Search

We review recent developments concerning the soft factorization of scattering amplitudes that arise in the large radius limit of four dimensional Anti-de Sitter (AdS4) spacetimes. This includes the presence of AdS radius dependent corrections of known flat spacetime soft factors and their implication on the relationship between soft theorems and Ward identities of the boundary conformai field theory. [ABSTRACT FROM AUTHOR]

Most works on Support Vector Regression (SVR) focus on kernel or loss functions, with the corresponding support vectors obtained using a fixed-radius ε -tube, affording good predictive performance on datasets. However, the fixed radius limitation prevents the adaptive selection of support vectors according to the data distribution characteristics, compromising the performance of the SVR-based methods. Therefore, this study proposes an "Alterable ε i -Support Vector Regression" (A ε i -SVR) model by applying a novel ε , named "Alterable ε i ," to the SVR model. Based on the data point sparsity at each location, the model solves the different ε i at the corresponding position, and thus zoom-in or zoom-out the ε -tube by changing its radius. Such a variable ε -tube strategy diminishes noise and outliers in the dataset, enhancing the prediction performance of the A ε i -SVR model. Therefore, we suggest a novel non-deterministic algorithm to iteratively solve the complex problem of optimizing ε i associated with every location. Extensive experimental results demonstrate that our approach can improve the accuracy and stability on simulated and real data compared with the baseline methods. [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 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]

For a simple connected graph G , the generalized distance matrix D α (G) is defined as D α (G) = α Tr (G) + (1 − α) D (G) , 0 ≤ α ≤ 1 , where Tr (G) and D (G) are, respectively, the diagonal matrix of vertex transmission degrees and the distance matrix of G. In this paper, we will study the spectral radius of the generalized distance matrix D α (G) of a connected graph G. We obtain some upper and lower bounds for the generalized distance spectral radius in terms of various parameters, like the vertex transmission degrees, the average transmission 2-degrees, etc., associated with the structure of the graph. We characterize the extremal graphs attaining these bounds. Further, we show that our bounds improve some previously known bounds existing in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a model based on constraint convex optimization is proposed for the radiation pattern synthesis in cylindrical and spherical microstrip conformal array antennas. The optimization algorithm is modeled to decrease the Euclidean distance between the obtained radiation pattern of the deformed array and the desired radiation pattern of the planar array by calculating the suitable amplitude and phase values for the individual array patches. Four prototypes of 2 × 2 , 3 × 3 , 4 × 4 , and 5 × 5 microstrip patch array antenna are used as the radiating elements which are deformed from planar arrangement and placed on the faces of prescribed spherical and cylindrical shapes with various radii of curvatures. The results reveal that the performance of optimization algorithm performs better in 5 × 5 array, followed by 4 × 4 array, 3 × 3 array, and 2 × 2 array. However, 5 × 5 array provides more degrees of freedom for tuning the radiation pattern in desired form. The 5 × 5 array computes suitable amplitude and phase values for the radiating elements of the array, which restore the radiation pattern in terms of mainlobe reconstruction, null locations, sidelobe levels, up to the deformation of 20   cm in both spherical and cylindrical configurations of conformal array. The proposed optimization technique when applied to conformal antenna array offers fast computational speed and good convergence accuracy for radiation pattern synthesis, which can be useful for various engineering applications. [ABSTRACT FROM AUTHOR]

We give some new bounds for the numerical radii of the off-diagonal parts of 2 × 2 operator matrices. A refinement of the triangle inequality for the operator norm is also given. [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]

Recent observations demonstrate that misalignments and other out-of-plane structures are common in protoplanetary discs. Many of these have been linked to a central host binary with an orbit that is inclined with respect to the disc. We present simulations of misaligned circumbinary discs with a range of parameters to gain a better understanding of the link between those parameters and the disc morphology in the wave-like regime of warp propagation that is appropriate to protoplanetary discs. The simulations confirm that disc tearing is possible in protoplanetary discs as long as the mass ratio, μ, and disc–binary inclination angle, i , are not too small. For the simulations presented here, this corresponds to μ > 0.1 and i ≳ 40°. For highly eccentric binaries, tearing can occur for discs with smaller misalignment. Existing theoretical predictions provide an estimate of the radial extent of the disc in which we can expect breaking to occur. However, there does not seem to be a simple relationship between the disc properties and the radius within the circumbinary disc at which the breaks appear, and furthermore the radius at which the disc breaks can change as a function of time in each case. We discuss the implications of our results for interpreting observations and suggest some considerations for modelling misaligned discs in the future. [ABSTRACT FROM AUTHOR]

