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Narrow escape theory deals with the first passage of a particle diffusing in a cavity with small circular windows on the cavity wall to one of the windows. Assuming that (i) the cavity has no size anisotropy and (ii) all windows are sufficiently far away from each other, the theory provides an analytical expression for the particle mean first-passage time (MFPT) to one of the windows. This expression shows that the MFPT depends on the only global parameter of the cavity, its volume, independent of the cavity shape, and is inversely proportional to the product of the particle diffusivity and the sum of the window radii. Amazing simplicity and universality of this result raises the question of the range of its applicability. To shed some light on this issue, we study the narrow escape problem in a cylindrical cavity of arbitrary size anisotropy with two small windows arbitrarily located on the cavity side wall. We derive an approximate analytical solution for the MFPT, which smoothly goes from the conventional narrow escape solution in an isotropic cavity when the windows are sufficiently far away from each other to a qualitatively different solution in a long cylindrical cavity (the cavity length significantly exceeds its radius). Our solution demonstrates the mutual influence of the windows on the MFPT and shows how it depends on the inter-window distance. A key step in finding the solution is an approximate replacement of the initial three-dimensional problem by an equivalent one-dimensional one, where the particle diffuses along the cavity axis and the small absorbing windows are modeled by delta-function sinks. Brownian dynamics simulations are used to establish the range of applicability of our approximate approach and to learn what it means that the two windows are far away from each other. [ABSTRACT FROM AUTHOR]

This study presents the effect of the flow velocity, which varies exponentially with time, on solute transport in a finite porous medium with radial geometry. The two-dimensional advection-dispersion equation in the cylindrical coordinate system is solved by using finite difference method. The concentration profiles are established for a duration of four hours of infiltration. It appears that the concentrations are lower in the case of the decreasing exponential velocity. The analysis of the effect of the injection radius showed that the retention of pollutants decreases when the injection radius increases. These findings can be used to design the size of a filter system for drinking water provision, and the environment protection. [ABSTRACT FROM AUTHOR]

A fractional matching of a graph G is a function f : E (G) → [ 0 , 1 ] such that for any v ∈ V (G) , ∑ e ∈ E G (v) f (e) ≤ 1 , where E G (v) = { e ∈ E (G) : e is incident with v in G }. The fractional matching number of G is μ f (G) = max { ∑ e ∈ E (G) f (e) : f is a fractional matching of G }. Let k ∈ (0 , n) is an integer. In this paper, we prove a tight lower bound of the spectral radius to guarantee μ f (G) > n − k 2 in a graph with minimum degree δ , which implies the result on the fractional perfect matching due to Fan et al. (2022) [6]. For a set { A , B , C , ... } of graphs, an { A , B , C , ... } -factor of a graph G is defined to be a spanning subgraph of G each component of which is isomorphic to one of { A , B , C , ... }. We present a tight sufficient condition in terms of the spectral radius for the existence of a { K 2 , { C k } } -factor in a graph with minimum degree δ , where k ≥ 3 is an integer. Moreover, we also provide a tight spectral radius condition for the existence of a { K 1 , 1 , K 1 , 2 , ... , K 1 , k } -factor with k ≥ 2 in a graph with minimum degree δ , which generalizes the result of Miao et al. (2023) [10]. [ABSTRACT FROM AUTHOR]

We first establish a lower bound on the size and spectral radius of a graph G to guarantee that G contains a fractional perfect matching. Then, we determine an upper bound on the distance spectral radius of a graph G to ensure that G has a fractional perfect matching. Furthermore, we construct some extremal graphs to show all the bounds are best possible. [ABSTRACT FROM AUTHOR]

The rail side wear in small radius curved track of metro lines is a serious problem in railway maintenance, which reduces the curve passing performance and shortens the service life of the wheel and rail. To improve the vehicle's curve passing performance and reduce rail wear, a localized grinding profile design method for sharp curves was developed. The GFC profile generation method was used to generate the profiles for the curved track of the metro line. Then a metro vehicle-track dynamic model was established to calculate the wheel rail contact parameters, objectives and constraints. The profiles are optimized by the KSM-PSO optimization algorithm. Finally, a simulation analysis of the curve passing performance and wheel-rail wear of the optimized profile was carried out. When the metro vehicle passes through the curved track with a curve radius of 450m, the optimized rail profile can effectively reduce the wear of the rail, the wear of the high rail in the curved track is reduced by 20.18%. The localized rail grinding of the curved track can effectively reduce the rail side wear, the GQI index is also significantly improved. This study can guide the design of rail grinding profiles for the metro lines. [ABSTRACT FROM AUTHOR]

