A DISCRETE CHARACTERIZATION OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES AND ITS APPLICATIONS

In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.

Minimax designs for linear regression models with bias in a reproducing kernel Hilbert space in a discrete set

Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the model bias comes from a reproducing kernel Hilbert space. Two different design criteria are proposed by applying the minimax approach for estimating the parameters of the regression response and extrapolating the regression response to points outside of the design space. A simulated annealing algorithm is applied to construct the minimax designs. These minimax designs are compared with the classical D-optimal designs and all-bias extrapolation designs. Numerical results indicate that the simulated annealing algorithm is feasible and the minimax designs are robust against bias caused by model misspecification.

Discrete state space method and modal extension method based impact sound synthesis model

The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on discrete state space（DSS） method and modal extension method（MEM）. This model is comprised of the whole three processes of the physical interaction, i.e., the Hertz contact process, the transient structural response process, and the sound radiation process. Firstly,the modal expanded DSS equations of the contact system are constructed and the transient structural response of the cylinder is obtained. Then the impact sound of the cylinder is acquired using improved discrete Raleigh integral. Finally, the proposed model is verified by comparing with existing models. The results show that the proposed impact sound synthesis model is more accurate and efficient than the existing methods and easy to be extended to the impact sound synthesis of other structures.

Spaces with σ-point-discrete N_0-weak bases

It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are： （1） A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-weak base; （2） Under （CH）, every separable space with a σ-point-discrete N_0-weak base has a countable N_0-weak base.

MULTI-PARAMETER HARDY SPACES VIA DISCRETE LITTLEWOOD-PALEY THEORY

In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces HP（Rn1× … ×Rnk） of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators onHP（Rn1× … ×Rnk） and fromHP（Rn1× … ×Rnk）toLP（Rn1× … ×Rnk）.

A Euclidean-Like Discrete Spacetime from the Unification of a Multitude of Hypercubic Lattices

An autonomous discrete space is proposed consisting of a huge number of four dimensional hypercubic lattices, unified along one of the four axes. The unification is such that the properties of the individual lattice are preserved. All the unifying axes are parallel, and the other axes have indeterminate mutual relations. The two kinds of axes are non-interchangeable resembling time and space of reality. The unification constitutes a framework without spatial properties. In case the axes with indeterminate relations are present at regular intervals in the time and the space, a Euclidean-like metric and goniometry can be obtained. In thus defined space-like structure, differences in speed and relativistic relations are only possible within regions of space enclosed by aberrations of the structure.

Spacetime Discreteness: Shedding Light on Two of the Simplest Observations in Physics

Loop quantum gravity is considered to be one of the two major candidates for a theory of quantum gravity. The most appealing aspect about this theory is it predicts that spacetime is not continuous;both space and time have a discrete nature. Simply, space is not infinitely divisible, but it has a granular structure, and time does not flow continuously like a smooth river. This paper demonstrates a review for two missed (unnoted) observations that support the discreteness of the spacetime. The content of this paper does not validate the specific model of quantized geometry of the spacetime which is predicted by the theory itself. Instead, it proves that time does not flow continuously. But it flows in certain, discrete steps, like a ticking of a clock, due to a simple observation which is absence of any possible value of time that can exist between the present and the future. Regarding space, it validates the spatial discreteness, and the existence of spatial granules (space quanta) due to a simple observation which is the existence of the origin position in a coordinates system. All of this is achieved by reviewing the concept of discreteness itself, and applied directly to the observations.

Physical Constants as Result of the Many Hypercubic Lattices of a Multidirectional Discrete Space

A multidirectional discrete space consists of numerous hypercubic lattices each of which contains one of the spatial directions. In such a space, several groups of lattices can be distinguished with a certain property. Each group is determined by the number of lattices it comprises, forming the characterizing numbers of the space. Using the specific properties of a multidirectional discrete space, it is shown that some of the characterizing numbers can be associated with a physical constant. The fine structure constant appears to be equal to the ratio of two of these numbers, which offers the possibility of calculating the series of smallest numerical values of these numbers. With these values, a reasoned estimate can be made of the upper limit of the smallest distance of the discrete space of approximately the Planck length.

A DISCRETE CHARACTERIZATION OF BESOV SPACES

The characterization of isotropic Besov spaces for in terms of progressive differences of a function on dyadic points is obtained. Moreover, for withan analogous characterization of anisotropic Besov spaces is presented.

Natural Numbers Applied to Physical Constants: Spacetime Discreteness

We analyze some physical concepts only using natural numbers. We assume a dis-crete space. Physical variables such as speed and momentum are considered as result of the sum of discrete contributions. Such discrete contributions can be calculated with natural numbers only. Elementary algebra is used in the analysis of physical subjects.