We develop a self-consistent and accurate halo model by partitioning matter according to the depletion radii of haloes. Unlike conventional models that define haloes with the virial radius while relying on a separate exclusion radius or ad hoc fixes to account for halo exclusion, our model distributes mass across all scales self-consistently and accounts for both the virialized and non-virialized matter distribution around each halo. Using a cosmological simulation, we show that our halo definition leads to very simple and intuitive model components, with the one-halo term given by the Einasto profile with no truncation needed, and the halo–halo correlation function following a universal power-law form down to the halo boundary. The universal halo–halo correlation also allows us to easily model the distribution of unresolved haloes as well as diffuse matter. Convolving the halo profile with the halo–halo correlation function, we obtain a complete description of the halo–matter correlation across all scales, which self-consistently accounts for halo exclusion at the transition scale. Mass conservation is explicitly maintained in our model, and the scale dependence of the classical halo bias is easily reproduced. Our model can successfully reconstruct the halo–matter correlation function within an accuracy of 9 per cent for halo virial masses in the range of 1011.5 h −1 M⊙ < M vir < 1015.35 h −1 M⊙ at z  = 0, and covers the radial range of 0.01 h −1 Mpc < r < 20 h −1 Mpc. We also show that our model profile can accurately predict the characteristic depletion radius at the minimum bias and the splash-back radius at the steepest density slope locations. [ABSTRACT FROM AUTHOR]

Extending certain scalar and norm inequalities, we present new inequalities for the numerical radius, which generalize and refine some known results. Applications of the obtained inequalities include a new original proof of the matrix arithmetic-geometric mean inequality and certain extensions of some well-established results from the literature for products of matrices. [ABSTRACT FROM AUTHOR]

Curved concrete box beams are commonly used for their superior integrality performance and greater torsional stiffness. This paper investigates the torsional behavior of these beams using both experimental and finite element analyses. The experiment is based on a 1:6 scale model of a three-span curved girder bridge with a small radius. The study examines six different load cases, including central vertical and eccentric vertical loads. The study reports the detailed reaction forces of the supports, as well as the displacements and strains of the mid-span section. Finite element models are established to analyze the warping behavior of the curved concrete box beams. Based on the experimental and FEM analysis, the following conclusions are noted. Firstly, in the central load case, the strain of the curved concrete box girder is close to a straight line, so the curved concrete box girders follows the plane-section assumption. Besides, the warping normal stress is produced in curved concrete box girder in eccentric load cases. Moreover, the ratio of warping normal stress to bending normal stress is smaller and smoother in the section with diaphragms than that without diaphragms. And this ratio decreases with an increase in the curvature radius and diaphragm number. This study contributes to the theoretical and numerical modeling of a large span curved girder bridge with a small radius. [ABSTRACT FROM AUTHOR]

Let B (H) be the algebra of all bounded linear operators on a Hilbert space H and let N (⋅) be a norm on B (H). For every 0 ≤ ν ≤ 1 , we introduce the w (N , ν) (A) as an extension of the classical numerical radius by w (N , ν) (A) : = sup θ ∈ R ⁡ N (ν e i θ A + (1 − ν) e − i θ A ⁎) and investigate basic properties of this notion and prove inequalities involving it. In particular, when N (⋅) is the Hilbert–Schmidt norm ‖ ⋅ ‖ 2 , we present several the weighted Hilbert–Schmidt numerical radius inequalities for operator matrices. Furthermore, we give a refinement of the triangle inequality for the Hilbert–Schmidt norm as follows: ‖ A + B ‖ 2 ≤ 2 w (‖ ⋅ ‖ 2 , ν) 2 ([ 0 A B ⁎ 0 ]) − (1 − 2 ν) 2 ‖ A − B ‖ 2 2 ≤ ‖ A ‖ 2 + ‖ B ‖ 2. Our results extend some theorems due to F. Kittaneh et al. (2019). [ABSTRACT FROM AUTHOR]

