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Saturated packing is a random packing state of particles widely applied in investigating the physicochemical properties of granular materials. Optimizing particle shape to maximize packing density is a crucial challenge in saturated packing research. The known optimal three-dimensional shape is an ellipsoid with a saturated packing density of 0.437 72(51). In this work, we generate saturated packings of three-dimensional asymmetric shapes, including spherocylinders, cones, and tetrahedra, via the random sequential adsorption algorithm and investigate their packing properties. Results show that the optimal shape of asymmetric spherocylinders gives the maximum density of 0.4338(9), while cones achieve a higher value of 0.4398(10). Interestingly, tetrahedra exhibit two distinct optimal shapes with significantly high densities of 0.4789(19) and 0.4769(18), which surpass all previous results in saturated packing. The study of adsorption kinetics reveals that the two optimal shapes of tetrahedra demonstrate notably higher degrees of freedom and faster growth rates of the particle number. The analysis of packing structures via the density pair-correlation function shows that the two optimal shapes of tetrahedra possess faster transitions from local to global packing densities. [ABSTRACT FROM AUTHOR]

Low-energy ion beam irradiation, combined with the introduction of impurities, presents a promising approach for nanopatterning silicon (Si) surfaces. In this research, we investigate the surface evolution of Si (100) surfaces irradiated by 75 eV helium (He) plasma, in the presence of tantalum (Ta), traditionally regarded as an impurity incapable of initiating pattern formation, as evidenced in prior studies. The Ta impurities are pre-deposited onto the Si surfaces using the magnetron sputtering method, which offers a more controlled and quantifiable approach compared with the conventional co-deposition route. After irradiation at 800 K, dense cone arrays are produced on the Si surface. The growth of the cones is explored for fluence spanning (1–10) × 1025 m−2. The cross-sectional scanning electron microscope images indicate that the cone lengths and base width are well characterized by t1/2 dependence. The kinetics of the cone growth follow Fick's law, characterized by an effective diffusive mechanism with the coefficients of diffusion: D = 6.49 ± 0.83 × 10−16 m−2 s−1. Transmission electron microscope observations reveal that the cone has distinct inner and outer parts with different microstructures and a clear interface. The growth mechanism of these cones is elucidated as a composite process involving preferential sputtering, the destabilizing influence of He bubbles, and the migration of adatoms. [ABSTRACT FROM AUTHOR]

The nonlinear forced vibration behavior of truncated open conical nanoshells is investigated in this paper. Nonlocal elasticity theory has been employed to modify the size-dependent effect of micro/nanostructure. Von Karman nonlinear strains are used to consider the geometric nonlinearity of the nanoshells. Using Hamilton's principle, the equations of motion and boundary conditions of truncated open conical nanoshells are derived. Galerkin method is used to solve the governing equations. Then, to determine the nonlinear forced vibration behavior of truncated open conical nanoshells, complex averaging and arc-length continuation methods are employed. Finally, the effect of nonlocal parameters, cone apex angle, the amplitude of harmonic excitation, structural damping coefficient, and geometrical parameters on the nonlinear frequency response of the truncated open conical nanoshells are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we compute the pseudo-effective cones of various projective bundles ℙX(E) over higher dimensional varieties X under some assumptions on X as well as on the vector bundle E. We also compute the volume function on fiber product ℙ(E) ×Cℙ(F) of two projective bundles over a smooth irreducible complex projective curve C. In particular, we show that the volume function on the fiber product of two ruled surfaces is of polynomial type. [ABSTRACT FROM AUTHOR]

The deposition and accumulation of inclusions is the dominant mechanism in nozzle clogging of the submerged entry nozzle. Previous modeling attempts of inclusion deposition have assumed that any contact between the inclusion and nozzle wall results in adhesion. Herein, an Eulerian–Lagrangian simulation with a stochastic adhesion model is used to study the effects of different inclusion‐wall sticking probability (Swall) on inclusion deposition. The results indicate that inclusion deposition is affected by both melt height and Swall. Lower melt heights result in increased deposition deeper into the nozzle and greater maximum particle area number density. The effect of Swall on the global deposition ratio can be divided into two regimes. When Swall increases from 0–0.05, there is a rapid rise in the global deposition ratio. When Swall > 0.05, the global deposition ratio increases only modestly with Swall. Changes to Swall also affect the location of deposition. When Swall decreases, the high and mid cases show greater relative deposition in the cone and taper sections of the nozzle, while the low melt height case shows greater relative deposition in the straight section of the nozzle. [ABSTRACT FROM AUTHOR]

In the present paper, we construct the existence of nontrivial solutions to a new kind of Hadamard fractional boundary value problem on an unbounded domain. With the contribution of some fixed point theorems in cone and the corresponding Green function, we ensure sufficient conditions for the Hadamard fractional boundary value problem. Also, the paper concludes with two examples to demonstrate our results. [ABSTRACT FROM AUTHOR]

We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a consequence of the series representation, we derive elementary proofs of some results of Bradley and Zhou for Mordell-Tornheim zeta values and give explicit formulas. The series representation for shuffle arborified zeta values also implies that they are conical zeta values. We characterise which conical zeta values are arborified zeta values and evaluate them as sums of multiple zeta values with rational coefficients. [ABSTRACT FROM AUTHOR]

