Some Generalizations of Monotonicity Condition and Applications

0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc..

Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws

With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati–Konno–Ichikawa(WKI) equation. Further, a new generalization of the Fokas–Lenells(FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained.

SOME GENERALIZATIONS ON THE BOUNDEDNESS OF BILINEAR OPERATORS

For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.

INTERPOLATION WITH LAGRANGE POLYNOMIALS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS GENERALIZATIONS

The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies the inequality then for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality 丨p^(k)(x)丨≤max{丨q^((k))(x)丨,丨1/k(x^2-1)q^(k+1)(x)+xq^((k))(x)丨}. This estimate leads to the Markov inequality for the higher order derivatives of polynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero. Some other results are established which gives evidence to the conjecture that under the conditions of Theorem 1 the inequality ‖p^((k))‖≤‖q^(k)‖holds.

Generalizations of Euler Numbers and Euler Numbers of Higher Order

The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.

SOME FURTHER GENERALIZATIONS OF KY FAN’S MINIMAX INEQUALITY AND ITS APPLICATIONS TO VARIATIONAL INEQUALITIES

The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the results presented in this paper to study the saddle . point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of[1-6]

Generalizations of Some Formulas of the Reciprocal Sum and Alternating Sum for Generalized Lucas Numbers

The purpose of this article is to provide the inversion relationships between the reciprocal sum S（1, 2,…, m） and the alternating sum T（1, 2,…, m） for generalized Lucas numbers which generalizes the Melham＇s results.

Properties of Elliptic Integrals and Their Generalizations

In this paper, a conjecture put forward by G. D. Anderson, S.-L. Qiu and M. K. Vamanamurthy in 1995 and concerning elliptic integrals is proved to be true, and some monotoneity and onvexity properties of certain combinations of generalized elliptic integrals are obtained.

Discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type

We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched.

Complementary roles of glial cells in generating region-specific neuroinflammatory responses and phagocytosis in Parkinson’s disease

Neuroinflammation is associated with Parkinson’s disease:Reactive gliosis and neuroinflammation are hallmarks of Parkinson’s disease(PD),a multisystem neurodegenerative disorder characterized by a progressive loss of dopaminergic neurons.Neuroinflammation has long been considered a mere consequence of neuronal loss,but whether it promotes PD or is a key player in disease progression remains to be determined.Human leukocyte antigen.

Research on Stock Price Prediction Method Based on the GAN-LSTM-Attention Model

Stock price prediction is a typical complex time series prediction problem characterized by dynamics,nonlinearity,and complexity.This paper introduces a generative adversarial network model that incorporates an attention mechanism(GAN-LSTM-Attention)to improve the accuracy of stock price prediction.Firstly,the generator of this model combines the Long and Short-Term Memory Network(LSTM),the Attention Mechanism and,the Fully-Connected Layer,focusing on generating the predicted stock price.The discriminator combines the Convolutional Neural Network(CNN)and the Fully-Connected Layer to discriminate between real stock prices and generated stock prices.Secondly,to evaluate the practical application ability and generalization ability of the GAN-LSTM-Attention model,four representative stocks in the United States of America(USA)stock market,namely,Standard&Poor’s 500 Index stock,Apple Incorporatedstock,AdvancedMicroDevices Incorporatedstock,and Google Incorporated stock were selected for prediction experiments,and the prediction performance was comprehensively evaluated by using the three evaluation metrics,namely,mean absolute error(MAE),root mean square error(RMSE),and coefficient of determination(R2).Finally,the specific effects of the attention mechanism,convolutional layer,and fully-connected layer on the prediction performance of the model are systematically analyzed through ablation study.The results of experiment show that the GAN-LSTM-Attention model exhibits excellent performance and robustness in stock price prediction.

5DGWO-GAN:A Novel Five-Dimensional Gray Wolf Optimizer for Generative Adversarial Network-Enabled Intrusion Detection in IoT Systems

The Internet of Things(IoT)is integral to modern infrastructure,enabling connectivity among a wide range of devices from home automation to industrial control systems.With the exponential increase in data generated by these interconnected devices,robust anomaly detection mechanisms are essential.Anomaly detection in this dynamic environment necessitates methods that can accurately distinguish between normal and anomalous behavior by learning intricate patterns.This paper presents a novel approach utilizing generative adversarial networks(GANs)for anomaly detection in IoT systems.However,optimizing GANs involves tuning hyper-parameters such as learning rate,batch size,and optimization algorithms,which can be challenging due to the non-convex nature of GAN loss functions.To address this,we propose a five-dimensional Gray wolf optimizer(5DGWO)to optimize GAN hyper-parameters.The 5DGWO introduces two new types of wolves:gamma(γ)for improved exploitation and convergence,and theta(θ)for enhanced exploration and escaping local minima.The proposed system framework comprises four key stages:1)preprocessing,2)generative model training,3)autoencoder(AE)training,and 4)predictive model training.The generative models are utilized to assist the AE training,and the final predictive models(including convolutional neural network(CNN),deep belief network(DBN),recurrent neural network(RNN),random forest(RF),and extreme gradient boosting(XGBoost))are trained using the generated data and AE-encoded features.We evaluated the system on three benchmark datasets:NSL-KDD,UNSW-NB15,and IoT-23.Experiments conducted on diverse IoT datasets show that our method outperforms existing anomaly detection strategies and significantly reduces false positives.The 5DGWO-GAN-CNNAE exhibits superior performance in various metrics,including accuracy,recall,precision,root mean square error(RMSE),and convergence trend.The proposed 5DGWO-GAN-CNNAE achieved the lowest RMSE values across the NSL-KDD,UNSW-NB15,and IoT-23 datasets,with values of 0.24,1.10,and 0.09,respectively.Additionally,it attained the highest accuracy,ranging from 94%to 100%.These results suggest a promising direction for future IoT security frameworks,offering a scalable and efficient solution to safeguard against evolving cyber threats.