F_(p) as a Discrete Metric Space

We define a metric that makes the algebraic closure of a finite field F_(p) into a UDBG(uniformly discrete with bounded geometry)metric space.This metric stems from algebraic properties of F_(p).From this perspective,for F_(p)we explore common research themes in metric spaces,reveal how peculiar properties naturally arise,and present it as a new type of example for certain well-studied questions.

PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL

We present an overview of the properties of the pseudohyperbolic metric in several real dimensions and study uniformly discrete sequences for the real unit ball in R^n.

On Discrete Cosmology, Gravitation and Mechanics

In this paper we will discretely reformulate the main fundamental magnitudes of mechanics and thermodynamics due to a new dynamic, discrete and irreversible nature for Time. The existence of a fundamental minimum time, implies that any physical system can only evolve discreetly according to this minimum time instead of a continuous evolution. Thus, the passage of Time must be considered a fundamental physical process and incorporated into Physics where the laws of Nature depend on a clear distinction between past, present and future. A time interval equals a loss of energy. The introduction of “dark matter”, “dark energy”, “ad hoc modifications of the laws of mechanics” or “fundamental constants varying” will prove to be unnecessary inasmuch as the view here to be developed will not require of a Universe provided with special properties. By considering that Universe can be expressed as the ensemble of N typical particles in motion of mass m, we will find possible solutions to some of the main problems of the current Physics, all from an existing deep connection between gravity, thermodynamics and quantum cosmology.

On Maximal, Discrete, and Area Operators

In this paper, we study the boundednesses of maximal operator g., the discrete operator gd, and the area operator A on Bergman spaces.

Is Nature Fundamentally Continuous or Discrete, and How Can These Two Different But Very Useful Conceptions Be Fully Reconciled?

Our contention is that reality is actually analog, but at a critical limit, when the Octonian gravity condition kicks in, for a time it is made to appear discrete. This is due to an initial phase transition just at the start of the big bang. Our second consideration is that symmetry breaking models, i.e. the Higgs boson, are in themselves not appropriate or necessary for the formation of particles with mass just before Octonionic gravity which could arise in pre-Planckian physics models without a potential. Finally, the necessity of potentials for pre-Octonionic gravity physics can be circumvented via judicious use of Scherrer k essence physics.

Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

面向外包空间数据库的查询验证机制设计实现

针对因外包数据库中数据基数大、身份特征难提取,导致的查询验证效率低、误差过大的问题,设计一种基于Hilbert曲线的查询验证机制。采用Hilbert曲线建立分析函数,线性贯穿二维、三维甚至更高维度的离散单元,描述外包空间数据库中数据在每个查询点的线性变化,将变化值映射到不同维度空间中,分别计算验证签名变化情况。求解数据在外包空间数据库中关键词权重,定义其为查询比对阈值,设定数据库中存在数据变换表,建立认证树,将计算得到的待验证数据节点权重输入至认证树中,查找对应信息,设定验证范围完成查询验证。实验结果表明,所提方法查询验证所需运算代价最小,在同等条件下验证耗时最少,验证结果与源数据存在高度一致性。

基于包装材料数字图像的RGB颜色空间色差评价方法研究

目的解决包装材料复杂颜色区域色差评价,目测检验方法存在判定标准复杂、结果一致性差等问题。方法提出一种基于包装材料高清数字图像的RGB颜色空间色差评价方法。通过搭建高清数字图像采集装置,获取包装材料标准样(上限、中限、下限)的全幅数字图像。通过采用RGB颜色空间降维的方法,对标准样测试区域的颜色空间进行离散边界拟合,构建标准样品测试区域的三限样RGB色差模型,与测试样对应测试区域的颜色空间进行对比;根据颜色空间模型的一致性判定测试样色差是否合格。结果对比多种离散边界拟合模型,采用滚球法边缘拟合模型的包含率和多出率分别达到100%、78.9%,模型拟合效果最佳。通过对包装材料色差缺陷样验证测试,采用上述色差评价方法准确率达到100%。结论本文提出的滚球法颜色空间边缘拟合模型和色差评价方法,可实现对包装材料复杂颜色区域的色差合格性判定,有利于提高企业生产的智能化检测水平。

天基信息支援体系离散事件仿真与效能评估

针对天基信息支援体系效能评估中存在的准确性与实时性无法兼顾的问题,以体系仿真为基础,提出一种基于离散事件仿真的效能评估模型构建方法。首先,基于仿真工具建立离散事件仿真模型,对体系的结构与运作流程进行模拟,并基于仿真模型构建评估指标体系,生成效能评估数据样本。之后,利用深度学习对复杂映射的强大表现能力基于深度置信网络构建效能评估代理模型,结合无监督预训练和有监督调优实现网络的训练和参数优化。最后,对仿真生成的测试集样本进行评估模型验证实验。结果表明,所提方法在计算快速的同时对原评估模型有很高的还原度。