PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

Finite Dimensional Approximation of the Monodromy Operator of a Periodic Delay Differential Equation with Piecewise Constant Orthonormal Functions

Using piecewise constant orthonormal functions, an approximation of the monodromy operator of a Linear Periodic Delay Differential Equation (PDDE) is obtained by approximating the integral equation corresponding to the PDDE as a linear operator over the space of initial conditions. This approximation allows us to consider the state space as finite dimensional resulting in a finite matrix approximation whose spectrum converges to the spectrum of the monodromy operator.

Effect of Nursing Intervention in Operating Room for Patients with Gastric Cancer during Anesthesia Recovery Period

Objective: To analyze the effect of nursing intervention in operating room for gastric cancer patients in anesthesia recovery period. Methods: From June 2021 to December 2021, 78 patients who underwent gastric cancer surgery in our hospital were selected for research. Combined with the random number table method, they were divided into the control group (providing routine nursing care in operating room) and the observation group (providing nursing intervention in operating room) with 39 patients in each group respectively. The body temperature of the two groups during operation, during abdominal closure and after operation, the time of leaving anesthesia room, extubation, postoperative wakefulness and hospitalization, degree of satisfaction with nursing work was compared. Results: Compared with the control group, the body temperature in the observation group tended to be more normal during operation, during abdominal closure and after operation (P 0.05). The time of leaving anesthesia room, extubation, postoperative wakefulness and hospitalization in the observation group were shorter than those in the control group (P 0.05). The satisfaction degree of the observation group with nursing work was higher than that of the control group (P 0.05). Conclusion: Nursing intervention in operating room is effective for gastric cancer patients in anesthesia recovery period, which can maintain their perioperative temperature stability, promote their postoperative recovery and enhance their satisfaction with nursing work. It is worth adopting.

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

Routine laboratory parameters in patients with necrotizing pancreatitis by the time of operative pancreatic debridement:Food for thought

BACKGROUND Timing of invasive intervention such as operative pancreatic debridement(OPD)in patients with acute necrotizing pancreatitis(ANP)is linked to the degree of encapsulation in necrotic collections and controlled inflammation.Additional markers of these processes might assist decision-making on the timing of surgical intervention.In our opinion,it is logical to search for such markers among routine laboratory parameters traditionally used in ANP patients,considering simplicity and cost-efficacy of routine laboratory methodologies.AIM To evaluate laboratory variables in ANP patients in the preoperative period for the purpose of their use in the timing of surgery.METHODS A retrospective analysis of routine laboratory parameters in 53 ANP patients undergoing OPD between 2017 and 2020 was performed.Dynamic changes of routine hematological and biochemical indices were examined in the preoperative period.Patients were divided into survivors and non-survivors.Survivors were divided into subgroups with short and long post-surgery length of stay(LOS)in hospital.Correlation analysis was used to evaluate association of laboratory variables with LOS.Logistic regression was used to assess risk factors for patient mortality.RESULTS Seven patients(15%)with severe acute pancreatitis(SAP)and 46 patients(85%)with moderately SAP(MSAP)were included in the study.Median age of participants was 43.2 years;33(62.3%)were male.Pancreatitis etiology included biliary(15%),alcohol(80%),and idiopathic/other(5%).Median time from diagnosis to OPD was≥4 wk.Median postoperative LOS was at the average of 53 d.Mortality was 19%.Progressive increase of platelet count in preoperative period was associated with shortened LOS.Increased aspartate aminotransferase and direct bilirubin(DB)levels the day before the OPD along with weak progressive decrease of DB in preoperative period were reliable predictors for ANP patient mortality.CONCLUSION Multifactorial analysis of dynamic changes of routine laboratory variables can be useful for a person-tailored timing of surgical intervention in ANP patients.

STOCHASTIC MODEL OF PERIODIC OPERATION PERFORMANCE FOR THE CONTINUOUS COUNTER－CURRENT ADSORPTION PROCESS

A stochastic model is developed to predict the peniodic operation performance ofthe continuous counter-current adsorption process. The model takes into account theeffects of random backmixing of particles, axial dispersion of liquid phase, liquid- film mass transfer, intraparticle diffusion and panticle shape, and can revealclearly the behavior of solid and liquid phase in adsorption process. The simulation results agree with the experimental data rather well.

