paper, we discuss the three-dimensional analysis for cone-shaped arc 3D display. In addition, we describe the actual fabrication of a cone-shaped arc 3D display and show that the 3D image can be displayed similarly with the analysis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the rough concept lattice and use the information flow to construct a second-order cone programming model for big data. Through the construction of the model, attribute reduction is performed on the original data of the noise in the formal background. Then, construct the concept lattice according to the reduced formal background, and then analyze the big data in the form of information flow. Then, based on the advantages of the β-upper and lower distribution reduction algorithms of the variable-precision rough set, combine the rough concept. The characteristics of the background of the lattice form, the second-order cone thought method theory is applied, and then a second-order cone calculation model is constructed. The rough concept lattice is applied to the processing of big data, and then it is analyzed and researched through concrete examples. The time required in traditional mode is between 118.3 min and 123.6 min, while the time required for second-order cone and concept lattice fitting is 92.4 min and 98.5 min. Experimental data show that the rough concept lattice uses information flow to construct a second-order cone programming model for big data, which results in a greatly reduced number of nodes in the rough concept lattice and an enhanced anti-noise capability of the system, which saves data statistics and calculation time. The traditional concept lattice algorithm can be traced back to the purification of the formal background, and the purification of the formal background can simplify the concept connotation and study attribute reduction from the perspective of lattice isomorphism. Experimental data show that the rough concept lattice uses information flow to construct a second-order cone programming model for big data, which greatly guarantees the integrity and security of the data by about 15%, and saves 20% of the data processing time compared with traditional and algorithms. It has guiding significance for the efficient and secure development of big data in the future. In this paper, data feature mining and information flow model construction are carried out, the power spectral density feature extraction of big data is carried out from a large number of noisy and fuzzy data, and the second-order cone programming model of big data information flow is carried out by rough concept lattice method. [ABSTRACT FROM AUTHOR]

This paper investigates the maximum principle for a nonlinear size structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. First, we show the existence of a unique non-negative solution of the system, and give a comparison principle. Next, we prove the existence of optimal policies by using maximizing sequence and Mazur's theorem in convex analysis. Then, we obtain necessary optimality conditions by using tangent-normal cones and adjoint system techniques. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper. [ABSTRACT FROM AUTHOR]

In this paper the authors introduce an analogue of the nilpotent cone, N, for a classical Lie superalgebra, g, that generalizes the definition for the nilpotent cone for semisimple Lie algebras. For a classical simple Lie superalgebra, g = g0 ⊕ g1 with Lie G0 = g0, it is shown that there are finitely many G0-orbits on N. Later the authors prove that the Duflo-Serganova commuting variety, X, is contained in N for any classical simple Lie superalgebra. Consequently, our finiteness result generalizes and extends the work of Duflo-Serganova on the commuting variety. Further applications are given at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the solar heating of a multi-layered spherical body with azimuthal symmetry is considered. The mathematical model is related to the determination of the steady state of the temperature distribution in the spherical cone consisting of concentric spherical layers. The solar heating is composed of two parts of the heat flux: direct and diffusion. Also, the simultaneous cooling of the cone by its outer surface (as convective heat flow to the environment) is taken into account. The proposed system of the partial differential equations supplemented by the adequate boundary conditions is solved in the analytical way by using, among others, the Legendre functions of the first kind. The sample results of temperature distribution in the cross-section of the cone with different polar angles are also presented. [ABSTRACT FROM AUTHOR]

New plastic solutions for the bearing capacity factors of conical footings on rock masses obeying the Hoek–Brown yield criterion are presented in the paper by using the lower and upper bound finite element limit analysis. A conical footing has a cone apex angle and is penetrated into a rock mass. The considered dimensionless parameters include the cone apex angle, the yield parameter, and the geological strength index of a rock mass, where the effects of these dimensionless parameters on the bearing capacity factor are compressively investigated. The collapse mechanisms of conical footings on rock masses are examined and discussed in the paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that fixed point theorem in cones can be applied to singular equations. Using the positivity of Green's function and the external force e(t), we prove the existence of a positive periodic solution for a damped singular equation with sub-linearity, semi-linearity and super-linearity conditions, and these results are applicable to weak and strong singularities. As applications, we consider the existence of a positive periodic solution for nonlinear elasticity model and Ermakov–Pinney equation [ABSTRACT FROM AUTHOR]

