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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]

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 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]

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]

The normalized distance Laplacian of a graph G is defined as D L (G) = T (G) − 1 / 2 (T (G) − D (G)) T (G) − 1 / 2 where D (G) is the matrix with pairwise distances between vertices and T (G) is the diagonal transmission matrix. In this project, we study the minimum and maximum spectral radii associated with this matrix, and the structures of the graphs that achieve these values. In particular, we prove a conjecture of Reinhart that the complete graph is the unique graph with minimum spectral radius, and we give several partial results towards a second conjecture of Reinhart regarding which graph has the maximum spectral radius. [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]

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]

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. 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]

The standard configuration of a sonic black hole (SBH) is a discrete set of rings with back cavities at a duct termination, whose inner radii decrease according to a power-law. Although several practical realizations of this type of slow-sound waveguide have been investigated, the continuous problem in which the number of ring/cavity sets goes to infinity has not been analyzed in depth. Understanding its performance is interesting in itself and could provide clues for new designs. For this purpose, we transform the generalized Webster equation for the acoustic pressure inside the ideal SBH into a spatially varying wavenumber Helmholtz equation for a new locally scaled pressure. We eliminate the singularity of the original problem at the SBH termination by considering a rigid residual surface that will be shown to play a role analogous to that of the acoustic black hole (ABH) residual thickness in beams and plates. The variational formulation of the Helmholtz equation is presented and solved by expanding the unknown scaled pressure in terms of a basis of Gaussian functions. The same framework is used to set up an eigenvalue problem that provides the SBH modes and thereby a modal decomposition for the pressure within the SBH. Once the theoretical foundations are established, the variation of the speed of sound and wavenumber in the SBH is presented. The dependence of the shape and distribution of the modes on the residual surface and damping helps to clarify the occurrence and disappearance of oscillations in the input admittance and reflection coefficient of the SBH at different frequencies. For the latter, a detailed parametric study is carried out. Alternative profiles to the power law are also investigated, some showing reflection coefficient values similar to those of the classical SBH. • Sonic black holes at the end of ducts provide minimal wave reflection. • A theoretical approach is proposed to solve the SBH governing equation. • The modal distribution in the SBH is strongly affected by the residual radius. • The modal distribution explains the oscillations in the reflection coefficient. • Alternative SBH profiles to the power law are studied. [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]

Let 0 < ρ ≤ 2 and w ρ (X) be the operator radius of a bounded linear Hilbert space operator X. In this paper we present characterizations of operators satisfying w ρ (X) ≤ 1. We also give an expression for the ρ -radii based on the numerical radius of a certain 2 × 2 block matrix. This enables us to investigate the properties of the operator radii w ρ (⋅). In particular, we obtain lower and upper bounds for the operator radii. In addition, we define a norm on Hilbert space operators, which generalizes the operator radii and prove some basic properties of this norm. Our results extend or improve some theorems due to Ando [4] , Bhatia–Jain [9] and Kittaneh [19]. [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]

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 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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]

A tree T with exactly one node u of degree larger than two is called a starlike tree and u is called the root node of T. Let S T n be a family of graphs consists of all starlike trees and the path with n + 1 nodes. For a fixed connected graph H with at least one edge, we construct a family of graphs F H (v) , n = { H (v) • T | T ∈ S T n } , where H (v) • T denotes the graph obtained by identifying some node, say v , of H with the root node of T. In this paper, we give an ordering of graphs in F H (v) , n by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. • The spectral radius of the graph powerfully characterizes dynamic processes on networks, such as virus spread and synchronization. • In this paper, we give an ordering of graphs in F H (v) , n by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. • The result generalizes the main result of Oliveira et al. in [10]. [ABSTRACT FROM AUTHOR]

