AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

基于EEMD、相关系数、排列熵和小波阈值去噪的新型水下声学信号去噪方法

The complexities of the marine environment and the unique characteristics of underwater channels pose challenges in obtaining reliable signals underwater,necessitating the filtration of underwater acoustic noise.Herein,an underwater acoustic signal denoising method based on ensemble empirical mode decomposition(EEMD),correlation coefficient(CC),permutation entropy(PE),and wavelet threshold denoising(WTD)is proposed.Furthermore,simulation experiments are conducted using simulated and real underwater acoustic data.The experimental results reveal that the proposed denoising method outperforms other previous methods in terms of signal-to-noise ratio,root mean square error,and CC.The proposed method eliminates noise and retains valuable information in the signal.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Entanglement and Volume Monogamy Features of Permutation Symmetric N-Qubit Pure States with N-Distinct Spinors: GHZ and States

We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.

The Influence of s-Conditional Permutability of Subgroups on the Structure of Finite Groups

Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized.

A color image encryption algorithm based on hyperchaotic map and DNA mutation

We devise a color image encryption scheme via combining hyperchaotic map,cross-plane operation and gene theory.First,the hyperchaotic map used in the encryption scheme is analyzed and studied.On the basis of the dynamics of hyperchaotic map,a color image encryption scheme is designed.At the end of the encryption process,a DNA mutation operation is used to increase the encoding images’randomness and to improve the encryption algorithm’s security.Finally,simulation experiments,performance analysis,and attack tests are performed to prove the effectiveness and security of the designed algorithm.This work provides the possibility of applying chaos theory and gene theory in image encryption.

Modified 2 Satisfiability Reverse Analysis Method via Logical Permutation Operator

The effectiveness of the logic mining approach is strongly correlated to the quality of the induced logical representation that represent the behaviour of the data.Specifically,the optimum induced logical representation indicates the capability of the logic mining approach in generalizing the real datasets of different variants and dimensions.The main issues with the logic extracted by the standard logic mining techniques are lack of interpretability and the weakness in terms of the structural and arrangement of the 2 Satisfiability logic causing lower accuracy.To address the issues,the logical permutation serves as an alternative mechanism that can enhance the probability of the 2 Satisfiability logical rule becoming true by utilizing the definitive finite arrangement of attributes.This work aims to examine and analyze the significant effect of logical permutation on the performance of data extraction ability of the logic mining approach incorporated with the recurrent discrete Hopfield Neural Network.Based on the theory,the effect of permutation and associate memories in recurrent Hopfield Neural Network will potentially improve the accuracy of the existing logic mining approach.To validate the impact of the logical permutation on the retrieval phase of the logic mining model,the proposed work is experimentally tested on a different class of the benchmark real datasets ranging from the multivariate and timeseries datasets.The experimental results show the significant improvement in the proposed logical permutation-based logic mining according to the domains such as compatibility,accuracy,and competitiveness as opposed to the plethora of standard 2 Satisfiability Reverse Analysis methods.

Cloud Resource Integrated Prediction Model Based on Variational Modal Decomposition-Permutation Entropy and LSTM

Predicting the usage of container cloud resources has always been an important and challenging problem in improving the performance of cloud resource clusters.We proposed an integrated prediction method of stacking container cloud resources based on variational modal decomposition(VMD)-Permutation entropy(PE)and long short-term memory(LSTM)neural network to solve the prediction difficulties caused by the non-stationarity and volatility of resource data.The variational modal decomposition algorithm decomposes the time series data of cloud resources to obtain intrinsic mode function and residual components,which solves the signal decomposition algorithm’s end-effect and modal confusion problems.The permutation entropy is used to evaluate the complexity of the intrinsic mode function,and the reconstruction based on similar entropy and low complexity is used to reduce the difficulty of modeling.Finally,we use the LSTM and stacking fusion models to predict and superimpose;the stacking integration model integrates Gradient boosting regression(GBR),Kernel ridge regression(KRR),and Elastic net regression(ENet)as primary learners,and the secondary learner adopts the kernel ridge regression method with solid generalization ability.The Amazon public data set experiment shows that compared with Holt-winters,LSTM,and Neuralprophet models,we can see that the optimization range of multiple evaluation indicators is 0.338∼1.913,0.057∼0.940,0.000∼0.017 and 1.038∼8.481 in root means square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE)and variance(VAR),showing its stability and better prediction accuracy.

