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In this paper, we study the existence of positive odd 2π-periodic solutions for second-order ordinary differential equations { − u ″ (t) = f (t , u (t) , v (t) , u ′ (t)) , t ∈ [ 0 , 2 π ] , − v ″ (t) = g (t , u (t) , v (t) , v ′ (t)) , t ∈ [ 0 , 2 π ] , u (0) = u (2 π) , u ′ (0) = u ′ (2 π) , v (0) = v (2 π) , v ′ (0) = v ′ (2 π) , where f , g : [ 0 , 2 π ] × R + × R + × R → R + are continuous, and f , g are 2π-periodic in t. Under the conditions that nonlinear terms f (t , x , y , p) and g (t , x , y , q) may be superlinear or sublinear growth on x , y , p and q as | (x , y , p) | → 0 , | (x , y , q) | → 0 or | (x , y , p) | → ∞ , | (x , y , q) | → ∞ . The existence results of positive periodic solutions are obtained, our proof is based on the fixed point index theory in cones. Finally, two examples are given to illustrate the applicability of the conclusions of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of nonnegative solutions to a fourth order singular boundary value problem at two points. Our result is based on a recent Birkhoff-Kellogg type fixed point theorem developed on translates of a cone on a Banach space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of multiple positive symmetric solutions for fourth order $\mathrm{p}$-Laplacian iterative system with integral boundary conditions. Initially, we establish the existence of at least one and two positive symmetric solutions for the fourth order problem using Krasnosel’skii fixed point theorem. Subsequently, we establish the existence of at least three positive symmetric solutions by applying five-functionals fixed point theorem.

Feedback at the photoreceptor synapse is the first neuronal circuit computation in vision, which influences downstream activity patterns within the visual system. Yet, the identity of the feedback signal and the mechanism of synaptic transmission are still not well understood. Here, we combined perturbations of cell-type-specific genes of mouse horizontal cells with two-photon imaging of the result of light-induced feedback in cones and showed that the electrogenic bicarbonate transporter Slc4a5, but not the electroneutral bicarbonate transporter Slc4a3, both expressed specifically in horizontal cells, is necessary for horizontal cell-to-cone feedback. Pharmacological blockage of bicarbonate transporters and buffering pH also abolished the feedback but blocking sodium-proton exchangers and GABA receptors did not. Our work suggests an unconventional mechanism of feedback at the first visual synapse: changes in horizontal cell voltage modulate bicarbonate transport to the cell, via Slc4a5, which leads to the modulation of feedback to cones. [Display omitted] • Feedback from horizontal cells to cones was measured by imaging calcium in cones • Slc4a5 is an electrogenic Na+-HCO 3 − cotransporter specific to horizontal cells • Knocking out or down Slc4a5 abolished horizontal cell-to-cone feedback • Blocking HCO 3 − transporters and buffering pH also abolished feedback Molecular mechanisms of horizontal cell-to-cone feedback in the retina have been under debate. Morikawa et al. show that Slc4a5, an electrogenic sodium-bicarbonate cotransporter specific to horizontal cells, is crucial for feedback. They suggest that Slc4a5, through its voltage-dependent transport of bicarbonate, regulates pH in the synaptic cleft that mediates feedback. [ABSTRACT FROM AUTHOR]

This article argues that the early Barth made too little of the concrete in a theologically spatiotemporal sense. In his wariness towards abstract a priori thinking, Barth refrained from developing a social imaginative poise that might embody a genuinely free, Christian creatureliness. In contrast, Bonhoeffer's insistence on the concrete command of Christ led to his assertion that the "Jewish question" required concrete action as a status confessionis for the Christian church in his context. Barth initially considered Bonhoeffer's radicalism to be extreme and hasty, yet he later came to view the events of the Confessing Church's resistance with some regret, having not immediately displayed the categorical opposition that Bonhoeffer had advocated. Cone's high esteem for Bonhoeffer reveals an important challenge regarding the integrity of Christian theology and ethics today in the brains and bodies of White scholars. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Using the fixed point theorem in partially ordered sets, we obtain sufficient conditions for the existence of a unique positive solution to a boundary-value problem of the Sturm–Liouville type for a nonlinear ordinary differential equation, and give an example illustrating the results obtained. [ABSTRACT FROM AUTHOR]

