Properties Of Cones Research Articles

Beyond The Sphere. Au20(PR3)8 as a Spherical Aromatic Cuboctahedron Cluster.

The icosahedral Au135+ core is a recurrent building block in ligand-protected gold clusters involving an 8-cluster electron 1S21P6 electronic shell. Such a prototypical structure enables a spherical aromatic behavior as given by long-range magnetic shielding. Recently, the Au20(tBu3P)8 cluster featuring a contrasting cuboctahedral core with formally neutral gold atoms appears as a novel core architecture with the potential to be considered as another potential building block towards functional nanostructures. Here, we explore the ligand-core interaction and spherical aromatic characteristics of Au20(tBu3P)8, in order to provide a direct connection to classical icosahedral spherical aromatic compounds, now involving a cuboctahedral core structure. Such characteristics suggest rationalization of their robustness in terms of certain electron counts, enabling a shielding cone property in ligand-protected metallic clusters, which favors bridging organic and inorganic planar/spherical aromatic species towards the unification of the aromaticity concept and designing guidelines for further achievements.

Exploring the sedative properties of natural molecules from hop cones (Humulus lupulus) as promising natural anxiolytics through GABA receptors and the human serotonin transporter.

This research work aimed to identify the main components that are responsible for the sedative properties of hop cones and allocate their targets. This investigation was performed through molecular docking, molecular dynamic simulations, root mean square fluctuation (RMSF) analysis, and DFT calculation techniques. The tested compounds from Humulus lupulus were compared to diazepam and paroxetine. Molecular docking showed that two-thirds of the compounds had a good affinity to gamma-aminobutyric acid (GABA), outperforming diazepam, while only three surpassed paroxetine on the SERT. Compounds 3,5-dihydroxy-4,6,6-tris(3-methylbut-2-en-1-yl)-2-(3-methylbutanoyl)cyclohexa-2,4-dien-1-one (5) and (S,E)-8-(3,7-dimethylocta-2,6-dien-1-yl)-5,7-dihydroxy-2-(4-hydroxyphenyl)chromen-4-one (15) showed stable binding and favorable energy parameters, indicating their potential for targeting GABA receptors and the SERT. This study provides a basis for future clinical research on these promising compounds.

Low-error, high-speed, and large-scale hardware implementation of retinal photoreceptor cells: Cone and rod cells

In recent times, there has been a significant focus on creating prosthetics and medical interventions to aid in the treatment of diseases, recovery, and the improvement of biological functions. Researchers have particularly directed their attention toward developing hardware models for delicate biological parts such as the brain, heart, nervous system, and. One area of particular interest is the retina, which is the thinnest and innermost layer of the eye. This research paper focuses on the development of a high-speed and low-error hardware implementation for retinal cone and rod cells. Current mathematical models often use multiple nonlinear functions to describe the behavior of these cells. However, these nonlinear functions can sometimes be limiting in terms of speed. In this study, we explore the use of trigonometric functions to approximate the non-linear properties of retinal cone and rod cells, allowing for improved performance. The results of the simulation show that the suggested model is in line with the functioning of primary cone and rod cells, particularly in relation to time characteristics, dynamic response, and margin of error. By implementing the proposed model in Large-Scale (300 cell) on a Virtex-5 Field Programmable Gate Array (FPGA) board, notable benefits were observed. One of these advantages includes increasing the synthesis frequency of the proposed model by 3.35 and 3.44 times faster than the original model for the cone cell and rod cell, respectively. Another advantage is the ability to implement 300 cells of the proposed models on the FPGA, compared to the implementation of a single cell of the original models, with only a two-fold increase in the amount of hardware resources used. The proposed framework is legitimate and features a compact hardware size and suitable network frequency, as demonstrated by the outcomes from implementing the hardware on the Virtex-5 reconfigurable board (FPGA).

