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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]

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]

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]

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]

The multi-objective optimisation of high-speed rail profile with small radius curve is studied in the paper. A multi-objective mathematical model for rail profile optimisation of high-speed railway is established. The CN60 rail profile is parameterised into a series of generalised functions of design variables. In order to guarantee the smoothness of the rail profile and meet the maximum grinding depth of rail in China, the constraints are employed. The wheel-rail vertical clearance and equivalent conicity of wheelset are taken as objective functions, and a rail wear prediction programme is compiled. Contact line method is employed to complete the detection algorithm of wheel-rail contact points. Finally, NSGA-II Algorithm is adopted to solve the Pareto-optimal front of the optimisation model. A set of solutions are retrieved from the Pareto optimal front solution as the optimised profile. The optimised rail profile and the original rail profile are matched with the LMA wheel profile (a certain worn type of wheel profiles for EMU in China) respectively. It is testified that the rail profile could effectively reduce the rail wear and improve curving performance. The new method proposed in this paper can provide some reference for the optimisation design of high-speed rail profile with small radius curve. [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]

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]

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]

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]

Ultrashort echo time (UTE) MRI techniques can be used to image the concentration of water in bones. Particularly, quantitative MRI imaging of collagen-bound water concentration (Cbw) and pore water concentration (Cpw) in cortical bone have been shown as potential biomarkers for bone fracture risk. To investigate the effect of Cbw and Cpw on the evaluation of bone mechanical properties, MRI-based finite element models of cadaver radii were generated with tissue material properties derived from 3 D maps of Cbw and Cpw measurements. Three-point bending tests were simulated by means of the finite element method to predict bending properties of the bone and the results were compared with those from direct mechanical testing. The study results demonstrate that these MRI-derived measures of Cbw and Cpw improve the prediction of bone mechanical properties in cadaver radii and have the potential to be useful in assessing patient-specific bone fragility risk. [ABSTRACT FROM AUTHOR]

A c-cyclic graph is a connected graph with n vertices and n + c−1 edges. In this paper, we consider the problem that: in the class of graphs, each of which is the complement graph of a c-cyclic graph with n vertices, which graph has the largest A α -spectral radius. We shall show that, for 0 ≤ c ≤ n − 4 , the extremal graph must be a graph with an isolated vertex. This implies that the maximum degree of G is larger, then the A α -spectral radius of its complement graph is also larger. We also determine the structure of the extremal graph with largest A α -spectral radius among the class of graphs, each of which is the complement graph of a c-cyclic graph with n vertices and maximum degree n−1 for 0 ≤ c ≤ n − 3 and n−2 for 0 ≤ c ≤ n − 4 , respectively. [ABSTRACT FROM AUTHOR]

During the magnetization of a granulated material with back filling of ferromagnetic spheres, the chains of contacting granules (spheres) serve as self-sufficient conductors of the magnetic flux. Each of such chains is characterized by a pronounced redistribution of the magnetic flux along its cross section. If in the chain of spheres with radius R the conditional core with radius r is selected, and then this core is surrounded by a loop placed between the contacting spheres in order to measure magnetic flux, it has been found that an increase in r decreases the thread density (magnetic induction). The data for magnetic flux are given for a different relative radius r/R of the cores of two chains differing only in R. For this purpose, the sensors created in the form of circular circuits based on thin printed circuit boards have been used. According to recorded magnetic flux, the detailed information on magnetic induction within the cores and their magnetic permeability under the magnetization of the chains in a solenoid has been obtained. It has been shown that as the ratio r/R increases, i.e., with the thickening in the conditional cores and the corresponding increase in magnetic flux, both magnetic induction and magnetic permeability significantly reduce. The complete mutual agreement of the corresponding r/R-dependence of magnetic induction and magnetic permeability is demonstrated for both chains, what indicates the potential in applying the results obtained for the chains of spheres of other radii. [ABSTRACT FROM AUTHOR]

