MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Prediction Method Study on the Remaining Useful Life of Plant New Varieties Rights Based on Weibull Survival Function and Gaussian Model——Taking Hybrid Rice Variety for Example

In view of the difficulty in determining remaining useful life of plant new variety right in economic analysis, Weibull Survival Analysis Method and Gaussian Model to were used to study how to accurately estimate the remaining useful life of plant new variety right. The results showed that the average life of the granted rice varieties was 10.013 years. With the increase of the age of plant variety rights, the probability of the same residual life Ttreaching x was smaller and smaller, the reliability lower and lower, while the probability of the variety rights becoming invalid became greater. The remaining useful life of a specific granted rice variety was closely related to the demonstration promotion age when the granted rice variety reached its maximum area and the appearance of alternative varieties, and when the demonstration promotion age of the granted rice variety reaching the one with the maximum area, the promotion area would be decreased once a new alternative variety appeared, correspondingly with the shortening of the remaining useful life of the variety. Therefore, Weibull Survival Analysis Method and Gaussian Model could describe the remaining useful life＇s time trend, as well as determine the remaining useful life of a concrete plant variety right, clarify the entire life time of varieties rights, and make the economic analysis of plant new varieties rights more accurate and reasonable.

基于改进ResNet的多标签胸部X光图像分类

针对目前胸部X光图像分类方法存在X光特异性特征表达不充分、高频图像特征提取效果差、疾病样本数量不平衡等问题,提出一种基于改进ResNet的多标签胸部X光图像分类方法(multi-label chest X-ray image classification based on improved ResNet, MLC-ResNet)。首先,设计一个多尺度特征提取和融合模块,以获取更丰富的特征信息;其次,将八度卷积替换为残差结构中的普通卷积,解决X光特异性特征表达不充分问题;再次,为改善高频特征提取效果,在ResNet中引入改进后的多层感知器(multilayer perception, MLP),更好地揭示图像的细节和整体结构,增加分类性能;最后,使用加权交叉熵损失函数增加样本数较少的类别权重,改善样本分布不平衡问题。在ChestX-Ray14和CheXpert数据集上进行实验测试,其平均AUC分别是0.858 7和0.844 7,相较于ResNet分类算法分别提高了4.47%和3.20%。通过与现有方法的对比实验,进一步证明MLC-ResNet模型具有更好的性能。

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

Functional Confirmation Using a Medical X-Ray System of a Semiconductor Survey Meter

In recent years, semiconductor survey meters have been developed and are in increasing demand worldwide. This study determined if it is possible to use the X-ray system installed in each medical facility to calculate the time constant of a semiconductor survey meter and confirm the meter’s function. An additional filter was attached to the medical X-ray system to satisfy the standards of N-60 to N-120, more copper plates were added as needed, and the first and second half-value layers were calculated to enable comparisons of the facility’s X-ray system quality with the N-60 to N-120 quality values. Next, we used a medical X-ray system to measure the leakage dose and calculate the time constant of the survey meter. The functionality of the meter was then checked and compared with the energy characteristics of the meter. The experimental results showed that it was possible to use a medical X-ray system to reproduce the N-60 to N-120 radiation quality values and to calculate the time constant from the measured results, assuming actual leakage dosimetry for that radiation quality. We also found that the calibration factor was equivalent to that of the energy characteristics of the survey meter.

Wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

A new kind of quantum non-Gaussian state with a vortex structure, termed a Bessel-Gaussian vortex state, is constructed, which is an eigenstate of the sum of squared annihilation operators a2 ＋ b2. The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that a quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.

