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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]

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]

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]

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]

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]

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]

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]

The estimation of temperature evolution in a solid material irradiated by a high-intensity laser beam is important for modelling of various laser-based heating processes. This paper proposes a three-dimensional analytical solution of temperature field based on the integral transform technique considering intensive convective boundary conditions. The proposed model evaluates the temperature of a laser-heated sheet as a function of geometric, material and laser attributes of the sheet. By comparing the findings of experimental investigation performed on 1.5 mm thick Al 6061-T6 sheets under the considered process conditions, the effectiveness of the proposed model is evaluated. Laser power and scanning speed varied during the experiments keeping laser beam radius and specimen geometry constant. The surface temperature of the laser-heated sheet is found to rise with increasing laser power. In contrast, the surface temperature drops with high scan speeds. The analytical and experimental results are in close agreement with errors less than 3 %. Eventually, the temperature evolution predicted by the analytical solution is compared numerically and it is found that the analytical model can effectively reduce the computing time for evaluating the temperature in the laser heating process. To broaden the application of the analytical model, the effect of process parameters, namely, laser beam radius, workpiece thickness and material properties on the temperature evolution are analyzed under different cooling schemes. This investigation is of significance towards developing an inverse method for determining laser process parameters quickly and inexpensively for various laser-based heating processes in near future works. [ABSTRACT FROM AUTHOR]

A single elliptical or ellipsoidal inclusion with an arbitrary uniform eigenstrain is known to achieve a constant stress field when embedded in an elastic medium provided the edge of the medium is sufficiently far from the inclusion (i.e. the interaction between the inclusion and the edge of the medium is negligible). In this paper, we aim to answer the question as to whether there exists an inclusion of certain configuration (with a uniform eigenstrain) that remains to possess a constant stress when embedded in a bounded medium whose edge interacts significantly with it. Specifically, we consider the anti-plane shear case of an inclusion with a uniform eigenstrain in a circular medium with a traction-free edge. We derive a sufficient and necessary condition ensuring the uniformity of the stress within the inclusion, which further leads to a nonlinear system of equations with respect to an infinite group of parameters characterizing the shape of the inclusion. We obtain convergent solutions for the truncated version of the nonlinear system using numerical techniques, and illustrate the corresponding shape of the inclusion in a few numerical examples. Our results for the case corresponding to small inclusion size and small edge-inclusion distance (relative to the radius of the medium) are well-consistent with the existing results for an inclusion with uniform stress in a semi-infinite medium with a traction-free surface, while those for centrally placed inclusions achieving uniform stress capture the classical case of centric circular inclusion accurately. The results presented in this paper provide a strong evidence for the existence of inclusions possessing uniform stress in an elastic bounded domain subjected to common external boundary conditions under anti-plane shear deformation. [ABSTRACT FROM AUTHOR]