A char cone, whose shape is similar to Bunsen flame and varies with oxidation conditions, was found in steady smoldering of biomass rods. In this short communication, characteristics of this char cone in natural downward smoldering of char rods with different diameters (2 – 7 mm) and ash contents (30–46%) were investigated via measuring propagation velocity and analyzing shape of char cone. Results showed that smoldering propagates steadily in all prepared char rods and the propagation velocity decreases with increasing diameter and ash content of char rods. Height of char cone is proportional to the mass flowrate of carbon, similar to the relationship between flame length and volume flowrate of gas fuel in laminar jet diffusion flame. It implies that oxygen diffusion through ash plays a dominant role in natural smoldering of char rod. This work provides some experimental basis for further investigation on mechanism of steady smoldering. [ABSTRACT FROM AUTHOR]

The phenomenon of droplet impingement on solid surfaces is prevalent in various natural and industrial contexts. Research on impact dynamics on conical surfaces keeps emerging, with superhydrophobic cones receiving more attention than hydrophilic ones. This study systematically investigates water droplet impact dynamics on both hydrophilic and superhydrophobic cones using a two-phase numerical solver under different Weber numbers (We) and cone angles (φ). Three distinct phases are identified in the We– φ map to describe the different outcomes on each type of cones. Generally, deposition occurs ultimately on hydrophilic cones, whereas rebounding is observed on superhydrophobic ones. The maximum spreading area β Amax on hydrophilic cones depends only slightly on φ but consistently increases with We, following a scaling law of We0.5 at higher We. In contrast, on superhydrophobic cones, β Amax increases significantly with both We and φ , and the exponent in the scaling laws of β Amax with respect to We increases notably as φ increases. Three characteristic times are defined to describe important motion states on both types of cones. Corresponding scaling laws for each time with We are established. Two theoretical models are developed to predict the maximum spreading position for droplets on hydrophilic cones and the rebound position on superhydrophobic cones, respectively. Gravitational potential energy is included in the energy budget for both models, and an auxiliary viscous dissipation due to spontaneous spreading is accounted for the hydrophilic case. Satisfactory agreement between the theoretical and numerical results is achieved. [ABSTRACT FROM AUTHOR]

The work establishes the unique solvability of a boundary value problem for a 3D linearized system of Navier–Stokes equations in a degenerate domain represented by a cone. The domain degenerates at the vertex of the cone at the initial moment of time, and, as a consequence of this fact, there are no initial conditions in the problem under consideration. First, the unique solvability of the initial-boundary value problem for the 3D linearized Navier–Stokes equations system in a truncated cone is established. Then, the original problem for the cone is approximated by a countable family of initial-boundary value problems in domains represented by truncated cones, which are constructed in a specially chosen manner. In the limit, the truncated cones will tend toward the original cone. The Faedo–Galerkin method is used to prove the unique solvability of initial-boundary value problems in each of the truncated cones. By carrying out the passage to the limit, we obtain the main result regarding the solvability of the boundary value problem in a cone. [ABSTRACT FROM AUTHOR]

This paper proposed an improved ant colony optimization named TSACO and an enhanced velocity obstacle (VO) to solve the UAV path planning problem. The TSACO incorporated non-uniform initial pheromone distribution, a turning heuristic function, and an elite ant system to improve the convergence speed and reduce the number of path corners during global planning. The enhanced VO integrated the UAV's dynamic equation, adaptive collision radius and emergency collision cone, along with an optimal velocity selection approach to increase real-time and safe local obstacle avoidance during local planning. Simulation experiments demonstrate that the proposed algorithms have better effectiveness in terms of path length, number of turns, and dynamic obstacle avoidance compared to other algorithms. [ABSTRACT FROM AUTHOR]

Facial asymmetry is defined as a bilateral difference between facial components. Correction, often desired by the patient, can be performed with the aim of bone born patient-specific solid implants designed using 3D CAD software. This treatment is embedded in the daily practice of today's healthcare. However, an analysis of the implant's accuracy of placement has not been reported. This case series describes the accuracy analysis of bone born aesthetic facial implants manufactured out of polyether-ether-ketone (PEEK). The accuracy analysis was based on postoperative (cone beam) computed tomography ((CB)CT) data and preoperative 3D planning. The analysis showed a median entry point error of 0.7 mm (min: 0.1, max: 3.3, interquartile range: 0.78). The median maximal orientation error was 5.5° (min: 0.1, max: 36.8, interquartile range: 7.13). Both parameters showed an excellent intraobserver and interobserver agreement with an ICC above 0.84. The described cases show that the analysis method is an objective approach for determining the accuracy of PSI placement and indicates that these implants can be placed accurately on the osseous face. [ABSTRACT FROM AUTHOR]

Purpose: To improve the spatial resolution and repeatability of a non‐contrast MRI technique for simultaneous time resolved 3D angiography and perfusion imaging by developing an efficient 3D cone trajectory design. Methods: A novel parameterized 3D cone trajectory design incorporating the 3D golden angle was integrated into 4D combined angiography and perfusion using radial imaging and arterial spin labeling (CAPRIA) to achieve higher spatial resolution and sampling efficiency for both dynamic angiography and perfusion imaging with flexible spatiotemporal resolution. Numerical simulations and physical phantom scanning were used to optimize the cone design. Eight healthy volunteers were scanned to compare the original radial trajectory in 4D CAPRIA with our newly designed cone trajectory. A locally low rank reconstruction method was used to leverage the complementary k‐space sampling across time. Results: The improved sampling in the periphery of k‐space obtained with the optimized 3D cone trajectory resulted in improved spatial resolution compared with the radial trajectory in phantom scans. Improved vessel sharpness and perfusion visualization were also achieved in vivo. Less dephasing was observed in the angiograms because of the short TE of our cone trajectory and the improved k‐space sampling efficiency also resulted in higher repeatability compared to the original radial approach. Conclusion: The proposed 3D cone trajectory combined with 3D golden angle ordering resulted in improved spatial resolution and image quality for both angiography and perfusion imaging and could potentially benefit other applications that require an efficient sampling scheme with flexible spatial and temporal resolution. [ABSTRACT FROM AUTHOR]