In this paper, we show that the radius of analyticity σ (t) of solutions to the one-dimensional nonlinear Schrödinger (NLS) equation i ∂ t u + ∂ x 2 u = | u | p − 1 u is bounded from below by c | t | − 2 3 when p > 3 and by c | t | − 4 5 when p = 3 as | t | → + ∞ , given initial data that is analytic with fixed radius. This improves results obtained by Tesfahun [On the radius of spatial analyticity for cubic nonlinear Schrödinger equations, J. Differential Equations 263(11) (2017) 7496–7512] for p = 3 and Ahn et al. [On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations, Discrete Contin. Dyn. Syst. 40(1) (2020) 423–439] for any odd integers p > 3 , where they obtained a decay rate σ (t) ≥ c | t | − 1 for larger t. The proof of our main theorems is based on a modified Gevrey space introduced in [T. T. Dufera, S. Mebrate and A. Tesfahun, On the persistence of spatial analyticity for the beam equation, J. Math. Anal. Appl. 509(2) (2022) 126001], the local smoothing effect, maximal function estimate of the Schrödinger propagator, a method of almost conservation law, Schrödinger admissibility and one-dimensional Sobolev embedding. [ABSTRACT FROM AUTHOR]

R. Lyons, R. Pemantle and Y. Peres (Ann. Probab. 24 (4), 1996, 1993–2006) conjectured that for a Cayley graph G with a growth rate gr(G) > 1, the speed of a biased random walk exists and is positive for the biased parameter λ ∈ (1, gr(G)). And Gabor Pete (Probability and geometry ´ on groups, Chaper 9, 2024) sheds light on the intricate relationship between the spectral radius of the graph and the speed of the biased random walk. Here, we focus on an example of a Cayley graph, a free product of complete graphs. In this paper, we establish the continuity of the spectral radius of biased random walks with respect to the bias parameter in this class of Cayley graphs. Our method relies on the Kesten-Cheeger-Dodziuk-Mohar theorem and the analysis of generating functions. [ABSTRACT FROM AUTHOR]

In this study, the effect of five geometric design features, including radius, superelevation, longitudinal grade, lane and shoulder width, on the average speed in the horizontal curve on a two-lane undivided rural road was investigated. The standardized regression coefficients showed that the most important factor affecting the speed was the radius (10.47) followed by the longitudinal grade (4.46). Superelevation and lane width had little effect. Shoulder width had no significant effect. This would be due to the wide width of the lanes. It was found that the relationships between speed and radius, longitudinal grade, superelevation and lane width were radical, quadratic, linear and linear, respectively. Increasing the longitudinal grade has increased the speed of the drivers. Increasing the superelevation was effective when its value changed from negative to positive. [ABSTRACT FROM AUTHOR]

This paper introduces several generalized extensions of some recent numerical radius inequalities of Hilbert space operators. More preciously, these inequalities refine the recent inequalities that were proved in literature. It has already been demonstrated that some inequalities can be improved or restored by concatenating some into one inequality. The main idea of this paper is to extend the existing numerical radius inequalities by providing a unified framework. We also present a numerical example to demonstrate the effectiveness of the proposed approach. Roughly, our approach combines the existing inequalities, proved in literature, into a single inequality that can be used to obtain improved or restored results. This unified approach allows us to extend the existing numerical radius inequalities and show their effectiveness through numerical experiments. [ABSTRACT FROM AUTHOR]

The goal of this study is to refine some numerical radius inequalities in a novel way. The new improvements and refinements purify some famous inequalities pertaining to Hilbert space operators numerical radii. The inequalities that have been demonstrated in this work are not only an improvement over old inequalities but also stronger than them. Several examples supporting the validity of our results are provided as well. [ABSTRACT FROM AUTHOR]

Lasers are used in various fields, however, in the medical field, they are mainly used for incision or chemotherapy. Photothermal therapy (PTT) is an anti-cancer treatment technique that uses lasers and the photothermal effect to increase the temperature of tumor tissue and induce its death. In this study, the therapeutic effect of PTT using gold nanoparticles as a photothermal converter was analyzed numerically for the occurrence of squamous cell carcinoma inside a skin section consisting four layers. Numerical modeling was implemented to calculate the temperature distribution inside the biological tissue while varying the distribution radius of gold nanoparticles in the tumor tissue, the number of injections, and the intensity of the irradiating laser. For the given situation, the optimal treatment effect was observed when the distribution radius ratio of the injected gold nanoparticles (GNPs) was 1, the number of injections was 7, and the intensity of the irradiated laser was 52 mW. Three apoptotic variables were used to quantitively evaluate the effect of PTT in each case and thus suggest the optimal treatment effect. However, although the temperature range at which apoptosis occurs is known, the maintenance of that temperature range is still under research and the temporal influence of apoptosis remains to be determined. [ABSTRACT FROM AUTHOR]