急性心肌梗死患者血清XIAP、PINK1水平及其与心肌缺血程度、心功能及预后的相关性

目的 探究急性心肌梗死患者血清X连锁凋亡抑制蛋白(XIAP)、PTEN诱导假定激酶1(PINK1)的表达水平及其与患者心肌缺血程度、心功能及预后的相关性。方法 收集2020年6月—2021年12月在宝鸡市人民医院接受治疗的86例急性心肌梗死患者作为研究组,另选取同期健康体检者80例作为对照组。依据血管狭窄程度将患者分为轻度组(27例)、中度组(34例)和重度组(25例)。对所有患者进行术后6个月随访,记录患者是否发生主要不良心血管事件(MACE)。检测各组血清XIAP和PINK1的表达水平;Pearson相关性分析XIAP、PINK与心肌缺血总负荷、心功能指标之间的关系;受试者工作特征(ROC)曲线分析血清XIAP、PINK1水平对急性心肌梗死患者预后的预测价值。结果 研究组患者XIAP、PINK1水平低于对照组,差异有统计学意义(t=17.802、24.295,P<0.05)。重度组和中度组患者XIAP、PINK1的表达水平低于轻度组,差异有统计学意义(F=164.194、303.700,P<0.05);重度组患者XIAP、PINK1的表达水平低于中度组,差异有统计学意义(P<0.05)。重度组和中度组患者心肌缺血总负荷高于轻度组,且重度组高于中度组(P<0.05)。患者血清XIAP、PINK1水平与心肌缺血总负荷、左心室舒张末期内径(LVEDD)、左心室收缩末期内径(LVESD)呈负相关(r=-0.554,-0.462,-0.488,-0.683,-0.474,-0.528,P<0.05),与左心室射血分数(LVEF)呈正相关(r=0.504,0.559,P<0.05)。MACE组患者XIAP、PINK1水平低于非MACE组,差异有统计学意义(t=15.845、22.566,P<0.05);血清XIAP、PINK1联合预测急性心肌梗死患者预后的曲线下面积(AUC)与XIAP单独预测AUC比较,差异无统计学意义(Z_(二者联合vs. XIAP)=0.839,P=0.402),但明显高于PINK1单独预测(Z_(二者联合vs. XIAP)=2.014,P=0.044)。结论 急性心肌梗死患者血清中XIAP和PINK1的水平降低,与患者心肌缺血程度、心功能及预后密切相关。

老年射血分数保留的心力衰竭病人血清CCL17、CXCL8与心功能及预后的关系

目的:分析血清C-C基序趋化因子配体17(CCL17)、C-X-C序列趋化因子配体8(CXCL8)与老年射血分数保留的心力衰竭(HFpEF)病人心功能及预后的关系。方法:选取2020年9月—2023年9月我院收治的168例HFpEF病人(HFpEF组)和81名心功能正常体检者(对照组)。采用酶联免疫吸附法检测血清CCL17、CXCL8水平;超声心动图测量左室收缩末期内径(LVESD)、左室舒张末期内径(LVEDD)、左室射血分数(LVEF)、二尖瓣舒张早期血流峰值(E)与舒张晚期血流峰值(A)比值。HFpEF病人出院后接受随访,统计随访期间不良心血管事件发生情况。Pearson相关性分析CCL17、CXCL8与超声心动图参数的相关性,多因素Logistic回归分析老年HFpEF病人预后的影响因素。受试者工作特征(ROC)曲线分析CCL17、CXCL8预测老年HFpEF病人预后的临床价值。结果:HFpEF组血清CCL17、CXCL8水平高于对照组,差异均有统计学意义(P<0.001)。HFpEF组LVESD、LVEDD高于对照组,LVEF、E/A比值低于对照组,差异均有统计学意义(P<0.001)。HFpEF病人血清CCL17、CXCL8水平与LVESD、LVEDD呈正相关(P<0.001),与LVEF、E/A比值呈负相关(P<0.01)。预后不良组纽约心脏病协会(NYHA)心功能Ⅳ级,血清CCL17、CXCL8、NT-proBNP水平,LVESD、LVEDD高于预后良好组(P<0.05),LVEF、E/A比值低于预后良好组(P<0.05)。NYHA心功能Ⅳ级、高CCL17、高CXCL8、高NT-proBNP是HFpEF病人预后不良的危险因素(P<0.05)。CCL17、CXCL8预测老年HFpEF病人预后不良的ROC曲线下面积(AUC)为0.776,0.800,联合CCL17、CXCL8后预测老年HFpEF病人预后不良的AUC为0.879,大于单独CCL17、CXCL8(Z值分别为2.333,2.193,P<0.05)。结论:老年HFpEF病人血清CCL17、CXCL8水平增高,其与心功能降低及预后不良有关,联合检测血清CCL17、CXCL8水平可预测不良预后风险。

医用X射线防护材料的研究进展

介绍了医用X射线与生物系统的相互作用机理及物理防护原理,分析了具有医用X射线屏蔽能力的柔性复合材料的研究进展。探讨了铅、铋、钨等防X射线功能颗粒及聚合物基材的性能特征,总结了涂层法、溶胶-凝胶法、纺丝法等成型方法的优缺点。研究表明,现有X射线防护材料在提升防护效果和使用便捷性方面具有重要意义,但面临性能优化和成本控制方面的挑战。未来研究应聚焦新型功能颗粒的开发、复合材料结构设计的优化及环保高效屏蔽材料的探索等方面,以进一步提升医用X射线防护材料的性能,拓宽其应用前景。