This study aimed to evaluate and compare the quality of matching single-cone obturation using three different single-file systems—WaveOne® Gold (Dentsply Sirona, Bensheim, Germany), Reciproc® blue (VDW GmbH, Munich, Germany), and Procodile® (Komet Medical, Gebr. Brasseler GmbH & Co. KG, Lemgo, Germany). The evaluation focused on the percentage of gutta-percha-filled areas (PGFAs), sealer-filled areas (PSFAs), and unfilled areas (PUAs) across three different sections of curved and straight root canals. Sixty extracted human teeth were categorized into six groups. Based on radiographically determined root canal curvature, thirty curved and thirty straight root canals were prepared using the single-file systems according to the manufacturers' instructions and obturated with matching gutta-percha cones using AH-Plus sealer. A total of 180 sections were evaluated digitally under the microscope and the results were statistically analyzed. The mean gutta-percha percentages for Reciproc® blue, Procodile®, and WaveOne® Gold were 83%, 82%, and 80%, respectively. No significant (p > 0.05) and relevant (ηp2 < 0.10) differences were found in the proportion of form-fitting gutta-percha cones between the systems in all sections. Similarly, canal anatomy showed no significant influence (p > 0.05). Ex vivo, all three systems showed comparable filling quality in all sections of curved and straight canals. Therefore, it can be concluded that all three file systems, in combination with their corresponding gutta-percha points, might be reliable methods for root canal obturation. Reciproc® Blue, Procodile®, and WaveOne® Gold consistently achieved comparable obturation results across various root configurations and levels of the root canal. [ABSTRACT FROM AUTHOR]

Objective: The purpose of this study was to evaluate the age-dependency of amplitudes and implicit times in the electroretinograms (ERGs) of healthy individuals and provide clinicians and researchers with a reference for a variety of stimulus paradigms. Design and methods: Full-field electroretinography was conducted on 73 healthy participants aged 14–73 using an extended ISCEV standard protocol that included an additional 9 Hz flicker stimulus for assessing rod function and special paradigms for isolated On–Off and S-cone responses. Correlation coefficients and best-fit regression models for each parameter's age-dependency were calculated. Results: Dark-adapted ERGs, in particular, displayed notable age-related alterations. The attenuation and delay of the b-wave with higher age were most significant in the dark-adapted, rod-driven 0.001 cd s/m2 flash ERG. The age-dependent reduction of the a-wave amplitude was strongest in the standard dark-adapted 3 cd s/m2 flash condition. Cone-driven, light-adapted responses to either flash or flicker stimuli displayed comparatively small alterations at higher age. S-cone function tended to diminish at an early age, but the effect was not significant in the whole population. Conclusion: The results suggest that rod and cone function decline at different rates with age, with rods being generally more affected by aging. Nonetheless, response amplitudes displayed a wide variability across the whole sample. [ABSTRACT FROM AUTHOR]

Porous tantalum metaphyseal cones may facilitate reconstructions of severe bone defects during revision total knee arthroplasty (TKA), but there remains a paucity of data on their outcomes at mean 5 years of follow-up. This study reports the component survivorship, patient satisfaction, functional outcomes, radiographic osseointegration, and complications of revision TKA with porous tantalum metaphyseal cones at mid-term (mean 5-year) follow-up. This study included 152 patients who had a mean age of 66 years (range, 33 to 86 years) undergoing revision TKA with porous tantalum metaphyseal cones. Indications for surgery included aseptic loosening (n = 87, 57.3%), second-stage reimplantation for infection (n = 42, 27.6%), osteolysis with well-fixed components (n = 20, 13.2%), and periprosthetic fracture (n = 3, 2.0%). Component survivorship, clinical outcomes, radiographic outcomes, and any complications were recorded. The mean follow-up time was 5.6 years (range, 2.2 to 13.7). Survivorship was 100% when the end point was revision of the metaphyseal cone (no cones were revised) and 83.8% (95% confidence interval: 77.9 to 90.2%) when the end point was reoperation for any reason at 5-year follow-up. Reoperations were performed for infection (n = 10), instability (n = 4), periprosthetic fracture (n = 2), and quadriceps rupture/dehiscence (n = 3). The mean patient satisfaction score was 78.8 ± 11.3 and the mean Forgotten Joint Score was 62.2 ± 16.7 at the final follow-up. The preoperative median University of California at Los Angeles score improved from 2 (interquartile range 2 to 3) to 6 points (interquartile range 5 to 6) (P <.001), and the preoperative Oxford knee score improved from 15.2 ± 3.8 to 39.4 ± 5.1 points (P <.001) at the final follow-up. All metaphyseal cones showed radiographic evidence of osteointegration without any subsidence or loosening. Porous tantalum metaphyseal cones enabled robust reconstructions of severe femoral and tibial bone defects during revision TKA. These reconstructions were associated with excellent survivorship, improvements in functional outcomes, and reproducible radiographic osseointegration at mean 5-year follow-up. The most common reasons for reoperation were infection and instability. [ABSTRACT FROM AUTHOR]

This paper is concerned with an inverse problem for steady potential hypersonic flow past a curved cone, for which we globally determine the curved cone with given uniform supersonic incoming flow and given shock position. Under suitable assumptions on given shock and given incoming flow, we construct the degenerate background solution for ρ∞ = 0 and establish its properties. Then, we apply scaling transformation and perturbation analysis to construct the global classical solution to the inverse problem for hypersonic incoming flow. [ABSTRACT FROM AUTHOR]