The motion of planetesimals initially located in the feeding zone of the planet Proxima Centauri c, at distances of 500 AU from the star to the star's Hill sphere radius of 1200 AU was considered. In the analyzed non-gaseous model, the primary ejection of planetesimals from most of the feeding zone of an almost formed planet c to distances greater than 500 AU from the star occurred during the first 10 million years. Only for planetesimals originally located at the edges of the planet's feeding zone, the fraction of planetesimals that first reached 500 AU over the time greater than 10 million years was more than half. Some planetesimals could reach the outer part of the star's Hill sphere over hundreds of millions of years. Approximately 90% of the planetesimals that first reached 500 AU from Proxima Centauri first reached 1200 AU from the star in less than 1 million years, given the current mass of the planet c. No more than 2% of planetesimals with aphelion orbital distances between 500 and 1200 AU followed such orbits for more than 10 million years (but less than a few tens of millions of years). With a planet mass equal to half the mass of the planet c, approximately 70–80% of planetesimals increased their maximum distances from the star from 500 to 1200 AU in less than 1 million years. For planetesimals that first reached 500 AU from the star under the current mass of the planet c, the fraction of planetesimals with orbital eccentricities greater than 1 was 0.05 and 0.1 for the initial eccentricities of their orbits eo = 0.02 and eo = 0.15, respectively. Among the planetesimals that first reached 1200 AU from the star, this fraction was approximately 0.3 for both eo values. The minimum eccentricity values for planetesimals that have reached 500 and 1200 AU from the star were 0.992 and 0.995, respectively. In the considered model, the disk of planetesimals in the outer part of the star's Hill sphere was rather flat. Inclinations i of the orbits for more than 80% of the planetesimals that first reached 500 or 1200 AU from the star did not exceed 10°. With the current mass of the planet c, the percentage of such planetesimals with i > 20° did not exceed 1% in all calculation variants. The results may be of interest for understanding the motion of bodies in other exoplanetary systems, especially those with a single dominant planet. They can be used to provide the initial data for models of the evolution of the disk of bodies in the outer part of Proxima Centauri's Hill sphere, which take into account gravitational interactions and collisions between bodies, as well as the influence of other stars. The strongly inclined orbits of bodies in the outer part of Proxima Centauri's Hill sphere can primarily result from bodies that entered the Hill sphere from outside. The radius of Proxima Centauri's Hill sphere is an order of magnitude smaller than the radius of the outer boundary of the Hills cloud in the Solar System and two orders of magnitude smaller than the radius of the Sun's Hill sphere. Therefore, it is difficult to expect the existence of a similarly massive cloud around this star as the Oort cloud around the Sun. [ABSTRACT FROM AUTHOR]

In light of the Alexander transformation, the class of spirallike functions is significant. The characteristics of special functions also appear very frequently in Geometric function theory. In this paper, we find the radii of γ -spirallike and convex γ -spirallike of order α of certain special functions. [ABSTRACT FROM AUTHOR]

We explore computationally tractable deformations of the SYK model. The deformed theories are described by the sum of two SYK Hamiltonians with differing numbers, q and q ~ , of interacting fermions. In the large N limit, employing analytic and numerical tools, we compute finite temperature correlation functions and thermodynamic quantities. We identify a novel analytically solvable model in the large q limit. We find that, under certain circumstances, the thermal RG flow in the strongly coupled infrared phase exhibits two regions of linear-in-temperature entropy, which we interpret in terms of Schwarzian actions. Using conformal perturbation theory we compute the leading relevant correction away from the intermediate near-conformal fixed point. Holographic spacetimes in two spacetime dimensions that reproduce the thermodynamics of the microphysical theory are discussed. These are flow geometries that interpolate between two Euclidean near-AdS2 spacetimes with different radii. The Schwarzian soft mode corresponding to the AdS2 region in the deep interior resides entirely within the geometric regime. [ABSTRACT FROM AUTHOR]

A solution of the Laplace equation in cylindrical coordinates is presented for a bounded cylinder with the known height and radius which is subject to inhomogeneous mixed boundary conditions of the third and second kinds on the surface. On the other surface, unmixed boundary conditions of the first or second kind are given. Through separation of variables, the Hankel integral transform, and the dual series equations, the solution of the mixed problem is reduced to solving the Fredholm integral equation of the second kind. [ABSTRACT FROM AUTHOR]

We propose a method for controlling the formation of microarray structures on the surface by using an electric field. In this study, a phase field model is employed to describe the formation of microstructures under the influence of the electric field. Initially, we utilize Cahn–Hilliard equation, Navier–Stokes equation, and Gaussian theory to construct the phase field model. Subsequently, we obtain the theoretical solution for the partial differential equations and apply numerical methods such as semi-implicit Fourier spectral and semi-implicit difference method. Finally, we establish the numerical model to observe the morphological changes on the polymer surface by changing the electric field strengths, the distribution and the radius of the electrode plate. Simulated observations show that the electric field induce the formation of microarray structures on the polymer surface successfully, and the microarray structures match the shape of the electric field. Additionally, higher electric field strength promotes the formation of morphological changes obviously. The distribution of microarray structures is controlled by changing the electric field distribution. These studies provide a theoretical basis for the fabrication of microarray structures. [ABSTRACT FROM AUTHOR]