The world of Christian theology mourns the passing of Jürgen Moltmann (1926–2024), one of the most prominent Protestant theologians of the twentieth century. Moltmann's death invites a first, albeit only cursory, review of his impact in the US. Since his first stay at Duke University in 1967–1968, he spent much time here, whether on lecture tours, conferences, or for visiting appointments. [ABSTRACT FROM AUTHOR]

In this article, we argue that public theologians have a rich tradition from which to argue for the right to self-determination of the Palestinian people. In particular, Dietrich Bonhoeffer's resistance to the co-opting of Christianity by the Nazi regime is frequently cited in theological circles as an exemplar. Yet, we find major public figures and theological societies, such as the Archbishop of Canterbury, Justin Welby, and the United Kingdom's Society for the Study of Theology (SST) to be wanting in this regard. From an examination of Welby's comments on the Israeli bombardment in Gaza, and the SST's response to our open letter and the lament from Palestinian Christians, we argue that theologians are failing. We draw on Palestinian liberation theology and anticolonial theologies to argue that the work of liberation is the raison d'être of theology and requires political activism. We conclude, therefore, that theological silence is complicity in injustice. [ABSTRACT FROM AUTHOR]

This paper establishes the existence of countably many positive solutions for a second order system of iterative system of two-point boundary value problems by using Hölder's inequality and Guo–Krasnoselskii's fixed point theorem for operator on a cone. [ABSTRACT FROM AUTHOR]

In this paper, we have defined A- cone and related concepts in Banach spaces and prove a result concerning convergence of a sequence in an A- cone. Also, atomic system for a subset of a Banach space is defined and proved that if a Banach space has an atomic system, then every subset of it also has an atomic system. [ABSTRACT FROM AUTHOR]

Highlights: Using sound insulation materials that do not impair indoor air quality and do not emit carbon. Increasing the sound insulation capacity with combinations of different natural materials. To enable to increase the intensity of use thanks to its economical production. Objective: The aim of the study is to develop new acoustic materials and panels that high sound transmission loss (STL), low carbon emissions, high sensitivity to human health, and also do not harm the indoor air quality. These materials are currently grown in Turkey and can be easily adopted in the industry. It has been comparatively analyzed that the developed materials can be alternatives to the synthetic materials on the market. Methods: In the experiment box similar to Alpha Cabin, which was designed and developed before, the STL values were obtained by conducting experiments in the frequency range 500–8000 Hz. with many natural and synthetic materials. In the study, low carbon emission natural materials with a STL of more than 30 dB were selected. Simulation: The experimentally measured samples were simulated in the acoustic module of the ANSYS program and compared with the results. Conclusion: The main purpose of choosing cones and walnut shells grown in our country is to contribute to the amount of oxygen in the atmosphere and green areas by increasing the cultivation of pine and walnut trees. In the tests of the samples, it was determined that the highest STL was 63.27 dB in the concave and egg-shaped sample, and 62.41 dB in the concave walnut shell and egg form. It is envisaged that the materials we obtained can be used in the sound insulation of machines and devices that produce 85 dB and above sound harmful to human health according to ILO and WHO standards. [ABSTRACT FROM AUTHOR]

Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for the number of generators, but also for the number of spanning trees, and for Tutte polynomial evaluations that count the recurrent sandpile configurations by their numbers of chips. [ABSTRACT FROM AUTHOR]

In this paper, we develop some new multiple fixed point theorems for the sum of two operators T + S where I - T is Lipschitz invertible and S is a k-set contraction on translate of a cone in a Banach space. New existence criteria for multiple positive solutions of a singular generalized Sturm-Liouville multipoint boundary value problem are established. The article ends with an illustrative example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of multiple positive symmetric solutions for fourth order p-Laplacian iterative system with integral boundary conditions. Initially, we establish the existence of at least one and two positive symmetric solutions for the fourth order problem using Krasnosel'skii fixed point theorem. Subsequently, we establish the existence of at least three positive symmetric solutions by applying fivefunctionals fixed point theorem. [ABSTRACT FROM AUTHOR]

This research presents an unsteady free convection magnetohydrodynamics (MHD) dusty fluid flow over a vertical cone enclosed inside a porous medium. The Crank–Nicolson approach is used to get the numerical solutions for these non-linear partial differential equations (PDEs). The velocity and temperature distributions are graphed numerically for a wide range of physical parameters to highlight important characteristics of the solutions. The results showed that increasing the porosity parameter leads to a rise in the velocity profile for the fluid and dust phases, while doing the reverse with the rise of the magnetic parameter, fluid-particle interaction parameter, and mass concentration of the particle phase parameter. Additionally, it is shown that the temperature profile rises as the magnetic parameter and the mass concentration of particle phase parameter grow, whereas the fluid-particle interaction parameter and porosity parameter show the opposite tendency.