关节镜联合C型臂X线机治疗胫骨平台骨折的疗效

目的探讨关节镜联合C型臂X线机治疗胫骨平台骨折的效果。方法方便选择2017年1月—2022年12月丹阳市人民医院收治的78例胫骨平台骨折患者为研究对象,以随机双盲法分为两组,每组39例。对照组行常规切开复位内固定术,观察组行关节镜联合C型臂X线机微创内固定术,对两组手术疗效、手术指标、膝关节功能恢复与并发症发生情况进行分析比较。结果观察组手术优良率(97.44%)明显高于对照组(82.05%),差异有统计学意义(χ^(2)=5.014,P<0.05);观察组手术治疗相关指标优于对照组,差异有统计学意义(P均<0.05)。术后6个月两组患者Lysholm、纽约特种外科医院(Hospital for Special Surgery,HSS)评分均升高,且观察组Lysholm、HSS评分明显高于对照组,差异有统计学意义(P均<0.05)。观察组术后并发症总发生率低于对照组,差异有统计学意义(P均<0.05)。结论胫骨平台骨折患者采用关节镜联合C型臂X线机治疗的疗效确切,患者创伤小、术后恢复快、并发症少,且对患者膝关节功能的恢复有着明显的促进作用。

表面基团对Ti_(3)C_(2)T_(x)吸附NO性能影响的第一性原理研究

本工作基于密度泛函理论的第一性原理方法,构建了Ti_(3)C_(2)O_(2)、Ti_(3)C_(2)O1.5(OH)0.5、Ti_(3)C_(2)O(OH)、Ti_(3)C_(2)O1.5F0.5和Ti_(3)C_(2)OF五种模型,从几何结构、电荷转移以及电子性质等方面研究了基团种类和比例对Ti_(3)C_(2)T_(x)吸附NO的影响。结果表明:相较于Ti_(3)C_(2)O_(2),含低比例-OH和-F基团的Ti_(3)C_(2)T_(x)对NO的吸附能更大,电荷转移更弱,不利于其探测NO,与实验结果一致;但随着-OH和-F比例的提高,吸附能分别减小和增大,电荷转移分别增强和减弱,表明高比例的-OH有利于Ti_(3)C_(2)T_(x)探测NO,而高比例的-F是不利的;同时,在吸附NO后,Ti_(3)C_(2)O_(2)在费米能级附近的能带极值曲率变小,电子有效质量增大,表明-O基团有利于Ti_(3)C_(2)T_(x)探测NO。在几何弛豫过程中NO分子总是以N原子靠近衬底,吸附距离均较小,而且最近邻原子的电子轨道出现杂化,电子的聚集和消散位于两端,表明最近邻原子间成键较弱且偏离子性。此计算结果可以为Ti_(3)C_(2)T_(x)探测和屏蔽NO提供理论指导,同时为Ti_(3)C_(2)T_(x)的表面改性提供思路。

回声构式“X是X”的构件特点、语义特征及互动功能

“X是X”构式借助于一定的语言手段重复前一说话人话语的部分内容“X”,以此表达说话人让步肯定的话语立场,同时,其整体意义的解读不能从组成成分的意义简单相加获得,可命名为回声构式。从构式的组成来看,“X是X”构式的前“X”是后一说话人从前一说话人话语中引入的回声成分,“是”是表示肯定的动词,起“复说”或“拷贝”作用且与后“X”一起表达后一说话人对前一说话人话语“X”的主观评价,不仅具备让步肯定的语义特征,同时还具备回声肯定的语义特征。“X是X”构式以绝对优势的比例使用于对话语体,且处于应答话轮的开端位置,这显示出构式具有极强的互动功能。如果把该类结构的考察范围从对话扩展到独白领域,会发现其评价立场的表达表现为显性互动和隐性互动两种类型。

Further Notes on the Gaussian Beam Expansion

We provide alternatively a simple way of computing the Fresnel field integral,a further extension to the Gaussianbeam expansion.With a known result that the circ function is approximately decomposed into a sum of Gaussian functions,the zero-order Bessel function of the first kind is similarly expanded by the Bessel-Fourior transform.Two expansions are together inserted in this integral,which is then expressible in terms of the simple algebraic functions.The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics.As examples,the calculation results for the uniform and the simply supported piston sources are presented,in a good agreement with those evaluated by numerical integration.

Gaussian Functions,Γ-Functions and Wavelets

The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following the train of thought in one dimensional situation, the relation between n dimensional Gaussian function and Γ function is given. By these, the possibility of arbitrary derivative of an n dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ function as well as in finding high dimensional mother wavelets.

Nb_(2)CT_(x) MXene: High capacity and ultra-long cycle capability for lithium-ion battery by regulation of functional groups

MXenes are well known for their potential application in supercapacitors due to their high-rate intercalation pseudocapacitance and long cyclability.However,the reported low capacity of pristine MXenes hinders their practical application in lithium-ion batteries.In this work,a robust strategy is developed to control the functional groups of Nb_2 CT_x MXene.The capacity of pristine Nb_2 CT_x MXene can be significantly increased by Li~+ intercalation and surface modification.The specific capacity of the treated Nb_2 CT_x is up to 448 mAh g^(-1) at 0.05 A g^(-1),and at a large current density of 2 A g^(-1) remains a high reversible capacity retention rate of 75% after an ultra-long cycle of 2000 cycles.These values exceed most of the reported pristine MXenes(including the most studied Ti_3 C_2 T_x) and carbon-based materials.It demonstrates that this strategy has great help to improve the electrochemical performance of pristine MXene,and the results enhance the promise of MXenes in the application of lithium-ion batteries.