The arithmetic-geometric spectral radius of a graph G is the largest eigenvalue of the arithmetic-geometric matrix of G whose (u, v)-entry is d u + d v 2 d u d v if u and v are adjacent and 0 otherwise for u , v ∈ V (G) , where d u denotes the degree of vertex u in G. We determine the graphs with the largest and the next largest arithmetic-geometric spectral radii over all n-vertex bicyclic graphs with n ≥ 5 . [ABSTRACT FROM AUTHOR]

Despite the extensive investigation on the stress and displacement distributions in tunnels, few have considered the influences of the damaged zone around a tunnel on the strength and stiffness parameters of the surrounding rock, including the gradual variation in the damaged factor D and dimensionless damaged radius ρ d , under the effect of excavation disturbance. In this paper, a numerical solution is presented for the stresses and displacement of a circular tunnel excavated in a Hoek–Brown rock mass considering the progressive destruction of the damaged zone. First, the results obtained using the proposed algorithm are compared with those obtained using other numerical solutions, demonstrating a high degree of accuracy through some examples. Second, the influences of the damaged factor D and dimensionless damaged radius ρ d on the stresses, radial displacement, plastic radii, and ground response curve are investigated. The results show that, as the damaged factor D increases, the radial displacement and plastic radius increase, whereas the tangential stress decreases. Both the plastic radius and displacement decrease with decreasing ρ d . This shows that the damaged factor D has a significant effect on tunnel convergence. [ABSTRACT FROM AUTHOR]

Let G be a graph and P be a property of graphs. A subset S ⊆ V (G) is called a P -admissible set of G if G - N [ S ] admits the property P . The P -admission number of G, denoted by η (G , P) , is the cardinality of a minimum P -admissible set in G. For a positive integer k, we say a graph G has the property R k if the radius of each component of G is at most k. In particular, η (G , R 1) is the cardinality of a smallest set S such that each component of G - N [ S ] has a universal vertex. In this paper, we establish sharp upper bound for η (G , R 1) for a connected graph G. We show that for a connected graph G ≠ C 7 of order n, η (G , R 1) ≤ n 4 . The bound is sharp. Several related problems are proposed. [ABSTRACT FROM AUTHOR]

We consider the problem of extreme partition of the complex plane well known in the geometric theory of functions. We obtain estimates for the maximum value of the product of some powers of inner radii of n disjoint domains in the complex plane with respect to n arbitrary points of the plane one of which can be located at infinity. The estimates established in the paper can be applied to various problems of the geometric theory of functions. [ABSTRACT FROM AUTHOR]

3D modeling of tool wear and optimization of hard turning have been performed in this study considering the tool geometry parameters, i.e., cutting edge and nose radii. Optimization is carried out using multiple objective and constraint, and it employs a meta-model that is developed using response surfaces based on radial basis functions. A 3D finite element model has been developed considering the tool geometry and is verified using force measurement during hard turning experiments on H-13. Chip formation simulations have been done using the coupled temperature displacement analysis based on explicit dynamics. The tool wear model is implemented using Usui's model for adhesive wear. This model takes input from the steady-state chip formation analysis, and the contact nodes on the tool are repositioned according to the wear rate and time increment. The model is able to predict chip morphology, force components, tool wear, stress, and temperature distributions. The effects of cutting edge and nose radii on tool stresses, tool wear, and temperature have been discussed. For optimization search genetic algorithm, MOGA-II is selected which has been used to optimize tool temperature and material removal rate during hard turning. Optimize solutions suggest the selection of high to moderate cutting edge and nose radii, large feeds, and low to moderate cutting speeds. [ABSTRACT FROM AUTHOR]