Let (H, 〈 · , · 〉) be a complex Hilbert space and A be a positive bounded linear operator on H. The semi-inner product 〈x, y〉A: = 〈Ax, y〉, x, y ∈ H, induces a semi-norm ∥ ⋅ ∥ A on H. Let ωA(T) and ∥ T ∥ A denote the A-numerical radius and the A-operator semi-norm of an operator T in semi-Hilbertian space (H, 〈 · , · 〉A), respectively. In this paper, some new bounds for the A-numerical radius of operators in semi-Hilbertian space are obtained, which improve the existing ones. In particular, a refinement of the triangle inequality for A-operator semi-norm is also shown. [ABSTRACT FROM AUTHOR]

Let G be a graph with order n and size m. For each real number α ∈ [ 0 , 1 ] , the A α -matrix of a graph G is defined as A α (G) := α D (G) + (1 − α) A (G) , where D (G) = d i a g (d 1 , ... , d n) is the degree matrix of G, and A (G) is its adjacency matrix. The functions s (G) = ∑ 1 ≤ i ≤ n d i − 2 m n a n d v a r (G) = 1 n ∑ 1 ≤ i ≤ n d i − 2 m n 2 have been already used elsewhere as measures of graph irregularity. In this paper, we find several bounds for the spectral radius λ (G) of the matrix A α (G). Especially, when G is non-empty we prove for α ∈ [ 0 , 1) that s 2 (G) 2 n 2 n (2 α − α 2) Δ 2 + 2 (1 − α) 2 m ≤ λ (G) − 2 m n ≤ 1 + (2 α − α 2) n Ω (G) 2 + (1 − α) 2 s (G) , where Ω (G) = Δ (G) − ⌈ 2 m / n ⌉ + 1 and Δ (G) is the maximum vertex degree of G. These inequalities extend to the A α -matrix a Nikiforov's result involving the spectral radius of the adjacency matrix. In addition, for fixed order and size, we determine the graphs minimizing the degree variance v a r (G) and compute the A α -spectrum of some blown-up graphs. [ABSTRACT FROM AUTHOR]

In this paper, we firstly establish new numerical radius inequalities which refine a result of Kittaneh in [Studia Math. 168, 73–80 (2005)], then present some numerical radius inequalities involving non-negative increasing convex functions for n × n operator matrices, which generalize the related results of Shebrawi in [Linear Algebra Appl. 523(15), 1–12 (2017)]. [ABSTRACT FROM AUTHOR]

The distance Laplacian matrix of a connected graph G is defined as L (G) = T r (G) − D (G) , where Tr(G) is the diagonal matrix of the vertex transmissions in G and D(G) is the distance matrix of G. The largest eigenvalue of L (G) is called the distance Laplacian spectral radius of G. In this paper, we determine the graphs with the maximum distance Laplacian spectral radius and the minimum distance Laplacian spectral radius among all the bicyclic graphs with given order, respectively. [ABSTRACT FROM AUTHOR]

Swirling gas flow is an important topic of research that helps in the design of rockets, atomizers,and gas turbine combustors. In the present work, swirl flow inside annular geometries with constant and varying cross-sectional areas are examined using computational fluid dynamics (CFD). Effects of changing the flow and geometric parameters on the swirl behaviour were studied. Reynolds number was found to increase the swirl number in straight and diverging cross-sectional geometries while no significant effect of Reynolds number was observed in converging cross-sectional geometry. Radius ratio, defined as the ratio of the inner to the outer radius of the annular geometry, was found to have a significant effect on the swirl number. Decreasing the radius ratio, in straight and diverging annular geometry decreases the swirl number, however, an opposite trend was observed in the case of converging annular geometry due to significant increase in axial velocity as a result of reduced cross-sectional area. Increasing the swirler vane angle increased the swirl number. At higher vane angles of 60° and 70°, a recirculation zone is developed near the exit of the swirler. Using small cone angles was found to lower the swirl decay rate in converging and diverging nozzles. [ABSTRACT FROM AUTHOR]