Gaussian process assisted coevolutionary estimation of distribution algorithm for computationally expensive problems

In order to reduce the computation of complex problems, a new surrogate-assisted estimation of distribution algorithm with Gaussian process was proposed. Coevolution was used in dual populations which evolved in parallel. The search space was projected into multiple subspaces and searched by sub-populations. Also, the whole space was exploited by the other population which exchanges information with the sub-populations. In order to make the evolutionary course efficient, multivariate Gaussian model and Gaussian mixture model were used in both populations separately to estimate the distribution of individuals and reproduce new generations. For the surrogate model, Gaussian process was combined with the algorithm which predicted variance of the predictions. The results on six benchmark functions show that the new algorithm performs better than other surrogate-model based algorithms and the computation complexity is only 10% of the original estimation of distribution algorithm.

Audio-Visual Underdetermined Blind Source Separation Algorithm Based on Gaussian Potential Function

Most existing algorithms for the underdetermined blind source separation(UBSS) problem are two-stage algorithm, i.e., mixing parameters estimation and sources estimation. In the mixing parameters estimation, the previously proposed traditional clustering algorithms are sensitive to the initializations of the mixing parameters. To reduce the sensitiveness to the initialization, we propose a new algorithm for the UBSS problem based on anechoic speech mixtures by employing the visual information, i.e., the interaural time difference(ITD) and the interaural level difference(ILD), as the initializations of the mixing parameters. In our algorithm, the video signals are utilized to estimate the distances between microphones and sources, and then the estimations of the ITD and ILD can be obtained. With the sparsity assumption in the time-frequency domain, the Gaussian potential function algorithm is utilized to estimate the mixing parameters by using the ITDs and ILDs as the initializations of the mixing parameters. And the time-frequency masking is used to recover the sources by evaluating the various ITDs and ILDs. Experimental results demonstrate the competitive performance of the proposed algorithm compared with the baseline algorithms.

On Development of Fuzzy Controller: The Case of Gaussian and Triangular Membership Functions

In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, we derived explicit Fourier series expressions for systematic and dynamic computation of grade of membership in the overlap and non-overlap regions of triangular Fuzzy sets. In another paper, we extended the methodology to cover cases of cosine, exponential and Gaussian Fuzzy sets by presenting explicit Fourier series representation for encoding fuzziness in the overlap and non-overlap domains of Fuzzy sets. This current paper presents the development of a “Fuzzy Controller” device, which incorporates the formal mathematical representation for computing grade of membership of Gaussian and triangular Fuzzy sets. It is shown that triangular approximation of Gaussian membership function in Fuzzy control can lead to wrong linguistic classification which may have adverse effects on operational and control decisions. The development of the Fuzzy controller demonstrates that the proposed technique can indeed be incorporated in engineering systems for dynamic and systematic computation of grade of membership in the overlap and non-overlap regions of Fuzzy sets;and thus provides a basis for the design of embedded Fuzzy controller for mission critical applications.

Mechanisms of Transforming CH_x to CO on Ni(111) Surface by Density Functional Theory

To elucidate feasible routes of producing CO from CH 3 and unravel the eff ect of adsorbed O on CH x transformation, the reactivity of CH x ( x = 1-3) with and without the assistance of adsorbed atomic O on Ni(111) was explored using density functional theory calculations. The adsorption energies of CH x ( x = 0-3) were found to be signifi cantly reduced on an O-preadsorbed Ni(111) surface compared to a pure surface. Furthermore, O-assisted one-step dehydrogenation of CH x ( x = 1-3) features energy barriers and thus is diffi cult to proceed. In terms of energy, the direct dissociation of CH 3 is favorable, except for the last CH dehydrogenation, which is energy intensive. Interestingly, in O-assisted two-step CH transformation to CO via CHO intermediate, the barrier is dramatically lowered. The successive dehydrogenations of CH x O ( x = 1-3) were also found to be a route for CO formation. Finally, two possible pathways from CH 3 to CO are proposed:(a) CH 3 → CH 2 → CH → CHO → CO;(b) CH 3 → CH 3 O → CH 2 O → CHO → CO.

The Non-standard Characteristics of Functional SpacesK(X) and C_0(X)

In this paper,the non standard characteristics of functional spaces K(X) and C 0(X) are presented and proved.