Hardy Spaces, Regularized BMO Spaces and the Boundedness of Calderón–Zygmund Operators on Non-homogeneous Spaces

One defines a non-homogeneous space (X,μ) as a metric space equipped with a non-doubling measure μ so that the volume of the ball with center x, radius r has an upper bound of the form r ⁿ for some n>0. The aim of this paper is to study the boundedness of Calderón–Zygmund singular integral operators T on various function spaces on (X,μ) such as the Hardy spaces, the L ^p spaces, and the regularized BMO spaces. This article thus extends the work of X. Tolsa (Math. Ann. 319:89–149, 2011) on the non-homogeneous space (? ⁿ ,μ) to the setting of a general non-homogeneous space (X,μ). Our framework of the non-homogeneous space (X,μ) is similar to that of Hytönen (2011) and we are able to obtain quite a few properties similar to those of Calderón–Zygmund operators on doubling spaces such as the weak type (1,1) estimate, boundedness from Hardy space into L ¹, boundedness from L ^∞ into the regularized BMO, and an interpolation theorem. Furthermore, we prove that the dual space of the Hardy space is the regularized BMO space, obtain a Calderón–Zygmund decomposition on the non-homogeneous space (X,μ), and use this decomposition to show the boundedness of the maximal operators in the form of a Cotlar inequality as well as the boundedness of commutators of Calderón–Zygmund operators and BMO functions.     

A Monte Carlo-Adjusted Goodness-of-Fit Test for Parametric Models Describing Spatial Point Patterns

Assessing the goodness-of-fit (GOF) for intricate parametric spatial point process models is important for many application fields. When the probability density of the statistic of the GOF test is intractable, a commonly used procedure is the Monte Carlo GOF test. Additionally, if the data comprise a single dataset, a popular version of the test plugs a parameter estimate in the hypothesized parametric model to generate data for the Monte Carlo GOF test. In this case, the test is invalid because the resulting empirical level does not reach the nominal level. In this article, we propose a method consisting of nested Monte Carlo simulations which has the following advantages: the bias of the resulting empirical level of the test is eliminated, hence the empirical levels can always reach the nominal level, and information about inhomogeneity of the data can be provided. We theoretically justify our testing procedure using Taylor expansions and demonstrate that it is correctly sized through various simulation studies. In our first data application, we discover, in agreement with Illian et al., that Phlebocarya filifolia plants near Perth, Australia, can follow a homogeneous Poisson clustered process that provides insight into the propagation mechanism of these plants. In our second data application, we find, in contrast to Diggle, that a pairwise interaction model provides a good fit to the micro-anatomy data of amacrine cells designed for analyzing the developmental growth of immature retina cells in rabbits. This article has supplementary material online.     

A characteristic difference method for the variable-order fractional advection-diffusion equation

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term (VOFADE-NST) on a finite domain. Combining the characteristic method and the finite difference method, a characteristic finite difference method for solving the VOFADE-NST is presented. Its stability and convergence are analyzed. This new method is shown to be more efficient and superior to the standard finite difference method. Numerical experiments are carried out and the results demonstrate the effectiveness of theoretical analysis.     

Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives

We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both necessary and sufficient higher-order conditions for weak efficiency in a general set-valued vector optimization problem without any convexity assumptions. Many examples are provided to explain advantages of our results over a number of existing ones in the literature.     

An Armijo-type method for pseudomonotone equilibrium problems and its applications

We present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the algorithms are established, among them the global convergence is proved under few assumptions. Applications to generalized variational inequalities and some numerical results are reported.     

Open critical area model and extraction algorithm based on the net flow-axis

In the integrated circuit manufacturing process, the critical area extraction is a bottleneck to the layout optimization and the integrated circuit yield estimation. In this paper, we study the problem that the missing material defects may result in the open circuit fault. Combining the mathematical morphology theory, we present a new computation model and a novel extraction algorithm for the open critical area based on the net flow-axis. Firstly, we find the net flow-axis for different nets. Then, the net flow-edges based on the net flow-axis are obtained. Finally, we can extract the open critical area by the mathematical morphology. Compared with the existing methods, the nets need not to divide into the horizontal nets and the vertical nets, and the experimental results show that our model and algorithm can accurately extract the size of the open critical area and obtain the location information of the open circuit critical area.     

