Ball Of Radius Research Articles

On p-harmonic measures in half-spaces

For all $1<p<\infty$ and $N\ge 2$ we prove that there is a constant $\alpha(p,N)>0$ such that the $p$-harmonic measure in $\R^N_+$ of a ball of radius $0 < \delta \leq 1$ in $\R^{N-1}$ is bounded above and below by a constant times $\delta ^{\alpha (p.N)}$. We provide explicit estimates for the exponent $\alpha(p,N)$

Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth-Order Convergence

The main contribution of this study is to present a new optimal eighth-order scheme for locating zeros with multiplicity m≥1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth-order convergence of the proposed scheme. Moreover, a local convergence study for the optimal fourth-order method defined by the first two steps of the new method is presented, allowing us to obtain the radius of the local convergence ball. Finally, numerical tests on some real-life problems, such as a Van der Waals equation of state, a conversion chemical engineering problem, and two standard academic test problems, are presented, which confirm the theoretical results established in this paper and the efficiency of this proposed iterative method. We observed from the numerical experiments that our proposed iterative methods have good values for convergence radii. Further, they not only have faster convergence towards the desired zero of the involved function but also have both smaller residual error and a smaller difference between two consecutive iterations than current existing techniques.

Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is a locally $\left(1-\frac{1}{n}\right)$-H\"older continuous function and so in particular it is continuous. Here for bounded geometry we mean that $M$ have $Ricci$ curvature bounded below and volume of balls of radius $1$, uniformly bounded below with respect to its centers. We prove also the equivalence of the weak and strong formulation of the isoperimetric profile function in complete Riemannian manifolds which is based on a lemma having its own interest about the approximation of finite perimeter sets with finite volume by open bounded with smooth boundary ones of the same volume. Finally the upper semicontinuity of the isoperimetric profile for every metric (not necessarily complete) is shown.

Study on the icosahedral fullerene structure with ultra-light and pressure resistance character.

An ultra-light icosahedral fullerene structure is described having 12 pentagonal faces at the vertices of the regular icosahedron and 20 triangular faces, which are expanded by hexagonal faces that consist of carbon atoms. When its size exceeds a critical value, the density of the icosahedron becomes lower than that of air. Since the hollow structure deforms under atmospheric pressure, we proposed the addition of helium atoms as a means to obtaining a floatable icosahedral fullerene with pressure-resistant character. According to these requirements, the radius of the midpoint ball of the edge is 493.33 μm; the total density of the helium-filled structure is 0.18 kg m-3; and the buoyancy per cubic meter in the air is 10.88 N. Theoretical calculation and simulation are combined to explore a new approach to ultra-light materials.

BEAT PATTERNS OF A PHYSICAL INCLINED PENDULUM AND THEIR REAL-WORLD APPLICATION

Ponte Academic JournalMar 2019, Volume 75, Issue 3 BEAT PATTERNS OF A PHYSICAL INCLINED PENDULUM AND THEIR REAL-WORLD APPLICATIONAuthor(s): Zharilkassin IskakovJ. Ponte - Mar 2019 - Volume 75 - Issue 3 doi: 10.21506/j.ponte.2019.3.3 Abstract:The paper develops dynamic and mathematical models of the physical inclined pendulum. The motion equations of a pendulum are solved by a stage-by-stage consideration method. The motion laws and amplitudes of oscillations, coordinates of the stagnation zone and their graphical representations are analyzed and discussed. The expressions of oscillation characteristic: period, amplitude, decrement of damping oscillations, quality of a pendulum are determined and considered depending on the angle of inclination and length of the thread, radius of the pendulum ball, rolling friction coefficient and other system parameters. For practical applications, working formulas have been found for determining the rolling friction coefficient at rest, the dynamic rolling friction coefficient and the rolling friction coefficient at the stagnation zone. As an example, the values of the coefficient of rolling friction of solid steel on steel are given. The investigation results can be used to develop new educational laboratory work, to design and create new instruments for determining rolling friction coefficients used in mechanical engineering. Download full text:Check if you have access through your login credentials or your institution Username Password

Extended Newton Methods for Multiobjective Optimization: Majorizing Function Technique and Convergence Analysis