Let D be a digraph of order n and let A (D) be the adjacency matrix of D. Let D e g (D) be the diagonal matrix of vertex out-degrees of D. For any real α ∈ [ 0 , 1 ] , the generalized adjacency matrix A α (D) of the digraph D is defined as A α (D) = α D e g (D) + (1 − α) A (D). The largest modulus of the eigenvalues of A α (D) is called the generalized adjacency spectral radius or the A α -spectral radius of D. In this paper, we obtain some lower bounds for the spectral radius of A α (D) in terms of the number of vertices, the number of arcs and the number of closed walks of the digraph D. The extremal graphs attained these lower bounds are determined. We also obtain some bounds for the spectral radius of A α (D) in terms of the vertex out-degrees, the vertex average 2-out-degrees of the vertices of D and parameter α. We characterize the extremal digraphs attaining these bounds. [ABSTRACT FROM AUTHOR]

For recognizing the coal-rock interface efficiently, the infrared thermal images of coal-rock interface excited by active thermal excitation are tested and extracted which results in rise of coal and rock with different spatiotemporal characteristics and the infrared temperature attenuation law of coal and rock surface are analysed. The coal-rock infrared image is segmented and denoised to recognize the coal-rock interface with different ratio. The experimental results show that: (1) Under the active thermal excitation, the infrared temperatures of coal, rock and transition layer increase at different rates with a faster temperature growth of coal and the growth of rock temperature is relatively gentle. With the increase of excitation distance, the temperature decreases gradually and fluctuation of surface temperature occurs due to closer distance;(2) No matter the coal seam or the rock stratum, the temperature decreases linearly during the cooling process; (3) The results of image recognition technology based on local optimization and adaptive radius constrained principal curve algorithm are consistent with the actual test samples of coal rock ratio and the maximum error is 0.56%. The analysis results in coal-rock interface recognition for improving the cutting efficiency of shearer and realizing intelligent drum height adjustment control. [ABSTRACT FROM AUTHOR]

This paper analyses the influence of friction coefficient and equivalent radius on the seismic reduction effect of friction pendulum bearings in the underground station under far-field and near-field earthquakes with different strength. It is found that the parameters of the friction pendulum bearings will obviously influence seismic reduction effectiveness. By combining genetic algorithm with finite element method, the parameters of friction pendulum bearings in the station can be optimized. By using this method, the optimal parameters range can be obtained, which can provide reference for parameter design of friction pendulum bearings in underground stations. [ABSTRACT FROM AUTHOR]

Free axisymmetric vibrations of uniform annular sandwich plates with relatively stiff core and membrane facings have been studied on the basis of Reddy's higher-order shear deformation theory. The core and facings are considered to be made up of isotropic materials. The governing equations of motion and natural boundary conditions are developed using Hamilton's principle. Chebyshev collocation technique is employed to obtain the frequency equations for clamped-clamped, clamped-simply supported and clamped-free edge conditions. The lowest three roots of these equations have been computed and reported as the values of frequency parameters for the first three modes of vibration. After validating the results of the proposed approach, detailed numerical results are given to analyze the effects of thickness of the core, face thickness and radii ratio on the natural frequencies. The results obtained for various plate parameters are compared numerically and graphically with those available in the literature. It also shows that the application of first-order theory is inappropriate for analyzing the vibration of annular sandwich plates with thick core. Three-dimensional mode shapes for a specified plate for all the three boundary conditions have been plotted. [ABSTRACT FROM AUTHOR]

