Desired Regularity Research Articles

ANALYSIS OF FACTORS RELATING TO PREGNANT WOMEN'S IRRANGEMENT IN CARRYING OUT PREGNANCY EXAMINATION AT THE KRUENG BARONA JAYA PUBLIC HEALTH CENTER, ACEH BESAR

Pregnancy is a physiological process that requires special attention in efforts to maintain the health of both mother and baby. One of the efforts that can be done is regular antenatal care (ANC) check-ups. However, there are still many pregnant women who have not undergone ANC with the desired regularity. Therefore, this study was conducted to identify factors related to the irregularity of prenatal check-ups. This study is a quantitative analytic study with a cross-sectional approach. The population in this study consisted of 294 pregnant women who had given birth in the Krueng Barona Jaya region, Aceh Besar. The sampling method used total sampling, where out of 294 pregnant women, 7 of them did not have or bring their KIA book, 39 could not be found or contacted, and 3 individuals were unwilling to become respondents. Hence, a total sample of 245 respondents was used in this study. The results of the analysis showed that factors related to the irregularity of ANC check-ups were poor knowledge (OR=15.61; 95% CI=2.50-97.39; P=0.003), lack of media exposure (OR=4.87; 95% CI=1.51-15.70; P=0.008), and previous experience (OR=2.99; 95% CI=1.02-8.76; P=0.046). The conclusion of this study is that knowledge, media exposure, and prior experiences influence the irregularity of prenatal check-ups. Here, prior experiences refer to the healthcare experiences received during previous check-ups or pregnancies. Attitude, as well as pregnancy intentions and planning, do not significantly correlate with irregular ANC check-ups. Therefore, efforts are needed to enhance knowledge and provide better media resources regarding the importance of prenatal examinations, as well as to improve the overall healthcare experience for pregnant women.

Isolating gasdynamic and chemical effects on the detonation cellular structure: A combined experimental and computational study

The dependence of detonation cell regularity on mixture gasdynamic and chemical kinetic properties are investigated through hydrogen-oxygen detonations with different diluent and ozone addition. A total of seven mixtures are specifically designed such that the post-shock specific heat ratio γVN, representing the gasdynamic effect, and the effective activation energy ϵi, representing the chemistry effect, can be varied independently among these mixtures. Both experiments and two-dimensional (2D) Navier-Stokes simulations are performed. For the ranges of γVN and ϵi considered, γVN is found to moderately affect cell regularity. For mixtures of relatively large γVN (≥1.3), detonation cells become slightly irregular with decreasing γVN. A clear increase in cell irregularity is found when γVN is small (<1.3). In contrast, the impact of ϵi on cell regularity is more notable: mixtures of large ϵi produce significantly more irregular cells, corresponding to frequent appearances of transverse detonation structures that dominate the global burning behavior. Finally, ozone is qualitatively and quantitatively shown to regulate the detonation structures in both simulations and experiments tested in this study, and results suggest that trace additives that alter the ϵi of a mixture can likely be used to tune the mixture for a desired regularity.

The smooth forcing extension method: A high-order technique for solving elliptic equations on complex domains

High-order numerical methods for solving elliptic equations over arbitrary domains typically require specialized machinery, such as high-quality conforming grids for finite elements method, and quadrature rules for boundary integral methods. These tools make it difficult to apply these techniques to higher dimensions. In contrast, fixed Cartesian grid methods, such as the immersed boundary (IB) method, are easy to apply and generalize, but typically are low-order accurate. In this study, we introduce the Smooth Forcing Extension (SFE) method, a fixed Cartesian grid technique that builds on the insights of the IB method, and allows one to obtain arbitrary orders of accuracy. Our approach relies on a novel Fourier continuation method to compute extensions of the inhomogeneous terms to any desired regularity. This is combined with the highly accurate Non-Uniform Fast Fourier Transform for interpolation operations to yield a fast and robust method. Numerical tests confirm that the technique performs precisely as expected on one-dimensional test problems. In higher dimensions, the performance is even better, in some cases yielding sub-geometric convergence. We also demonstrate how this technique can be applied to solving parabolic problems and for computing the eigenvalues of elliptic operators on general domains, in the process illustrating its stability and amenability to generalization.