We consider the extended Newton method for approaching a Pareto optimum of a multiobjective optimization problem, establish quadratic convergence criteria, and estimate a radius of convergence ball under the assumption that the Hessians of objective functions satisfy an $L$-average Lipschitz condition. These convergence theorems significantly improve the corresponding ones in [J. Fliege, L. M. G. Drummond, and B. F. Svaiter, SIAM J. Optim., 20 (2009), pp. 602--626]. As applications of the obtained results, convergence theorems under the classical Lipschitz condition or the $\gamma$-condition are presented for multiobjective optimization, and the global quadratic convergence results of the extended Newton method with Armijo/Goldstein/Wolfe line-search schemes are also provided.

Study for tool life of small radius ball endmill in nitride cast iron cutting

Study for tool life of small radius ball endmill in nitride cast iron cutting

Critical elliptic equations via a dynamical systems approach

In this work we consider the existence of positive solutions to various equations of the form −Δu(x)=(1+g(|x|,u))u(x)pin BR,u=0on ∂BR,where BR is the open ball of radius R in RN centered at the origin and p=N+2N−2. We will generally assume g is nonnegative. Our approach will be to utilize some dynamical systems approaches.

A quantitative Carleman estimate for second-order elliptic operators

AbstractWe prove a Carleman estimate for elliptic second-order partial differential expressions with Lipschitz continuous coefficients. The Carleman estimate is valid for any complex-valued function u ∈ W2,2 with support in a punctured ball of arbitrary radius. The novelty of this Carleman estimate is that we establish an explicit dependence on the Lipschitz and ellipticity constants, the dimension of the space and the radius of the ball. In particular, we provide a uniform and quantitative bound on the weight function for a class of elliptic operators given explicitly in terms of ellipticity and Lipschitz constant.

On the complexity of quasiconvex integer minimization problem

In this paper, we consider the class of quasiconvex functions and its proper subclass of conic functions. The integer minimization problem of these functions is considered in the paper, assuming that an optimized function is defined by the comparison oracle. We will show that there is no a polynomial algorithm on $\log R$ to optimize quasiconvex functions in the ball of integer radius $R$ using only the comparison oracle. On the other hand, if an optimized function is conic, then we show that there is a polynomial on $\log R$ algorithm. We also present an exponential on the dimension lower bound for the oracle complexity of the conic function integer optimization problem. Additionally, we give examples of known problems that can be polynomially reduced to the minimization problem of functions in our classes.

Effects of endothermic chain-branching reaction on spherical flame initiation and propagation

A theoretical model is developed to describe the spherical flame initiation and propagation. It considers endothermic chain-branching reaction and exothermic recombination reaction. Based on this model, the effects of endothermic chain-branching reaction on spherical flame initiation and propagation are assessed. First, the analytical solutions for the distributions of fuel and radical mass fraction as well as temperature are obtained within the framework of large activation energy and quasi-steady assumption. Then, a correlation describing spherical flame initiation and propagation is derived. Based on this correlation, different factors affecting spherical flame propagation and initiation are examined. It is found that endothermicity of the chain-branching reaction suppresses radical accumulation at the flame front and thus reduces flame intensity. With the increase of endothermicity, the unstretched flame speed decreases while both flame ball radius and Markstein length increases. Endothermicity has a stronger effect on the stretched flame speed with larger fuel Lewis number. The Markstein length is found to increase monotonically with endothermicity. Furthermore, the endothermicity of the chain-branching reaction is shown to affect the transition among different flame regimes including ignition kernel, flame ball, propagating spherical flame, and planar flame. The critical ignition power radius increases with endothermicity, indicating that endothermicity inhibits the ignition process. The influence of endothermicity on ignition becomes relatively stronger at higher crossover temperature or higher fuel Lewis number. Moreover, one-dimensional transient simulations are conducted to validate the theoretical results. It is shown that the quasi-steady-state assumption used in theoretical analysis is reasonable and that the same conclusion on the effects of endothermic chain-branching reaction can be drawn from simulation and theoretical analysis.