Short-Term Prediction of Photovoltaic Power Generation Based on LMD Permutation Entropy and Singular Spectrum Analysis

The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete randomness.With the development of new energy economy,the proportion of photovoltaic energy increased accordingly.In order to solve the problem of improving the energy conversion efficiency in the grid-connected optical network and ensure the stability of photovoltaic power generation,this paper proposes the short-termprediction of photovoltaic power generation based on the improvedmulti-scale permutation entropy,localmean decomposition and singular spectrum analysis algorithm.Firstly,taking the power output per unit day as the research object,the multi-scale permutation entropy is used to calculate the eigenvectors under different weather conditions,and the cluster analysis is used to reconstruct the historical power generation under typical weather rainy and snowy,sunny,abrupt,cloudy.Then,local mean decomposition(LMD)is used to decompose the output sequence,so as to extract more detail components of the reconstructed output sequence.Finally,combined with the weather forecast of the Meteorological Bureau for the next day,the singular spectrumanalysis algorithm is used to predict the photovoltaic classification of the recombination decomposition sequence under typical weather.Through the verification and analysis of examples,the hierarchical prediction experiments of reconstructed and non-reconstructed output sequences are compared.The results show that the algorithm proposed in this paper is effective in realizing the short-term prediction of photovoltaic generator,and has the advantages of simple structure and high prediction accuracy.

A Relationship between the Partial Bell Polynomials and Alternating Run Polynomials

In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce an explicit formula of the alternating run polynomials in terms of the partial Bell polynomials.

日间手术和择期手术的手术相关时长差异性分析

对腹腔镜胆囊切除术(以下简称LC)日间手术病人和择期手术病人的手术时长、术后恢复时长、占用手术间时长和术后住院时长分别进行了K-S检验和Permutation检验。结果显示LC日间手术和择期手术病人的手术时长、术后恢复时长、占用手术间时长和术后住院时长均值不相等,分布不相同,样本均来自不同的总体。科研工作者在研究过程中如果涉及到手术时长、术后恢复时长、占用手术间时长和术后住院时长,应考虑是否需要根据是日间手术还是择期手术加以区别对待。

两个一维总体分布相等性的permutation检验

检验两个一维总体分布的相等性,采用理论证明和数值模拟的方法,在Prastgaard提出的Kolmogorov-Smirnov统计量T1及相应的permutation统计量T 1基础上,提出了基于K-S统计量的新统计量T2及相应的permutation统计量T 2,研究了在一维的情形下T2与T 2的分布,并进行了数值模拟.结果表明:新统计量在原假设下有相同的极限分布,数值模拟结果优于原统计量.该方法对检验两总体分布的相等性有一定的参考价值.

新疆喀什-乌恰交汇区潮汐触发地震活动的统计检验

基于Schuster检验及Permutation检验方法,对喀什-乌恰交汇区地震活动受固体潮触发情况进行日尺度及月尺度检验。其中日尺度分别选取引潮力南北分量、东西分量及潮汐体应力作为潮汐曲线。研究结果显示,该地区地震活动均较多的发生于3种潮汐的最大值(相位0°)附近,优势发震相位分别为-5.86°、6.60°以及-15.52°,且发生地震的频次随潮汐力的增大而增加;利用3种潮汐曲线(引潮力日尺度南北分量、东西分量以及潮汐体应力)对所有地震进行Schuster检验所得pS值分别为10.52%、2.40%以及2.06%,Permutation检验所得pP值分别为10.90%、2.40%以及2.06%,其中基于引潮力东西分量及潮汐体应力的pS、pP值均低于潮汐触发地震的阈值0.05。月尺度Schuster检验pS值及Permutation检验pP值结果均非常小(接近于0),远低于潮汐触发地震阈值0.05,优势发震相位φ为-1.91°,较为接近月尺度下的固体潮最大值0°(即农历朔、望)。对潮汐触发地震的统计学检验结果即东西向潮汐触发效应大于南北向触发效应的原因进行了初步解释。

Bootstrap和Permutation方法在样本率多重比较中的应用

目的介绍Bootstrap和Permutation方法在样本率多重比较中的应用。方法调用SAS中的MULTTEST过程,编写程序实现样本率的两两比较和与控制组比较,并通过实例说明效果。结果运用Bootstrap和Permutation方法能较好解决样本率的多重比较问题。结论使用Bootstrap和Permutation方法的SAS程序,简单明了,结果准确,使用方便。

流水车间排列排序专家系统—PFSCH

流水车间排列排序问题可以简单表示为:n/m/p/Fmax,其含义为,n个不同的工件（J1,J2,…,Jn）要经m台机器（M1,M2…,Mm）加工;加工路线为M1—M2—…—Mm,n个工件在每台机器上的加工顺序都一样;p表示排列排序;目标函数是使最长流程时间Fmax（加工周期）最短.n个工件有n!种不同的加工顺序.现已证明,n/m/p/Fmax（m≥3）问题属于NP难题,找不到多项式时间算法.因此,人们提出了若干个启发式算法,其中最著名的是Campbell等人提出的启发式算法（简称为CDS法）.Dannenbring曾比较过11种不同的启发式算法的效果,指出“快速接近扩展搜索法（RAES法）”的结果最好.但是,RAES法实质上还是一种列举法,它不从问题本身的结构出发,具有很大的盲目性.