In this paper. A new definition of discrete topological graph is introduced. Some properties of this graph are proved. If n > 2 are evaluated Gτ has no pendant vertex, not tree, also the value of the diameter and the minimum degree of Gτ . If n ≥ 2, Gτ has (2n − 3) complete bipartite induced subgraphs, Gτ is connected graph, simple graph, has no odd cycle, the clique number also proved, the value of the radius, the maximum degree and the chromatic number of Gτ have been studied. [ABSTRACT FROM AUTHOR]

We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]

Numerical simulation of fatigue crack growth (FCG) is presented, based on the application of the extended finite element method (XFEM). Couple of case studies are presented, as a review of recent experience of the Belgrade school of XFEM simulations, established at the Faculty of Mechanical Engineering. Case studies comprised Charpy specimen with initial crack at the notch tip, oil rig pipe with an axial surface crack, pressure vessels with a crack at the welded joint with connecting pipe, turbine shaft with a crack at the transition radius, optimization of a wing spar in respect to FCG, the effect of mesh size on fatigue life estimation of a stringer panel, fatigue life estimation of wing‐to‐fuselage connecting lug, geometry effect on fatigue life of orthopedic plates and fatigue life of hip implant. Based on these case studies, XFEM is discussed in respect to its accuracy and efficiency. It is concluded that XFEM is a versatile tool for simulation of FCG, providing an excellent option for precise and reliable fatigue life of a cracked component. [ABSTRACT FROM AUTHOR]

In this paper, we study a Riemann-Liouville-type fractional Riemann-Stieltjes integral boundary value problem under some conditions regarding the spectral radius of the relevant linear operator. The existence of nontrivial solutions is obtained using topological degree, and our results improve and generalize some results in the literature. [ABSTRACT FROM AUTHOR]

We present the observational mass–radius (M–R) relation for a sample of 47 magnetized white dwarfs (WDs) with the magnetic field strength (B) ranging from 1 to 773 MG, identified from the SDSS data release 7 (DR7). We derive their effective temperature, surface gravity (log g), luminosity, radius, and mass. While atmospheric parameters are derived using a Virtual Observatory Spectral Energy Distribution Analyzer (VOSA), the mass is derived using their location in the HR diagram in comparison with the evolutionary tracks of different masses. We implement this mass measurement instead of a more traditional method of deriving masses from log g , which is unreliable as is based on SED and generates errors from other physical parameters involved. The main disadvantage of this method is that we need to assume a core composition of WDs. As it is complicated to identify the exact composition of these WDs from low-resolution spectra, we use tracks for the masses 0.2 to 0.4 M⊙ assuming a He-core, 0.5 to 1.0 M⊙ assuming CO core, and above M⊙ assuming O–Ne–Mg core. We compare the observed M–R relation with those predicted by the finite temperature model by considering different B , which are well in agreement considering their relatively low-surface fields, ≲109 G. Currently, there is no direct observational detection of magnetized WDs with B > 109 G. We propose that our model can be further extrapolated to higher B , which may indicate the existence of super-Chandrasekhar mass (M > 1.4 M⊙) WDs at higher B. [ABSTRACT FROM AUTHOR]

Establish a new classification system of distal radius fracture based on computed tomographic (CT), and evaluate its reliability and reproducibility preliminarily, and provide a new theoretical reference for clinicians to use the clinical classification system. The imaging data and clinical data of 204 inpatients with distal radius fracture during 6 years from January 1, 2014 to January 1, 2019 in orthopaedic department were analyzed retrospectively and classified based on CT. Three observers evaluated the image data of 48 randomly selected cases based on CT at different time nodes of T1 and T2. Cohen's kappa was used to calculate the consistency. At the last follow-up, patients' Disabilities of the Arm, Shoulder and Hand (DASH), Patient Rated Wrist Evaluation (PRWE), and VAS scores were collected. Among 204 cases, there were 12 cases of type 1, including 6 cases of type 1-D, 4 cases of type 1-V and 2 cases of type 1-R. There were 6 cases of type 2, including 2 cases of type 2-DV, 2 cases of type 2-DR and 2 cases of type 2-VR. There were 186 cases of type 3, including 32 cases of type 3–0, 127 cases of type 3–1 and 27 cases of type 3–2. There was no significant difference in DASH, PRWE and VAS scores among all types (P > 0.05). The results of interobserver reproducibility were kappa = 0.985, ICC = 0.984 in the first evaluation, kappa = 0.986, ICC = 0.986 in the second evaluation. The results of intraobserver reproducibility were O1 = 0.991, O2 = 0.991, O3 = 0.989 respectively. The new classification system of distal radius fracture based on CT has theoretical and practical significance for incision selection, fracture reduction and internal fixation. 123 classification system is clear, comprehensive, easy to understand and remember. Moreover, it has higher interobserver reliability and intraobserver reproducibility than other systems reported at present. [ABSTRACT FROM AUTHOR]