A supertree is a connected and acyclic hypergraph. Let T m △ , △ be the set of the r-uniform supertrees with m edges and exactly two vertices of maximum degree ▵, where m ≥ 5 and 3 ≤ △ ≤ [ (m + 1) / 2 ]. We investigate the supertree with the minimum spectral radius among T m △ , △ . Several useful grafting operations are introduced for comparing the spectral radii of supertrees. The supertree with the minimum spectral radius among T m △ , △ is characterized. In addition, a new simple method is demonstrated to obtain the supertree with the minimum spectral radius among the set of r-uniform supertrees with m edges. [ABSTRACT FROM AUTHOR]

The scattering of a linearly polarized electromagnetic plane-wave from a sphere composed of an orthorhombic dielectric–magnetic medium having concentric layer of the chiral material is considered. The incident, the internal, and the scattered field phasors are expanded in terms of suitable sets of vector waves. By ensuring the continuity of the tangential components of electromagnetic fields across the chiral/ free-space and the chiral/ orthorhombic dielectric-magnetic interfaces, a relation between the incident and the scattered fields expansion coefficients by a transition matrix is obtained. Thereafter, the total scattering, absorption, forward-scattering, and backscattering efficiencies of the scattered field were calculated. The influences of the chirality parameter on various cross sections for different core–shell radii ratio are discussed numerically. [ABSTRACT FROM AUTHOR]

Let G be a digraph and A (G) be the adjacency matrix of G. Let D (G) be the diagonal matrix with outdegrees of vertices of G. For any real α ∈ [ 0 , 1 ] , define the matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G). The largest modulus of the eigenvalues of A α (G) is called the A α spectral radius of G. In this paper, we determine the digraphs which attain the maximum (or minimum) A α spectral radius among all strongly connected digraphs with given parameters such as girth, clique number, vertex connectivity or arc connectivity. We also propose an open problem. [ABSTRACT FROM AUTHOR]

One of the most crucial aspects of biaxial testing is the geometry of the cruciform specimen. The optimised cruciform geometry leads to obtain adequate stress-strain data. Different geometries of the cruciform specimen were investigated in the last few years, but none of them could be considered as a standard cruciform geometry. It is desirable to have more homogeneous stress and maximum plastic strain in the central area of the specimen. The parameters such as slit width, corner radius, and thickness of the specimen were varied during the FE simulation. The FE tool Abaqus Explicit with von Mises yield criterion was used. Nine alternatives were framed by using Taguchi L9 orthogonal array approach for parametric randomisation. The Technique of Order Preference by Similarity to Ideal Solution (TOPSIS) and Simple Additive Weighting (SAW) methods were employed to evaluate the overall performance of each alternative. The optimised geometry was further analysed with different stress ratios and slit width by keeping other parameters constant. It was noticed that the average plastic strain was decreased from 1.43% to 1.35% and 3.66% to 3.33% with the change in slit width from 0.2 mm to 0.6 mm at loading ratio 1:1 and 2:1, respectively. [ABSTRACT FROM AUTHOR]

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for H -matrices. The computational model can be thought of as a two-stage alternating iterative method, which well suits to the well-known Hermitian and skew-Hermitian splitting (HSS) approach, with the particularity here of considering only one inner iteration. Experimental parallel performance comparison is conducted between the generalized minimal residual (GMRES) algorithm, the standard HSS and our asynchronous variant, on both real and complex non-Hermitian linear systems, respectively, arising from convection–diffusion and structural dynamics problems. A significant gain on execution time is observed in both cases. [ABSTRACT FROM AUTHOR]

In this paper, we establish some numerical radius inequalities for 2 × 2 bounded linear operator defined on a complex Hilbert space. As a natural application, the existence of the all polynomial zeros is identified in a specific small disk. Moreover, we provide a refinement of an earlier numerical radius inequality due to Herzallah et al. [Numerical radius inequalities for certain 2 × 2 operator matrices. Integr Equ Oper Theory. 2011;71:129–147] and a generalization of Shebrawi's inequality [Numerical radius inequalities for certain 2 × 2 operator matrices II. Linear Algebra Appl. 2017;523:1–12]. [ABSTRACT FROM AUTHOR]

