Optimum selection of the dental implant diameter and length in the posterior mandible with poor bone quality – A 3D finite element analysis

This study aimed to evaluate continuous and simultaneous variations of dental implant diameter and length, and to identify their relatively optimal ranges in the posterior mandible under biomechanical consideration. A 3D finite element model of a posterior mandibular segment with dental implant was created. Implant diameter ranged from 3.0 to 5.0 mm, and implant length ranged from 6.0 to 16.0 mm. The results showed that under axial load, the maximum Von Mises stresses in cortical and cancellous bones decreased by 76.53% and 72.93% respectively, with the increasing of implant diameter and length; and under buccolingual load, by 83.97% and 84.93%, respectively. Under both loads, the maximum displacements of implant-abutment complex decreased by 58.09% and 75.53%, respectively. The results indicate that in the posterior mandible, implant diameter plays more significant roles than length in reducing cortical bone stress and enhancing implant stability under both loads. Meanwhile, implant length is more effective than diameter in reducing cancellous bone stress under both loads. Moreover, biomechanically, implant diameter exceeding 4.0 mm and implant length exceeding 12.0 mm is a relatively optimal combination for a screwed implant in the posterior mandible with poor bone quality.     

Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems

This paper examines the influence of two major aspects on the solution quality of surrogate model algorithms for computationally expensive black-box global optimization problems, namely the surrogate model choice and the method of iteratively selecting sample points. A random sampling strategy (algorithm SO-M-c) and a strategy where the minimum point of the response surface is used as new sample point (algorithm SO-M-s) are compared in numerical experiments. Various surrogate models and their combinations have been used within the SO-M-c and SO-M-s sampling frameworks. The Dempster–Shafer Theory approach used in the algorithm by Müller and Piché (J Glob Optim 51:79–104, 2011) has been used for combining the surrogate models. The algorithms are numerically compared on 13 deterministic literature test problems with 2–30 dimensions, an application problem that deals with groundwater bioremediation, and an application that arises in energy generation using tethered kites. NOMAD and the particle swarm pattern search algorithm (PSWARM), which are derivative-free optimization methods, have been included in the comparison. The algorithms have also been compared to a kriging method that uses the expected improvement as sampling strategy (FEI), which is similar to the Efficient Global Optimization (EGO) algorithm. Data and performance profiles show that surrogate model combinations containing the cubic radial basis function (RBF) model work best regardless of the sampling strategy, whereas using only a polynomial regression model should be avoided. Kriging and combinations including kriging perform in general worse than when RBF models are used. NOMAD, PSWARM, and FEI perform for most problems worse than SO-M-s and SO-M-c. Within the scope of this study a Matlab toolbox has been developed that allows the user to choose, among others, between various sampling strategies and surrogate models and their combinations. The open source toolbox is available from the authors upon request.     

A divide-and-conquer bound for aggregate’s quality and algebraic connectivity

We establish a divide-and-conquer bound for the aggregate’s quality and algebraic connectivity measures, as defined for weighted undirected graphs. Aggregate’s quality is defined on a set of vertices and, in the context of aggregation-based multigrid methods, it measures how well this set of vertices is represented by a single vertex. On the other hand, algebraic connectivity is defined on a graph, and measures how well this graph is connected. The considered divide-and-conquer bound for aggregate’s quality relates the aggregate’s quality of a union of two disjoint sets of vertices to the aggregate’s quality of the two sets. Likewise, the bound for algebraic connectivity relates the algebraic connectivity of the graph induced by a union of two disjoint sets of vertices to the algebraic connectivity of the graphs induced by the two sets.     

Modeling voluntary participation in a cost‐sharing agricultural water quality management program

This economic analysis of farmers' voluntary adoption of water quality management alternatives integrates three biophysical simulators to predict crop yields and soil erosion/water quality impacts under uncertain weather and market conditions. Farmers' willingness to costshare was used to estimate expectations of net returns and associated water and soil pollution based upon government costshare scenarios. Simulations integrated into mathematical programming results indicate that irrigation and nitrogen fertilizer applications do not alter water quality in the Gum Creek Watershed as much as generally anticipated. Under limited government payments, pollution abatement through reduction of irrigation and/or nitrogen fertilizer applications significantly reduces farmers' net revenues and hence, without threats of other regulatory means, more farmers opt out of a voluntary program. Abatement of nitrogen runoff and leaching should consider other management alternatives and include nonagricultural sources of pollution.     

