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.

A Bioequivalence Study of Empagliflozin/Metformin Fixed-Dose Combination in Healthy Subjects under Fasting Conditions

Background: This study evaluated the bioequivalence of empagliflozin 12.5 mg/metformin 1000 mg tablets compared to Synjardy® (Empagliflozin 12.5 mg/metformin 1000 mg) tablets in healthy male subjects under fasting conditions. Methods: This was a phase I, randomized, single-dose, two-period, two-sequence, crossover study to evaluate the bioequivalence (BE) profiles of two fixed-dose combinations (FDCs) of empagliflozin/metformin. Cmax, AUC0-t and AUC0-∞ from test and reference formulations were evaluated to access BE. The plasma concentrations were measured using a validated liquid chromatography-mass spectrometry (LC-MS/MS) method. Of the 24 subjects enrolled, 23 completed both periods of the study. The two formulations test and reference were considered bioequivalent if 90% confidence interval (CI) fell within 80.00% - 125.00% for Cmax, AUC0-t and AUC0-∞. Tolerability and safety were assessed throughout the study. Results: The pharmacokinetic (PK) parameters were similar between the test product (T) and reference product (R) Synjardy®. The 90% CI of the test/reference ratios of log-transformed PK parameters point estimates was Cmax: 89.87% (85.68% - 94.27%), AUC0-t: 87.91% (83.65% - 92.39%) and AUC0-∞: 87.16% (82.80% - 91.75%) to empagliflozin and Cmax: 92.19% (87.95% - 96.65%), AUC0-t: 91.38% (84.42% - 98.91%) and AUC0-∞: 93.78% (83.82% - 104.93%) to metformin respectively (90% CI for all PK parameters fell within 80.00% - 125.00%). Conclusion: Our results demonstrated BE between the test and reference formulations of oral tablets of empagliflozin 12.5 mg/metformin 1000 mg (FDC) in healthy male subjects under fasting conditions.

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.

Simultaneous Adsorption of Aqueous Pb2+, Cu2+, Zn2+, and Cd2+ Using Surfactant-Modified and Unmodified Activated Carbon in a Fixed Bed Column

The goal of this work is to improve the simultaneous removal of Pb2+, Cu2+, Zn2+, and Cd2+ ions from synthetic wastewater in a fixed bed column by incorporating sodium dodecyl sulfate (SDS) onto the surface of activated carbon made from coconut shells. The activated carbons were characterized using Fourier transform infrared spectroscopy (FT-IR) and scanning electron microscopy-energy dispersive x-ray (SEM-EDX). The adsorption column dynamics were studied by varying the flow rates (5, 10 and 15 mL/min), bed heights (10, 15 and 20 cm), and initial concentrations (50, 150, and 250 mg/L). The activated carbon has a pore volume of 0.715 cm3/g and a BET-specific surface area of 1410 m2/g. Sodium dodecyl sulfate (SDS) surfactant incorporation onto the surface of the activated carbon enhances its capacity for simultaneous adsorption of Pb2+, Cu2+, Zn2+, and Cd2+ from the aqueous medium. The affinity of the heavy metals to both unmodified (AC) and modified (AC-SDS) activated carbons followed the order of Pb2+ > Cu2+ > Zn2+ > Cd2+. The dynamic adsorption of the column depends on the flow rate, bed height, initial metal concentration, and SDS surface modification. With a 5 mL/min flow rate, a 20 cm bed height, and a 50 mg/L initial metal concentration, a maximum break-through time of 150 minutes for the unmodified activated carbon (AC) and 180 minutes for the SDS-modified activated carbon (AC-SDS) was reached.

A Study on the Internal Control and Countermeasures of Fixed Assets in Private Universities:A Case Study of N College

Fixed assets in universities occupy an important position in university management due to their wide coverage and large amount of money.Due to insufficient funding supply,private universities mainly focus on the allocation and utilization of fixed assets,which reflects the overall characteristics of cautious allocation,maximum utilization,and delayed elimination in the actual management of fixed assets.This article aims to conduct research and analysis on the entire lifecycle process of the allocation,use,and disposal of fixed assets in private universities,summarize the problems existing in the internal control of fixed assets in private universities,and propose corresponding countermeasures and suggestions in a targeted manner.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

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.

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.

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.

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.

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.

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.

Integrated Guidance and Control of Homing Missiles Against Ground Fixed Targets

This paper presents a scheme of integrated guidance and autopilot design for homing missiles against ground fixed targets. An integrated guidance and control model in the pitch plane is formulated and further changed into a normal form by nonlinear coordinate transformation. By adopting the sliding mode control approach, an adaptive nonlinear control law of the system is designed so that the missile can hit the target accurately with a desired impact attitude angle. The stability analysis of the closed-loop system is also conducted. The numerical simulation has confirmed the usefulness of the proposed design scheme.

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。