截面数据异方差问题检验技术的比较

在忽略异方差的情况下,进行模型的OLS参数估计会导致严重的后果,因此,研究异方差性的检验、选取适当的检验方法是非常重要的理论与实践问题。文章基于蒙特卡罗随机模拟技术,分别在PermutationTest与传统形式下对异方差检验的主要方法有:White检验、Park检验、Goldfeld-Quandt检验、Breusch-Pagan/Godfrey检验、Glejser检验,在不同的异方差假定形式下、在不同的样本容量下对这五种检验方法的第一类错误率的控制、检验功效等方面进行充分、完备的研究和讨论,并给出结论供实践工作者参考。

Quantitative Precipitation Forecast Experiment Based on Basic NWP Variables Using Deep Learning

The quantitative precipitation forecast(QPF)performance by numerical weather prediction(NWP)methods depends fundamentally on the adopted physical parameterization schemes(PS).However,due to the complexity of the physical mechanisms of precipitation processes,the uncertainties of PSs result in a lower QPF performance than their prediction of the basic meteorological variables such as air temperature,wind,geopotential height,and humidity.This study proposes a deep learning model named QPFNet,which uses basic meteorological variables in the ERA5 dataset by fitting a non-linear mapping relationship between the basic variables and precipitation.Basic variables forecasted by the highest-resolution model(HRES)of the European Centre for Medium-Range Weather Forecasts(ECMWF)were fed into QPFNet to forecast precipitation.Evaluation results show that QPFNet achieved better QPF performance than ECMWF HRES itself.The threat score for 3-h accumulated precipitation with depths of 0.1,3,10,and 20 mm increased by 19.7%,15.2%,43.2%,and 87.1%,respectively,indicating the proposed performance QPFNet improved with increasing levels of precipitation.The sensitivities of these meteorological variables for QPF in different pressure layers were analyzed based on the output of the QPFNet,and its performance limitations are also discussed.Using DL to extract features from basic meteorological variables can provide an important reference for QPF,and avoid some uncertainties of PSs.

Phase Ⅱ open-label study of recombinant circularly permuted TRAIL as a single-agent treatment for relapsed or refractory multiple myeloma

Background: Despite the recent development of new therapies, multiple myeloma(MM) remains an incurable disease. Thus, new, efective treatments are urgently needed, particularly for relapsed or refractory MM(RRMM). In an earlier phase I study, a novel form of recombinant human Apo2L/tumor necrosis factor-related apoptosis-inducing ligand(TRAIL) that is currently in clinical development for the treatment of hematologic malignancies, i.e., circularly permuted TRAIL(CPT), was well tolerated at a dose of 2.5 mg/kg per day and showed promising preliminary activity in patients with RRMM. This phase II, open-label, multicenter study further investigated the eicacy and safety of 2.5-mg/kg per day CPT as single-agent therapy for patients with RRMM.Methods: Patients with RRMM were treated once daily with CPT(2.5 mg/kg, intravenously) for 14 consecutive days for each 21-day cycle. Clinical response and toxicity were assessed after each treatment cycle.Results: Twenty-seven patients received CPT. Using the European Group for Blood and Marrow Transplantation criteria, we calculated the overall response rate of 33.3% with 1 near-complete response(n CR) and 8 partial responses(PRs). The clinical beneit rate(48.1%) included 1 nCR, 8 PRs, and 4 minimal responses. The most common treatmentrelated adverse events(TRAEs) were fever, aspartate aminotransferase elevation, alanine aminotransferase elevation, leucopenia, rash, neutropenia, and thrombocytopenia. We graded toxicity using the Common Toxicity Criteria for Adverse Events, version 3.0, and determined that 37.0% of patients had at least 1 grade 3–4 TRAE.Conclusions: CPT as a single agent can elicit a response in patients with RRMM and is well tolerated. Further clinical investigation is warranted.

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

CONSTRUCTION OF COMPACTLY SUPPORTED BIVARIATE ORTHOGONAL WAVELETS BY UNIVARIATE ORTHOGONAL WAVELETS

After some permutation of conjugate quadrature filter, new conjugate quadrature filters can be derived. In terms of this permutation, an approach is developed for constructing compactly supported bivariate orthogonal wavelets from univariate orthogonal wavelets. Non-separable orthogonal wavelets can be achieved. To demonstrate this method, an example is given.