Uniform Smoothness Research Articles

Effect of solvent/disinfectant ethanol on the micro-surface structure and properties of multiphase denture base polymers

Aim of the studyThe aim of this study was to evaluate the effect of solvent/disinfectant ethanol on the surface of denture base polymers. Changes in surface roughness, topography and some nanomechanical properties were assessed by SEM and nanoindentation plotted against different concentrations of ethanol on heat cured and autopolymerized polymetyl methacrylate based acrylic denture base polymers. Materials and methodsTest specimens (10×10×3mm3) of heat-curing (HC) and auto-polymerizing (AP) acrylic resin were prepared and polished to obtain uniform smoothness which were further grouped into 3 sub-groups HC1, HC2, HC3 and AP1, AP2, AP3 respectively 10 specimens (n) in each group. HC1 and AP1, HC2 and AP2, HC3 and AP3 were treated with 99.9%, 70% and 40% respectively for 30, 60 and 120s followed by analysis of surface roughness (Sa), topographical changes and some nanomechanical properties. ResultsBoth HC and AP resins showed changes in their Sa and nanomechanically measured modulus of elasticity and surface hardness after being treated at different concentrations of ethanol and at different lengths of time. Surface changes were most clearly seen in autopolymerizing denture base polymer, especially at the interface region between the PMMA polymer bead and polymer matrix. There was a correlation (R2=0.83, r=0.91, P<0.001) between the time of treatment by ethanol and thickness of the affected area of denture base polymer. ConclusionThe present study demonstrated that denture base polymers, especially autopolymerized denture base polymer is prone for surface crazing and dissolving by solvent/disinfectant ethanol. The interphase region between the PMMA polymer bead and the polymer matrix was most affected by the ethanol.

A voxelation-corrected non-stationary 3D cluster-size test based on random field theory

Cluster-size tests (CSTs) based on random field theory (RFT) are commonly adopted to identify significant differences in brain images. However, the use of RFT in CSTs rests on the assumption of uniform smoothness (stationarity). When images are non-stationary, CSTs based on RFT will likely lead to increased false positives in smooth regions and reduced power in rough regions. An adjustment to the cluster size according to the local smoothness at each voxel has been proposed for the standard test based on RFT to address non-stationarity, however, this technique requires images with a large degree of spatial smoothing, large degrees of freedom and high intensity thresholding. Recently, we proposed a voxelation-corrected 3D CST based on Gaussian random field theory that does not place constraints on the degree of spatial smoothness. However, this approach is only applicable to stationary images, requiring further modification to enable use for non-stationary images. In this study, we present modifications of this method to develop a voxelation-corrected non-stationary 3D CST based on RFT. Both simulated and real data were used to compare the voxelation-corrected non-stationary CST to the standard cluster-size adjusted non-stationary CST based on RFT and the voxelation-corrected stationary CST. We found that voxelation-corrected stationary CST is liberal for non-stationary images and the voxelation-corrected non-stationary CST performs better than cluster-size adjusted non-stationary CST based on RFT under low smoothness, low intensity threshold and low degrees of freedom.

The projection methods in countably normed spaces

It is well known that a normed space is uniformly convex (smooth) if and only if its dual space is uniformly smooth (convex). We extend the notions of uniform convexity (smoothness) from normed spaces to countably normed spaces ‘in which there is a countable number of compatible norms’. We get some fundamental links between Lindenstrauss duality formulas. A duality property between uniform convexity and uniform smoothness of countably normed spaces is also given. Moreover, based on the compatibility of those norms, it is interesting to show that ‘from any point in a real uniformly convex complete countably normed space, the nearest point to a nonempty convex closed subset of the space is the same for all norms’, which is helpful in further studies for fixed points.

Study of Hybrid Printing Based on Printed Electronics

With the development of technologies in printed electronics, they are perfect for low performance applications, such as displays, labels, clothing, and batteries. Flexible, electrical circuits can be printed using functional inks and printing methods, such as screen printing, gravure and inkjet. Uniform ink surface, smoothness, fine lines, and registration are keys in determining the capability of printed electronics. Screen mesh count, printing methods and emulsion thickness are all variables that are involved in screen printing and need to be quantified in order to determine optimal operational conditions. Inkjet printing is used to conductive traces based on its tiny drop. This study attempted to control human errors during operation that might influence electrical conductivity with inkjet and screen printing.

Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces

The present paper is devoted to the study of the generalized projectionπK:X∗→K, whereXis a uniformly convex and uniformly smooth Banach space andKis a nonempty closed (not necessarily convex) set inX. Our main result is the density of the pointsx∗∈X∗having unique generalized projection over nonempty close sets inX. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.

Iterative Methods for Nonconvex Equilibrium Problems in Uniformly Convex and Uniformly Smooth Banach Spaces

We suggest and study the convergence of some new iterative schemes for solving nonconvex equilibrium problems in Banach spaces. Many existing results have been obtained as particular cases.

Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces

Let \(C\) be a convex compact subset of a uniformly convex Banach space. Let \(\{T_t\}_{t \geq0}\) be a strongly-continuous nonexpansive semigroup on \(C\). Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on \(\{c_k\}\) and \(\{t_k\}\), the sequence \(\{x_k\}_{n=1}^\infty\) converges strongly to a common fixed point of the semigroup \(\{T_t\}_{t \geq0}\). There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.

Asymptotic geometry of Banach spaces and uniform quotient maps

Recently, Lima and Randrianarivony pointed out the role of the property ( β ) (\beta ) of Rolewicz in nonlinear quotient problems and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of ( β ) (\beta ) of the domain space. We also provide conditions under which this comparison can be improved.

Maximal Marcinkiewicz multipliers

Let \(\mathcal{M} =\{m_{j}\}_{j=1}^{\infty}\) be a family of Marcinkiewicz multipliers of sufficient uniform smoothness in \(\mathbb{R}^{n}\). We show that the Lp norm, 1<p<∞, of the related maximal operator $$M_Nf(x)= \sup_{1\leq j \leq N} |\mathcal{F}^{-1} ( m_j \mathcal{F} f)|(x) $$ is at most C(log(N+2))n/2. We show that this bound is sharp.

Asymptotic analysis and upper semicontinuity with respect to rotational inertia of attractors to von Karman plates with geometrically localized dissipation and critical nonlinearity

In this study we consider the von Karman evolution equations accounting for rotational inertial forces along with a nonlinear localized damping. Under suitable hypotheses we prove the existence, regularity and finite dimensionality of a compact attractor Aα,R. The main result of the paper is upper semicontinuity of attractors with respect to rotational inertia terms. The main obstacles are: criticality of the nonlinear term of the equation combined with geometrically constrained dissipation. The flux multiplier used for propagation of the damping does not cooperate with the nonlinear term which is of critical exponent. A new method based on uniform compactness is developed in order to handle such cases. The method allows to establish uniform smoothness of the elements from the attractor which is the key ingredient in proving that the attractor is upper semicontinuous with respect to the rotational inertia α>0 and conclude that it “converges” to the attractor AR obtained (in the case α=0) in Geredeli et al. (2013) [23] when α→0.

High Frequency Waves and the Maximal Smoothing Effect for Nonlinear Scalar Conservation Laws

The article first studies the propagation of well prepared high frequency waves with small amplitude $\varepsilon$ near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating solutions are used to highlight a conjecture of Lions, Perthame, and Tadmor [J. Amer. Math. Soc., 7 (1994), pp. 169--192] about the maximal regularizing effect for nonlinear conservation laws. For this purpose, a definition of smooth nonlinear flux is stated and compared to classical definitions. Then it is proved that the uniform smoothness expected by these authors in Sobolev spaces cannot be exceeded for all smooth nonlinear fluxes.

The Effect of Implant Surfaces sputter-coated with Hydroxyapatite Target

The aim of this study was to develop experimental titanium implants sputter-coated from a hydroxyapatite target and to evaluate peri-implant tissue responses in an animal experiment. The experimental implants were prepared from plastic rods, each of which was 1.6 mm in diameter and 7 mm in length. A thin titanium film was deposited onto the rods by DC magnetron sputtering. The surface of each rod was subsequently sputter-coated from a hydroxyapatite target by RF magnetron sputtering. The experimental implants were placed in the tibiae of 8-week-old male SD rats. Titanium-coated implants were placed as controls using the same method. Tissue samples were obtained 3, 5, 7, 10, 14, and 28 days after implant placement. Histological evaluation was performed using a light microscope, and the bone-implant contact ratios (BICs) were measured. Microstructural observations of implant-bone interfaces were made using a transmission electron microscope (TEM). Peri-implant osteoblastic activity was evaluated using samples obtained 5, 7, and 10 days after implant placement. Immunohistochemical evaluation of type I collagen, osteopontin, and osteocalcin was performed. Uniform smoothness of experimental implant surfaces was confirmed by scanning electron microscope(SEM) images. In the calcium phosphate layer, the compositional ratio of the experimental implant surface was Ca:P:O=1.0:0.79:2.8 based on the results of X-ray photoelectron spectroscopy(XPS). In the trabecular bone region, the BIC ratio was significantly higher in the experimental group than in the control group at 5, 7, 10, and 28 days after implant placement. Type I collagen, osteopontin, and osteocalcin immunostaining revealed that the experimental group tended to show positive results earlier than the control group. The results of this study suggest that surface treatment using a hydroxyapatite target and RF magnetron sputtering can enhance new bone formation during implant osseointegration.

