On Enforcing Dyadic-type Homogeneous Binary Function Product Constraints in MatBase

Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.

V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.

THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS

The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.

A MAXIMAL FUNCTION CHARACTERIZATION 0F HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE

A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.

GENERALIZED HOMOGENEOUS FUNCTIONS AND THE TWO-BODY PROBLEM

A generalization of the homogeneous function concept is studied.An application is done with a solution of the two-body problem.

A Proof for the Nonexistence of Some Homogeneous Bent Functions

By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.

Solving Cauchy Issues of Highly Nonlinear Elliptic Equations Using a Meshless Method

In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).

Subdifferential Representation of Homogeneous Functions and Extension of Smoothness in Banach spaces

In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction F, we extend the smoothness of sphere and differentiability of norm function in Banach space.

Local synchronization and amplitude of the fluctuation of spontaneous brain activity in attention-deficit/hyperactivity disorder:a resting-state fMRI study

Regional homogeneity（ReHo）and the amplitude of low-frequency fluctuation（ALFF）are two approaches to depicting different regional characteristics of resting-state functional magnetic resonance imaging（RS-fMRI）data.Whether they can complementarily reveal brain regional functional abnormalities in attention-deficit/hyperactivity disorder（ADHD）remains unknown.In this study,we applied ReHo and ALFF to 23 medication-na ve boys diagnosed with ADHD and 25 age-matched healthy male controls using whole-brain voxel-wise analysis.Correlation analyses were conducted in the ADHD group to investigate the relationship between the regional spontaneous brain activity measured by the two approaches and the clinical symptoms of ADHD.We found that the ReHo method showed widely-distributed differences between the two groups in the fronto-cingulo-occipitocerebellar circuitry,while the ALFF method showed a difference only in the right occipital area.When a larger smoothing kernel and a more lenient threshold were used for ALFF,more overlapped regions were found between ALFF and ReHo,and ALFF even found some new regions with group differences.The ADHD symptom scores were correlated with the ReHo values in the right cerebellum,dorsal anterior cingulate cortex and left lingual gyrus in the ADHD group,while no correlation was detected between ALFF and ADHD symptoms.In conclusion,ReHo may be more sensitive to regional abnormalities,at least in boys with ADHD,than ALFF.And ALFF may be complementary to ReHo in measuring local spontaneous activity.Combination of the two may yield a more comprehensive pathophy-siological framework for ADHD.

Effects of methylphenidate on resting-state brain activity in normal adults: an fMRI study

Methylphenidate （MPH） is one of the most commonly used stimulants for the treatment of attention deficit hyperactivity disorder （ADHD）. Although several studies have evaluated the effects of MPH on human brain activation during specific cognitive tasks using functional magnetic resonance imaging （fMRI）, few studies have focused on spontaneous brain activity. In the current study, we investigated the effect of MPH on the intra-regional synchronization of spontaneous brain activity during the resting state in 18 normal adult males. A handedness questionnaire and the Wechsler Adult Intelligence Scale were applied before medication, and a resting-state fMRI scan was obtained 1 h after medication （20 mg MPH or placebo, order counterbalanced between participants）. We demonstrated that： （1） there were no significant differences in the performance of behavioral tasks between the MPH and placebo groups; （2） the left middle and superior temporal gyri had stronger MPH-related regional homogeneity （ReHo）; and （3） the left lingual gyrus had weaker MPH-related ReHo. Our findings showed that the ReHo in some brain areas changes with MPH compared to placebo in normal adults, even though there are no behavioral differences. This method can be applied to patients with mental illness who may be treated with MPH, and be used to compare the difference between patients taking MPH and normal participants, to help reveal the mechanism of how MPH works.

On the Construction of p-Harmonic Morphisms and Conformal Actions

We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.

THE SIMPLE BLOCK ITERATIVE ALGORITHM OF AN EXTENDED ENTROPY MODEL AND ITS CONVERGENCE

The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equations. Because the algorithm gives consideration to the characteristic of the model, it has better effect in our practice. The paper also studies the existence and uniqueness of the solution and convergence of the algorithm.