The eccentricity matrix ɛ (G) of a graph G is obtained from the distance matrix D (G) by retaining only for each row and each column the largest distance, and setting the remaining elements as 0. In this paper, we firstly show that the eccentricity matrix of clique trees is irreducible. We identify the t -clique trees with given diameter odd d having the maximum ɛ -spectral radius, and the corresponding extremal graphs are also determined. We determine the upper bounds for the ɛ -spectral radius of t -clique trees which d and n satisfy that one is odd and the other is even. Finally, we propose some potential topics for further study. [ABSTRACT FROM AUTHOR]

Most computer‐aided optimization procedures for horizontal alignment optimization of roads require the use of information such as horizontal points of intersection (PIs) to determine an alignment. In these methods, to obtain parameters such as the radius of the curve corresponding to a specific PI, the previous and next PIs must be known. In this paper, a sequential exploration algorithm (SEA) is proposed, and the algorithm continuously explores the entire optimization space through certain steps. Only the parameters of the previous node are required to determine the current node's parameters during the exploration process, avoiding the tight coupling between PIs in traditional optimization algorithms. Furthermore, the proposed SEA does not require assumptions about the positions and numbers of the PIs, and it can design near‐optimal road alignments that match geometric restrictions and automatically take transition curves into account. Another feature of the proposed algorithm is that it directly optimizes the geometric element parameters based on the actual milepost, and it is a fully collaborative optimization approach that does not require secondary optimization nesting during the optimization process. Analyses comparing the optimization effects of different algorithms are performed on a numerical case, that is, a problem of avoiding obstacles, and two actual cases from the literature, that is, a new road design problem and an existing road reconstruction problem. It is discovered that the proposed SEA results in an approximately 3% to 10% improvement in optimization effects when compared to two current cutting‐edge optimization algorithms. This work offers a new perspective on road alignment optimization by merging discrete and continuous optimizations, with a discrete component handling optimization accuracy and a continuous component handling real optimization. [ABSTRACT FROM AUTHOR]

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

Let A be a bounded linear operator defined on a complex Hilbert space and let | A | = (A * ⁢ A) 1 2 . Among other refinements of the well-known numerical radius inequality w 2 ⁢ (A) ≤ 1 2 ⁢ ∥ A * ⁢ A + A ⁢ A * ∥ , we show that w 2 ⁢ (A) ≤ 1 4 ⁢ w 2 ⁢ (| A ⁢ | + i | ⁢ A * |) + 1 8 ⁢ ∥ | A | 2 + | A * | 2 ∥ + 1 4 ⁢ w ⁢ (| A | ⁢ | A * |) ≤ 1 2 ⁢ ∥ A * ⁢ A + A ⁢ A * ∥ . Also, we develop inequalities involving the numerical radius and the spectral radius for the sum of the product operators, from which we derive the inequalities w p ⁢ (A) ≤ 1 2 ⁢ w ⁢ ( | A | p + i ⁢ | A * | p ) ≤ ∥ A ∥ p for all p ≥ 1 . Further, we derive new bounds for the zeros of complex polynomials. [ABSTRACT FROM AUTHOR]

We prove that if every bounded linear operator (or N-homogeneous polynomials) on a Banach space X with the compact approximation property attains its numerical radius, then X is a finite dimensional space. Moreover, we present an improvement of the polynomial James' theorem for numerical radius proved by Acosta, Becerra Guerrero and Galán [Q. J. Math. 54 (2003), pp. 1–10]. Finally, the denseness of weakly (uniformly) continuous 2-homogeneous polynomials on a Banach space whose Aron-Berner extensions attain their numerical radii is obtained. [ABSTRACT FROM AUTHOR]