Finding the coefficients in the new representation of the solution of the Riemann–Hilbert problem using the Lauricella function

The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F _D ^(N). The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.     

On the Relationship Between the Baum-Katz-Spitzer Complete Convergence Theorem and the Law of the Iterated Logarithm

For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which （i） lim sup n→∞ ｜｜Sn｜｜/an〈∞ a.s.and ∞ ∑n=1（1/n）P（｜｜Sn｜｜/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞） are equivalent; （ii） For all constants λ ∈ [0, ∞）, lim sup ｜｜Sn｜｜/an =λ a.s.and ^∞∑ n=1（1/n） P（｜｜Sn｜｜/an ≥ε）{〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables.     

Note on the Norm Involved in the Definition of the ε-spectrum

There exist many definitions of the ε-spectrum. Unlike the spectrum, the ε-spectrum definitions depend on the choice of the norm. We propose to study the conditions on the norm that make all these definitions equivalent. The spectral radius of a related matrix is a useful tool in the eigenvalues perturbation analysis. The study of its connection with the ε-spectrum provides a new definition of the ε-spectrum. In most articles dealing with this subject, the chosen norm is the spectral one. In this paper, we intend to justify this choice.     

On the order of the operators in the Douglas–Rachford algorithm

The Douglas–Rachford algorithm is a popular method for finding zeros of sums of monotone operators. By its definition, the Douglas–Rachford operator is not symmetric with respect to the order of the two operators. In this paper we provide a systematic study of the two possible Douglas–Rachford operators. We show that the reflectors of the underlying operators act as bijections between the fixed points sets of the two Douglas–Rachford operators. Some elegant formulae arise under additional assumptions. Various examples illustrate our results.     

On the Uniqueness of the ADS Spacetime

The uniqueness of the ADS spacetime among all static vacuum spacetimes with the same conformal infinity is proved for dimension n≤7. For dimension n 〉 7, the same result is established under the spin assumption.     

The quality of bank forecasts: The dollar-pound exchange rate, 1990–1993

A general framework for examining the quality of currency forecasts is described. This framework incorporates existing accuracy measures and modifies them to give components of accuracy that are appropriate for statistically derived and judgementally based forecasts. The framework is described and applied to one week ahead US$/UK£ forecasts from three major banks over a three year period between 1990 and 1993. The results suggest that, while overall forecast performance was poor, some aspects of the predictions could still be useful in a practical setting.     

Why do the microstructures of the main pulse and the interpulse of the pulsar in the Crab nebula differ so dramatically?

Theoretical and Mathematical Physics - Pulsars are magnetized neutron stars. They are not resolved by modern radio telescopes and are studied only by radiation coming from the regions of the...     

On the sphericity of the subgroup PSL2(ℝ) in the group of diffeomorphisms of the circle

It is shown that the group PSL₂(?) is a spherical subgroup in the group of C³-diffeomorphisms of the circle.     

On the non-round points of the boundary of the numerical range ∗

Let A be a bounded linear operator acting on a Hilbert space. It is well known (Donoghue, 1957) that comer points of the numerical range W(A) are eigenvalues of A. Recently (1995), this result was generalized by Hiibner who showed that points of infinite curvature on the boundary of W(A) lie in the spectrum of A. Hübner also conjectured that all such points are either corner points or lie in the essential spectrum of A. In this paper, we give a short proof of this conjecture.     

On the behavior of the solution of the dissipative Camassa–Holm equation with the arbitrary dispersion coefficient

In this paper, we consider the dissipative Camassa–Holm equation with arbitrary dispersion coefficient and compactly supported initial data. We demonstrate the simple conditions on the initial data that lead to finite time blow-up of the solution in finite time or guarantee that the solution exists globally. Also, propagation speed for the equation under consideration is investigated.     

On the regularity of the solutions to the 3D Navier–Stokes equations: a remark on the role of the helicity

We show that if velocity and vorticity are orthogonal at each point (and they become orthogonal fast enough) then solutions of the 3D Navier–Stokes equations are smooth. This condition implies that the helicity is identically zero and, in a certain sense, the flow resembles the 2D geometric situation. To cite this article: L.C. Berselli, D. Córdoba, C. R. Acad. Sci. Paris, Ser. I 347 (2009).