This paper uses vehicle system dynamics simulations to investigate curving resistance generated from the wheel-rail interface. More than 600 simulations were conducted using a freight wagon model to investigate the implications of curve radii, vehicle speeds and track superelevation for curving resistance, as well as the changes of curving resistance with wheelset Angle of Attack (AoA) and track cant deficiency. The results show that with the same curve radius, vehicle speeds and track superelevation can change the simulated curving resistance by 13–26%. Comparatively, vehicle speeds have stronger influences; resistance variations due to speed changes were about 16% larger than those due to superelevation changes. When the speed of the specific wagon was lower than 60 km/h, curving resistance decreases with both the increase of speed and the decrease of track superelevation. However, these trends can change to their opposite directions when speed reaches 70 or 80 km/h. Curving resistance increases with the increase of AoA and with the decrease of curve radii. The analyses of cant deficiency show that overbalanced speed cases generally have lower curving resistance. The results of the specific wagon indicated that zero cant deficiency did not generate the minimum curving resistance. [ABSTRACT FROM AUTHOR]

In low-permeability reservoirs, the average pore throat radius is small and the heterogeneity is severe, and the threshold pressure gradient exists obviously. Because of the pore throat radius sorting of porous media, the threshold pressure gradients of the pore throats with different radius are different, which leads to the asynchronism of the fluid participating in flow in the pore throats with different radius. The apparent permeability of the rock is a variable value before it reaches the average permeability of the rock, which makes low-velocity nonlinear porous flow come into being. The essence of nonlinear porous flow is the process of the fluid participating in porous flow gradually according to pore throat radius from large to small in pore throats with different radius under the combined action of threshold pressure gradient and pore throat radius sorting. This is an inevitable stage before the porous media reaches Darcy flow. The porous media keeps in nonlinear porous flow stage before all the pore throats participate in flowing. Based on the pore throat radius sorting of porous media, the nonlinear porous flow equation in low-permeability reservoirs was established using unequal-diameter parallel capillary bundle model with the capillary radius commonly in accordance with normal distribution. The equation can not only reveal low-velocity nonlinear porous flow mechanism but also describe the forming process of nonlinear porous flow. Furthermore, the equation is a general equation. Both Darcy's law and the pseudo-Darcy equation with the threshold pressure gradient in low-permeability reservoirs are the particular cases. [ABSTRACT FROM AUTHOR]

In this article, we consider the condition pseudospectrum of bounded linear operators on a Banach space. The condition pseudospectrum of normal matrices and Jordan blocks are characterized and condition pseudospectral radius of the classes are found. Sub-additivity and sub-multiplicativity of the condition pseudospectral radius for commuting pairs of bounded linear operators are proved. It is shown that the condition pseudospectral radius becomes a complete algebra norm in a commutative complex unital Banach algebra. Certain examples are given to illustrate the results. The results developed are also extended to a general setting. [ABSTRACT FROM AUTHOR]

The radius of robust feasibility is the maximal size of uncertain set in which the robust feasible set for an uncertain program is nonempty. In this paper, we employ robust optimization technique to study a class of uncertain convex conic program, and give its formulas for radius of robust feasibility under several data uncertain sets. First, with aid of the distance from the origin to the so-called epigraphcal set, we provide computable upper and lower bounds of the radius of robust feasibility for convex conic program in face of ball uncertainty. Second, a formula is presented for the radius of robust feasibility for robust convex optimization problem with SOS-convex polynomial constraints under ball uncertain sets. Finally, some exact formulas of radius of robust feasibility are given for convex conic program with piecewise linear function constraints under boxes or polytopes uncertain sets. [ABSTRACT FROM AUTHOR]