Constructions of Uniformly Convex Functions

AbstractWe give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.

On asymptotically uniformly smooth Banach spaces

The class of asymptotically uniformly smoothable Banach spaces has been considered in connection with several problems of Nonlinear Functional Analysis, as the differentiability of Lipschitz functions, the uniform classification of Banach spaces or the fixed point property. The known characterizations for those spaces come from p-estimates when finite dimensional block decompositions are available or via duality by means of the Szlenk index. In this paper we found a geometrical characterization for the existence of asymptotically uniformly smooth renorming using an ordinal type index defined for subsets of the space. Among the applications, we prove that the modulus of asymptotic uniform smoothness is the same for all the non-asymptotically uniformly smoothable Banach spaces.

On Landweber–Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces

In this paper, iterative regularization methods of Landweber–Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case).

Growth and properties of GaAs and GaN films and low-dimensional GaAs/QWsInGaAs structures on Si substrates with a Ge buffer layer

The conditions for producing mirror-smooth Ge buffer layers of uniform size on Si(100) and Si(111) substrates by means of hot wire chemical vapor deposition (HW-CVD) at a low temperature (350°C) are determined. Single-crystal GaN and GaAs films and low-dimensional GaAs/QWInGaAs/ GaAs/QWInGaAs/GaAs/Ge/Si structures of uniform smoothness are obtained via MOVPE at reduced pressures. Their quantum wells are found to be characterized by intense photoluminescence comparable in intensity to that produced on GaAs substrates.

On the computational content of convergence proofs via Banach limits

This paper addresses new developments in the ongoing proof mining programme, i.e. the use of tools from proof theory to extract effective quantitative information from prima facie ineffective proofs in analysis. Very recently, the current authors developed a method of extracting rates of metastability (as defined by Tao) from convergence proofs in nonlinear analysis that are based on Banach limits and so (for all that is known) rely on the axiom of choice. In this paper, we apply this method to a proof due to Shioji and Takahashi on the convergence of Halpern iterations in spaces X with a uniformly Gâteaux differentiable norm. We design a logical metatheorem guaranteeing the extractability of highly uniform rates of metastability under the stronger condition of the uniform smoothness of X. Combined with our method of eliminating Banach limits, this yields a full quantitative analysis of the proof by Shioji and Takahashi. We also give a sufficient condition for the computability of the rate of convergence of Halpern iterations.

Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in q‐Uniformly Smooth and Strictly Convex Banach Spaces

We introduce a new iterative scheme with Meir‐Keeler contractions for an asymptotically nonexpansive mapping in q‐uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.

Orbits of linear operators and Banach space geometry

Let $T$ be a bounded linear operator on a (real or complex) Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers tending to 0. Then, the set of $x \in X$ such that $\|T^nx\| \geqslant a_n \|T^n\|$ for infinitely many $n$'s has a complement which is both $\sigma$-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents $q>0$, such that for every non nilpotent operator $T$, there exists $x \in X$ such that $(\|T^nx\|/\|T^n\|) \notin \ell^{q}(\mathbb{N})$, using techniques which involve the modulus of asymptotic uniform smoothness of $X$.

Approximation of zeros of inverse strongly monotone operators in Banach spaces

In this paper, we consider the projection algorithm studied by Iiduka and Takahashi (2008) [10] for finding a solution of the variational inequality problem for an inverse strongly monotone operator in a Banach space. We first remark that, under the assumptions imposed on the operator in their paper, the iterative sequence converges weakly to a zero of the operator, not just a solution of the variational inequality problem. In our proof, slightly modified from the original, we do not assume the uniform smoothness of a space as was the case there. Finally, using Halpern’s type method, we modify this algorithm to obtain the strong convergence to a zero of an inverse strongly monotone operator which is nearest to the initial element of the algorithm in the sense of the Bergman distance associated with the function 1 2 ‖ ⋅ ‖ 2 .