A central vertex of a graph is a vertex whose eccentricity equals the radius. The center of a graph is the set of all central vertices. The central ratio of a graph is the ratio of the cardinality of its center to its order. In 1982, Buckley proved that every positive rational number not exceeding one is the central ratio of some graph. In this paper, we obtain more detailed information by determining which cardinalities are possible for the center of a graph with given order and radius. There are unexpected phenomena in the results. For example, there exists a graph of order 14 and radius 6 whose center has cardinality s if and only if s ∈ { 1 , 2 , 3 , 4 , 9 , 10 , 11 , 12 , 14 }. The turning value (3 n + 2) / 8 for the radius seems mysterious. We also prove a related uniqueness result. [ABSTRACT FROM AUTHOR]

The calibration of areal surface topography measuring instruments is of high relevance to estimate the measurement uncertainty and to guarantee the traceability of the measurement results. Calibration structures for optical measuring instruments must be sufficiently small to determine the limits of the instruments. Besides other methods, micro-milling is a suitable process for manufacturing areal material measures. For the manufacturing by micro-milling with ball end mills, the tool radius (effective cutter radius) is the corresponding limiting factor: if the tool radius is too large to penetrate the concave profile details without removing the surrounding material, deviations from the target geometry will occur. These deviations can be detected and excluded before experimental manufacturing with the aid of a kinematic simulation. In this study, a kinematic simulation model for the prediction of the dimensional accuracy of micro-milled areal material measures is developed and validated. Subsequently, a radius study is conducted to determine how the tool radius r of the tool influences the dimensional accuracy of an areal crossed sinusoidal (ACS) geometry according to ISO 25178-70 [1] with a defined amplitude d and period length p. The resulting theoretical surface texture parameters are evaluated and compared to the target values. It was shown that the surface texture parameters deviate from the nominal values depending on the effective cutter radius used. Based on the results of the study, it can be determined with which effective tool radius the measurands Sa and Sq of the material measures are best met. The ideal effective radius for the application considered is between 50 and 75 μm. [ABSTRACT FROM AUTHOR]

To study the influence mechanisms of tool geometry parameters on surface quality and subsurface damage when nanocutting polycrystalline NiFeCr superalloys, based on the theory of molecular dynamics, a three-dimensional nanocutting model is established. By investigating the mechanisms of material removal, cutting force, friction coefficient, surface roughness, residual stress, dislocation density, and phase transformation atoms, the influences of the tool rake angles, edge radii, and clearance angles on the surface and subsurface structures are analysed in detail. At the initial cutting stage, the material removal mechanism is dominated by tool extrusion, and as cutting continues, the dominant removal mechanism transforms into shearing. When the tool rake angle changes from negative to positive, the surface roughness improves, the dislocation density and phase transformation atoms decrease, and the tensile residual stress increases. As the edge radius increases, the surface roughness and dislocation density increase, the tensile residual stress decreases, and the phase transformation atoms first increase and then decrease. With the increased tool clearance angle, the surface roughness and phase transformation atoms decrease, the tensile residual stress increases first and then decreases, and the dislocation density shows fluctuating characteristics. In addition, an analysis of dislocation and defect evolution reveals the plastic deformation and subsurface damage mechanisms during nanocutting. In particular, grain boundaries help to inhibit the proliferation of defect damage and dislocations, and the interactions of dislocations form new dislocations. [ABSTRACT FROM AUTHOR]

The angular distributions for the 11.28, 11.82, and 13.79 MeV states were obtained and analyzed from the scattering of light particles by the Be nucleus. The MDM method was used to estimate the radii. The radius of the 11.82 MeV state turned out to be equal to the radius of the ground state. For the 11.28 MeV the radius turned out to be increased. As for the 13.79 MeV state, the obtained value of the diffraction radius was ambiguous. The spin–parity values were estimated using the semiempirical Bohr–Mottelson formula. A conclusion was made on assignment of these states to the corresponding bands in the Be nucleus. [ABSTRACT FROM AUTHOR]