Exponential stability of periodic solutions for a hematopoiesis model with two time delays

In applied mathematics, many practical problems involving heat flow, species interaction, microbiology, neural networks, and more are associated with delay differential equations. To elucidate regulation and control mechanisms in physiological systems, Mackey and Glass introduced new mathematical models as a representation of hematopoiesis (blood-cell formation) in their influential and highly referenced 1977 paper. The presence of multiple delays, rather than a single delay, can lead to a new range of dynamics: an equation that was stable with one delay may become unstable when the delays are not equal, resulting in sustained oscillations. The dynamics of the non-autonomous Mackey-Glass model with two variable delays have not been thoroughly explored yet, which is presented as an open problem by Berezansky and Braverman. This paper focuses on the existence, uniqueness, and exponential stability of positive periodic solutions of a generalized class of the Hematopoiesis Model with two variable delays. Initially, using properties of cones and a fixed point theorem for a concave and increasing operator, we establish conditions ensuring the existence of a unique positive periodic solution for the model with almost periodic coefficients and delays. Subsequently, we employ a suitable Lyapunov functional method and differential inequality techniques to derive sufficient conditions guaranteeing the exponential stability of the unique positive periodic solution of the system. This approach covers a broad range of models that were previously studied. Additionally, an illustrative example with a numerical simulation is provided to validate the efficiency and reliability of the theoretical results. Our approach can be applied to the case of positive almost periodic solutions and positive pseudo almost periodic solutions of the model under consideration.

Nontrivial solutions for resonance quasilinear elliptic systems

Abstract We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically ( p , q ) \left(p,q) -linear at infinity. The proof relies on a cohomological linking in a product Banach space where the properties of cones of the sublevels are missing, differently from the single quasilinear equation. We also perform critical group computations of the energy functional at the origin, in spite of the lack of its C 2 {C}^{2} regularity, to exclude that the found mini-max solution is trivial. Finally, we furnish a local condition which guarantees that the found solution is not semi-trivial.

Partner Curves in Three Dimensional Degenerated Space Form

Using elementary and effective methods we study cone curves and their associated curves or partner curves in the three dimensional lightlike cone $\Q^3$, which is called three dimensional degenerated space form of the four dimensional Minkowski space $\E^4_1$. We define the associated curve of the cone curve and also partner curves of some special curves, such as a Bertrand curve and a Mannheim curve. We consider the properties and relations of a curve and its associated curve or partner curve. Some geometric characterizations of these curves are also given.

Optimal boundary control for a competitive population system with size structure and time delay in a polluted environment

In this paper, we consider the optimal boundary control problem of a two-species competitive system with time delay and size structure in a polluted environment. First, the well posedness of the system is studied by using the characteristic line method and the fixed point principle. Second, the necessary conditions for optimal boundary control are obtained by conjugate system and normal cone property. Finally, the existence and uniqueness of the optimal strategy are proved by Ekeland variational principle.

Interior point algorithm for second-order cone optimization based on a new kernel function

Second-order cone optimization (SOCO) problems are crucial in various fields such as engineering, finance, and machine learning due to their ability to model complex convex optimization tasks efficiently. In this article, we propose an interior point algorithm tailored for SOCO, leveraging a novel kernel function to enhance optimization performance. Traditional interior point methods for SOCO often encounter challenges in scalability and efficiency, particularly with large-scale problems. These methods typically rely on barrier functions that may suffer from slow convergence rates, especially when dealing with highly ill-conditioned or degenerate cones. To address these limitations, our approach introduces a new kernel function that exploits the geometric properties of second-order cones, thereby improving convergence behavior and computational efficiency. The key innovation of our algorithm lies in the construction of the kernel function, which incorporates insights from the structure of second-order cones to efficiently capture the curvature information of the optimization problem. By exploiting this curvature information, our algorithm can effectively navigate the optimization landscape, leading to faster convergence and enhanced robustness compared to traditional methods. Furthermore, our algorithm is equipped with advanced techniques for handling various challenges encountered in SOCO, such as dealing with degenerate cones and exploiting problem structure to accelerate convergence. Additionally, we incorporate strategies for warm-starting and adaptive step-size selection to further improve efficiency, particularly in iterative optimization processes. Finally, our proposed interior point algorithm for second-order cone optimization, based on a new kernel function, derives the iteration bounds O (Nlog (N/∊)) for large update methods. Here denotes N the number of second-order cones in the problem formulation and ∊ the desired accuracy. These iteration bounds are currently the best known bounds for such methods.

Genetic programming to understand the influence of new sustainable powder materials in the fresh performance of cement pastes

This study focused on pastes that incorporate metakaolin, biomass ash, and granite powder as supplementary cementitious materials to obtain specific expressions to predict rheological properties in pastes and to define the most appropriate dosage parameters using genetic programming. For this purpose, a dataset was developed following a central composite design, and some fresh properties were measured: Marsh cone and rheological properties, such as yield stress and plastic viscosity. The models generated by genetic programming presented robust statistical indices for the properties studied. The influence of supplementary cementitious materials on rheological properties was also analysed through a parametric analysis. After analysing the factors affecting paste rheology, it was concluded that the most important aspects affecting fresh behaviour were water demand and particle interaction, as well as the relation between both effects.