Ignition electrodes have an immense impact on the accurate measurement of the flame propagation spherical radius. In this study, a flame-radius calculation method is designed. The method is able to eliminate effects due to the ignition electrodes. The adaptability and optimization effects of the proposed method are analyzed. The results show that the ratio of the angle is affected by the ignition electrodes under the Han II method. There are three obvious divisions include a high-value area, a sharp-variation area, and a mild-variation area. The ratio of the angle affected by the ignition electrodes is only applicable to the mild-variation region when the flame presents respective convex and concave distributions. For these distributions, the increment rate of the mean radius is 0.4–0.85% and 0.42–3.19%. The reduced rate of the standard deviation of the radius extraction value is 11.91–22.1% and 5.13–17.99%, and the reduced rate of the radius extraction value range is 20.32–39.51% and 0.32–8.09%. [ABSTRACT FROM AUTHOR]

Let H be a complex Hilbert space. Assume that the power series with complex coefficients f (z) := ∑∞k=0 akzk is convergent on the open disk D(0, R), fa (z) := ∑∞k=0 |ak| zk that has the same radius of convergence R and A, B, C ∊ B (H) with ||A|| < R, then we have the following Schwarz type inequality ... for α ∊ [0, 1] and x, y ∊ H. Some natural applications for numerical radius and p-Schatten norm are also provided. [ABSTRACT FROM AUTHOR]

In this work, we give an improved new argument to prove that the solution of the Cauchy problem for the nonlinear spatially homogeneous Landau equation with hard potentials with $ L^2(\mathbb{R}^3) $ initial datum enjoys a analytic Gelfand-Shilov regularizing effect in the class $ S^1_1(\mathbb{R}^3) $, the evolution of analytic radius is similar to the heat equation. [ABSTRACT FROM AUTHOR]

A graph G is called fractional [ a , b ] -covered if for every edge e of G there is a fractional [ a , b ] -factor with the indicator function h such that h (e) = 1. In this paper, we provide a tight spectral radius condition for graphs being fractional [ a , b ] -covered. [ABSTRACT FROM AUTHOR]

Transfer entropy (TE) has proven to be an effective tool for determining the causal connection between two processes. For example, TE has been used to classify leader and follower agents in collective dynamics in the Vicsek model (VM). However, previous results have limited interaction radii, which are precisely the same among all agents, which is not realistic in practice. Here, we propose a modified version of the VM where the domains in which an agent can be influenced by others vary from agent-to-agent, which matches more closely with a real-life setting where not all agents have the same physical traits. We demonstrate that the TE vs cut-off technique is robust and efficacious in determining the maximum distance at which two interacting agents can transfer information in the system. We find that for two agents with different interaction domains, the derivative of the average inward TE can determine the individual agent's interaction domain. In a system with numerous agents, the TE vs cut-off technique is shown to be effective in predicting the average interaction domain of all agents, where the interaction domain of each agent was randomly selected from a Gaussian distribution. [ABSTRACT FROM AUTHOR]

Let G be a graph and let k ⩾ 2 be an integer. A { K 1 , j : 1 ⩽ j ⩽ k } -factor of G is a spanning subgraph of G , in which each component is isomorphic to a member in { K 1 , j : 1 ⩽ j ⩽ k }. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a { K 1 , j : 1 ⩽ j ⩽ k } -factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a { K 1 , j : 1 ⩽ j ⩽ k } -factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible. [ABSTRACT FROM AUTHOR]

In the non-uniform k-center problem, the objective is to cover points in a metric space with specified number of balls of different radii. Chakrabarty, Goyal, and Krishnaswamy [ICALP 2016, Trans. on Algs. 2020] (CGK, henceforth) give a constant factor approximation when there are two types of radii. In this paper, we give a constant factor approximation for the two radii case in the presence of outliers. To achieve this, we need to bypass the technical barrier of bad integrality gaps in the CGK approach. We do so using "the ellipsoid method inside the ellipsoid method": use an outer layer of the ellipsoid method to reduce to stylized instances and use an inner layer of the ellipsoid method to solve these specialized instances. This idea is of independent interest and could be applicable to other problems. [ABSTRACT FROM AUTHOR]