On Bohr radii of finite dimensional complex Banach spaces

We study the Bohr radius of the unit ball of a~complex $n$-dimensional Banach space with an $1$-unconditional basis in terms of its lattice convexity/concavity constants. As an application we give asymptotic estimates of the Bohr radius of the unit ball of the $n$-th section of Lorentz and Marcinkiewicz sequence spaces.

Analytical modeling of ultrasonic surface burnishing process: Evaluation of through depth localized strain

During surface treatment process, microstructure change beneath the surface layers and relevant mechanical properties depend to amount of work hardening occurs through depth of the treated samples. In the present work, an analytical model of surface plastic strain based on contact mechanic theorem is proposed to analyze the ultrasonic burnishing parameters. The model comprises effect of factors such static force, feed rate, ball diameter and ball material as well as ultrasonic vibration parameters such as amplitude and frequency. To incorporate effect of feed rate, two important parameters such as linear coverage coefficient and overlapping ratio have been defined and contributed in the model. The through depth localized plastic strain has been verified by 3D finite element simulation model for different parameter combination. Since, in surface treatment process such as ultrasonic burnishing the surface hardness and microstructure is directly influenced by the plastic strain, a series of experiments have been carried out and through depth hardness profiles has been obtained. It was found from the results that the through depth plastic strain distribution is consistent well with that derived from FE simulation. According to the analytical model, surface plastic strain and relevant affected depth increases by increase of static force and vibration amplitude. Also, it decreases by increase of ball radius and feed rate. On the other hand, it was found that using tungsten carbide ball significantly enhances the surface plastic strain compared to the ball made of steel and silicon nitride. The analytical model of strain and relevant affected depth was completely in line with the variation of through depth hardness and relevant hardened depth.

Remarks on Rawnsley’s $$\varvec{\varepsilon }$$ε-function on the Fock–Bargmann–Hartogs domains

In this paper, we mainly study a family of unbounded non-hyperbolic domains in $$\mathbb {C}^{n+m}$$, called Fock–Bargmann–Hartogs domains $$D_{n,m}(\mu )$$ ($$\mu >0$$) which are defined as a Hartogs type domains with the fiber over each $$z\in \mathbb {C}^{n}$$ being a ball of radius $$e^{-\frac{\mu }{2} {\Vert z\Vert }^{2}}$$. The purpose of this paper is twofold. Firstly, we obtain necessary and sufficient conditions for Rawnsley’s $$\varepsilon $$-function $$\varepsilon _{(\alpha ,g)}(\widetilde{w})$$ of $$\big (D_{n,m}(\mu ), g(\mu ;\nu )\big )$$ to be a polynomial in $$\Vert \widetilde{w}\Vert ^2$$, where $$g(\mu ;\nu )$$ is a Kahler metric associated with the Kahler potential $$\nu \mu {\Vert z\Vert }^{2} -\ln (e^{-\mu {\Vert z\Vert }^{2}}-\Vert w\Vert ^2)$$. Secondly, using above results, we study the Berezin quantization on $$D_{n,m}(\mu )$$ with the metric $$\beta g(\mu ;\nu )$$$$(\beta >0)$$.

Beta-complex versus Alpha-complex: Similarities and Dissimilarities.

The beta-complex is a construct derived from the Voronoi diagram of spherical balls of arbitrary radii and has proven a powerful capability for proximity reasoning among spherical balls in three-dimensional space. Important applications related to molecular shapes in structural/computational molecular biology have been correctly, efficiently, and conveniently solved in the unified framework of the beta-complex and the Voronoi diagram. The beta-complex is a generalization of the ordinary alpha-complex. However, there are similarities and dissimilarities between the two complexes and it is necessary to correctly understand these similarities and dissimilarities to choose the right complex to solve application problems at hand. This paper presents the similarities and dissimilarities between these constructs and illustrates the consequence of the dissimilarity in application problems from both theoretical and practical points of view using examples of atomic arrangements.