Bistable metal sheets with a coiled transport geometry and an unfolded profile as second stable state, are of great interest as lightweight components. It is well known that a specific distribution of residual stresses is necessary to enable bistable properties. With the help of numerical FE models, the optimal process parameters for production of such sheets are evaluated. Afterwards, incremental bending and roll forming experiments are conducted in order to analyse possible continuous production methods for bistable metallic profiles. Finally, the influence of bending and rolling radii on bistability and profile geometries in stable states are investigated. [ABSTRACT FROM AUTHOR]

We consider a biharmonic problem Δ2uω = fω with Navier type boundary conditions uω = Δuω = 0, on a family of truncated sectors Ωω in ℝ2 of radius r, 0 < r < 1 and opening angle ω, ω ∈ (2π/3, π] when ω is close to π. The family of right-hand sides (fω)ω∈(2π/3, π] is assumed to depend smoothly on ω in L2(Ωω). The main result is that uω converges to uπ when ω → π with respect to the H2-norm. We can also show that the H2-topology is optimal for such a convergence result. [ABSTRACT FROM AUTHOR]

We consider a well-known problem of the geometric theory of functions on the extreme partition of the complex plane. For this problem, we establish estimates for the maximum value of the product of inner radii of n nonoverlapping domains with respect to n arbitrary points in the complex plane one of which may be infinitely remote. At present, the exact solutions of this problem are known only for n = 2, 3, 4. We establish estimates that can be used in various extreme problems of the geometric theory of functions. [ABSTRACT FROM AUTHOR]

The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This determines when the robust feasible set is non-empty. Otherwise, the robust counterpart of an uncertain program is not well defined as a robust optimization problem. In this paper, we address a key fundamental question of robust optimization: How to compute the radius of robust feasibility of uncertain linear conic programs, including linear programs? We first provide computable lower and upper bounds for the radius of robust feasibility for general uncertain linear conic programs under the commonly used ball uncertainty set. We then provide important classes of linear conic programs where the bounds are calculated by finding the optimal values of related semi-definite linear programs, among them uncertain semi-definite programs, uncertain second-order cone programs and uncertain support vector machine problems. In the case of an uncertain linear program, the exact formula allows us to calculate the radius by finding the optimal value of an associated second-order cone program. [ABSTRACT FROM AUTHOR]

The two well-known numerical radius inequalities for the tensor product A ⊗ B acting on H ⊗ K , where A and B are bounded linear operators defined on complex Hilbert spaces H and K , respectively are 1 2 ‖ A ‖ ‖ B ‖ ≤ w (A ⊗ B) ≤ ‖ A ‖ ‖ B ‖ and w (A) w (B) ≤ w (A ⊗ B) ≤ min { w (A) ‖ B ‖ , w (B) ‖ A ‖ }. In this article, we develop new lower and upper bounds for the numerical radius w (A ⊗ B) of the tensor product A ⊗ B and study the equality conditions for those bounds. [ABSTRACT FROM AUTHOR]

Electrical Discharge Machining (EDM) is an established non-conventional process, which is particularly efficient for the processing of hard-to-cut materials, in order to obtain high dimensional accuracy and surface integrity. However, in order to determine the appropriate parameters for machining novel materials, it is necessary to investigate the EDM process in depth, both by experiments and numerical models, taking into consideration the fundamental physical phenomena occurring during this process and be able to predict the surface morphology and microstructural alterations under various conditions. One of the challenging issues of EDM simulation models that still remain open is the representation of the evolution of plasma channel radius, for which various approaches have been proposed such as a linear, power law, or a more complex piecewise relation, in respect to time. Thus, in this work, the effect of different relations for the plasma channel radius evolution on energy absorption coefficient, plasma flushing efficiency (PFE), and crater morphology is compared under various conditions with a numerical model, which is also compared to experimental data. The results indicate that the energy absorption coefficient is dependent on the plasma column radius function, as slower growth of plasma channel leads to lower absorption coefficient and more efficient material removal, whereas a lower variation and different trends under different conditions were observed regarding PFE values, in respect to the power law exponent. Finally, the crater dimensions were shown to be consistently more narrow and deeper with higher exponents; thus, based on actual observations of indicative craters, it was revealed that the appropriate values for the exponent of the power law plasma radius function are below 0.25. [ABSTRACT FROM AUTHOR]