The Shock Cone Instabilities and Quasi-Periodic Oscillations around the Hartle–Thorne Black Hole

To explain the observed X-ray data in a black hole–accreting matter system and understand the physical mechanisms behind QPOs, we have numerically modeled the dynamical and oscillation properties of the shock cone formed around both slowly and rapidly rotating Hartle–Thorne black holes, resulting from the mechanism of Bondi–Hoyle–Lyttleton (BHL). According to the numerical simulations, an increase in the quadrupole parameter leads to a decrease in the shock cone opening angle around the black hole. A larger quadrupole parameter results in more matter falling into the black hole within the cone. The combination of the quadrupole parameter and black hole rotation causes the matter inside the cone to exhibit chaotic motion. These dynamical changes and chaotic behavior of the shock cones excite the fundamental oscillation modes. Moreover, new frequencies have been formed due to the nonlinear coupling of the fundamental modes. Conversely, we have numerically studied the behavior of cones formed around rapidly rotating Hartle–Thorne black holes and found differences and similarities to those obtained from slowly rotating cases. Finally, comparing the outcomes obtained fromHartle–Thorne gravity with the results fromKerr and Einstein–Gauss–Bonnet (EGB) gravities reveals the impact of the quadrupole parameter on the shock cone and QPOs.

Minimum intensity projection of embossed quadrant-detection images for improved photoreceptor mosaic visualisation.

Non-confocal split-detection imaging reveals the cone photoreceptor inner segment mosaic in a plethora of retinal conditions, with the potential of providing insight to ageing, disease, and response to treatment processes, in vivo, and allows the screening of candidates for cell rescue therapies. This imaging modality complements confocal reflectance adaptive optics scanning light ophthalmoscopy, which relies on the waveguiding properties of cones, as well as their orientation toward the pupil. Split-detection contrast, however, is directional, with each cone inner segment appearing as opposite dark and bright semicircles, presenting a challenge for either manual or automated cell identification. Quadrant-detection imaging, an evolution of split detection, could be used to generate images without directional dependence. Here, we demonstrate how the embossed-filtered quadrant-detection images, originally proposed by Migacz etal. for visualising hyalocytes, can also be used to generate photoreceptor mosaic images with better and non-directional contrast for improved visualisation. As a surrogate of visualisation improvement between legacy split-detection images and the images resulting from the method described herein, we provide preliminary results of simple image processing routines that may enable the automated identification of generic image features, as opposed to complex algorithms developed specifically for photoreceptor identification, in pathological retinas.

Minimal piecewise linear cones in $\mathbb{R}^4$

We consider three dimensional piecewise linear cones in $\mathbb{R}^4$ that are mass minimal with respect to Lipschitz maps in the sense of [Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165] as in [Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489–539]. There are three that arise naturally by taking products of $\mathbb{R}$ with lower dimensional cases and earlier literature has demonstrated the existence of two with 0-dimensional singularities. We classify all possible candidates and demonstrate that there are no piecewise linear minimizers outside these five.

Cone property and measure density condition

Cone property and measure density condition

Intercluster B-H and B-B aggregation in iso- and trans-[B20H18]2-. Spherical aromaticity in borane dimers.

The formation of molecular-based functional materials is a key step towards the development of technologies at the nanoscale. Recently, it has been shown that after oxidation of closo-[B10H10]2- anions, an induced aggregation of two cluster units is achieved, retaining their parent B10 backbones as persistent building blocks. Such characterization provides an interesting scenario to further understand relevant factors leading to aggregation in a minimal structure involving two units. Here, we explore the interaction between closo-[B10H10]2- units in two isomers, namely, iso- and trans-[B20H18]2-, involving different intercluster contacts based on B-B and B-H interactions, respectively. Our results show that the inherent spherical aromatic characteristics of the parent closo-[B10H10]2- cluster are persistent in both iso- and trans-[B20H18]2- isomers as an interplay between the spherical aromatic properties from both B10 motifs, leading to an overlap of the shielding regions from shielding cone properties, ascribed as a dual spherical-spherical aromatic cluster. From 11B-NMR features, it came out that trans-[B20H18]2- involves larger differences in comparison to closo-[B10H10]2-, owing to the variation of the B10-B10 backbone provided by the intercluster B-interaction, thus resulting in a more effective aggregation connecting such building units, towards boron-based cluster materials.

