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.

Twin-block在骨性Ⅱ类错[牙合]下颌后缩患儿中的应用

目的:探讨Twin-block在骨性Ⅱ类错[牙合]下颌后缩患儿中的应用效果。方法:选取2019年1月-2021年1月笔者医院接收的84例骨性Ⅱ类错[牙合]下颌后缩患儿设置为研究对象,按随机抽签法分为对照组、研究组,各42例,对照组采用直丝弓矫治器,研究组采用Twin-block矫治器。比较两组治疗前后咀嚼功能、牙齿咬合力、下颌骨变化、软组织面型变化、上气道矢状径,并统计家属治疗满意度。结果:治疗后,研究组咀嚼功能、牙齿咬合力、下颌骨变化指标、软组织面型变化指标均优于对照组(P<0.05);治疗后,研究组上气道矢状径高于对照组(P<0.05);研究组家属治疗满意度(95.24%)明显高于对照组(73.81%)(P<0.05)。结论:Twin-block应用于骨性Ⅱ类错[牙合]下颌后缩患儿治疗中,能改善咀嚼功能,增强牙齿咬合力,促进下颌骨生长,提高面型美观度,扩大上气道矢状径,利于改善呼吸功能,获得家属对治疗效果的高度评价。

Twin-Block双期矫治与单纯直丝弓矫正技术在早期下颌后缩矫正患儿中的疗效对比

目的探讨Twin-Block双期矫治与单纯直丝弓矫正技术在替牙及恒牙早期错(牙合)畸形矫正患儿中的疗效对比。方法选取我院2020年9月到2023年9月收治的60例恒牙早期错(牙合)畸形患儿作为研究对象,按照治疗方法不同分为观察组与对照组,各组均为30例。所有患儿均采取矫正治疗,对照组患儿采取直丝弓矫正技术进行治疗,观察组患儿采取Twin-Block矫治器及直丝弓矫治技术进行双期治疗。对比两组患儿临床疗效,及矫治时间,治疗前头影测量及关节改建情况,采用口腔锥形束扫描成像进行检测两组患儿关节窝宽径、关节前间隙、关节后间隙、关节上间隙、髁突前后径、髁突高度相关参数表达水平,最后对比两组患儿治疗前后上下齿槽座(ANB)角、下齿槽座(SNB)角、上齿槽座(SNA)角、下颌平面角(Mp-SN)、下颌综合长度(Ar-Po)、下颌升支高度(Ar-Go)、下颌体长(Go-Gn)、上中切牙-SN平面角(U1-SN)、下中切牙-下颌平面角(L1-Mp)、上唇审美平面距(Ls-E)、下唇审美平面距(Li-E)、鼻唇角。结果观察组治疗总有效率96.67%明显高于对照组76.67%(P<0.05);治疗后,观察组矫治时间长于对照组(P<0.05);治疗前,两组患儿关节窝宽径、关节前间隙、关节后间隙、关节上间隙、髁突前后径、髁突高度对比无明显差异(P>0.05),治疗后,两组患儿关节窝宽径对比无明显差异,关节前间隙减小,观察组(1.21±0.28)mm高于对照组,关节后间隙、关节上间隙、髁突前后径、髁突高度均增加,且观察组高于对照组(P<0.05);治疗前,两组患儿ANB角、SNB角、SNA角、Mp-SN、Ar-Po、Ar-Go、Go-Gn、U1-SN、L1-Mp、Ls-E、Li-E、鼻唇角对比无明显差异(P>0.05),治疗后,两组患儿SNB、Mp-SN、Ar-Po、Ar-Go、Go-Gn、鼻唇角均增大,ANB、U1-SN、L1-Mp、Li-E、Ls-E减小,且观察组变化大于对照组(P<0.05)。结论Twin-Block矫治器配合直丝弓矫治技术双期矫治器与单纯直丝弓矫正技术相比治疗替牙及恒牙早期错(牙合)畸形疗效显著,可作为儿童恒牙早期错(牙合)畸形的首选治疗方案。

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.