Gear hobbing is a well-established manufacturing process for cylindrical spur gears. The cutting edge of a hobbing tool is, among others, characterized by the cutting edge radius and the form-factor K. The magnitude of these parameters is ideally chosen based on the machining conditions given by the workpiece and cutting material and the cutting parameters as well as the gear and tool geometry. However, the influence of the cutting edge geometry on tool life and wear behavior is hardly known, which complicates an optimized tool design. Furthermore, the preparation process regarding the coating thickness distribution on the wear behavior is equally relevant. Therefore, the objective was to identify the influence of the cutting edge radius, the form-factor K, and the preparation process on the wear behavior of gear hobbing tools made of powder metallurgical high-speed steel (PM-HSS). Fly-cutting trials were performed as an analogy process for gear hobbing in order to study the wear behavior and identify the respective tool lives. The trials indicated that the form-factor K influences the wear behavior, while a variation of the cutting edge radius did not have a significant effect. A homogenous coating thickness could extend the tool life significantly. [ABSTRACT FROM AUTHOR]

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius R and width w subject to a magnetic flux. We consider the case where the crystal symmetry is locally modified through dislocations created by replacing the original carbon hexagon by a pentagon, square, heptagon or octagon. To model this type of defect, we include appropriate boundary conditions for the angular coordinate. The electrons are then confined to a finite width strip in the radial direction by setting an infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel functions and their asymptotic behavior allows to derive quantized energy levels in the presence of an energy gap. We also investigate the persistent currents that appear in the quantum ring in the presence of a quantum flux at the center of the ring and how wedge disclination influences different quantum transport quantities. [ABSTRACT FROM AUTHOR]

Let S (m, d, k) be the set of k-uniform supertrees with m edges and diameter d, and S1 (m, d, k) be the k-uniform supertree obtained from a loose path u1, e1, u2, e2, ..., ud, ed, ud+1 with length d by attaching m–d edges at vertex u⌊d/2⌋+1. In this paper, we mainly determine S1 (m, d, k) with the largest signless Laplacian spectral radius in S (m, d, k) for 3 ⩽ d ⩽ m − 1. We also determine the supertree with the second largest signless Laplacian spectral radius in S (m, 3, k). Furthermore, we determine the unique k-uniform supertree with the largest signless Laplacian spectral radius among all k-uniform supertrees with n vertices and pendent edges (vertices). [ABSTRACT FROM AUTHOR]

Given an elliptic integrand of class C 2 , α , we prove that finite unions of disjoint open Wulff shapes with equal radii are the only volume-constrained critical points of the anisotropic surface energy among all sets with finite perimeter and reduced boundary almost equal to its closure. [ABSTRACT FROM AUTHOR]

Based on the elementary solutions and new integral equations, a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries. The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method, the numerical solution of the finite element method, and the analytical-numerical solutions of the series expansion and Laurent series methods. Some numerical examples are presented to investigate the effects of the hole geometry parameters (radii and relative positions) and loading conditions (remote stresses and surface stresses) on the interacting tangential stresses and interacting stress concentration factors. The results show that whether the interference effect is shielding (k < 1) or amplifying (k > 1) depends on the relative orientation of holes (α) and remote stresses (

The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph. It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph, and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph. In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius, where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph. [ABSTRACT FROM AUTHOR]