We continue the study of the properties of graphs in which the ball of radius r around each vertex induces a graph isomorphic to the ball of radius r in some fixed vertex-transitive graph F, for various choices of F and r. This is a natural extension of the study of regular graphs. More precisely, if F is a vertex-transitive graph and r ∈ ℕ, we say a graph G is r-locally F if the ball of radius r around each vertex of G induces a graph isomorphic to the graph induced by the ball of radius r around any vertex of F. We consider the following random graph model: for each n ∈ ℕ, we let Gn = Gn (F, r) be a graph chosen uniformly at random from the set of all unlabelled, n-vertex graphs that are r-locally F. We investigate the properties possessed by the random graph Gn with high probability, i.e. with probability tending to 1 as n → ∞, for various natural choices of F and r. We prove that if F is a Cayley graph of a torsion-free group of polynomial growth, and r is sufficiently large depending on F, then the random graph Gn = Gn (F, r) has largest component of order at most n5/6 with high probability, and has at least exp(nδ) automorphisms with high probability, where δ > 0 depends upon F alone. Both properties are in stark contrast to random d -regular graphs, which correspond to the case where F is the infinite d -regular tree. We also show that, under the same hypotheses, the number of unlabelled, n-vertex graphs that are r-locally F grows like a stretched exponential in n, again in contrast with d -regular graphs. In the case where F is the standard Cayley graph of ℤd, we obtain a much more precise enumeration result, and more precise results on the properties of the random graph Gn (F, r). Our proofs use a mixture of results and techniques from geometry, group theory and combinatorics. We make several conjectures regarding what happens for Cayley graphs of other finitely generated groups. [ABSTRACT FROM AUTHOR]

A design method for the allpass-based infinite impulse response multi-notch filters with identical pole radiuses is derived in the paper. According to the standard procedure when design of the allpass-based filters is considered, the multi-notch filters' magnitude response specifications are first formulated as the phase response specifications of the corresponding allpass filter. Then, for the specified identical pole radiuses, it is shown that unknown allpass filter coefficients can be obtained determined from the square system of linear equations. On the other hand, the minimum value of the pole radius, such that specifications of the the magnitude response are satisfied in all passbands, can be determined using the bisection method. Results of comparison with some of the existing design methods lead to the conclusion that proposed filters have higher area under the squared passbands magnitude response compared to filters with the same maximum pole radius. Furthermore, utilization of the proposed method can result in transfer functions that have the lowest possible maximum pole radius. [ABSTRACT FROM AUTHOR]

To explore the curvature dependence of solid–fluid interfacial thermodynamics, we calculate, using Grand Canonical Monte Carlo simulation, the surface free energy for a 2d hard-disk fluid confined in a circular hard container of radius R as a function of the bulk packing fraction η and wall curvature C ̄ = − 1 / R. (The curvature is negative because the surface is concave.) Combining this with our previous data [Martin et al., J. Phys. Chem. B 124, 7938–7947 (2020)] for the positive curvature case (a hard-disk fluid at a circular wall, C ̄ = + 1 / R), we obtain a complete picture of surface thermodynamics in this system over the full range of positive and negative wall curvatures. Our results show that γ is linear in C ̄ with a slope that is the same for both positive and negative wall curvatures, with deviations seen only at high negative curvatures (strong confinement) and high density. This observation indicates that the surface thermodynamics of this system is consistent with the predictions of so-called morphometric thermodynamics at both positive and negative curvatures. In addition, we show that classical density functional theory and a generalized scaled particle theory can be constructed that give excellent agreement with the simulation data over most of the range of curvatures and densities. For extremely high curvatures, where only one or two disks can occupy the container at maximum packing, it is possible to calculate γ exactly. In this limit, the simulations and density functional theory calculations are in remarkable agreement with the exact results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the q-numerical radius $ \omega _{q}(.) $ ω q (.) of bounded linear operators on Hilbert spaces. More precisely, first, we show that $ \omega _{q}(.) $ ω q (.) defines a norm which is equivalent to the operator norm. Next, the following compatible generalization of Kittaneh's inequality $$\begin{align*} \frac{1}{4}\left(\frac{q}{2-q^{2}}\right)^{2}\parallel T^{*}T +TT^{*}\parallel & \leq \omega_{q}^{2}(T) \leq \frac{(q+2\sqrt{1-q^2})^2}{2}\\ & \quad\times \Vert T^{*}T+TT^{*}\Vert. \end{align*}$$ 1 4 (q 2 − q 2 ) 2 ∥ T ∗ T + T T ∗ ∥ ≤ ω q 2 (T) ≤ (q + 2 1 − q 2 ) 2 2 × ‖ T ∗ T + T T ∗ ‖. is obtained. Finally, some generalizations of q-numerical radius inequalities for composition of operators are established. [ABSTRACT FROM AUTHOR]