This work presents the idea of a symmetric Ncone metric space and explore the convergence properties of sequences within this framework. Furthermore, we show fixedpoint theorems for maps that satisfy certain contractive conditions and present examples to illustrate our point. Our findings complement, expand, and consolidate numerous established conclusions in the literature. [ABSTRACT FROM AUTHOR]

In this paper the authors consider the existence of positive solutions to a two point boundary value problem for nonlinear second-order impulsive systems. They use a vector version of Krasnosel'skii's fixed point theorem in cones in their proofs. Examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

In geometry, there are problems that if solved by conventional methods are very long and sometimes impossible to solve. But if you find a suitable configuration, solving problems will be much simpler. The following is a method to find a sphere inscribed in a cone to solve some advanced problems in geometry. This method allows combining the distance problem with the angle problem into an easily solvable tangent problem. [ABSTRACT FROM AUTHOR]

In this study, we investigate and propose an improved theoretical method to more accurately predict the performance of a field-emission electric propulsion (FEEP) thruster with its complex configuration. We identify critical flaws in the previous theoretical methods and derive corrected equations. Additionally, we define and implement the overall half angle of the Taylor cone to account for variations in the Taylor cone's half angle depending on the applied voltage. Next, we also establish an improved method of the electric filed simulation in a three-dimensional domain to accurately predict a trajectory of extracted ions and a resulting spatial beam distribution of the FEEP thruster by incorporating a configuration of the Taylor cone with the estimated overall half angle from the results of the present theoretical method. Through comparison with the experimental measurements, we found that the present improved methods for theoretical and electric field simulations can yield more accurate predictions than those of the previous methods, especially for higher V and Iem regimes, which correspond to the actual operating conditions of the FEEP thruster. Consequently, we anticipate that the proposed methods can enhance the reliability and efficiency of the design process by accurately predicting performance when developing the new FEEP thruster with its non-symmetric complex configuration to match specific thrust or spatial beam requirements. [ABSTRACT FROM AUTHOR]

The valley degree of freedom, as a new information carrier, is important for basic physical research and the development of advanced devices. Herein, using first-principle calculations, we predict that two-dimensional Hf2TeIX (X = I, Br) monolayers harbor intriguing valley properties. Without considering spin–orbit coupling (SOC), the Hf2TeI2 monolayer has a semi-metallic nature, with Dirac cones located at the high-symmetry point K, and feature, with considerable Fermi velocity. When the SOC is taken into account, a band gap opening of 271 meV can be observed at the Dirac cones. More interestingly, the Hf2TeIBr monolayer exhibits intrinsic spatial inversion symmetry breaking, which leads to the emergence of valley-contrasting physics under SOC. This is demonstrated by the presence of spin–valley splitting and opposite Berry curvature at adjacent K points. Besides, the spin–valley splitting, the band gap and magnitude of the Berry curvature of the Hf2TeIBr monolayer can be effectively tuned by strain engineering. These findings contribute significantly to the design of valleytronic devices and extend opportunities for exploring two-dimensional valley materials. [ABSTRACT FROM AUTHOR]

Objective/Background: Taxodium distichum (L.) Rich., a plant of the Cupressaceae family, is known for its leaves and cones rich in essential oils, which are traditionally used in folk medicine. This study employed hydrodistillation to extract essential oils from three parts of T. distichum, namely its leaves, twigs, and cones, and evaluated the yield and composition of these oils as well as their anti-mildew property on paper. Methods: The chemical compositions of the essential oils from the three parts were analyzed using gas chromatography with flame ionization detection (GC-FID) and gas chromatography mass spectrometry (GC-MS). The anti-mildew properties were assessed on paper against seven mold fungi, namely Aspergillus clavatus, A. niger, Chaetomium globosum, Cladosporium cladosporioides, Myrothecium verrucaria, Penicillium citrinum, and Trichoderma viride, following standards such as TAPPI T487 cm-93 and CNS 2690. Furthermore, the essential oil demonstrating the strongest anti-mildew properties was selected from the oils extracted from three different parts, underwent column chromatography for isolation, and the main active compounds were identified. Results: Among the three parts, cones had the highest essential oil yield (0.53 ± 0.03 mL/100 g), followed by leaves (0.46 ± 0.02 mL/100 g) and twigs (0.06 ± 0.01 mL/100 g). The main components were limonene (39.8%) and α-pinene (37.1%) in leaves; limonene (16.8%), α-pinene (15.8%), and ferruginol (11.0%) in twigs; and ferruginol (43.2%) and caryophyllene oxide (12.5%) in cones. The cone oils exhibited the most effective anti-mildew properties on paper. Furthermore, the cone oils were fractionated into six fractions (CO1–CO6), with the CO4 fraction exhibiting the best activity. CO4's main components were ferruginol, caryophyllene oxide, and β-caryophyllene. Ferruginol showed the best anti-mildew performance, with 100% inhibition at 200 μg/cm² for all strains. Conclusion: The study results indicated that essential oils from the cones of T. distichum and ferruginol exhibit promising anti-mildew effects on paper. Therefore, further research and development are highly warranted for their application in inhibiting fungal growth on paper. [ABSTRACT FROM AUTHOR]