Higher H\xf6lder regularity for nonlocal equations with irregular kernel

We study the higher Hölder regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interesting feature of our main result is that the obtained regularity is better than one might expect when considering corresponding results for local elliptic equations in divergence form with continuous coefficients. Therefore, in some sense our result can be considered to be of purely nonlocal type, following the trend of various such purely nonlocal phenomena observed in recent years. Our approach can be summarized as follows. First, we use certain test functions that involve discrete fractional derivatives in order to obtain higher Hölder regularity for homogeneous equations driven by a locally translation invariant kernel, while the global behaviour of the kernel is allowed to be more general. This enables us to deduce the desired regularity in the general case by an approximation argument.

Irregular Double Obstacle Problems with Orlicz Growth

We study an irregular double obstacle problem with Orlicz growth over a nonsmooth bounded domain. We establish a global Calderon–Zygmund estimate by proving that the gradient of the solution to such a nonlinear elliptic problem is as integrable as both the nonhomogeneous term in divergence form and the gradient of the associated double obstacles. We also investigate minimal regularity requirements on the relevant nonlinear operator for the desired regularity estimate.

Some regularity results on stochastic convolutions in point delay differential equations perturbed by noise

In this work, we obtain some regularity results on stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded coefficient operators driven by white noise. We first establish some estimates on fundamental solutions which play an important role in the subsequent theory. Then we apply these estimates to some stochastic convolutions arising in stochastic delay differential equations to obtain the desired regularity property.

On regularity of stochastic convolutions of functional linear differential equations with memory

In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates on fundamental solutions which are time delay versions of those on $ C_0 $-semigroups. To this end, we develop a scheme of constructing the resolvent operators for the integrodifferential equations of Volterra type since the equation under investigation is of this type in each subinterval describing the segment of its solution. Then we apply these estimates to stochastic convolutions of our equations to obtain the desired regularity property.

Partition of unity extension of functions on complex domains

We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in 2D. Function extension plays a fundamental role in extending the applicability of boundary integral methods to inhomogeneous partial differential equations with embedded domain techniques. Overlapping partitions are placed along the boundaries, and a local extension of the function is computed on each patch using smooth radial basis functions; a trivially parallel process. A partition of unity method blends the local extrapolations into a global one, where weight functions impose compact support. The regularity of the extended function can be controlled by the construction of the partition of unity function. We evaluate the performance of the PUX method in the context of solving the Poisson equation on multiply connected domains using a boundary integral method and a spectral solver. With a suitable choice of parameters the error converges as a tenth order method down to 10−14.

Higher integrability for constrained minimizers of integral functionals with ([formula omitted])-growth in low dimension

We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations ∫Ωf(x,Du(x))dx,u:Ω⊂Rn→SN−1,with growth conditions of (p,q)-type: |ξ|p≤f(x,ξ)≤C(|ξ|q+1),p<q,in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients.

The Singular Set for a Semilinear Unstable Problem

We study the regularity of solutions of the following semilinear problem $${\Delta}u = -\lambda_{+}(x) (u^{+})^{q}+\lambda_{-} (x) (u^{-})^{q} \qquad \text{in} \;\; B_{1}, $$ where B 1 is the unit ball in ℝ n , 0 < q < 1 and λ ± satisfy a Holder continuity condition. Our main results concern local regularity analysis of solutions and their nodal set {u = 0}. The desired regularity is C [κ],κ−[κ] for κ = 2/(1 − q) and we divide the singular points in two classes. The first class contains the points where at least one of the derivatives of order less than κ is nonzero, the second class which is named $\mathcal {S}_{\kappa }$ , is the set of points where all the derivatives of order less than κ exist and vanish. We prove that $\mathcal {S}_{\kappa }=\varnothing $ when κ is not an integer. Moreover, with an example we show that $\mathcal {S}_{\kappa }$ can be nonempty if κ ∈ ℕ. Finally, a regularity investigation in the plane shows that the singular points in $\mathcal {S}_{\kappa }$ are isolated.