In this study, we analytically investigate the performances of annular fins with rectangular and hyperbolic profiles under partially wet conditions. We propose four equations for the profiles of enthalpy difference, four equations for heat transfer rates, and four equations for fin efficiency which is a function of interface radius. We then present four equations for evaluating interface radius. Results indicate that the heat transfer rate and efficiency of an annular fin with a rectangular profile is higher than that with a hyperbolic profile. The efficiency under partially wet conditions is between those under fully dry and fully wet conditions. The efficiency of fully dry fins is independent of relative humidity; however, for fully wet and partially wet conditions, efficiencies increase with decreasing relative humidity. At the same relative humidity, heat transfer rate increases with an increasing ratio of outside radius to inside radius. In contrast, fin efficiency decreases. By analytical method, the partially wet annular fin performances are investigated. Partially wet fin efficiency of annular fin of rectangular profile is presented. Partially wet fin efficiency of annular fin of hyperbolic profile is presented. [ABSTRACT FROM AUTHOR]

The design of rolling bearings must be optimized to get an improved fatigue life. As the fatigue life is directly affected by the dynamic capacity, therefore the later is considered as an objective function, which is to be maximized using a robust design optimization. Such design procedures enhance the qualities and reliability of products by ensuring that they are insensitive to the source of variabilities or uncertainties present in them, without eliminating these sources and at the same time maintaining the design feasibility with probabilistic constraints. In the present work, deep groove ball bearings (DGBBs) are designed in such a way that it will have minimum variation in the objective function due to the variation in design variables. A nonlinear constrained optimization problem is formulated with one objective function, ten design variables and a set of total thirty-five constraints. The real-coded genetic algorithm (GA) is used as the optimization tool. The result obtained shows the optimized bearings have improved fatigue life. A convergence study is performed to ensure global optima in the design space and further a sensitivity analysis is performed. The analysis shows that the dynamic capacity is the most sensitive to the variation in the inner groove curvature radius and least sensitive to the bearing pitch diameter. This paper allows the designers to design the rolling bearings by optimizing the fatigue life along with the minimization of their variations, which are due to variations or having tolerances in input design variables during its manufacturing. Moreover, the proposed design methodology is not limited to the bearings only, but can also be enforced in the design of any machine components (like clutches, gears, cams, levers, springs, etc.) having substantial uncertainties in their geometry or material, such as the residual strain, modulus, thickness, density, etc. [ABSTRACT FROM AUTHOR]

In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other inequalities, it is shown that if A is a bounded linear operator on a complex Hilbert space, then w 2 (A) ≤ ∫ 0 1 t A + 1 − t A ∗ 2 d t ≤ 1 2 A 2 + A ∗ 2 where w (A) and A are the numerical radius and the usual operator norm of A, respectively. [ABSTRACT FROM AUTHOR]

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in the literature. In this article, we present many new inequalities for the numerical radius of accretive matrices. The importance of this study is the presence of a new approach that treats a specific class of matrices, namely the accretive ones. While some of these inequalities can be considered as refinements of other existing ones, others present new insight to some known results for positive matrices. [ABSTRACT FROM AUTHOR]

New numerical radius inequalities for Hilbert space operators are given. These inequalities improve a well-known inequality of F. Kittaneh. We also show that the inequalities obtained here are sharp. A refinement of the triangle inequality is also shown. [ABSTRACT FROM AUTHOR]

The main goal of this article is to present generalized extensions of numerical radius inequalities involving the Euclidean operator radius and the numerical radius of some well-known operator quantities such as Heinz means, arithmetic mean and f-connection. [ABSTRACT FROM AUTHOR]

