Fixed-Time Consensus-Based Nash Equilibrium Seeking

Dear Editor,This letter examines the fixed-time stability of the Nash equilibrium(NE)in non-cooperative games.We propose a consensus-based NE seeking algorithm for situations where players do not have perfect information and communicate via a topology graph.The proposed algorithm can achieve NE in a fixed time that does not depend on initial conditions and can be adjusted in advance.

Secure Tracking Control via Fixed-Time Convergent Reinforcement Learning for a UAV CPS

Dear Editor,This letter is concerned with the secure tracking control problem in the unmanned aerial vehicle(UAV) system by fixed-time convergent reinforcement learning(RL). By virtue of the zero-sum game,the false data injection(FDI) attacker and secure controller are viewed as game players.

Effect of the Particle Packing Configuration on Fixed Bed Performance

Fixed-bed reactors are generally considered the optimal choice for numerous multi-phase catalytic reactions due to their excellent performance and stability.However,conventional fixed beds often encounter challenges related to inadequate mass transfer and a high pressure drop caused by the non-uniform void fraction distribution.To enhance the overall performance of fixed beds,the impact of different packing configurations on performance was investigated.Experimental and simulation methods were used to investigate the fluid flow and mass transfer performances of various packed beds under different flow rates.It was found that structured beds exhibited a significantly lower pressure drop per unit length than conventional packed beds.Furthermore,the packing configurations had a critical role in improving the overall performance of fixed beds.Specifically,structured packed beds,particularly the H-2 packing configuration,effectively reduced the pressure drop per unit length and improved the mass transfer efficiency.The H-2 packing configuration consisted of two parallel strips of particles in each layer,with strips arranged perpendicularly between adjacent layers,and the spacing between the strips varied from layer to layer.

Relay-Switching-Based Fixed-Time Tracking Controller for Nonholonomic State-Constrained Systems:Design and Experiment

Dear Editor,This letter investigates the fixed-time trajectory tracking controller design for nonholonomic chained systems with static state constraints.Firstly,a fixed-time tracking control law is given to carry out relay switching,which divides the controller development process into two stages.

Vision-Based Fixed-Time Uncooperative Aerial Target Tracking for UAV

Dear Editor,In this letter,a vision-based fixed-time control is proposed for an unmanned aerial vehicle(UAV)with actuator saturation to track an uncooperative target.The fixed-time control is designed in backstepping framework.The relative states between UAV and the target are not directly measured,and are estimated by an onboard monocular camera.

Liquid-phase esterification of methacrylic acid with methanol catalyzed by cation-exchange resin in a fixed bed reactor:Experimental and kinetic studies

The kinetic behavior of esterification between methacrylic acid and methanol catalyzed by NKC-9 resin was studied in a fixed bed reactor.The reaction was conducted in the temperature range of 323.15 to 368.15 K with the molar ratio of reactants from 0.8 to 1.4 under certain pressure.The measurement data were regression with the pseudo-homogeneous(P-H),Eley-Rideal(E-R),and Langmuir-Hinshelwood(L-H)heterogeneous kinetic models.Independent adsorption experiments were implemented to gain the adsorption equilibrium constants of four components.Among the above three models,the L-H model exhibited the best fitting results.The stability of NKC-9 was evaluated by long-term running with the yield of methyl methacrylate no decrease during 3000 h operation.The structure and physicochemical properties of the new and used catalyst were performed by several characterizations including thermogravimetric analysis(TG),scanning electron microscope(SEM),X-ray diffraction(XRD)and Fourier transform infrared spectroscopy(FT-IR)and so on.

Efficacy and safety of latanoprost/timolol fixed combination dosed twice daily compared to once daily in patients with primary open angle glaucoma

AIM:To evaluate whether latanoprost/timolol fixed combination(LTFC)dosed twice daily may provide further intraocular pressure(IOP)reduction and evaluate the safety profile at this dose.METHODS:This is an open-labeled,randomized,prospective crossover study on fourty primary open angle glaucoma patients.Two weeks of washout period were followed by randomization to either once daily(OD,group A)or twice daily dosing(BD,group B)of LTFC for 4wk.After another 2-week washout period,the patients’treatment dose was crossed-over for another 4wk.IOP reduction alongside ocular and systemic side effects were evaluated.RESULTS:Mean baseline IOP was 18.57±2.93 and 17.8±3.01 mm Hg before OD and BD dose respectively,(P=0.27).Mean IOP after BD dose was statistically lower(12.49±1.59 mm Hg)compared to OD(13.48±1.81 mm Hg,P=0.017).Although IOP reduction after BD dose was more(5.32±3.24 mm Hg,29.89%)than after OD dosing(5.04 mm Hg,27.14%),it did not reach statistical significance(P=0.68).Patients switched from OD to BD(group A)showed mean IOP reduction by 0.69 mm Hg[95%confidence interval(CI):-0.09 to 1.48 mm Hg,P=0.078];but patients switched from BD to OD(group B)had significantly higher mean IOP by 1.25 mm Hg(95%CI:-2.04 to-0.46 mm Hg,P=0.006).BD dose had more ocular side effects albeit mild.CONCLUSION:Mean IOP after LTFC dosed twice daily is statistically lower,with additional mild side effects.