Frictional properties of red pine cones harvested under different conditions

The climbing of trees to pick pinecones is a high-risk exercise. In this study, a mechanical gripper jaw was designed. Frictional characteristics between the pinecones and the mechanical gripper jaw during pinecone picking under different conditions were investigated using a workbench simulation, homemade inclined friction meter, and mass tester. Three-level orthogonal and one-factor tests were conducted. The relationship between the water content and friction properties and between the water content and hardness were investigated, and conclusions were drawn on how water content affected friction properties by influencing hardness. The results showed that the contact material greatly affected the friction properties. The pinecone water content was maintained between 24% and 28% to ensure that the coefficient of friction was maximized and that the pinecones were sufficiently hard to dislodge. Additionally, a prototype machine was used to perform pinecone-gripping experiments to validate the experimental and simulation results. Consequently, the results of this study provide a useful reference for the structural design of pinecone picking robots and the picking reason.

Euclidean volumes of hyperbolic knots

The hyperbolic structure on a 3 3 –dimensional cone–manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an algebraic number, which is reminiscent of Sabitov’s theorem (the Bellows Conjecture). This fact also stands in contrast to hyperbolic volumes whose number–theoretic nature is usually quite complicated.

Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space

In this paper Gaussian, Mean and total curvature formulae of Rational Bezier Curves with asymptotic frame field are calculated by using its curvatures in 3- dimensional lightlike cone in Minkowski 4- Space. Our main intention is to introduce and investigate some differential geometric properties of the the Rational Bezier Curves with asymptotic frame field in 3- dimensional lightlike cone in Minkowski 4- Space by using its curvatures.

The preliminary in vitro study and application of deep learning algorithm in cone beam computed tomography image implant recognition

To properly repair and maintain implants, which are bone tissue implants that replace natural tooth roots, it is crucial to accurately identify their brand and specification. Deep learning has demonstrated outstanding capabilities in analysis, such as image identification and classification, by learning the inherent rules and degrees of representation of data models. The purpose of this study is to evaluate deep learning algorithms and their supporting application software for their ability to recognize and categorize three dimensional (3D) Cone Beam Computed Tomography (CBCT) images of dental implants. By using CBCT technology, the 3D imaging data of 27 implants of various sizes and brands were obtained. Following manual processing, the data were transformed into a data set that had 13,500 two-dimensional data. Nine deep learning algorithms including GoogleNet, InceptionResNetV2, InceptionV3, ResNet50, ResNet50V2, ResNet101, ResNet101V2, ResNet152 and ResNet152V2 were used to perform the data. Accuracy rates, confusion matrix, ROC curve, AUC, number of model parameters and training times were used to assess the efficacy of these algorithms. These 9 deep learning algorithms achieved training accuracy rates of 100%, 99.3%, 89.3%, 99.2%, 99.1%, 99.5%, 99.4%, 99.5%, 98.9%, test accuracy rates of 98.3%, 97.5%, 94.8%, 85.4%, 92.5%, 80.7%, 93.6%, 93.2%, 99.3%, area under the curve (AUC) values of 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00. When used to identify implants, all nine algorithms perform satisfactorily, with ResNet152V2 achieving the highest test accuracy, classification accuracy, confusion matrix area under the curve, and receiver operating characteristic curve area under the curve area. The results showed that the ResNet152V2 has the best classification effect on identifying implants. The artificial intelligence identification system and application software based on this algorithm can efficiently and accurately identify the brands and specifications of 27 classified implants through processed 3D CBCT images in vitro, with high stability and low recognition cost.

The unique tangent cone property for weakly holomorphic maps into projective algebraic varieties

The unique tangent cone property for weakly holomorphic maps into projective algebraic varieties

Analogues of Poisson-type limit theorems in discrete bm-Fock spaces

In this paper, we present analogues of the Poisson limit distribution for the noncommutative bm-independence, which is associated with several positive symmetric cones. We construct related discrete Fock spaces with creation, annihilation and conservation operators, and prove Poisson type limit theorems for them. Properties of the positive cones, in particular the volume characteristic property they enjoy, and the combinatorics of labeled noncrossing partitions, play crucial role in these considerations.