A non-iterative method is proposed to evaluate surface tension and contact angle simultaneously from a sessile drop observation in gravity using two universal figures. A theory of the sessile drop in gravity is used assuming an axisymmetric profile of the drop. Numerical calculation is carried out to prepare the two figures. The first one of the figures is a relation between the normalized curvature at the top of the drop and the geometry ratio of height to radius of a point on the drop surface. The second one of the figures is a relation between the normalized curvature and the normalized height of the point. The position and the tangential angle of the point on the drop surface are obtained from the sessile drop observation. Using the first figure, the normalized curvature can be determined from the position and the tangential angle of the point. Using the second figure, the normalized height of the point can be determined from the normalized curvature determined. Since the height and the normalized heights can be obtained from the measurement, the normalizing factor can be obtained. Because the factor is a function of the gravity and the surface tension of the liquid, we can evaluate the surface tension of the liquid from the point on the sessile drop surface. By taking average using several points, we can improve accuracy of the surface tension evaluated. Also, the first figure can be used to evaluate the contact angle from the position of the drop edge without measurement of angle. The present method is demonstrated using a pure water droplet on a water-repellent surface. It shows a successful evaluation of the surface tension and the contact angle, simultaneously from the droplet observation, without any iterative calculation. [ABSTRACT FROM AUTHOR]

It is well known that the numerical stability of many finite difference time-stepping algorithms for solving the Kolmogorov differential equations for Markov jump processes depends on the magnitude of the spectral radius of the rate matrix. In this paper, we develop bounds on the spectral radius that rigorously establish that the spectral radius typically scales in proportion to the maximal jump rate. Our analysis also provides rigorous bounds on the stiffness of the rate matrix, when the process is reversible. [ABSTRACT FROM AUTHOR]

We explore the analysis of exact three-dimensional free vibrations of visco-thermoelastic solid cylinder, which has been considered at a uniform temperature and undeformed initially in the framework of generalized thermoelasticity. The formulation has been implemented with two relaxation time parameters, i.e., mechanical and thermal relaxation parameters. The series solution has been implemented to solve the differential equations along with the evaluation of stresses, displacements, and temperature by applying stress-free, rigidly fixed, thermally insulated and isothermal boundary conditions. The relations of frequency equations for the existence of different modes of visco-thermoelastic solid cylinder have been developed in compact form using assumed boundary conditions. Thermoelastic damping and frequency shift are presented graphically from the data generated by computations and simulations of numerical results. Also, the natural frequencies are represented in the form of tables which show that with an increase in the ratio of length to the radius and axial wave-number, the variation of vibrations keeps increasing. [ABSTRACT FROM AUTHOR]

The governing equations of electro-elastic bending problem are derived for size-dependent electro-elastic analysis of three-layered piezoelectric doubly curved nano shells. The three-layered nano shell is composed of an elastic homogeneous core and two piezoelectric nano layers at top and bottom. The doubly curved piezoelectric nano shell is subjected to applied electric potential and transverse loads. A comparative study is presented for validation of formulation and solution. The influence of nonlocal parameter, applied electric potential, and geometric parameters such as radii of curvature and ratio of thickness is studied on the electro-elastic results of the simply-supported doubly curved nano shell. [ABSTRACT FROM AUTHOR]

Poor coordination between geometric elements of horizontal curves can lead to unsafe speed. This study evaluated the effect of horizontal curve geometry on vehicle speed distribution for a four-lane divided highway and developed prediction models for mean speed and standard deviation. Spot speed data of passenger cars (PC), heavy commercial vehicles and light commercial vehicles were collected at 24 horizontal curves. Statistical analysis of the speed data of randomly selected 10 sites revealed PC as the critical vehicle category. Hence, the effects of horizontal curve geometry on PC speed were analyzed and radius was identified as the most influencing parameter. Radius beyond 400 m had similar influence on speed distributions. Appropriate models were developed using regression analysis. Degree of curvature was found as the most significant predictor. Benefits of the proposed models over traditional 85th percentile speed in designing and evaluating horizontal curves for consistency and safety were discussed. [ABSTRACT FROM AUTHOR]