A fixed point theorem for Proinov mappings with a contractive iterate

In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.

Adsorption dynamics of ethane from air in structured fixed beds with different microfibrous composites

Adsorption dynamics of ethane in two granular fixed beds and structured fixed beds with microfibrous composites was studied.5A zeolite membrane 5A/PSSF(paper-like sintered stainless steel fiber)and microfibrous entrapped activated carbon(MEAC)composites were prepared by wet layup papermaking/sintering technique and in-situ hydrothermal method.Microfibrous composites were characterized by X-ray diffraction,scanning electron microscopy and N2 adsorption/desorption.Structured fixed beds were designed by filling granular adsorbents(5A zeolite or activated carbon)and microfibrous composites at the inlet and outlet of the beds,respectively.Effects of flow rate,bed height and structure on the breakthrough curves were investigated.The length of unused bed(LUB)was determined,and Yoon–Nelson model was used to fit the breakthrough curves.The experimental results showed ethane was effectively adsorbed on the granular adsorbents and microfibrous composites.Both composites could decrease the LUB values and enhance bed utilization.All breakthrough curves fitted well to Yoon–Nelson model,with correlation coefficient exceeding 0.89.The adsorption rate of ethane could be improved in the structured fixed beds,which showed an enhanced mass transfer efficiency for ethane adsorption.LUB values of structured fixed beds with 5A/PSSF composites were larger,the bed utilization values were lower,and the adsorption rate constants were higher than those with MEAC composites under the same conditions.

An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.

On Some Novel Fixed Point Results for Generalized F-Contractions in b-Metric-Like Spaces with Application

The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

The Impact of Nitrogen-Fixing Bacteria, Iron, and Zinc Foliar Application on Dry Land Yellow Mustard (Brassica juncea) Grain and Oil Production

The study, conducted at the Research Farm of the College of Agriculture, University of Tabriz in 2021, focused on the effects of various nitrogen-fixing bacterial isolates, biofertilizers containing nitrogen and phosphorus, as well as iron and zinc foliar applications on mustard growth under rainfed conditions. The results indicated that biofertilizers, whether used alone or in combination with chemical fertilizers, produced comparable grain and oil outputs compared to chemical fertilizers alone. Additionally, the application of iron and zinc through foliar spraying significantly enhanced both grain and oil production. These findings suggest that integrating nitrogen-fixing bacteria and biofertilizers could reduce reliance on chemical nitrogenous fertilizers, leading to decreased production expenses, improved product quality, and minimized environmental impact. This study highlights the potential for sustainable agricultural practices in dry land farming as a viable alternative to traditional chemical-intensive methods. Substituting chemical nitrogenous fertilizers with nitrogen-fixing bacteria or biofertilizers could result in cost savings in mustard grain and oil production while promoting environmental sustainability.

A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.

CyberKnife中Fixed/Iris准直器对肝癌患者治疗计划的影响及评价

目的:探讨及评价不同准直器(Fixed/Iris)的选择对治疗计划剂量学特点的影响。方法:选取12例肝癌患者影像数据,统一给予靶区剂量50 Gy/5 F,在相同条件下分别对每例患者选择Fixed与Iris准直器进行治疗计划设计,通过靶区适形度指数(CI)、均匀性指数(HI)、梯度指数(GI)、正常肝脏平均受量以及治疗时间等参数,分析评估计划优化质量及实施效率。结果:Iris组计划执行的平均治疗时间明显优于Fix组[(48.33±1.92)min vs(51.50±1.88)min,t=4.23,P=0.001],而CI(0.79±0.07 vs 0.80±0.08,t=0.52,P=0.613)、HI(0.42±0.14 vs 0.41±0.14,t=0.35,P=0.733)、GI(3.66±0.61 vs 3.60±0.50,t=1.15,P=0.273)、处方剂量归一值[(76.92±6.55)%vs(77.00±6.34)%,t=0.18,P=0.857]以及正常肝脏平均受量[(5.15±1.25)Gy vs(5.16±1.27)Gy,t=0.63,P=0.542]则无统计学差异。结论:CyberKnife系统中使用Iris相对Fixed准直器而言,除治疗时间明显缩短外,没有显著的剂量学差异。而对于其他部位肿瘤患者的治疗计划有无差异,还需进一步探讨和研究。