Dirac cones are difficult to achieve in a square lattice with full symmetry. Here, we have theoretically investigated a bipartite tetragonal lattice composed of tetragons and octagons using both Tight-Binding (TB) model and density functional theory (DFT) calculations. The TB model predicts that the system exhibits nodal line semi-metallic properties when the on-site energies of all atoms are identical. When the on-site energies differ, the formation of an elliptical Dirac cone is predicted. Its physical properties (anisotropy, tilting, merging, and emerging) can be regulated by the hopping energies. An exact analytical formula is derived to determine the position of the Dirac point by the TB parameters, and a criterion for the existence of Dirac cones is obtained. The "divide-and-coupling" method is applied to understand the origin of the Dirac cone, which involves dividing the bands into several groups and examining the couplings among inter-groups and intra-groups. Various practical systems computed by DFT methods, e.g., t-BN, t-Si, 4,12,2-graphyne, and t-SiC, are also examined, and they all possess nodal lines or Dirac cones as predicted by the TB model. The results provide theoretical foundation for designing novel Dirac materials with tetragonal symmetry. [ABSTRACT FROM AUTHOR]

The magnetic field B induced along the axis of symmetry of axially magnetized cones was studied analytically and experimentally for various cone angles α. An explicit algebraic equation was derived for sharp-pointed and truncated cones. A sharp cone is characterized by singularities of B and ∇ B at its apex point. For a truncated cone, the maximum values of these quantities are achieved for α m a x ∼ 54.7 ° and α ∇ ∼ 39.2 ° , respectively. Two truncated cones with α u n i ∼ 63.4 ° positioned in a mirrored co-apex configuration produce a uniform axial field in the free-space gap. For smaller angles, the minimum field is located in the center of the airgap, while for larger, it is at the cones' surfaces with extremum at α m i n ∼ 71.6 °. These predictions were investigated using a tunable apparatus in which Co–Fe cones are magnetized by cylindrical NdFeB magnets. Strong ∼ 4 T B-field was achieved. Experimental results are discussed in detail, including incomplete magnetization and other secondary effects. [ABSTRACT FROM AUTHOR]

The northern boreal forest treeline is usually considered to be the result of climate limiting tree reproduction. Although climate also influences the cycling of nutrients, the effects of nutrient availability on the treeline have largely been ignored. Various animal activities can alter nutrient cycling, creating microsites of highly fertile soil. Red foxes (Vulpes vulpes) act as ecosystem engineers in the nutrient-poor northern boreal woodlands by concentrating soil nutrients through their denning activities, increasing white spruce (Picea glauca) tree growth. Here, we examined how denning activity affects reproduction in white spruce by determining the number cones per tree, seeds per cone (with or without endosperm, i.e., filled or not) and their viability. Overall, seed production in the study region was low, with an average of 3.7 filled seeds and 0.73 viable seeds per cone. Denning activity affected all stages of seed production, with trees on dens producing an average of two times more cones, three times more total seeds, four times more filled seeds, and 18 times more viable seeds than trees growing away from dens. While cone counts per tree were a good predictor of filled seeds per tree, they were less reliable at predicting viable seeds per tree. Additionally, the number of cones on a tree does not predict the number of filled seeds in a cone, making it difficult for granivores like squirrels and birds to assess food availability from cone abundance. Overall, these results suggest that nutrient availability can play a crucial role in tree reproduction at the treeline and denning activities can create hotspots of seed production and seed viability, acting as a potential food source for granivores and locations for tree reproduction.

This paper is dedicated to the study of the converse implication in Hilbert 17th problem for a general commutative ring. We introduce the notions of central and precentral prime cones which generalize the notion of central real points of irreducible real algebraic varieties. We study these families of prime cones which both live in the real spectrum of the ring and allow to state new Positivstellensätze and to obtain an equivalence in Hilbert 17th problem. [ABSTRACT FROM AUTHOR]

In this paper, we characterise point sets having the same intersection numbers with respect to hyperplanes as an ovoidal cone. In particular, we show that a set of points of PG(4,q) $\text{PG}(4,q)$ which blocks all planes and intersects solids in q+1 $q+1$, q2+1 ${q}^{2}+1$ or q2+q+1 ${q}^{2}+q+1$ points is a plane or an ovoidal cone, and determine all examples that arise when the blocking condition is omitted. [ABSTRACT FROM AUTHOR]

We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface M n ⊂ R n + 1 , 2 ≤ n ≤ 6 , with an isolated conical singularity is modeled on the level set flow of the cone. In particular, the flow fattens (instantaneously) if and only if the level set flow of the cone fattens. [ABSTRACT FROM AUTHOR]

Introduction: The potential neuroprotective and regenerative properties of electrical stimulation (ES) were studied in rhodopsin knockout mice (Rho-/-), a murine model of inherited retinal degeneration. The study focused on assessing the impact of varying ES frequencies on visual functions and photoreceptor cell survival in Rho-/- mice. Methods: To elucidate the impact of electrical stimulation on cone survival, Rho-/- mice received either sham or transpalpebral ES using biphasic ramp or rectangular waveforms at 100 µA amplitude, starting at six weeks of age. The treatment duration spanned from one to three weeks. The optimal treatment frequency of ES sessions was determined by applying ES every one, two, or three days in three separate groups of Rho-/- mice. The sham group received daily treatments without the application of ES. Results: Our study revealed significant improvement of visual function in Rho-/- mice following daily or every-other-day noninvasive transpalpebral ES, as evidenced by electroretinogram and optomotor response-based visual behavior assays. Concurrently, assessment of outer nuclear thickness and immunohistochemistry for the cone photoreceptor cell marker PNA demonstrated pronounced increases in the survival of rods and cones and improvement in the morphology of the inner and outer segments. Discussion: This study underscores the protective effect of non-invasive ES in rhodopsin knockout-induced retinal degenerative disorders, providing a foundation for developing targeted therapeutic interventions for retinitis pigmentosa. [ABSTRACT FROM AUTHOR]