We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in Ricketson and Chacón (2020) [36] to include finite Larmor-radius (FLR) effects in the presence of electric-field length-scales comparable to the particle gyro-radius (the gyro-kinetic limit). We introduce two modifications to the earlier scheme. The first is the explicit gyro-averaging of the electric field at the half time-step, along with an analogous modification to the current deposition, which we show preserves total energy conservation in implicit PIC schemes. The number of gyrophase samples is chosen adaptively, ensuring proper averaging for large timesteps and the recovery of full-orbit dynamics in the small time-step limit. The second modification is an alternating large and small time-step strategy that ensures the particle trajectory samples gyrophases evenly. We show that this strategy relaxes the time-step restrictions on the scheme, allowing even larger speed-ups than previously achievable. We demonstrate the new method with several single-particle motion tests in a variety of electromagnetic field configurations featuring gyro-scale variation in the electric field. The results demonstrate the advertised ability to capture FLR effects accurately even when significantly stepping over the gyration time-scale. • An asymptotic-preserving, implicit time integrator for charged particles in arbitrary electromagnetic fields is presented. • Method captures finite Larmor radius (FLR) effects, making it the first asymptotic-preserving scheme to do so. • Method preserves desired properties of correct gyroradius, first-order guiding center drifts, and energy conservation. • A new alternating time-step technique relaxes time-step constraints, allowing larger speed-ups than previously achievable. • Numerical results show dramatic accuracy improvement over prior schemes. [ABSTRACT FROM AUTHOR]

[Display omitted] • The choice of nozzle height is almost independent of nozzle height for R ≥ 80 mm. • H significantly affects cartridge cleaning performance with smaller R. • Peak static pressure distribution along filter cartridge height. • The main vortex reduces the static pressure inside the cartridge. The inner cone double-layer filter cartridges have the capability to guide the flow, which can optimize the airflow distribution inside the cartridge and reduce the cartridge's incomplete cleaning. However, the selection of different cone radius and nozzle heights can affect the cartridge's cleaning performance. More thorough investigations of the static pressure distribution properties within double-layer cartridges are required to improve their design and optimization. The results show that double-layer cartridges' peak static pressure at different nozzle heights has a similar distribution law. Peak static pressure increases progressively with cartridge height in the middle and lower sections (OM3-OM5, IM2-IM5), with the lower section having a larger peak static pressure. The cleaning performance of cartridges with a cone radius of R ≥ 80 mm is little impacted by the nozzle height. The stability of the cartridge's cleaning performance improves and then deteriorates as the cone radius increases, with the best cleaning effect and stability reached at R = 80 mm. In practical applications, double-layer filter cartridges with larger cone radius should be considered. [ABSTRACT FROM AUTHOR]

Within the framework of effective mass approximation and with the use of finite element method, we calculate the energy states of an electron in a double toroidal quantum ring with a Hopf link structure. The study includes the influence of externally applied static electric and magnetic fields, and considers different geometric combinations of radii and link positions. We have found that geometric manipulations have significant impact on the energy values and the distribution of electronic probability densities in either one or both linked rings. Similar effects can be achieved with the application of the electromagnetic probes. • Novel Hopf link quantum ring system has been modeled in finite potential barriers. • Electrical and magnetic fields tune the density probability of one confined electron. • Some geometric configurations allow overcoming the isolation of potential barriers. • Energy oscillations under magnetic field are only evident for excited states. [ABSTRACT FROM AUTHOR]

A celebrated result of Beck shows that for any set of N points on S d there always exists a spherical cap B ⊂ S d such that number of points in the cap deviates from the expected value σ (B) ⋅ N by at least N 1 / 2 − 1 / 2 d , where σ is the normalized surface measure. We refine the result and show that, when d ≢ 1 (mod 4) , there exists a (small and very specific) set of real numbers such that for every r > 0 from the set one is always guaranteed to find a spherical cap C r with the given radius r for which the result holds. The main new ingredient is a generalization of the notion of badly approximable numbers to the setting of Gegenbauer polynomials: these are fixed numbers x ∈ (− 1 , 1) such that the sequence of Gegenbauer polynomials (C n λ (x)) n = 1 ∞ avoids being close to 0 in a precise quantitative sense. [ABSTRACT FROM AUTHOR]