Background: Abnormalities in cone photoreceptor topography are closely associated with the development of various ocular diseases, including axial myopia. Adaptive Optics Scanning Laser Ophthalmoscopy (AOSLO) enables high-resolution, single-cell imaging of the living human retina. Methods: This study aimed to investigate the potential relationship between cone topography and axial myopia using a commercial AOSLO system. A total of 74 participants (148 eyes; 30 men, 40.5 %) with a mean age of 31.8 ± 10.4 years were included. Cone mosaics were imaged at 3° and 5° eccentricities of the fovea centralis. The relationships between cone parameters (linear cone density, cone spacing, cone dispersion, and cone regularity) and axial length were analyzed. Results: Linear cone density significantly decreased with increasing axial length at both 3° and 5° eccentricities (all P < 0.001). Cone spacing significantly increased with greater axial length and reduced cone density. After adjusting for axial length, cone spacing was significantly associated only with linear cone density at both 3° and 5° eccentricities (all P < 0.001). Cone dispersion significantly increased with longer axial length and lower cone density. After adjusting for axial length, cone dispersion remained significantly associated with linear cone density only at the inferior 3° (β = -0.43, P = 0.014) and inferior 5° eccentricities (β=-0.4, P = 0.003). Cone regularity significantly increased with higher linear cone density at certain 3° eccentricities (nasal: β=0.34, P < 0.001; temporal: β=0.25, P = 0.006; inferior: β = 0.2, P = 0.04) and significantly decreased with longer axial length at temporal 5° eccentricity (β = -0.57, P < 0.001). Conclusions: Linear cone density was significantly reduced in axial myopia. The uniformity of cone distribution was disrupted as a result of the reduction in cone density. Additionally, cone regularity was significantly diminished in axial myopia, potentially due to the direct effects of axial elongation at 5° eccentricity or reductions in cone density at 3° eccentricity.

A boundary value problem for a nonlinear second-order functional-differential equation on the interval with integral boundary conditions is considered. Sufficient conditions for the existence of at least one positive solution of the problem under consideration are found by using special topological tools. A nontrivial example in which the sufficient conditions for the unique solvability of the problem are satisfied is given. [ABSTRACT FROM AUTHOR]

An investigation of the impacts of magnetic field, heat generation/absorption and thermal radiation on unsteady free convection dusty fluid flow over a non-isothermal vertical cone enclosed inside a porous medium is explored. The Crank–Nicolson approach is used to get the numerical solutions for these nonlinear, coupled partial differential equations (PDEs). The interaction of physical parameter range on temperature and velocity distribution is calculated and graphically presented. The results demonstrate that when the porosity, heat generation/absorption, and thermal radiation parameters are increased, the velocities rise, whereas the magnetic and mass concentration of particle phase parameters have an opposite effect. Furthermore, raising the fluid-particle interaction parameter causes a rise in dust phase velocity but a reduction in fluid phase velocity. [ABSTRACT FROM AUTHOR]

In this paper we consider second order iterative boundary value problem with Sturm Liouville type boundary conditions and establish the existence of countably many positive symmetric solutions by using Krasnoselskii's fixed point theorem for operator on a cone. [ABSTRACT FROM AUTHOR]

The paper studies a symmetric eigenvalue problem with nonlinear dependence on the spectral parameter in a Hilbert space which is a vector lattice with a cone of positive elements. The existence of a positive simple minimum eigenvalue corresponding to a single normalised positive eigenelement is established. The approximation of the problem in a finite-dimensional subspace is investigated. Results on the convergence and error of approximations to the minimum eigenvalue and the corresponding positive eigenelement are obtained. Computational methods for solving matrix eigenvalue problems with nonlinear dependence on the spectral parameter are developed and justified. The results of numerical experiments illustrating theoretical conclusions are given. [ABSTRACT FROM AUTHOR]