WELL-POSEDNESS AND PEAKON SOLUTIONS FOR A HIGHER ORDER CAMASSA-HOLM TYPE EQUATION

In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.

Further Generalizations of Opial’s Inequality

Let C1[a,b] denote the set of all continuously differentiable functions on theclosed finite interval [a,b],and Iet AC [a,b] be the set of all absolutely continuousfunctions on [a,b].Z.Opial proved that if f∈C1[O,h],f(O)-f(h)=0 andf(x)>0 when x∈(O,h),then

基于ADRV9009的雷达干扰系统设计

如何快速高效地实现高灵活性、高集成度、可配置性好、低成本且易于维护的雷达干扰系统是当前雷达对抗领域的研究重点。针对以上需求,采用高集成度宽带射频收发器ADRV9009和FPGA芯片XC7Z100来设计雷达干扰系统,实现从射频到基带的全链路信号收发,提高了系统的集成度。通过串口通信对雷达干扰参数进行实时配置,提高了雷达干扰系统的灵活性和可配置性。采用System Generator开发工具对雷达干扰系统进行层次化、模块化设计,缩短了系统开发周期,提高了系统的可维护性。

GENERALIZATIONS OF J-HOMOMORPHISM AND THE ROHLIN THEOREM

Ⅰ. INTRODUCTIONThroughout this note all manifolds are assumed to be compact,connected and differentiable. A theorem of Rohlin asserts that the first Pontrjagin class of a 4-manifold M is congruent to zero modulo 48, provided w1（M）=w2 （M）=0. This result has been generalized to higher dimensions by Milnor and Kervaire.

Computational Experiments for Complex Social Systems:Experiment Design and Generative Explanation

Powered by advanced information technology,more and more complex systems are exhibiting characteristics of the cyber-physical-social systems(CPSS).In this context,computational experiments method has emerged as a novel approach for the design,analysis,management,control,and integration of CPSS,which can realize the causal analysis of complex systems by means of“algorithmization”of“counterfactuals”.However,because CPSS involve human and social factors(e.g.,autonomy,initiative,and sociality),it is difficult for traditional design of experiment(DOE)methods to achieve the generative explanation of system emergence.To address this challenge,this paper proposes an integrated approach to the design of computational experiments,incorporating three key modules:1)Descriptive module:Determining the influencing factors and response variables of the system by means of the modeling of an artificial society;2)Interpretative module:Selecting factorial experimental design solution to identify the relationship between influencing factors and macro phenomena;3)Predictive module:Building a meta-model that is equivalent to artificial society to explore its operating laws.Finally,a case study of crowd-sourcing platforms is presented to illustrate the application process and effectiveness of the proposed approach,which can reveal the social impact of algorithmic behavior on“rider race”.

基于System Generator的卷积加速结构设计与实现

为解决卷积神经网络中卷积运算耗时长、运算复杂的问题,针对卷积运算的并行性特征,提出一种基于分块的流水线加速方法,并基于该方法在System Generator上进行了电路设计。通过在FPGA(Field-programmable Gate Array)上进行实验验证,该设计模型能正确输出卷积运算结果;在结构和输入数据相同的情况下,该设计模型在计算速度上相比于普通CPU最高可加速258倍,相比于服务器级CPU提高了近40倍,具有良好的加速效果。

May ChatGPT be a tool producing medical information for common inflammatory bowel disease patients’questions?An evidencecontrolled analysis

Artificial intelligence is increasingly entering everyday healthcare.Large language model(LLM)systems such as Chat Generative Pre-trained Transformer(ChatGPT)have become potentially accessible to everyone,including patients with inflammatory bowel diseases(IBD).However,significant ethical issues and pitfalls exist in innovative LLM tools.The hype generated by such systems may lead to unweighted patient trust in these systems.Therefore,it is necessary to understand whether LLMs(trendy ones,such as ChatGPT)can produce plausible medical information(MI)for patients.This review examined ChatGPT’s potential to provide MI regarding questions commonly addressed by patients with IBD to their gastroenterologists.From the review of the outputs provided by ChatGPT,this tool showed some attractive potential while having significant limitations in updating and detailing information and providing inaccurate information in some cases.Further studies and refinement of the ChatGPT,possibly aligning the outputs with the leading medical evidence provided by reliable databases,are needed.