Background: TheWagner Cone Prosthesis was designed to address complex femoral deformities during total hip arthroplasty (THA), but its mid-term component survivorship and functional outcomes remain undetermined. The objectives of this study were to determine the implant survivorship, patient satisfaction, functional outcomes, osseointegration as seen radiographically, implant subsidence, and complications of THA using the Wagner Cone Prosthesis stem at intermediate-term follow-up. Methods: This study involved 302 patients with proximal femoral deformities, including developmental hip dysplasia and Legg-Calv'e-Perthes disease, who underwent a total of 320 primary THAs using the Wagner Cone Prosthesis. The average age at the time of surgery was 49.4 ± 14.5 years (range, 18.8 to 85.6 years). Patient satisfaction was recorded using a self-administered questionnaire assessing satisfaction in 4 domains. The University of California at Los Angeles (UCLA) activity score, the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), the Oxford Hip Score (OHS), the Forgotten Joint Score (FJS), radiographic outcomes, and complications were recorded. The mean follow-up time was 10.1 years (range, 5.2 to 15.5 years). Results: Survivorship of the Wagner Cone Prosthesis was 98.7% (95% confidence interval [CI]: 97.2% to 100%) with stem revision as the end point and 95.8% (95% CI: 93.5% to 98.2%) with reoperation for any reason as the end point at 10 years postoperatively. In total, 3 stems were revised: 2 for infection and 1 for chronic hip dislocation. The median patient satisfaction score was 95 (interquartile range [IQR], 80 to 100), median UCLA score was 6 (IQR, 6 to 7), median WOMAC score was 18 (IQR, 16 to 22), median OHS was 40 (IQR, 36 to 47), and median FJS was 80 (IQR, 76 to 88) at the time of final follow-up. All Wagner Cone stems that were not revised showed radiographic evidence of osseointegration, with a mean stem subsidence of 0.9 ± 0.8 mm at the most recent follow-up. Conclusions: The use of the Wagner Cone Prosthesis stem in patients with complex femoral anatomy undergoing primary THA is associated with excellent component survivorship, high levels of patient satisfaction, good functional outcomes, and reliable osseointegration with minimal stem subsidence as seen on radiographs at intermediate-term follow-up. Level of Evidence: Therapeutic Level IV. See Instructions for Authors for a complete description of levels of evidence. [ABSTRACT FROM AUTHOR]

Vision plays a crucial role in the survival of animals, and the visual system has particularly selectively evolved in response to the visual environment, ecological niche, and species habitats in vertebrate species. To date, a horizontal streak of retinal ganglion cell (RGC) distribution pattern is observed across mammal species. Here, we report that the giant panda's vertically oriented visual streak, combined with current evidence of the animal's forward‐placed eyes, ocular structure, and retinal neural topographic distribution patterns, presents the emergence of a well‐adapted binocular visual system. Our results suggest that the giant panda may use a unique way to processing binocular visual information. Results of mathematical simulation are in favor of this hypothesis. The topographic distribution properties of RGCs reported here could be essential for understanding the visual adaptation and evolution of this living fossil. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fourth-order three-point boundary value problem. Despite the fact that the corresponding Green's function changes its sign on the square of its definition, we obtain the existence of at least one positive and decreasing solution under some suitable conditions. The results are based on the classical Krasosel'skii's fixed point theorem in cones. Then, we impose some sufficient conditions that allow us to deduce nonexistence results. In the end, some examples are given in order to illustrate our main results. [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]

A predator-prey model with prey-taxis under homogeneous Dirichlet boundary conditions was established. Based on the prior estimate of positive solutions, the asymptotic stability of trivial and semi-trivial solutions was obtained by using the eigenvalue theory of linearization operators and spectral theory. The existence of positive steady-state solutions was established using the fixed point index theory in a cone. By analyzing two related eigenvalues, the coexistence region with respect to the growth rates of two species was obtained. The results show that prey-taxis has an obvious influence on the steady-state solutions. [ABSTRACT FROM AUTHOR]

The objective of this study was to evaluate the relationship between the excision type and the persistence/recurrence of CIN2–3. A total of 227 women with CIN2–3 who were treated with LLETZ were evaluated. The types of excision according to the IFCPC 2011, volume, cone dimensions, margins of resection, post-cone high-risk human papillomavirus (HR-HPV) status, and viral load were studied. The time to recurrence was assessed using Kaplan–Meier curves. Persistent/recurrent CIN2–3 was found in 12 cases (5.2%). Type 1 excision was performed in 107 patients, with 7 recurrences (6.5%); type 2 excision in 74 patients, with 4 recurrences (5.4%); and type 3 excision in 46 patients, with 1 recurrence (2.1%). The percentage of clear margins in type 1 excisions was 44.9%, that in type 2 excisions was 59.5%, and that in type 3 excisions was 69.6% (p = 0.008). Type 1 excision was associated with 28.5% post-LLETZ HR-HPV positivity, that in type 2 reached 20.6%, and that in type 3 reached 11.4%; this difference was non-significant (p = 0.24). (4) Conclusions: Type 3 excision was associated with a larger proportion of clear margins and lower post-cone HR-HPV positivity, with a lower incidence of the persistence/recurrence of CIN2–3. [ABSTRACT FROM AUTHOR]