Bendway weirs are low-level transverse structures constructed on the outer bank of a channel bend to improve navigation, create aquatic habitat and control bend migration. This experimental study was aimed at investigating the erosion and sedimentation patterns in a 90° bend by varying the relative curvature radius (i.e. normalized to the channel width), in the absence and in the presence of bendway weirs, under different flow conditions. A series of flat weirs with relative heights of 30% and 70% were considered. The results indicate that as the relative curvature increases, the erosion near the weirs decreases while the point-bar at the inner bend wall extends. Regardless of the weir height, the increase in the relative curvature leads to a deeper scour depth at the tip of the weirs. Bendway weirs with submergence ratio of 70% are found to be the most efficient in protecting the outer bank from erosion. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The microsphere profile of probe tips has to be measured and compensated to improve the measurement accuracy of micro-coordinate measuring machines (micro-CMMs) to less than several hundred nanometers. A high-precision radius and sphericity measurement method for the microsphere of the CMM probe tip is proposed in this article. Different circumferences of the tested microsphere are measured, and the true radius of any measuring point on the surface can be obtained after separating the runout errors. Then the sphericity of the tested microsphere can be evaluated by the minimum zone sphere method. A corresponding measuring system is developed based on the analysis of the primary error model and mechanical model, and verification experiments are conducted using a ruby microsphere (A-5000-7801, Renishaw Corporation) as the reference, whose claimed diameter and sphericity are 700 µm and 130 nm, respectively. Six groups of repeated experiments are performed, and 18 000 measurement points on 15 circumferences are recorded in each group of experiments. Results show that the average radius of the tested microsphere is 350.003 µm, and the average sphericity error is 208 nm with a standard deviation of 5.3 nm. Finally, the expanded uncertainty of the measurement results of the developed system is calculated as 209 nm (k = 1.96, normal distribution). The proposed method and system can be used in the precision measurements and compensations for probe tips of micro-CMMs and other parts, such as microspheres used in micro-bearings and micro-manufacturing machines. [ABSTRACT FROM AUTHOR]

A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical tube inserted into a streambed (Solomon et al., 2020, https://doi.org/10.1029/2019WR026983). The ability to infer flux values with high temporal resolution relies on an accurate interpretation of water level dynamics inside the tube. Here, we reduce the three‐dimensional hydrodynamic problem that describes the ASM water level in a variety of field conditions to a single ordinary differential equation. This novel general analytical solution for estimating ASM responses is more comprehensive and flexible than previous approaches and is applicable to the entire range of field conditions, including steady or transient stream stages, evaporation, rainfall, and noise. For example, our analysis determines the timing of the nonmonotonic ASM response to a monotonic linear stream stage variation and explains previously used empirical parabolic approximation for estimating fluxes. We present algorithms for simultaneous inference of vertical interface flux and hydraulic conductivity values together with an example code. We quantify how the accuracy of parameter estimation depends on test duration and noise amplitude and propose how our analysis can be used to optimize field test protocols. On this basis, changing the ASM geometry by increasing the radius and decreasing tube insertion depth may enable ASM field test protocols that estimate interface flux and hydraulic conductivity faster while maintaining desired accuracy. Potential applications of joint parameter estimation are suggested. Key Points: A generalized equation of water level dynamics in the Automatic Seepage Meter valid for a variety of field conditionsThe theory considers surface water level fluctuations, evaporation, rainfall, and ambient noiseWater flux and vertical hydraulic conductivity estimation accuracy is analyzed with examples and recommendations [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]

This paper proposes two effective nonmonotone trust-region frameworks for solving nonlinear unconstrained optimization problems while provide a new effective policy to update the trust-region radius. Conventional nonmonotone trust-region algorithms apply a specific nonmonotone ratio to accept new trial step and update the trust-region radius. This paper recommends using the nonmonotone ratio only as an acceptance criterion for a new trial step. In contrast, the monotone ratio or a hybrid of monotone and nonmonotone ratios is proposed as a criterion for updating the trust-region radius. We investigate the global convergence to first- and second-order stationary points for the proposed approaches under certain classical assumptions. Initial numerical results indicate that the proposed methods significantly enhance the performance of nonmonotone trust-region methods. [ABSTRACT FROM AUTHOR]