The convergence-confinement method (CCM) is a standard design tool to study the ground-structure interaction. Constitutive model selection is a critical issue in the correct application of the CCM to represent the real behavior of rock mass and plastic zone. In this paper, the post-failure behavior of rock mass is formulated and incorporated by a numerical approach and the results are compared with the experimental observations. Elastic perfectly plastic (EPP) and strain softening (SS) models, are used and compared for a circular tunnel to be applied in the CCM method. The results show that elastic parts of the ground reaction curve and the longitudinal deformation profiles for both models are similar. But when the rock failure occurs and tunnel face exceeds 0.5D, differences in the curves are significant. Based on the results, the maximum displacement in different amount of K (in-situ stress ratios) for the SS model is more than 3 times of the EPP model. Plastic radius in the SS model is about 2 times the radius in the EPP model. In addition to precisely identifying the plastic zone and its distribution, the modified numerical approach in this paper, can determine the critical support pressure within residual and softening regions. [ABSTRACT FROM AUTHOR]

The interface tends to behave as a circular shape under the effect of surface tension in the two-dimensional two-phase fluid flow. In this study, based on the coupled volume-of-fluid and level set (VOSET) method, an accurate circle-based interface reconstruction (CIR) algorithm for structured meshes is proposed, which features a straightforward implementation procedure. A portion of the standard circle is employed to approximate the curve interface, without the need for complex classification, coordinate transformation, and equation transformation. The radius of this circle is computed simply by the curvature and signed distance at the mixed cell center, and the center of this circle is determined using a straightforward dichotomy method under the mass conservation constraints. Results indicate that the coupled VOSET and CIR (VOSET-CIR) method maintains superior computational accuracy in the signed distance, interface curvature, and dynamic interface reconstruction compared to the coupled VOSET and piecewise linear interface calculation (VOSET-PLIC) method, with accuracy improvements ranging from 34% to 1490% across different test cases. Furthermore, the VOSET-CIR method outperforms the efficient least squares volume-of-fluid interface reconstruction (ELVIRA) and PLIC algorithms in reconstructing random circles and surpasses the quadratic spline based interface reconstruction (QUASI) algorithm in reconstructing random squares. In terms of computational efficiency, except for the initial PLIC algorithm, the time costs of the VOSET-CIR method are substantially lower than those of the ELVIRA and QUASI algorithms, as well as the VOSET-PLIC method. [ABSTRACT FROM AUTHOR]

In this work, we give several new upper and lower bounds for the p-numerical radii of operators as well as for n × n operator matrices. An application to 2-nilpotent operators is provided, and a p-numerical radius power inequality is also given. [ABSTRACT FROM AUTHOR]

A dominating set S in a graph G is called a radius dominating set if for each vertex V ∈ v -- S there is at least one vertex in u ∈ S S such that d(u, v) = rad(G). The cardinality of the minimum radius dominating set is called the radius domination number of G, denoted by γrd(G). In this article, we study the properties of this parameter. The radius domination number of some families of standard graphs are obtained and the bounds are estimated. [ABSTRACT FROM AUTHOR]

We present several upper bounds for the numerical radii of 2 × 2 operator matrices. We employ these bounds to improve on some known numerical radius inequalities for powers of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then for every r ≥ 1 and α ∈ [0, 1]. This substantially improves on the existing inequality. Here w(.) and ||.|| denote the numerical radius and the usual operator norm, respectively. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical technique based on Taylor's series method namely DTM has been used to solve the differential equation which governs the motion of three types of annular FGM plates. The differential equation has been obtained using Hamilton principle and classical plate theory. The mechanical properties of the plate (Young's modulus and density) are considered to be graded in thickness direction and vary following the power-law. The behaviour of volume fraction index and radii ratio has been investigated onto first three modes of frequency parameter for all three plates. Moreover, the novelty of this paper is the application of the versatile technique DTM to study the effect of radii ratio and volume fraction index on three different types of annular FGM plates. A comparison has been made between the obtained numerical results and the results are available in the literature. A good agreement of the results verifies the accuracy of the present technique. Three-dimensional mode shapes for all three plates are also presented. [ABSTRACT FROM AUTHOR]

Any 3D AFM image is a convolution of the geometry of the AFM tip and the profile of the scanned sample, especially when the dimensions of the scanned sample are comparable to those of the AFM tip shape. The precise profile of the scanned sample can be extracted from the 3D AFM image if the geometry of the AFM tip is known. Therefore, in order to separate the geometry of the AFM probe tip from the 3D AFM image of a diffraction grating with a rectangular profile and to correct for the topographic convolutions induced by the AFM probe tip, a method is used to quantitatively evaluate the geometry of the AFM probe tip, including the tip radius and the included angle. A model for reconstructing the measured AFM image is proposed to correct topography convolutions caused by the AFM tip shape when scanning a diffraction grating with rectangular profiles. A series of experiments were performed to verify the effectiveness of the proposed AFM tip geometry evaluation method, and comparison experiments were conducted to demonstrate the feasibility and reliability of the proposed reconstruction model. [ABSTRACT FROM AUTHOR]