In this work, we provide upper and lower bounds for the numerical radius of an n × n off-diagonal operator matrix, which extends some results by Abu-Omar and Kittaneh (Stud. Math. 216:69–75, 2013; Linear Algebra Appl. 468:18–26, 2015; Rocky Mt. J. Math. 45(4):1055–1065, 2015), and Paul and Bag (Appl. Math. Comput. 222:2731–2943, 2013). [ABSTRACT FROM AUTHOR]

In this paper, we consider the unimodality of the principal eigenvector of graphs. A unimodal lemma of the principal eigenvector on internal paths is obtained. This unimodal lemma is used to establish a cycle version of Li–Feng transformation with respect to the spectral radius. Another application of unimodal lemma is to determine the unicyclic graph with minimal spectral radius. [ABSTRACT FROM AUTHOR]

For a connected graph G and α ∈ [ 0 , 1) , the distance α-spectral radius of G is the spectral radius of the matrix D α (G) defined as D α (G) = α T (G) + (1 − α) D (G) , where T (G) is a diagonal matrix of vertex transmissions of G and D (G) is the distance matrix of G. We give bounds for the distance α-spectral radius, especially for graphs that are not transmission regular, propose local graft transformations that decrease or increase the distance α-spectral radius, and determine the graphs that minimize and maximize the distance α-spectral radius among several families of graphs. [ABSTRACT FROM AUTHOR]

In order to solve the problem that the traditional DV-Hop location algorithm has a large error in locating unknown nodes, this paper proposes an improved DV-Hop algorithm based on dual communication radius. By adding a communication radius, the algorithm updates the minimum hop number obtained by the unknown node closer to the beacon node to a smaller hop value and keeps the minimum hop number information of unknown nodes farther away. This method reflects the gap between the actual distances in terms of hop number, which solves the problem of the large difference between the actual distances of the same hops to a certain extent. Therefore, it is more advantageous to estimate the more accurate average jump distance and can calculate the more precise distance between them and obtain the more precise coordinates of unknown nodes. MATLAB simulation results show that the improved algorithm based on dual communication radius DV-Hop can effectively reduce the location error and improve the location accuracy and stability compared with the traditional DV-Hop location algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we establish some Brauer-type bounds for the spectral radius of Hadamard product of two nonnegative tensors based on Brauer-type inclusion set, which are shown to be sharper than the existing bounds established in the literature. The validity of the obtained results is theoretically and numerically tested. [ABSTRACT FROM AUTHOR]

In this paper, we study the numerical radius parallelism for bounded linear operators on a Hilbert space (H , ⟨ · , · ⟩) . More precisely, we consider bounded linear operators T and S which satisfy ω (T + λ S) = ω (T) + ω (S) for some complex unit λ , and is denoted by T ‖ ω S . We show that T ‖ ω S if and only if there exists a sequence of unit vectors { x n } in H such that lim n → ∞ | ⟨ T x n , x n ⟩ ⟨ S x n , x n ⟩ | = ω (T) ω (S). We then apply it to give some applications. [ABSTRACT FROM AUTHOR]

The smoothed particle hydrodynamics simulation model of micromachining of industrial pure iron was established to study the effect of tool edge radius on chip formation in this paper. The process of chip production was studied by particle displacement method, and cutting force and stress were analyzed. Meanwhile, the mechanism of chip formation was revealed. The simulation results show that the tool edge radius has significant effects on chip formation in micromachining. When the depth of cut is 0.16 times of the tool edge radius, the chips begin to produce. And the minimum cutting thickness decreases with the increase of the ratio of the cutting depth to the tool edge radius, which means that chips are more easily to be produced with the decrease of the tool edge radius. Meanwhile, the larger the tool edge radius is, the wider the stress distribution area is and the greater the fluctuation of the cutting force is. Finally, values of the minimum cutting thickness under different ratios obtained by the theoretical formula are basically consistent with the simulation results, verifying the correctness of the simulation results. This paper provided valuable insights into reasonable selection of tool parameters for improving machining precision. [ABSTRACT FROM AUTHOR]