Large values and gradients of stress and strain, triggering concentrated stress and strain, arise in angular areas of a structure. The strain action, leading to the finite loss of contact between structural elements, also triggers concentrated stress. The loss of contact reaches an irregular point and a line on the boundary. The theoretical analysis of the stress–strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous strain is reduced to the study of singular solutions to the homogeneous problem of elasticity theory with power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the area located near the vertex of an angular cutout in the boundary features substantial strain and rotations, and it corresponds to higher values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighborhood of an irregular boundary point. As far as these areas are concerned, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of strain, to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equilibrium equation in the polar system of coordinates for a V-shaped area under the action of temperature-induced strain, taking into account geometric non-linearity and physical linearity. [ABSTRACT FROM AUTHOR]

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

In this paper, we characterize bounded linear operators A,B on a complex Hilbert space such that inf λ∈C ||A+B-λ I|| = inf λ∈C ||A-λ I||+ inf λ∈C ||B-λ I||, where I is the identity operator. We also establish some inequalities satisfied by the distance from scalar operators for products of two complex Hilbert space operators. [ABSTRACT FROM AUTHOR]

Generalizing the notion of numerical range and numerical radius of an operator on a Banach space, we introduce the notion of joint numerical range and joint numerical radius of tuple of operators on a Banach space. We prove that on a finite-dimensional Banach space, the joint numerical radius can be retrieved from the extreme points. Furthermore, we introduce a notion of joint numerical index of a Banach space. We explore the same for direct sum of Banach spaces. Applying these results, finally we compute the joint numerical index of some classical Banach spaces. [ABSTRACT FROM AUTHOR]

The local metric dimension is one of many topics in graph theory with several applications. One of its applications is a new model for assigning codes to customers in delivery services. Let G be a connected graph and V(G) be a vertex set of G. For an ordered set W = fx1; x2;: :: ; xkg - V(G), the representation of a vertex x with respect to W is rG(xjW) = f(d(x; x1); d(x; x2);: :: ; d(x; xk)g. The set W is said to be a local metric set of G if r(xjW), r(yjW) for every pair of adjacent vertices x and y in G. The eccentricity of a vertex x is the maximum distance between x and all other vertices in G. Among all vertices in G, the smallest eccentricity is called the radius of G and a vertex whose eccentricity equals the radius is called a central vertex of G. In this paper, we developed a new concept, so-called the central local metric dimension by combining the concept of local metric dimension with the central vertex of a graph. The set W is a central local metric set if W is a local metric set and contains all central vertices of G. The minimum cardinality of a central local metric set is called a central local metric dimension of G. In the main result, we introduce the definition of the central local metric dimension of a graph and some properties, then construct the central local metric dimensions for trees and establish results for the grid graph. [ABSTRACT FROM AUTHOR]

The purpose of this note is to present upper bounds estimations for the numerical radius of a products and Hadamard products of special matrices, including sectorial and accretivedissipative matrices. [ABSTRACT FROM AUTHOR]

Our aim in this article is to establish several new norm and numerical radius inequalities for products and sums of operators acting on a complex Hilbert space (H , 〈 · , · 〉) . Some of the obtained inequalities improve well known ones. In addition, by using new techniques, we prove certain new inequalities related to ω A (·) and | | · | | A , where ω A (T) and | | T | | A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (H , 〈 · , · 〉 A) , respectively. Here 〈 x , y 〉 A : = 〈 A x , y 〉 for every x , y ∈ H . [ABSTRACT FROM AUTHOR]

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

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]

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]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of China University of Petroleum is the property of China University of Petroleum and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which are generalizations of Hilbert spaces. We demonstrate how these new inequalities can be employed to derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator in a complex Hilbert space. Some of our novel A-numerical radius inequalities expand upon the existing literature on numerical radius inequalities with Hilbert space operators, which are important tools in functional analysis. We use techniques from semi-Hilbert space theory to prove our results and highlight some applications of our findings. [ABSTRACT FROM AUTHOR]