The performance of tactile and optical surface sensors for nano and micro coordinate measuring machines is currently limited by the lack of precisely characterised micro spheres, since established strategies have mainly been developed for spheres in the range of millimetres or above. We have, therefore, recently focused our research efforts towards a novel strategy for the characterisation of spheres in the sub-millimetre range. It is based on a set of atomic force microscope (AFM) surface scans in conjunction with a stitching algorithm. To obtain an uncertainty statement, the uncertainty about the shape of the reference surface needs to be propagated via the shape of the AFM tip to the actual measurement object. However, the sampling process of an AFM is non-linear and the processing of AFM scans requires complex algorithms. We have, therefore, recently begun to model the characterisation of micro spheres through simulations. In this contribution, this model is extended by the influence of the tip and reference surface. The influence of the tip's shape and reference surface is investigated through virtual and real experiments. The shape of the tip is varied by using tips with mean radii of 200 nm and 2 μm while sampling the same ruby sphere with a mean radius of 150 μm. In general, the simulation results imply that an uncertainty of less then 10 nm is achievable. However, an experimental validation of the model is still pending. The experimental investigations were limited by the lack of a suitable cleaning strategy for micro parts, which demonstrates the need for further investigations in this area. Although the characterisation of a full sphere has already been demonstrated, the investigations in this contribution are limited to equator measurements. [ABSTRACT FROM AUTHOR]

In Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function's radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones. [ABSTRACT FROM AUTHOR]

Building a 15-minute radius livelihood service circle from the needs of residents is a topdown process of optimizing urban layout and promoting high-quality development implemented by the government. In September 2022, Xicheng District of Beijing served as a national pilot of the 15-minute radius livelihood service circle. Based on the data of POI, urban walking network and building outline, this paper studies the coverage of commercial service facilities in the 15-minute radius livelihood service circle of Chunshu Street by using kernel density analysis and urban network analysis tools. The research shows that the commercial facilities are concentrated in Zhuangsheng Square and Dazhalan commercial district. There are large gaps in housekeeping and couriers logistics facilities, which need to be further improved. [ABSTRACT FROM AUTHOR]

The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius r on networks. Furthermore, the radius r is flexible and the objective function is the conic combination of the traditional 1-median function and the value r. We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network G = (V,E) in O(|E||V|³) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree. [ABSTRACT FROM AUTHOR]

In this paper, we introduced s-index weakly positive tensors and discussed the calculation of the spectral radius of this kind of nonnegative tensors. Using the diagonal similarity transformation of tensor and Perron-Frobenius theory of nonnegative tensor, the calculation method of the maximum H-eigenvalue of s-index weakly positive tensors was given. A variable parameter was introduced in each iteration of the algorithm, which is equivalent to a translation transformation of the tensor in each iteration to improve the calculation speed. At the same time, it was proved that the algorithm is linearly convergent for the calculation of the spectral radius of s-index weakly positive tensors. The final numerical example shows the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Traffic noise mapping frequently employs Kriging, Inverse Distance Weighted (IDW), and Triangular Irregular Networks (TIN) spatial interpolations. This study uses the Henk de Kluijver noise model to evaluate the performance of spatial interpolations. Effective traffic noise mapping requires that noise observation points (Nops) be designed as 2 m grids. The upper and lower slopes function as noise barriers to reduce sound levels. Therefore, assessment of accuracy is essential for visualising noise levels in undulating and level terrain. In addition, this work gives an accurate comparison of traffic noise interpolation in undulating areas. The elements of spatial interpolations, such as the weighting factor, variogram, radius, and number of points influence the interpolation accuracy. The Kriging with a Gaussian variogram, where the radius is 5 m and the number of points is 12 demonstrates the highest level of precision. However, there is no direct relationship between accuracy validation and cross-validation. In cross-validation, however, the accuracy of the Gaussian variogram with a 7 m radius and 18 points is more accurate. In addition, this study demonstrates that Kriging is superior for extrapolating noise levels in undulating regions. Accurate visualising traffic noise levels requires a prior understanding of spatial interpolations. [ABSTRACT FROM AUTHOR]

The univalent function ϕ SG (z) : = 2 / (1 + e − z) maps the open unit disk | z | < 1 onto a sigmoid domain | log (w / (2 − w)) | < 1. The sharp radii constants have been computed for the classes involving ratios f / g and g / (z p) of analytic functions f , g and p defined in | z | < 1 such that p is subordinate to ϕ SG , the other two ratios are subordinate to 1 + z , e z or z + 1 + z 2 and the quantity z f ′ / f lies in a certain region of the right half plane. [ABSTRACT FROM AUTHOR]