Thyroid hormone (TH) plays an essential role in cell proliferation, differentiation, and metabolism. Experimental and clinical studies have shown a potential association between TH signaling and retinal degeneration. The suppression of TH signaling protects cone photoreceptors in mouse models of retinal degeneration, whereas excessive TH signaling induces cone degeneration, manifested as reduced light response and a loss of cones. This work investigates the genes/transcriptomic alterations that might be involved in TH-induced cone degeneration in mice using single-cell RNA sequencing (scRNAseq) analysis. One-month-old C57BL/6 mice received triiodothyronine (T3, 20 µg/mL in drinking water) for 4 weeks as a model of hyperthyroidism/excessive TH signaling. At the end of the experiments, retinal cells were dissociated, and cell viability was analyzed before being subjected to scRNAseq. The resulting data were analyzed using the Seurat package and visualized using the Loupe browser. Among 155,866 single cells, we identified 14 cell clusters, representing various retinal cell types, with rod and cone clusters comprising 76% and 4.1% of the total cell population, respectively. Cone cluster transcriptomes demonstrated the most alterations after the T3 treatment, with 450 differentially expressed genes (DEGs), accounting for 38.5% of the total DEGs. Statistically significant changes in the expression of genes in the cone cluster revealed that phototransduction and oxidative phosphorylation were impaired after the T3 treatment, along with mitochondrial dysfunction. A pathway analysis also showed the activation of the sensory neuronal/photoreceptor stress pathways after the T3 treatment. Specifically, the eukaryotic initiation factor-2 signaling pathway and the cAMP response element-binding protein signaling pathway were upregulated. Thus, excessive TH signaling substantially affects cones at the transcriptomic level. The findings from this work provide an insight into how excessive TH signaling induces cone degeneration. [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]

A symmetric variational eigenvalue problem in the Hilbert space with a cone is investigated. New sufficient conditions on the bilinear forms, the Hilbert space, and the cone of the variational problem guaranteeing the existence of a unique normalized positive eigenelement corresponding to a positive simple minimal eigenvalue are proposed and justified. The obtained abstract results are illustrated by an example of the generalized eigenvalue problem for the second order self-adjoint elliptic differential operator. [ABSTRACT FROM AUTHOR]

The article introduces the concept of an interior point of a cone of a partially ordered space, which makes it possible to determine the topology in it. This topology turns a given linear space into a topological linear space, which is the main achievement of the article. [ABSTRACT FROM AUTHOR]

The functionality of photoreceptors, rods, and cones is highly dependent on their outer segments (POS), a cellular compartment containing highly organized membranous structures that generate biochemical signals from incident light. While POS formation and degeneration are qualitatively assessed on microscopy images, reliable methodology for quantitative analyses is still limited. Here, we developed methods to quantify POS (QuaPOS) maturation and quality on retinal sections using automated image analyses. POS formation was examined during the development and in adulthood of wild-type mice via light microscopy (LM) and transmission electron microscopy (TEM). To quantify the number, size, shape, and fluorescence intensity of POS, retinal cryosections were immunostained for the cone POS marker S-opsin. Fluorescence images were used to train the robust classifier QuaPOS-LM based on supervised machine learning for automated image segmentation. Characteristic features of segmentation results were extracted to quantify the maturation of cone POS. Subsequently, this quantification method was applied to characterize POS degeneration in "cone photoreceptor function loss 1" mice. TEM images were used to establish the ultrastructural quantification method QuaPOS-TEM for the alignment of POS membranes. Images were analyzed using a customwritten MATLAB code to extract the orientation of membranes from the image gradient and their alignment (coherency). This analysis was used to quantify the POS morphology of wild-type and two inherited retinal degeneration ("retinal degeneration 19" and "rhodopsin knock-out") mouse lines. Both automated analysis technologies provided robust characterization and quantification of POS based on LM or TEM images. Automated image segmentation by the classifier QuaPOS-LM and analysis of the orientation of membrane stacks by QuaPOS-TEM using fluorescent or TEM images allowed quantitative evaluation of POS formation and quality. The assessments showed an increase in POS number, volume, and membrane coherency during wild-type postnatal development, while a decrease in all three observables was detected in different retinal degeneration mouse models. All the code used for the presented analysis is open source, including example datasets to reproduce the findings. Hence, the QuaPOS quantification methods are useful for in-depth characterization of POS on retinal sections in developmental studies, for disease modeling, or after therapeutic interventions affecting photoreceptors. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of solutions to fourth order nonlinear boundary value problem involving systems of differential equations and two point boundary conditions. The nonlinearity f ∈ C([0, 1] × R+n × Rn × Rn × Rn, Rn) considered in this paper includes derivatives up to order three. Using recent fixed point results for the sum of two operators, we impose a growth condition on f to establish new existence criterion that ensure the existence of at least one and the existence of at least two nonnegative solutions. [ABSTRACT FROM AUTHOR]