A new study aims to clarify the analytical and mathematical dimensions of the tangent hyperbolic fluid through the plate and cone with useful uses in technical devices like the handling of biomass pyrolysis and viscometer. The presence of chemical process and mixed convection in the natural characteristics of liquid is taken into account. By implementing the homotopy analysis approach, the achieved coupling system is inspected. The influence of the flow control variables on the related profiles is evaluated quantitatively and qualitatively in order to get a full understanding of the current pagination. Through the deep study, it is calculated that convective thermal and surface drag factor for the plate is greater in magnitude than for the cone. The superiority is also observed for the plate in the thermal field relative to that in the cone. The results shows that the heat transfer improves as Hartmann number (M) and Brownian motion factor (Nt) increase but it decreases with an increase of thermophoresis factor (Nb). Also it can be found that effect of drag coefficient is more pronounced or higher for cone as compared to plate. [ABSTRACT FROM AUTHOR]

Although hinged prostheses have been used successfully in complex revision total knee arthroplasty (TKA), concerns exist regarding early failure due to aseptic loosening and other mechanical complications. The use of metaphyseal cones and hybrid cement fixation have been studied in unlinked constrained primary or revision TKA, but their impact on the survivorship of hinged prostheses has yet to be investigated. We identified a consecutive series of 164 hinged prostheses and collected data on demographics, indications, complications, and re-revisions in patients who had fully cemented versus hybrid stems, with and without metaphyseal cones. A multivariate analysis was performed to identify independent variables associated with re-revision as the primary end point. In total, 84 patients (51.2%) had fully cemented stems, and 80 patients (48.8%) had hybrid stems. Cones were used in 73 patients (44.5%). At a mean follow-up of 3.4 ± 2.2 years, 42 patients underwent re-revision (25.8%), most commonly for infection (12.2%), followed by loosening (6.7%) and periprosthetic fracture (3.7%). Patients who had fully cemented stems had lower re-revision rates than hybrid fixation constructs (19 versus 26%, P =.043). Using multivariable regression, a construct with hybrid fixation with cones (odds ratio = 2.39; P =.037) was an independent risk factor for failure. Utilization of cones alone did not have an effect on re-revision rates at 3.4-year follow-up. While we found no difference with the use of cones, patients undergoing revision TKA with a hinge prosthesis and fully cemented stems had better overall survivorship than hybrid stems. [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]

We prove that |$\omega \Delta ^{\prime}_{e_{k}}e_{n}|_{t=0}$|⁠ , the symmetric function in the Delta Conjecture at |$t=0$|⁠ , is a skewing operator applied to a Hall-Littlewood polynomial, and generalize this formula to the Frobenius series of all |$\Delta $| -Springer modules. We use this to give an explicit Schur expansion in terms of the Lascoux-Schützenberger cocharge statistic on a new combinatorial object that we call a battery-powered tableau. Our proof is geometric, and shows that the |$\Delta $| -Springer varieties of Levinson, Woo, and the second author are generalized Springer fibers coming from the partial resolutions of the nilpotent cone due to Borho and MacPherson. We also give alternative combinatorial proofs of our Schur expansion for several special cases, and give conjectural skewing formulas for the |$t$| and |$t^{2}$| coefficients of |$\omega \Delta ^{\prime}_{e_{k}}e_{n}$|⁠. [ABSTRACT FROM AUTHOR]

The numerical investigation regarding the impact of Hall current and non-linear slip on the flow of hybrid nanofluid past a vertical rotating cone is carried out in the present study. Each hybrid nanofluid comprises two nanoparticles and two base fluids such as water and sodium alginate. The numerical solution is devised by Fourth order Runge-Kutta scheme cum shooting technique. The obtained outcomes are that tangential velocity and swirl velocity ameliorate subject to rise in magnetic parameter and Hall parameter for water and sodium alginate based hybrid nanofluids. Tangential and swirl velocities exhibit opposite subject to non-linear slip condition. Heat transfer rate attains greatest magnitude for TiO2 + Cu/H2O hybrid nanofluid among all the remaining hybrid nanofluids. [ABSTRACT FROM AUTHOR]

The pull-off of a sphere from an elastic substrate follows the well-known JKR solution, and a similar but less known solution is valid for a cone. The two differ qualitatively in the parametric dependences of the pull-off load, so we study the case of a viscoelastic substrate using a well-known Gent and Schultz approach for the effective work of adhesion, with the assumption that the elastic modulus in the bulk of the specimen is the relaxed one. The rate of peeling of the contact line (for given remote withdrawing speed) depends on elastic modulus for the spherical case, and not for the cone. However, for the spherical geometry, we predict that the highest load amplification should be actually smaller than the highest work of adhesion amplification, while for the cone the opposite is true, although of a smaller factor. [ABSTRACT FROM AUTHOR]

Perceiving direct gaze — the perception of being looked at — is important in everyday life. The gaze cone is a concept to define the area in which observers perceive gaze as direct. The most frequently used methods to measure direct gaze threshold fall into two broad groups: First, a variant of the method of constant stimuli, firstly introduced by Gibson and Pick (The American Journal of Psychology, 76, 386–394, 1963). Second, a variant of the method of adjustment, firstly introduced by Gamer and Hecht (Journal of Experimental Psychology: Human Perception and Performance, 33, 705–715, 2007). Previous studies found a considerable range of thresholds, and although some influences on thresholds are already known (uncertainty, clinical groups), thresholds often vary for no apparent reason. Another important method is a triadic gaze-perception task, which usually finds triadic gaze direction judgments to be overestimated. In two experiments, we compare the method of adjustment with the method of constant stimuli. Experiment 1 additionally examines the influence of the overestimation effect found in the triadic task. Results indicate that thresholds are larger when measured by the method of adjustment than by constant stimuli. Furthermore, Experiment 1 finds a nonlinear overestimation factor, indicating that gaze directions near 0° are less overestimated than larger eccentricities. Correcting the thresholds with individually obtained overestimation factors widens the gaze cone but does not eliminate the average difference between the methods of adjustments and constant stimuli. [ABSTRACT FROM AUTHOR]