Semicontinuity of the Approximate Solution Sets of Multivalued Quasiequilibrium Problems

We consider two kinds of approximate solutions and approximate solution sets to multivalued quasiequilibrium problems. Sufficient conditions for the lower semicontinuity, Hausdorff lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity, and closedness of these approximate solution sets are established. Applications in approximate quasivariational inequalities, approximate fixed points, and approximate quasioptimization problems are provided.     

Multifractional Markov Processes in Heterogeneous Domains

In this article, we introduce a class of Markov processes whose transition probability densities are defined by multifractional pseudodifferential evolution equations on compact domains with variable local dimension. The infinitesimal generators of these Markov processes are given by the trace of strongly elliptic pseudodifferential operators of variable order on such domains. The results derived provide a pseudomultifractal version of some existing special classes of multifractional Markov processes. In particular, pseudostable processes are defined on domains with variable local dimension in this framework. In the case where the local dimension of the domain and the local Hölder exponents of the transition probability densities are constant, the existing results on fractal versions of Lévy processes are recovered.     

Methoxyflavone Inhibitors of Cytochrome P450

Abstract  Cytochrome P450 enzymes are a superfamily of enzymes involved in the metabolism of endogenous compounds as well as xenobiotics. Due to the large number of reactions catalyzed by these enzymes and their importance in drug metabolism and carcinogenesis, they have been the focus of many studies over the years. Based on the knowledge that flavones are natural substrates of certain P450 enzymes (such as P450 1A2) involved in carcinogenesis, we have synthesized and studied a number of flavonoids as potential inhibitors of these enzymes. These compounds are structurally very similar to the natural flavone substrates of these enzymes but have methoxy substituents at various positions. Here we are reporting the synthesis, structural analysis, X-ray crystal structures, and preliminary inhibition studies of four methoxyflavones from this series. Crystallographic data: 2′-methoxyflavone, P-1, a = 7.2994(8) ?, b = 8.3322(7) ?, c = 10.8240(10) ?, α = 97.905(8)°, β = 92.779(10)°, γ = 111.105(8)°, V = 604.9(1) ?³; 3′-methoxyflavone, P2₁/n, a = 15.1313(16) ?, b = 3.9699(4) ?, c = 19.9454(16) ?, β = 91.673(8)°, V = 1197.6(2) ?³; 4′-methoxyflavone, P2₁/n, a = 16.451(12) ?, b = 3.881(1) ?, c = 19.529(16) ?, β = 106.65(1)°, V = 1195.1(4) ?³; 3′,4′-dimethoxyflavone, C2/c, a = 30.819(5) ?, b = 4.0857(7) ?, c = 26.100(3) ?, β = 124.21(1)°, V = 2717.6(7) ?³. Index Abstract  Methoxyflavone Inhibitors of Cytochrome P450 Michael McKendall, Tasha Smith, Kien Anh, Jamie Ellis, Terri McGee, Maryam Foroozesh, Naijue Zhu and Cheryl L. Klein Stevens* This paper is a report of the synthesis, structural analysis, X-ray crystal structures, and preliminary inhibition studies of 2′-methoxyflavone, 3′-methoxyflavone, 4′-methoxyflavone, and 3′,4′-dimethoxyflavone.

New indications of potential rat intestinal α-glucosidase inhibition by Syzygium zeylanicum (L.) and its hypoglycemic effect in mice

Research on Chemical Intermediates - Natural α-glucosidase inhibitors (aGIs) have been considered effective agents for type 2 diabetes management. In this study, Syzygium zeylanicum (L.)...