On Partition of Unities Generated by Entire Functions and Gabor Frames in $$ L^2({\mathbb R}^d) $$ L 2 ( R d ) and $$\ell ^2({\mathbb Z}^d)$$ ℓ 2 ( Z d )

We characterize the entire functions P of d variables, $$d\ge 2,$$ for which the $${\mathbb Z}^d$$ -translates of $$P\chi _{[0,N]^d}$$ satisfy the partition of unity for some $$N\in \mathbb N.$$ In contrast to the one-dimensional case, these entire functions are not necessarily periodic. In the case where P is a trigonometric polynomial, we characterize the maximal smoothness of $$P\chi _{[0,N]^d},$$ as well as the function that achieves it. A number of especially attractive constructions are achieved, e.g., of trigonometric polynomials leading to any desired (finite) regularity for a fixed support size. As an application we obtain easy constructions of matrix-generated Gabor frames in $$ L^2({\mathbb R}^d) ,$$ with small support and high smoothness. By sampling this yields dual pairs of finite Gabor frames in $$\ell ^2({\mathbb Z}^d).$$

Scrambled Geometric Net Integration Over General Product Spaces

Quasi-Monte Carlo (QMC) sampling has been developed for integration over $[0,1]^s$ where it has superior accuracy to Monte Carlo (MC) for integrands of bounded variation. Scrambled net quadrature gives allows replication based error estimation for QMC with at least the same accuracy and for smooth enough integrands even better accuracy than plain QMC. Integration over triangles, spheres, disks and Cartesian products of such spaces is more difficult for QMC because the induced integrand on a unit cube may fail to have the desired regularity. In this paper, we present a construction of point sets for numerical integration over Cartesian products of $s$ spaces of dimension $d$, with triangles ($d=2$) being of special interest. The point sets are transformations of randomized $(t,m,s)$-nets using recursive geometric partitions. The resulting integral estimates are unbiased and their variance is $o(1/n)$ for any integrand in $L^2$ of the product space. Under smoothness assumptions on the integrand, our randomized QMC algorithm has variance $O(n^{-1 - 2/d} (\log n)^{s-1})$, for integration over $s$-fold Cartesian products of $d$-dimensional domains, compared to $O(n^{-1})$ for ordinary Monte Carlo.

On knife-edge conditions with unbounded growth

Imagine an economic process modeled with help of ordinary differential equations with some fixed initial conditions and suppose that a solution to the system under consideration, for some reason, should enjoy desired conditions. It appears that small changes in the system describing the modeled process may have devastating effect on the fulfillment of the desired conditions by solutions of the perturbed system. Such a feature of a system is called a knife-edge condition in the literature on economic growth and it has recently found some deeper interest in that literature. However, the available results seem to be unclear and not correct – this paper shows how to correct and improve these results, creating consistent mathematical foundations of that theory. The main contribution of the paper is that knife-edge conditions are present whenever long-term unbounded growth of an economic variable is required as (or implied by) a desired regularity condition.

A Distributed Control Problem for Two Coupled Fluids in a Porous Medium

The purpose of this article is to introduce and study a mathematical model and a distributed control problem associated with the interaction between two nonmiscible fluids in a porous medium, when on their interface there exists a jump of temperature. By means of the Schauder's fixed point theorem we obtain the existence of a solution for the variational formulation of the physical problem. Throughout this work, we study certain variational problems with a priori regularity of the weak solutions. We obtain the existence of less regular solutions and then we prove the desired regularity of these solutions. In order to examine the pressure distribution in the two fluids, we consider a distributed control problem which permits us to determine the radiant sources that provide an optimal configuration for the pressure. Since the solution of the problem is not unique, the control variable does not appear explicitly in the definition of our cost functional. To overcome this difficulty, we introduce a family of p...

A high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of variable-coefficient conservative fractional diffusion equations