In this paper, we analyze minimal representations of (p, α)-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case α and p are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location. [ABSTRACT FROM AUTHOR]

Introduction/purpose: This article introduces the concept of revised fuzzy cone contraction by using the concept of a traiangular conorm and Revised Fuzzy Cone contractive conditions. Methods: This article established new Revised Fuzzy Cone Contraction (RFC-C) type unique coupled Fixed Point theorems (FP theorems) in revised fuzzy cone metric spaces (RFCMS) by using the triangular property of RFCMS. Results: The obtained results on fixed points in revised fuzzy cone metric spaces generalize some known results in the litrature and present illustrative examples to support the main work. Conclusion: The RFC contractive conditions generalize some important contraction types and examine the existence of a fixed point in revised fuzzy cone metric spaces. In addition, the Lebesgue integral type mapping is applied to get the existence result of a unique coupled fixed point in RFCMS to validate the main work. [ABSTRACT FROM AUTHOR]

This paper describes a Pennsylvanian lycophyte cone collected from a highway cut along the southbound lanes of U.S. Interstate Highway 24 (I-24) north of Vienna, Illinois (USA) and stratigraphically belonging to the basal Tradewater Formation, under the Reynoldsburg Coal Bed (upper Bashkirian, lowermost Pennsylvanian). The cone is incomplete, more than 135 mm long and 26 mm wide, mainly representing the distal part with a missing base. The in situ spores from the cone represent trilete cingulizonate microspores belonging to the Lycospora brevijuga Group. Based on these spores together with morphological characters, the cone was compared with already existing species and differs sufficiently to warrant establishing a new species, here named Lepidostrobus willardii sp. nov. • Key words: Lepidostrobus, Lycospora, Tradewater Formation, Pennsylvanian, Illinois Basin. [ABSTRACT FROM AUTHOR]

The moduli space Y=Y(E6)$Y = Y(E_6)$ of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth‐century work of Cayley and Salmon. Modern interest in Y$Y$ was restored in the 1980s by Naruki's explicit construction of a W(E6)$W(E_6)$‐equivariant smooth projective compactification Y¯${\overline{Y}}$ of Y$Y$, and in the 2000s by Hacking, Keel, and Tevelev's construction of the Kollár–Shepherd‐Barron–Alexeev (KSBA) stable pair compactification Y∼${\widetilde{Y}}$ of Y$Y$ as a natural sequence of blowups of Y¯${\overline{Y}}$. We describe generators for the cones of W(E6)$W(E_6)$‐invariant effective divisors and curves of both Y¯${\overline{Y}}$ and Y∼${\widetilde{Y}}$. For Naruki's compactification Y¯${\overline{Y}}$, we further obtain a complete stable base locus decomposition of the W(E6)$W(E_6)$‐invariant effective cone, and as a consequence find several new W(E6)$W(E_6)$‐equivariant birational models of Y¯${\overline{Y}}$. Furthermore, we fully describe the log minimal model program for the KSBA compactification Y∼${\widetilde{Y}}$, with respect to the divisor KY∼+cB+dE$K_{{\widetilde{Y}}} + cB + dE$, where B$B$ is the boundary and E$E$ is the sum of the divisors parameterizing marked cubic surfaces with Eckardt points. [ABSTRACT FROM AUTHOR]

Objective: Both porous metal cones and metaphyseal sleeves are excellent implants for reconstructing severe bone defects in the knee joint, but they both exhibit design limitations. The porous metal cone, especially, has significant room for improvement in its shape design. The existing porous metal cones often feature a conical external surface with a relatively small taper, potentially compromising both rotational and axial stability. To improve both axial and rotational stability in porous metal cones, we developed a 3D‐printed stepped porous metal cone. This study aimed to assess the short‐term clinical outcome of the 3D‐printed stepped porous metal cone and to compare it with the clinical outcome of patients who underwent revision total knee arthroplasty (rTKA) with the metaphyseal sleeves during the same period. Method: Patients who underwent total knee arthroplasty revision with metaphyseal bone defect reconstruction from 2019 to 2021 were retrospectively analyzed. A total of 61 patients were enrolled in the study, including 15 patients using 3D‐printed stepped porous metal cones and 46 patients using metaphyseal metal sleeves. Thirty patients using metaphyseal sleeves were screened by propensity score matching method and compared with those using stepped cones. Analysis included the American Knee Society Score, the Hospital for Special Surgery knee score, the Western Ontario and McMaster Universities Arthritis index, the Short Form 12 (SF‐12) health survey, and radiographic assessment with a mean follow‐up of 28.5 ± 8.3 months. To conduct comparative analyses, unpaired Student's t‐tests were employed for continuous variables, while categorical variables were analyzed using the appropriate Fisher exact or chi‐squared test. Results: In this study, the survival rates of both the stepped cone and metaphyseal sleeve were 100%. There was no statistically significant difference in postoperative knee function scores between the two groups (p > 0.05). However, patients in the cone group had significantly higher mental component summary scores on the SF‐12 scale (p < 0.05) and higher increases in mean postoperative physical component summary scores than patients in the sleeve group (p < 0.05). In addition, patients in the cone group experienced fewer intraoperative and postoperative complications compared to the sleeve group. Conclusion: The 3D‐printed stepped porous metal cone can effectively reconstruct bone defects in complex rTKA and provide satisfactory early clinical and radiographic results. The 3D‐printed stepped cone provides a more stable structure similar to the sleeve while maintaining the original benefits of the cone making it a promising choice for rTKA. [ABSTRACT FROM AUTHOR]

The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier. [ABSTRACT FROM AUTHOR]