For a system of nonlinear integral equations on the semiaxis, we study a boundary value problem whose matrix kernel has unit spectral radius. This boundary value problem has applications in various areas of physics and biology. In particular, such problems arise in the dynamical theory of -adic strings for the scalar field of tachyons, in the mathematical theory of spread of epidemic diseases, in the kinetic theory of gases, and in the theory of radiative transfer. The questions of the existence, absence, and uniqueness of a nontrivial solution of this boundary value problem are discussed. In particular, it is proved that a boundary value problem with a zero boundary conditions at infinity has only a trivial solution in the class of nonnegative and bounded functions. It is also proved that if at least one of the values at infinity is positive, then this problem has a convex nontrivial nonnegative bounded and continuous solution. At the end of this paper, examples of the matrix kernel and nonlinearity are provided that satisfy all the conditions of the proved theorems. [ABSTRACT FROM AUTHOR]

Simple Summary: Traumatic brain injuries, a primary global health concern, can lead to severe disabilities. Acute subdural haematoma is one type of traumatic brain injury resulting from the rupture of bridging veins in the brain. Existing numerical models often oversimplify these structures. This study's main goals were to understand how the cerebral vein's cross-sectional shape affects its response, more akin to real-life testing, and to introduce a hyperelastic model for these veins that captures their non-linear behaviour. The results reveal that the vein's shape significantly influences its response to stretching, highlighting the need for more realistic geometries in modelling. Additionally, hyperelastic models, like the Marlow and polynomial models, were successfully implemented. This research provides valuable insights into the mechanical properties of bridging veins and their response to tensile loading, potentially improving our understanding of traumatic brain injuries. Traumatic brain injury (TBI) is a serious global health issue, leading to serious disabilities. One type of TBI is acute subdural haematoma (ASDH), which occurs when a bridging vein ruptures. Many numerical models of these structures, mainly based on the finite element method, have been developed. However, most rely on linear elasticity (without validation) and others on simplifications at the geometrical level. An example of the latter is the assumption of a regular cylinder with a constant radius, or the geometry of the vein acquired from medical images. Unfortunately, these do not replicate the real conditions of a mechanical tensile test. In this work, the main goal is to evaluate the influence of the vein's geometry in its mechanical behaviour under tensile loading, simulating the real conditions of experimental tests. The second goal is to implement a hyperelastic model of the bridging veins where it would be possible to observe its non-linear elastic behaviour. The results of the developed finite element models were compared to experimental data available in the literature and other models. It was possible to conclude that the geometry of the vein structure influences the tensile stress–strain curve, which means that flattened specimens should be modelled when validating constitutive models for bridging veins. Additionally, the implementation of hyperelastic material models has been verified, highlighting the potential application of the Marlow and reduced polynomial (of fourth and sixth orders) constitutive models. [ABSTRACT FROM AUTHOR]

The effect of cutting edge radius (rß) on the chip formation mechanism during the finish turning of Ti6Al4V is studied. An increase in rß decreases the cutting to thrust force ratio and produces lower chip thickness due to the increase in plowing zone depth. Larger radius tools produce thinner loosely curled chips whereas tightly curled thicker chips are formed for the unprepared edge tool (36 µm). As rß increases, the chip flow angle (ß) increases and free-flowing chips with reduced up-curl but increased side and lateral curl and consequently larger resultant chip curl radius are produced. The chip serration height to overall chip thickness ratio increases whereas chip core thickness reduces owing to the increased plowing action as rß increases. Chip segmentation analysis reveals increased serration height, thermal instability, and shear localisation in the shear zone due to the increased ploughing effect beyond ~60 µm edge radius. [ABSTRACT FROM AUTHOR]

This article presents a new DIRECT-type SCABALL (scattering balls) algorithm with a new partition method for derivation-free optimization problems. It does not focus on dividing the region of interest into specific geometric shapes, but rather scatters several balls to cover it. In SCABALL, several potential optimal regions are selected at each iteration, and they are covered by smaller balls sequentially. In this way, the SCABALL ensures the everywhere dense convergence. The center points and radii of the scattered balls significantly influence the efficiency of SCABALL; therefore, the minimax designs are used in the initial and sequential stages to obtain better coverage. The SCABALL parameters, including the number of balls and their radii, were analyzed by numerical investigation. We provided the empirical choices for those parameters and found that the balls' radii can be contracted to balance efficiency and global convergence. Numerical experiments show that the SCABALL algorithm is locally biased and robust. [ABSTRACT FROM AUTHOR]