安氏Ⅱ类错[牙合]畸形佩戴Twin-block矫治器时上颌骨的应力分布

背景:Twin-block矫治器常用于安氏Ⅱ类错[牙合]畸形的矫治,其刺激下颌骨生长的作用机制已得到许多研究证实,但对上颌骨生长的影响尚不清楚。目的:通过有限元法分析安氏Ⅱ类错[牙合]畸形患者佩戴Twin-block矫治器时上颌骨复合体、周围骨缝及上颌牙列的应力分布。方法:选择在山东省康复大学青岛医院/青岛市市立医院口腔正畸科进行正畸治疗的安氏Ⅱ类错[牙合]畸形患者1例,测量患者佩戴Twin-block矫治器时的咬合力数据,采集其锥形束CT数据,建立包含上颌骨复合体、周边各骨缝、Twin-block矫治器及上颌牙列在内的有限元模型,通过ABAQUS软件模拟患者戴入Twin-block时上颌骨、骨缝及上颌牙列的应力分布与位移。结果与结论:①上颌前牙受到的等效应力明显小于后牙,两侧牙齿的最大等效应力分别为4.7975 MPa和8.7161 MPa,均位于第一前磨牙处;最大位移呈现在两侧上颌切牙处,分别为0.0805 mm和0.0810 mm;②骨缝的最大等效应力为1.284 MPa,主要集中在两侧翼腭缝及额颌缝,其余骨缝受力情况几乎无差异;骨缝的最大位移为0.07 mm,其中翼腭缝的位移量最大,其次是额颌缝;③上颌骨复合体受到的最大等效应力为27.18 MPa,主要集中在上颌骨前面梨状孔两侧、鼻额缝周边及颚骨后部翼腭缝附近;上颌骨的最大位移值为0.07 mm,主要集中于上颌牙槽骨;④结果显示,咬合力通过Twin-block矫治器作用于上颌骨复合体,导致上颌骨顺时针旋转、牙合平面变陡,应采取相应措施补偿这种趋势,例如建牙合过程中考虑上颌磨牙伸长、下颌磨牙压低,不仅能够将牙合平面整平,同时有利于下颌前伸,这将进一步提高Ⅱ类错[牙合]正畸治疗效果。

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.

安氏Ⅱ类Ⅰ分类青少年Twin-Block矫治前后的上气道研究

目的 应用锥束型电脑断层扫描(cone beam computed tomography,CBCT)测量分析安氏Ⅱ类Ⅰ分类青少年患者在佩戴Twin-Block矫治器前后上呼吸道的容积变化。方法 选择就诊于我院的安氏Ⅱ类Ⅰ分类患者28例,佩戴Twin-Block矫治器矫治,在治疗开始前与结束后均拍摄直立位吸气末CBCT及头颅侧位片,三维重建CBCT分析上气道治疗前后的形态及体积变化,测量头颅侧位片ANB及舌骨垂直与水平方向的位置变化,分析其变化量与上气道各指标变化量的相关性。结果 (1)上气道变化:与矫治前相比,矫治后患者的腭咽容积、舌咽容积、口咽容积、腭咽最小横截面积、舌咽最小横截面积、最小矢状径、最小冠状径均明显增加,差异有统计学意义(P<0.05),鼻咽段容积和鼻咽段最小横截面积改变较小,差异无统计学意义(P>0.05)。(2)舌骨位置变化:舌骨垂直方向(即H-PS)与舌骨水平方向(即H-VPS)均发生明显改变。(3)相关性分析:ANB与腭咽体积、腭咽最小横截面积、舌咽最小横截面积、最小矢状径成明显负相关,代表舌骨垂直方向位置变化的H-PS与腭咽最小横截面积、舌咽最小横截面积、上气道最小矢状径成明显正相关,其余指标之间无明显相关性。结论 Twin-Block矫治器可以使上气道体积增加,有助于改善患者呼吸问题。

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.