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.

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.

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.

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.

Oxidative coupling of methane in a fixed bed reactor over perovskite catalyst:A simulation study using experimental kinetic model

The oxidative coupling of methane （OCM） to ethylene over a perovskite titanate catalyst in a fixed bed reactor was studied experimentally and numerically. The two-dimensional steady state model accounted for separate energy equations for the gas and solid phases coupled with an experimental kinetic model. A lumped kinetic model containing four main species CH4, O2, COx （CO2, CO）, and C2 （C2H4 and C2H6） was used with a plug flow reactor model as well. The results from the model agreed with the experimental data. The model was used to analyze the influence of temperature and feed gas composition on the conversion and selectivity of the reactor performance. The analytical results indicate that the conversion decreases, whereas, C2 selectivity increases by increasing gas hourly space velocity （GHSV） and the methane conversion also decreases by increasing the methane to oxygen ratio.

Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.

Pixel and Column Fixed Pattern Noise Suppression Mechanism in CMOS Image Sensor

A double sampling circuit to eliminating fixed pattern noise(FPN) in CMOS image sensor (CIS) is presented. Double sampling is implemented by column switch capacitor amplifier directly, and offset compensation is added to the amplifier to suppress column FPN. The amplifier is embedded in a 64×64 CIS and successfully fabricated with chartered 0.35 μm process. Theory analysis and circuit simulation indicate that FPN can be suppressed from millivolt to microvolt. Test results show that FPN is smaller than one least-significant bit of 8 bit ADC. FPN is reduced to an acceptable level with double sampling technique implemented with switch capacitor amplifier.

Study and Commercial Application of Graded Optimization of Catalysts for Fixed Bed Residue Upgrading Unit

The SHIFT-G technology of inverse catalyst loading is used to optimize the catalyst grading in the residue hydrotreating unit. The results, taken from pilot tests and commercial units, have showed that the optimized catalyst grading system can reasonably distribute the reaction load, effectively improve the prop- erties of hydrotreated products, prolong the operating cycle and promote economic benefits.

Numerical simulation of fixed bed reactor for oxidative coupling of methane over monolithic catalyst

A three-dimensional geometric model was set up for the oxidative coupling of methane(OCM) fixed bed reactor loaded with Na_3PO_4-Mn/SiO_2/cordierite monolithic catalyst,and an improved Stansch kinetic model was established to calculate the OCM reactions using the computational fluid dynamics method and Fluent software.The simulation conditions were completely the same with the experimental conditions that the volume velocity of the reactant is 80 ml·min^(-1) under standard state,the CH_4/O_2 ratio is 3 and the temperature and pressure is800 ℃ and 1 atm,respectively.The contour of the characteristic parameters in the catalyst bed was analyzed,such as the species mass fractions,temperature,the heat flux on side wall surface,pressure,fluid density and velocity.The results showed that the calculated values matched well with the experimental values on the conversion of CH4 and the selectivity of products(C_2H_6,C_2H_4,CO,CO_2 and H_2) in the reactor outlet with an error range of±4%.The mass fractions of CH_4 and O_2 decreased from 0.600 and 0.400 at the catalyst bed inlet to 0.445 and0.120 at the outlet,where the mass fractions of C_2H_6,C_2H_4,CO and CO_2 were 0.0245,0.0460,0.0537 and 0.116,respectively.Due to the existence of laminar boundary layer,the mass fraction contours of each species bent upwards in the vicinity of the boundary layer.The volume of OCM reaction was changing with the proceeding of reaction,and the total moles of products were greater than reactants.The flow field in the catalyst bed maintained constant temperature and pressure.The fluid density decreased gradually from 2.28 kg·m^(-3) at the inlet of the catalyst bed to 2.18 kg·m^(-3) at the outlet of the catalyst bed,while the average velocity magnitude increased from 0.108 m·s-1 to 0.120 m·s^(-1).

Variation of toxic pollutants emission during a feeding cycle from an updraft fixed bed gasifier for disposing rural solid waste

The variation of toxic pollutants emission during a feeding cycle was examined by field monitoring from a batch feeding updraft fixed bed gasifier for disposing rural domestic solid waste. Results showed that the content of oxygen in flue gas gradually increased, while SO_2 and HCl in flue gas decreased with time after feeding in a whole feeding cycle. Although large amount of CO was produced during the gasifying, low CO content in flue gas could be obtained after the heat treatment with an electric heating device. The distribution characteristics of dioxin congeners in flue gas indicted the re-synthesis of dioxins after flue gas heating, and the increase of oxygen promoted the synthesis of dioxins. The emission content of dioxins could meet the standard(0.1 ng I-TEQ·m^(-3),GB18458-2014) of China when the oxygen content was controlled below 8.3%. Hence, for a batch feeding gasifier,low oxygen condition should be offered by reducing air intake at the later stage of feeding cycle in order to decrease the re-synthesis of dioxins after the flue gas heating.

Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.

Differential Spontaneous Photon Emissions from Cerebral Hemispheres of Fixed Human Brains: Asymmetric Coupling to Geomagnetic Activity and Potentials for Examining Post-Mortem Intrinsic Photon Information

The emissions of biophotons have been considered a ubiquitous property of living systems and their components. We measured the “spontaneous” photon emissions from fixed whole and sectioned human brains within hyper-dark settings. Significant differences in photon counts were measured from different spatial planes. The flux densities were in the order of 2 × 10-12 W per m2. The right hemispheres but not the left hemispheres displayed more photon emissions whose spectral power density profiles exhibited a conspicuous amplitude peak between 7.9 and 8 Hz. Brains measured in the hyperdark (~10-12 W·m2) after removal from the typical lighting of the laboratory emitted more photons than those that had been maintained in the hyperdark for one week. The significant correlation between the numbers of photons emitted from the left hemisphere (but not the right) and global geomagnetic activity also exhibited energy equivalence between the photon flux densities and the geomagnetic shift within the cerebral volumes. These results indicate that what has been assumed to be fixed unresponsive human brain tissue still emits small numbers of photons that may be residuals from ambient light and can potentially interact with global geomagnetic activity. The medical implications for post-mortem intrinsic photonic information based upon the anisotropic microstructures within the hemispheres of the human cerebrum are discussed.

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.

Entanglement of Two-Superconducting-Qubit System Coupled with a Fixed Capacitor

We study thermal entanglement in a two-superconducting-qubit system in two cases,either identical or distinct.By calculating the concurrence of system,we find that the entangled degree of the system is greatly enhanced in the case of very low temperature and Josephson energies for the identical superconducting qubits and our result is in a good agreement with the experimental data.

Instability of the Random Fixed Point of Renormalization Group for the Spin Systems with Quenched Disorder

The replica trick used in the renormalization group(RG)for the disordered spin systems is discussed.The recursion relations of RG are derived in a more general situation in which the coupling constants can have arbitrary symmetry to the replica indices.It is shown that the random fixed point found by Luther,Grinstein and Lubensky is unstable.This instability implies that the replica symmetry should be broken in the RG for the disordered systems.

COUPLED FIXED POINTS OF SKEW INCREASINGOPERATORS AND APPLICATIONS

In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.