A Natural Diffusion Distance and Equivalence of Local Convergence and Local Equicontinuity for a General Symmetric Diffusion Semigroup

In this paper, we consider a general symmetric diffusion semigroup Ttft≥0 on a topological space X with a positive σ-finite measure, given, for t&gt;0, by an integral kernel operator: Ttf(x)≜∫X‍ρt(x,y)f(y)dy. As one of the contributions of our paper, we define a diffusion distance whose specification follows naturally from imposing a reasonable Lipschitz condition on diffused versions of arbitrary bounded functions. We next show that the mild assumption we make, that balls of positive radius have positive measure, is equivalent to a similar, and an even milder looking, geometric demand. In the main part of the paper, we establish that local convergence of Ttf to f is equivalent to local equicontinuity (in t) of the family Ttft≥0. As a corollary of our main result, we show that, for t0&gt;0, Tt+t0f converges locally to Tt0f, as t converges to 0+. In the Appendix, we show that for very general metrics D on X, not necessarily arising from diffusion, ∫X‍ρt(x,y)D(x,y)dy→0 a.e., as t→0+. R. Coifman and W. Leeb have assumed a quantitative version of this convergence, uniformly in x, in their recent work introducing a family of multiscale diffusion distances and establishing quantitative results about the equivalence of a bounded function f being Lipschitz, and the rate of convergence of Ttf to f, as t→0+. We do not make such an assumption in the present work.

A hard-core stochastic process with simultaneous births and deaths

We introduce and examine a class of stochastic spatial point processes with births and deaths, related to spatial loss networks introduced in Ferrari et al. In these processes, a point stays in the system until it is removed due to interaction with a conflicting new arrival. In particular, we consider an interaction scheme where two points are conflicting if closed balls of radius 1/2 around them overlap and a new arriving point “ kills” each conflicting point independently with probability ρ. The new point is accepted if all conflicting points are killed. We construct this process on the whole Euclidean space , . If ρ is large enough, we show existence of a stationary regime and exponential convergence to the stationary distribution. Such stochastic models have been studied earlier as models for populations of interacting individuals or as spatial queuing and resource sharing networks.

On spectral radii of unraveled balls

Given a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We prove a lower bound on the maximum spectral radius of unraveled balls of fixed radius, and we show, among other things, that if the average degree of G after deleting any ball of radius r is at least d then its second largest eigenvalue is at least 2d−1cos⁡(πr+1).

Characterization of half-radial matrices

Numerical radius r(A) is the radius of the smallest ball with the center at zero containing the field of values of a given square matrix A. It is well known that r(A)≤‖A‖≤2r(A), where ‖⋅‖ is the matrix 2-norm. Matrices attaining the lower bound are called radial, and have been analyzed thoroughly. This is not the case for matrices attaining the upper bound where only partial results are available. In this paper we consider matrices satisfying r(A)=‖A‖/2, and call them half-radial. We summarize the existing results and formulate new ones. In particular, we investigate their singular value decomposition and algebraic structure, and provide other necessary and sufficient conditions for a matrix to be half-radial. Based on that, we study the extreme case of the attainable constant 2 in Crouzeix's conjecture. The presented results support the conjecture of Greenbaum and Overton, that the Crabb–Choi–Crouzeix matrix always plays an important role in this extreme case.

On the Constraint Factor and Tabor Coefficient Pertinent to Spherical Indentation

Measuring the uniaxial stress–strain response from indentation testing has been of great interest to the materials community ever since the seminal work on spherical indentation by David Tabor. In this regard, spherical indentation is the primary choice due to the ability to access a wide range of strains in a single test. While indentation testing is fairly simple to perform, the conversion factors required to calculate the uniaxial flow stress from hardness, which is commonly referred to as constraint factor and uniaxial strain from indentation contact radius and ball radius, which is called the Tabor coefficient, are not necessarily constant and most of the prior work involves assumptions about one of these conversion factors to calculate the other. In this work, we present a finite element analysis-based approach to independently determine the constraint factor and Tabor coefficient in the fully plastic indentation regime which is a pre-requisite for this analysis. The criteria to determine whether fully plastic indentation regime is satisfied has also been presented. The proposed approach has been validated by comparing the uniaxial stress–strain response from spherical indentation tests on OFHC copper and the data obtained by conventional uniaxial testing. Excellent agreement has been found between the two approaches which can be readily applied for measuring the uniaxial stress–strain response of coatings which is otherwise difficult to determine.