In this study, the wetting states and wetting transition of droplets on the microstructured surfaces are investigated using the multiphase lattice Boltzmann method. The Cassie-Baxter (Cassie) and Wenzel wetting states on the rough surfaces are captured through the simulations, and the stability of Cassie state and the wetting transition are then studied and discussed by simulating the evaporation of droplets on several specified microstructured surfaces. The simulated apparent contact angles of the droplet on various rough surfaces fit the theoretical predictions very well. The results also present the coexistence of the Wenzel and Cassie states when the substrate is moderately hydrophobic with its Young's angle smaller than the critical angle. In addition, the "De-pinning" wetting transition from Cassie to Wenzel state is observed for the moderately hydrophobic substrate once the droplet reduces to its critical radius, while the stable Cassie state is obtained when the substrate's Young's angle larger than the critical angle. The simulated critical radii for wetting transition are in quantitative agreements with the analytical values for different surface geometries and Young's angles. This work provides mesoscopic information necessary for understanding the wetting phenomena on microstructured rough surfaces. [ABSTRACT FROM AUTHOR]

The novel implementation of three evolutionary optimisation algorithms, namely quantum particle swarm optimisation (QPSO), teaching-learning based optimisation (TLBO) and symbiotic organism search (SOS) for thinning of multiple concentric circular array antenna with isotropic array elements for the simultaneous optimisation of the sidelobe levels (SLLs) as well as peak directivity is presented in this work. The performance studies as cases 1 and 2 are made with two control parameters: interring radii and number of switched 'on–off' elements in each ring. The comparative study of the three algorithms has been carried out using common parameters. Finally, experimental results show that case 2 outperforms case 1 with regard to SLL and directivity. Apart from this, the results of SOS have been shown to be better than the other two state of art meta-heuristic optimisation after comparing their effectiveness based on SLL, peak directivity, mean value, and standard deviation along with best cost. For statistical validation of both cases, t-test has been done for testing the stability of SOS over QPSO and TLBO. [ABSTRACT FROM AUTHOR]

Description of convergence domains for multiple power series is a quite difficult problem. In 1889 J.Horn showed that the case of hypergeomteric series is more favourable. He found a parameterization formula for surfaces of conjugative radii of such series. But until recently almost nothing was known about the description of convergence domains in terms of functional inequalities ρ j (| a 1 | , ... , | a m |) < 0 relatively moduli | a i | of series variables. In this paper we give a such description for hypergeometric series representing solutions to tetranomial algebraic equations. In our study we use the remarkable observation by M. Kapranov (1991) consisting in the fact that the Horn's formulae give a parameterization of discriminant locus for a corresponding A-discriminant. We prove that usually the considered convergence domains are determined by a signle or two inequalities ρ (| a t | , | a s |) ≶ 0 , where ρ is a reduced discriminant. [ABSTRACT FROM AUTHOR]

In this paper, by characterizing the ratio of the smallest and largest values of a Perron vector, we propose some Ostrowski-type bound estimations for the spectral radius of weakly irreducible nonnegative tensors which improve the existing results. Based on Brualdi-type eigenvalue inclusion sets and Gershgorin eigenvalue inclusion sets, we establish some new Ky Fan-type theorems for weakly irreducible nonnegative tensors. [ABSTRACT FROM AUTHOR]

In this paper we consider the spectral radii of a special set system called hypertrees, i.e. connected acyclic hypergraphs. By employing the theory of matching polynomial of hypertrees and ordering of hypertrees, we determine the largest spectral radius of hypertrees with m edges and given size of matching. [ABSTRACT FROM AUTHOR]

Mud and gravel deposition often occurs in circulation systems of pumps. In this paper, a liquid-solid coupling method combining CFD and DEM is proposed to study two-phase flow behavior of water, The flow characteristics of water-clay mud and the motion characteristics of gravel were simulated under different discharge pipe bending radii and geometry shape conditions. Numerical results showed that for a circular cross section pipe with a fixed bending radius, the collision times between the gravel particles and the pipe wall decreased with the increase of the bending radius. [ABSTRACT FROM AUTHOR]