It is shown that the front of the flame of a thoroughly mixed diluted methane-oxygen mixture at 298 K and 100–300 Torr propagating to the ends of hollow cylindrical and conical obstacles does not form a von Kármán path (vortex shedding) behind them; however, this instability occurs under the same conditions in the flow of hot products after obstacles. The reason that vortex shedding is not observed behind an obstacle during flame propagation but appears in the course of propagation of a reflected stream of hot products is that thermal conductivity reduces the curvature of the flame and leads to its stabilization. Indeed, the convex areas of the chemical reaction zone in a combustible mixture give off more heat in relation to cold ones than in a flat flame: the heat from them is not only transmitted forward in the direction of flame propagation but also in the lateral directions. The resulting cooling of the reaction zone causes the flame regions that burst forward to lag behind. The opposite situation is observed in concave areas, where the temperature rises for the same reasons. The rate of reactions increases and they spread forward faster as the flame spreads. Thus, the surface of the curved front of the flame is evened out. In other words, thermal conductivity has a stabilizing effect on a curved flame. This effect is missing in non-reactive gas. This effect is absent in a nonreacting gas. Calculations based on the acoustic approximation of the Navier–Stokes equations for a compressible reacting medium make it possible to take into account the main observed feature of the flame front approaching an obstacle in the form of a cylinder: vortex shedding is not observed behind the obstacle during flame propagation. Thus, a qualitative model allows obtaining both the mode of the emergence of a von Kármán instability in a chemically inert gas and its absence during flame propagation. [ABSTRACT FROM AUTHOR]

The current study investigates to characterize the Complex Programming Problem (CPP) solution in a fuzzy environment. The paper is divided into two parts: 1) the first presents a Fuzzy Complex Programming Problem (F-CPP) with fuzzy complex constraints, and 2) the second presents the optimality criteria using the fuzzy complex cone. The CPP is suggested by involving fuzzy numbers in the constraints in parts. Using the cut set concepts, the problem is converted into the complex programming. A number of basic theorems with proofs are established concerning the basic results for the fuzzy complex set of solutions for the F-CPP, and the optimality criteria of the saddle point for F-CPP with fuzzy cones is derived.

The information about main results on geometry of developable surfaces with an edge of regression which have a directrix ellipse in the base is gathered. These surfaces constitute a group called “Ruled surfaces of conical type on elliptical base”. This group includes elliptical cones, torses with two ellipses defined in the parallel planes, equal slope surfaces, and ruled surfaces with the main frame of three superellipses that are ellipses in one coordinate plane and broken straight lines in the other two coordinate planes. The paper presents a method for developing torses onto a plane, approximation of torses by folded surfaces, and parabolic ending of a thin sheet from elastic material into a torse shell. A brief review of the methods of stress-strain and buckling analysis of the considered ruled shells is given, including the displacement-based finite element method and variational energy method. It is shown that analytical methods can be used only in the case of applying the momentless shell theory for ruled thin shells of conical type. The analytical formulae for determining the normal and tangent internal forces in any momentless conic shell with a superellipse in the base are derived. References to forty four scientific articles of other authors, working or having worked on the subject of the paper are given. These references confirm the conclusions of the author and the perspectives of investigations of the considered ruled surfaces and shells.