[Display omitted] • Depth-controlled TiO 2 nanotraps are constructed by an area-selective atomic layer method. • TiO 2 nanotrap's depth determines both the exposed sites and the electronic states of Au. • The particle migration-coalescence of Au can be suppressed by TiO 2 nanotraps. • Balance between stability and activity of Au can be achieved by tuning nanotraps' depth. The sintering of nanoparticles has always been a great challenge for supported Au catalysts. Herein, we fabricate a depth-controlled TiO 2 nanotrap via area-selective atomic layer deposition (ALD) method to balance the activity and anti-sintering properties of Au nanoparticles. Au nanoparticles anchored by a 2.31 nm deep TiO 2 nanotrap prepared by 25 ALD cycles of TiO 2 exhibit the best overall activity for CO oxidation, where the depth of TiO 2 nanotrap is close to the geometric radius of Au nanoparticle. It exhibits enhanced sintering resistance while retaining an activity similar to that of pure Au catalyst. The average size of sintered Au (8.4 ± 2.7 nm) is three times smaller than that of pure Au catalyst (21.1 ± 7.1 nm) after calcination in air at 700 °C. The performance of TiO 2 nanotrapped Au catalyst breaks the conventional trade-off between the activity and anti-sintering capability of Au by exposing active sites, and hindering Au migration-coalescence simultaneously, which serves as a promising strategy to design highly stable Au catalysts. [ABSTRACT FROM AUTHOR]

The dispersive and Strichartz estimates are essential for establishing well posedness results for nonlinear equations as well as long time behaviour of solutions to the equation. While in the boundary-less case these estimates are well understood, the case of boundary the situation can become much more difficult. In this work, we establish local in time dispersive estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains ⊂ Ω R³ with smooth boundary ∂Ω ≠ ø. In this paper, we provide detailed proofs of the results established in [16, 17]. Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair, Smith, Sogge [4, 5]. Optimal estimates in strictly convex domains have been obtained in [12]. Our case of cylindrical domains is an extension of the result of [12] in the case when the nonnegative curvature radius depends on the incident angle and vanishes in some directions. [ABSTRACT FROM AUTHOR]

A structural solution was proposed to enable passive control of the wheelsets of a motorised metro car on curved track with a small curve radius. This effect was achieved by varying the stiffness of the guidance of the wheelsets in the horizontal plane of the frame of each bogie on which the wagon body rests. This ensured the required critical speed of the metro wagon when moving on straight track, and allowed for reduced mechanical wheel wear and better steering of the bogies when moving on curved track with a small radius of curvature. Parameters specific to the design of modern metro cars were taken into account. Current knowledge of non-linear lateral dynamics of rail vehicles and the specialist computer programme Vi-Rail were used to perform the calculations involving simulation models. [ABSTRACT FROM AUTHOR]

This paper presents the theoretical and experimental results of a study investigating a new method for tube bending. The method involves three-point bending of a tube without using a mandrel. The bending process was conducted with a small bending radius of Rg = 1.5Dz (where Dz is the outside diameter of the bent tube) and a large bending angle of 180°. The novelty of the proposed solution is the use of new shapes of bending roll impression. Instead of the standard circular-shaped impression, an elliptical-shaped impression was used. The aim of the study on the proposed small radius tube bending technique was to optimize the shape of roll impression in terms of minimizing ovalization and flattening of the tube cross section in the bending zone. Previous studies only showed that circular impressions were inefficient. The tube bending process conducted with a circular impression roll, without the use of a mandrel or other type of filling to achieve an angle ranging 90°÷180°, led to the flattening of the cross section. The tube wall in the upper zone would crack or its cross section would become deformed and oval. This theoretical and experimental study was conducted on tubes with an outside diameter of Dz = 20 mm and a wall thickness of g = 2 mm, made of 16Mo3 boiler steel and EN-AW 6060 aluminum alloy. Obtained results were then used to determine the ranges of bending roll impression parameters that ensured that the product would meet the standardized conditions of cross-sectional ovalization in the bending zone. The tool developed for this study can be applied in industrial practice. [ABSTRACT FROM AUTHOR]

First principles based beyond Born–Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin–orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A′, 22A′, and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn–Teller (JT) type conical intersections between the two A′ states translate along C2 v and linear geometries in F + H2. In addition, A′ and A″ states undergo Renner–Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system. [ABSTRACT FROM AUTHOR]