We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue λ on a d -dimensional closed Riemannian manifold contains a ball of radius c λ − 1 2 (log ⁡ λ) − d − 2 2 . This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain. [ABSTRACT FROM AUTHOR]

In this study, we explored the complex effects of electric fields in three unique directions and axial magnetic field on a GaAs-Variant Quantum Ring Quarter Cross-Section (VQRQCS), particularly when there is an off-center shallow donor impurity. The investigation explores the impact of these fields on various physical attributes, including electronic energy, binding energy, magnetic shift, Stark shift, average electron impurity distance, and diamagnetic susceptibility. Using effective mass approximation and three-dimensional finite difference methods we solved the Schrodinger equation. Our result shows that the geometric radius of the VQRQCS has an essential impact on electronic energy. Notably, as the radius increases, the electronic energy decreases, regardless of the presence of fields. In particular, we found that magnetic fields amplify the electronic energy of the ground state. The angle of curvature of the nanostructure and the direction of the electric field also play an important role. Additionally, the electron–impurity binding energy decreases with the growth of the nanostructure, with external fields intensifying this effect. The average distance between the electron and the impurity, analyzed in the context of simultaneously applied fields, provides insight into the Coulomb interaction. Diamagnetic susceptibility, measuring the response of a material to an external magnetic field, is studied, indicating opposition to the external field. In summary, this research highlights the nuanced interactions between electric and magnetic fields that determine the properties of a GaAs quantum ring, providing critical insights for quantum ring-based technological advancements. • Exploration of the intricate effects of electric fields in three unique directions and an axial magnetic field on a quantum ring nanostructure. • Electronic properties, magnetic shift, Stark shift, average electron–impurity distance, and diamagnetic susceptibility have been studied. • Discovery that the geometrical parameters of the quantum ring significantly influence the electronic energy. • The angle of curvature of the nanostructure and the direction of the electric field are found to be crucial factors. • Diamagnetic Susceptibility: Examination of how the material responds to an external magnetic field. [ABSTRACT FROM AUTHOR]

For objects belonging to a known model set and observed through a prescribed linear process, we aim at determining methods to recover linear quantities of these objects that are optimal from a worst-case perspective. Working in a Hilbert setting, we show that, if the model set is the intersection of two hyperellipsoids centered at the origin, then there is an optimal recovery method which is linear. It is specifically given by a constrained regularization procedure whose parameters can be precomputed by semidefinite programming. This general framework can be applied to several scenarios, including the two-space problem and problems involving ℓ 2 -inaccurate data. It can also be applied to the problem of recovery from ℓ 1 -inaccurate data. For the latter, we reach the conclusion of existence of an optimal recovery method which is linear, again given by constrained regularization, under a computationally verifiable sufficient condition. [ABSTRACT FROM AUTHOR]

Metal additive manufacturing (AM) technology has been utilized in many industries including automotive, aerospace, and medical. AM Ti6Al4V (Ti64) alloy is highly noticed for production of medical instruments such as dental implants and the machining process is mostly needed during the production or post-processing of these components. Numerical model, as a powerful tool, can be efficiently used for analyzing the machining process. A customized model was employed using a user-written subroutine in this work to evaluate machinability and microstructural changes in cryogenic machining of AM Ti64 alloy. For this purpose, the microstructural changes were simulated as the new numerical outputs. The numerical results of cutting forces, temperature, nano-hardness, and alpha lamellae thickness (grain size) were successfully verified by corresponding experiments from literature. Then, the impact of tool geometry (including rake and clearance angles, cutting edge radius, and nose radius) on the machinability performance was examined. It was found that, the variation of clearance and rake angles were more effective on depth of the hardened layer compared to the other parameters. Thickness of alpha lamellae phase near the machined surface and depth of the affected layer by nano-hardness changes were changed from 0.9 to 1.58 µm, and from 18 to 40 µm, respectively. Overall, it was concluded that the variation of insert positioning made by tool holder (change in rake and clearance angles) was an effective parameter on the process outputs when machining AM Ti64 alloy. [ABSTRACT FROM AUTHOR]