Fractional diffusion equations were shown to provide an adequate and accurate description of transport processes exhibiting anomalous diffusion behavior. Recently, spectral Galerkin methods were developed for space-fractional diffusion equations aiming at achieving exponential convergence. An optimal order error estimate in the fractional energy norm was proved under the assumption that the true solution to the fractional diffusion equation has the desired regularity. An optimal order error estimate in the L2 norm was proved via the well known Nitsche lifting technique under the assumption that the true solution to the corresponding boundary-value problem of the fractional diffusion equation has the required regularity for each right-hand side.In this paper we show that the true solution to the Dirichlet boundary-value problem of a conservative fractional diffusion equation of order 2−β with 0<β<1 as well as a constant diffusivity coefficient and a constant source term is not in the fractional Sobolev space H3/2−β in general, but is still in the Besov space B∞3/2−β(L2). Hence, the provable convergence rate of a spectral Galerkin method in the L2 norm is at most of the order O(N−(3/2−β)), where N is the degree of the polynomial space in the numerical method. Numerical experiments show that the spectral Galerkin method exhibits a subquadratic convergence in the L2 norm for any 0<β<1.We develop a high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of one-sided variable-coefficient conservative fractional diffusion equations. The method has a proved high-order convergence rate of arbitrary order (i) without requiring the smoothness of the true solution u to the given boundary-value problem, but only assuming that the diffusivity coefficient and the right-hand source term have the desired regularity; (ii) for a variable diffusivity coefficient; and (iii) for an inhomogeneous Dirichlet boundary condition. Numerical experiments substantiate the theoretical analysis and show that the method exhibits exponential convergence provided the diffusivity coefficient and the right-hand source term have the desired regularity.

Global Existence for the Critical Dissipative Surface Quasi-Geostrophic Equation

In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in $${\mathbb{R}^2}$$ . Motivated by the study of the homogeneous statistical solutions of this equation, we show that for any large initial data θ 0 liying in the space $${\Lambda^{s} (\dot{H}^{s}_{uloc}(\mathbb{R}^2)) \cap L^\infty(\mathbb{R}^2)}$$ the critical (SQG) has a global weak solution in time for 1/2 < s < 1. Our proof is based on an energy inequality verified by the equation $${(SQG)_{R,\epsilon}}$$ which is nothing but the (SQG) equation with truncated and regularized initial data. By classical compactness arguments, we show that we are able to pass to the limit ( $${R \rightarrow \infty}$$ , $${\epsilon \rightarrow 0}$$ ) in $${(SQG)_{R,\epsilon}}$$ and that the limit solution has the desired regularity.

On the Global Well-posedness for the Boussinesq System with Horizontal Dissipation

In this paper, we investigate the Cauchy problem for the tridimensional Boussinesq equations with horizontal dissipation. Under the assumption that the initial data is an axisymmetric without swirl, we prove the global well-posedness for this system. In the absence of vertical dissipation, there is no smoothing effect on the vertical derivatives. To make up this shortcoming, we first establish a magic relationship between $\frac{u^{r}}{r}$ and $\frac{\omega_\theta}{r}$ by taking full advantage of the structure of the axisymmetric fluid without swirl and some tricks in harmonic analysis. This together with the structure of the coupling of \eqref{eq1.1} entails the desired regularity.

Construction of ${\mathcal L}^{{p}}$ -strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions

We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated semigroup and resolvents of kernels having the $\mathcal L^p$-strong Feller property. They allow us to construct a process which solves the corresponding martingale problem for all starting points from a known set, namely the set where the regularity assumptions hold. We apply this result to construct elliptic diffusions having locally Lipschitz matrix coefficients and singular drifts on general open sets with absorption at the boundary. In this application elliptic regularity results imply the desired regularity assumptions.

Hole filling on surfaces by discrete variational splines

This paper concerns about a method to fill polygonal holes in a given surface by using smoothing variational splines. We develop two different approaches of this technique: discontinuous filling and regular filling. In the discontinuous case, we fill the holes with spline functions in a finite element space that minimizes an energy functional. Such fillings are chosen to be smooth and as close as possible to the original surface in the neighborhoods of the holes. In this approach the global reconstructed surface will not be continuous. On the contrary, in the regular case, we do not only fill the holes, but we also replace the known surface with another very similar in such a way that the global reconstructed surface will have the desired regularity. We give convergence results and we illustrate the developed theory with several graphical and numerical examples.

A new family of high regularity elements

AbstractIn this article, we propose a new family of high regularity finite element spaces. The global approximation spaces are obtained in two steps. We first build an open cover of the computational domain and local approximation spaces on each patch of the cover. Then we construct partition of unity functions subordinate to the open cover depending on the regularity requirement. The basis functions of the global space is given by the products of the local basis functions and the corresponding partition of unity functions. The method can be used to construct finite element spaces of any desired regularity. Approximation properties and implementation details are discussed. Numerical examples for the biharmonic equation are presented to show the effectiveness of the proposed method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 1–16, 2012