In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the ALM have been established in the literature. Recently, it has been shown in [Cui, Sun, and Toh, Math. Program., 178 (2019), pp. 381-415] that if the quadratic growth condition holds at an optimal solution for the dual problem, then the KKT residual converges to zero R-superlinearly when the ALM is applied to the primal problem. Moreover, Cui, Ding, and Zhao [SIAM J. 0ptim., 27 (2017), pp. 2332-2355] provided sufficient conditions for the quadratic growth condition to hold under the metric subregularity and bounded linear regularity conditions for solving composite matrix optimization problems involving spectral functions. Here, we adopt these recent ideas to analyze the convergence properties of the ALM when applied to SOCPs. To the best of our knowledge, no similar work has been done for SOCPs so far. In our paper, we first provide sufficient conditions to ensure the quadratic growth condition for SOCPs. With these elegant theoretical guarantees, we then design an SOCP solver and apply it to solve various classes of SOCPs, such as minimal enclosing ball problems, classical trust-region subproblems, square-root Lasso problems, and DIMACS Challenge problems. Numerical results show that the proposed ALM based solver is efficient and robust compared to the existing highly developed solvers, such as Mosek and SDPT3. [ABSTRACT FROM AUTHOR]

Solutions of singular differential equations with the Bessel operator of negative order are studied. In this regard, of great interest are the solutions of the singular differential Bessel equation , which are presented in the paper as linearly independent functions and , . Some properties of the functions expressed in terms of the properties of the Bessel–Levitan -function are considered. The direct and inverse -Bessel transforms are introduced, and the -pseudoshift operator that commutes with the Bessel operator is defined. The fundamental solution of the ordinary singular differential operator is found. A representation of the fundamental solution of the Kipriyanov -operator with a singularity at the point and on the cone in the Euclidean -dimensional half-space is given. [ABSTRACT FROM AUTHOR]

Circle geometries are incidence structures that capture the geometry of circles on spheres, cones and hyperboloids in three‐dimensional space. In a previous paper, the author characterised the largest intersecting families in finite ovoidal circle geometries, except for Möbius planes of odd order. In this paper we show that also in these Möbius planes, if the order is greater than 3, the largest intersecting families are the sets of circles through a fixed point. We show the same result in the only known family of finite nonovoidal circle geometries. Using the same techniques, we show a stability result on large intersecting families in all ovoidal circle geometries. More specifically, we prove that an intersecting family ℱ ${\rm{ {\mathcal F} }}$ in one of the known finite circle geometries of order q $q$, with ∣ℱ∣≥12q2+22q+8 $| {\rm{ {\mathcal F} }}\,| \ge \frac{1}{\sqrt{2}}{q}^{2}+2\sqrt{2}q+8$, must consist of circles through a common point, or through a common nucleus in case of a Laguerre plane of even order. [ABSTRACT FROM AUTHOR]

This paper focuses on the design of a new optical cone and pendulum scanning imaging mode for micro-nanosatellites. This kind of satellite uses a high-resolution camera with a small imaging plane to achieve high-resolution and ultra-wide coverage imaging through the three-dimensional motion of the camera's wobble, satellite spin, and satellite orbital motion. First, this paper designs a single-camera constant speed OCPSI (optical cone and pendulum scanning imaging) mode. On the premise of ensuring coverage, the motion parameters and imaging parameters are derived. Then, in order to improve the performance and imaging quality of the system, a dual-camera variable speed OCPSI mode is designed. In this method, in order to reduce the overlap ratio, the camera is oscillated at a variable speed. Turn on the cameras in turn at the same time to minimize the overlap. This paper details these working modes. The simulation experiment is carried out using the satellite orbit of 500 km, the focal length of 360 mm, the pixel size of 2.5 μm, the resolution of [5120 × 5120], the number of imaging frames in the pendulum scanning hoop of 10, and the initial camera inclination angle of 30°. The single-camera constant speed OCPSI mode has an effective swath of 1060 km at a ground sampling distance of 5.3 m. The dual-camera variable speed OCPSI mode has an effective width of 966 km under the same conditions. Finally, the ground experiment prototype of OCPSI imaging theory is designed. We choose a camera with a pixel size of 3.45 μm, a resolution of [1440 × 1080], and a focal length of 25 mm. The ground experiment was carried out at the initial camera inclination angle of 10°, the number of imaging frames in the pendulum scanning hoop of 3, and the orbit height of 11 m. The experimental result is that the effective width of OCPSI imaging mode reaches 10.8 m. Compared with the traditional push-broom mode using the same camera, the effective width of 1.64 m is increased by seven times, and the effective width of 3.83 m is increased by three times compared to the traditional whisk-broom imaging mode. This study innovatively integrates three-dimensional motion imaging into aerospace remote sensing and provides a reference for the research on the realization of high-resolution and ultra-wide coverage of micro-nano remote sensing satellites. [ABSTRACT FROM AUTHOR]