A malunited distal radius fracture can lead to symptomatic ulnar impaction syndrome, which is a common cause for ulnar-sided wrist pain. If conservative treatment fails and symptoms persist after an arthroscopic ulnocarpal debridement, ulnar shortening osteotomy (USO) is the treatment of choice. Since the first USO described by Milch in 1941 after a malunited Colles fracture, many techniques have been described varying in surgical approach, type of osteotomy and osteosynthesis material used. Many studies demonstrated good to very good functional results after USO, reporting, however, a delayed union or non-union rate up to 18%. A modern, low profile, locking plate showed in our short-term study very good functional results and no implant-associated complications, in particular no non-union. [ABSTRACT FROM AUTHOR]

Although the literature generally agrees that displaced distal radius fractures require surgery, no single consensus exists concerning the length of immobilization and type of post-operative physiotherapeutic rehabilitation program. Palmar locking plate fixation represents a very stable fixation of the distal radius, and was assessed biomechanically in various studies. Surprisingly, most authors report additional immobilization after plate fixation. One reason might be due to the pain caused during active wrist mobilization in the early post-operative stages or secondly to protect the osteosynthesis in the early healing stages preventing secondary loss of reduction. This article addresses the biomechanical principles, current available evidence for early mobilization/immobilization and impact of physiotherapy after operatively treated distal radius fractures. [ABSTRACT FROM AUTHOR]

Wrist arthroscopy is mainly used to assist fracture reduction and fixation and to diagnose and treat concomitant injuries mainly to the scapholunate (SL), lunotriquetral (LT) ligament and the triangular fibrocartilage complex (TFCC). Arthroscopy is beneficial in improving anatomical reduction of fracture steps and gaps in intra-articular distal radius fractures (DRFs). Yet, the literature that the functional outcome correlates with the use of arthroscopy, is limited. Non-surgical treatment and immobilization is recommended for Geissler grade I-III Sl-ligament injuries, while open reduction, ligament suture and/or K-wire pinning is mandatory for complete ligament tears according to Geissler grade IV. This manuscript describes the current literature and gives insight into the authors' opinions and practice. [ABSTRACT FROM AUTHOR]

In the recent years, treatment of distal radius fractures (DRF) has advanced considerably. Surgical fixation with palmar angular stable plate has gained popularity, due to a reported lower complication rate when compared to dorsal fixation. The type of trauma or injury, surgical procedure and impaired bone quality are all contributors to complications in DRF. The main aim of this review is to summarize the most common complications and possible therapeutic solutions. In addition, strategies for minimizing these complications will be discussed. [ABSTRACT FROM AUTHOR]

Distal Radius fractures (DRF) are one of the most common injuries in the upper extremity and incidence is expected to rise due to a growing elderly population. The complex decision to treat patients operatively or conservatively depends on a large variety of parameters which have to be considered. No unanimous consensus has been reached yet, which operative approach and fixation technique would produce the best postoperative functional results with lowest complication rates. This article addresses the available evidence for indications, approaches, reduction, and fixation techniques in treating DRF. [ABSTRACT FROM AUTHOR]

Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell overcrowding may hamper cells from moving in certain directions or even from sensing beyond regions that practically act like physical barriers. We extend the non-local kinetic model proposed by Loy and Preziosi (J Math Biol, 80, 373–421, 2020) to include situations in which the sensing radius is not constant, but depends on position, sensing direction and time as the behaviour of the cell might be determined on the basis of information collected before reaching physically limiting configurations. We analyse how the actual possible sensing of the environment influences the dynamics by recovering the appropriate macroscopic limits and by integrating numerically the kinetic transport equation. [ABSTRACT FROM AUTHOR]