Abies is an important genus of the family Pinaceae, with about 50 species found in the highlands of Asia, Europe, North Africa, and North and Central America. The principal aim of the present work was to investigate the chemical content and biological potential of the resin and cone from Abies nordmanniana subsp. bornmulleriana and Abies nordmanniana subsp. equi-trojani, respectively. The flavonoid and phenolic contents of the resin and cones were evaluated using liquid chromatography-high resolution mass spectrometry (LC-HRMS). Additionally, the essential oil and fatty acid compositions were analyzed using gas chromatography-mass spectrometry (GC-MS) and gas chromatography-flame ionization detector (GC-FID), respectively. Cytotoxicity of the extracts and essential oils were screened against certain cancer cell lines, namely, human prostate adenocarcinoma cell line (PC3), human lung adenocarcinoma cell line (A549), human pancreatic cancer cell line (PANC-1), human hepatocellular carcinoma cell line (HepG2), human breast cancer cell line (MDA-MB231), and normal human lung fibroblast cell line (CCD-34-LU), with MTT [3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-2H-tetrazolium bromide] assay. According to the MTT results, hexane extracts of both cone (CH) and resin (RH), ethanol-water (CEW), dichloromethane (CD), and acetone (CA) extracts of the cone mostly inflict cytotoxicity in HepG2 cell line. Antiviral activities of Abies nordmanniana subsp. extracts at doses of 5 µg/g and 10 µg/g were also evaluated in ovo for their virucidal activity against avian coronavirus. Abies nordmanniana subsp. extracts exhibited concentration-dependent antiviral activity on specific pathogen-free embryonated chicken eggs. Significantly, cone acetone extract (CA), cone ethanol extract (CE), and cone dichloromethane extract (CD) of Abies nordmanniana subsp. exhibited strong inhibition of the virus at a concentration of 10 µg/g. The most potent virucidal activity was observed with ethanol-water extract of conifer form (CEW). According to these results, it was proved that Abies nordmanniana species could be a potential, sustainable, and renewable drug source, especially considering the impressive antiviral and significant cytotoxic activity potentials. [ABSTRACT FROM AUTHOR]

We consider the solutions of the Klein–Gordon equation in the 2 + 1 -dimensional space-time which gravity is analyzed, i.e., the manifold ℝ t × ℝ + × ℝ / 2 ⁢ π ⁢ α ⁢ ℤ created by a massive point particle. Using the Schwartz kernel of resolvent and spectral measure for Schrödinger operator on the spinless cone, we prove the dispersive estimates and Strichartz estimates for the Klein–Gordon equation. In a future paper, we will consider the problem on the spinning cone. [ABSTRACT FROM AUTHOR]

Tests of a streamlined cone with a rear hemispherical part were carried out in a supersonic wind tunnel using an installation of free oscillations along the pitch angle at Mach number M = 1.75 and for several values of the body inertia moment (calculated relative to the axis of rotation). In all tests, after the completion of the transient process, undamped oscillations of the cone were recorded with an amplitude depending on the reduced frequency. The dependence for the of undamped oscillation amplitude on the reduced frequency exhibits a pronounced resonant behavior. [ABSTRACT FROM AUTHOR]

By means of a recent Birkhoff-Kellogg type theorem, we discuss the solvability of a fairly general class of parameter-dependent fourth order retarded differential equations subject to functional boundary conditions. We seek solutions within a translate cone of nonnegative functions. We provide an example to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

AbstractThe present article examines the double diffusion mixed convective nanofluid flow over a wedge and cone in which slip effects as Brownian motion and the thermophoretic parameter are considered. Mixed convective flow over wedges and cones is applied in different technical fields such as fiber technology, nuclear cooling systems, surface treatment, spray deposition techniques, and polymer production. Double diffusion is increasingly significant in scientific fields like astronomy, geosciences, oceanography, and chemical processes. Mixed convection occurs in several applications such as electric devices, solar panels, nuclear power plants, heat exchangers, radiators, and atmospheric boundary layer fluxes. The governing equations of the study are highly coupled nonlinear partial differential equations with surface constraints. The process of similarity transformation used to converts partial differential equations into nondimensional ordinary differential equations, which can be resolved using the MATLAB Bvp5c function. The graphical representation and detailed analysis of variations in velocity, temperature, and concentration distributions of nanofluids are presented. As the mixed convection parameter increases, the fluid’s velocity rises, with a more pronounced effect observed in the cone compared to the wedge. As the Brownian diffusion parameter grows, the fluid temperature increases, and velocity is more pronounced in the wedge scenario compared to the cone. Moreover, an increase in the thermophoresis parameter results in an elevation in the fluid’s temperature. Additionally, the wedge has a higher concentration of fluid and nanoparticles compared to the wedge. Fluid concentration falls with increasing Schmidt number, but fluid nanoparticle concentration decreases with increasing Lewis number. [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]