一种改进的Fixed-base Comb安全快速算法

本文从分析椭圆曲线上Fixed-baseComb算法出发,根据其特点,利用牺牲乘法操作以降低求逆操作的方法,分别用2kP、2P+Q的快速算法对Fixed-baseComb算法的预计算阶段和赋值阶段进行改进,极大地提高了计算效率:在素数域上预计算阶段提高70%～80%,而赋值阶段提高38%～43%,同时,改进算法通过对k的预处理,使得算法能够抵抗边际信道攻击.

基于ICA Fixed-Point算法的信号图像分析

从ICA算法的基准点出发,探讨了固定点算法中寻找W叠代公式的原理和方法,对分离一个独立成分和分离n个独立成分的运算方法进行了推导和分析;模拟试验表明:逐一分离的效果较好。

Treatment of coke plant wastewater by SND fixed biofilm hybrid system

In this article, coke plant wastewater was treated by a simultaneous nitrifying and denitrifying （SND） fixed biofilm hybrid system. The results showed that suitable parameters of the system were important for the performance of the bio-degradation system. The chemical oxygen demand （COD） removal efficiency in this system was satisfactory, higher than 94%, and ammonia nitrogen was higher than 95%. The effluent COD concentration could meet the discharge standard, except for very few situations. The results showed that a sufficient carbon source was important for making ammonia nitrogen concentration meet the discharge standard. Then the TiN removal efficiency in this system can be brought higher than 94%. Dissolved oxygen （DO） is very important to the performance of the SND bio-degradation system, and the suitable DO is about 3.5-4.0 mg/L at the forepart of reactor. In addition, the performance of the system was almost not affected by pH value. The results show that the system is feasible to treat coke plant wastewater.

Distributions of chlorophyll a and carbon fixed strength of phyto-plankton in autumn of the southern Huanghai Sea waters

Chlorophyll a （Chl a） concentration and primary productivity （PP）, namely, carbon fixed strength of phytoplankton along four transects in the southern Huanghai Sea （SHS） were studied for their distribution features and controlling mechanisms based on the investigations from 17 October to 3 November 2005. The Chl a concentration in the study waters dynamically changed spatially. Surface Chl a concentrations ranged from 0.11 to 2.38 mg/m^3 with higher and lower values observed in the nutrient-laden inshore waters and central part of the SHS occupied by oligotrophic current, respectively. The vertical distribution of Chl a concentration showed a predominant pattern of subsurface concentration maximum profile. It followed the previous result of the deep dissolved oxygen concentration maximum profile, which was significantly correlated with phytoplankton and regional water mass. The primary productivity of carbon in autumn of the SHS, ranging from 95 to 1 634 rag/（ m^2· d） mainly varied with nutrient condition, especially phosphate concentration in seawater and hydrological condition. Furthermore, associating the present study results together with previous studies, the annual value of carbon fixed production of phytoplankton in the entire marginal seas of East China （including the Bohai Sea, the Huanghai Sea and the East China Sea） was estimated to be 222 Mt, which accounted for 2% of that in the global margins. Besides, it was as 16.2 times as the annual value of apparent carbon sink strength （ 13.96 Mt） in the marginal seas of East China. This multiple was different in different sea areas （ 3.0 in the Bohai Sea, 6. 7 in the Huanghai Sea and 81.6 in the East China Sea）.

Influence of control strategy on stability of dual-spin projectiles with fixed canards

Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise of meeting guidance system requirements, the influence of control moment provided by a motor on the flight stability is analyzed in this paper. Firstly, the effect of the rolling movement on stability is analyzed based on the stability criterion derived using the Hurwitz stability theory. Secondly, the evaluation parameters combining the features of different control periods that could assess the variation of stability features after the motor torque are obtained. These effective formulas are used to indicate that, to reduce the flight instability risks, the stabilized rolling speed of roll speed keeping period should be as small as possible; the variation trend of motor torque during the rolling speed controlling period and the roll angle of the forward body during roll angle switching period are recommended corresponding to the projectile and trajectory characteristics. Moreover,detailed numerical simulations of 155 mm dual-spin projectile are satisfactory agreement with the theoretical results.