The preoperative preparation and postoperative care of interventional treatment for coronary heart disease

The well performance of everything in the peripheral operative period is important to improve successful rate, decrease complications and assure favorable convalescence of patients for interventional treatment of coronary heart disease. It is mentioned that the primary management of peripheral operative period and main notes for interventional treatment of coronary heart disease in the paper summarily.

Existence of Periodic Solutions of Nonlinear Neutral Differential Equation with Deviating Argument

Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.

The Problem of Periodic Solutions fora Class of Dynamical System(Ⅱ)

In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability,and show that there are not any periodic solutions in some a neibourhood of the equilibrium points of the dynamical systems.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.

Existence of Positive Periodic Solutions for Two Species Population Growth Model

Existence and nonexistence criteria are established for the positive periodic solutions of two species population growth with periodic delay by applying continuation theorem of coincidence degree theory.

Optimization on Water Resource System Operation Policy during Drought

The mixed linear programming model is commonly recognized to be an effective means for searching optimal reservoir operation policy in water resources system. In this paper a multi-objective mixed integer linear programming model is set up to obtain the optimal operation policy of multi-reservoir water supply system during drought, which is able to consider the operation rule of reservoir-group system within longer-term successive drought periods, according to the basic connotation of indexes expressing the water-supply risk of reservoir during drought, that is, reliability, resilience and vulnerability of reservoir water supply, and mathematical programming principles. The model-solving procedures, particularly, the decomposition-adjustment algorithm, are proposed based on characteristics of the model structure. The principle of model-solving technique is to decompose the complex system into several smaller sub-systems on which some ease-solving mathematical models may be established. The objective of this optimization model aims at maximizing the reliability of water supply and minimizing the maximum water-shortage of single time-period within water- supply system during drought. The multi-objective mixed integer linear programming model and proposed solving procedures are applied to a case study of reservoir-group water-supply system in Huanghe-Huaihe River Basin, China. The desired water-shortage distribution within the system operation term and the maximum shortage of single time-period are achieved. The results of case study verifies that the lighter water-shortage distributed evenly among several time-periods can avoid the calamities resulted from severe water shortage concentrated on a few time-periods during drought.

Role of Periodic Input Composition and Sweeping Gas for Improvement of Hydrogen Production in a Palladium Membrane Reactor by Partial Oxidation of Methane

The partial oxidation of methane under periodic operation over Ni/y/-Al2O3 catalyst was investigated in a Pd-membrane reactor. The effects of key parameters such as the inlet composition and the sweeping, gas on methane conversion and the hydrogen recovery are numerically estalallshed with two penodtc input ttmctlons. In order to analyze the effect of the inputs modulation, the reaction was performed under low steam to methane ratio at a mod-erate temperature and pressure. It was obtained that to achieve process intensification is to operate the process in a periodic way. The main results show that the periodic input functions can improve the performance of the process compared to the optimal steady state operation. Moreover, there is an optimum amplitude of manipulated inputs leads to a maximum of hydrogen recovery. It is noteworthy that the comparison between the predicted performancevia the sinusoidal and the＇square ways show that the better＇average performance was obtainedwith the square way.

Discrete Pseudo Almost Periodic Solutions for Some Difference Equations

In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic sequences to show the main results of this work. For the illustration, some applications are provided for a second order differential equation with piecewise constant arguments.

Positive Periodic Solutions for Prey-predator Model with Saturation

By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.

Existence and Uniqueness of Positive Periodic Solutions for First-order Functional Differential Equations

In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.

Multi-Waves,Breathers,Periodic and Cross-Kink Solutions to the(2+1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

The present article deals with multi-waves and breathers solution of the(2+1)-dimensional variable-coefficient CaudreyDodd-Gibbon-Kotera-Sawada equation under the Hirota bilinear operator method.The obtained solutions for solving the current equation represent some localized waves including soliton,solitary wave solutions,periodic and cross-kink solutions in which have been investigated by the approach of the bilinear method.Mainly,by choosing specific parameter constraints in the multi-waves and breathers,all cases the periodic and cross-kink solutions can be captured from the 1-and 2-soliton.The obtained solutions are extended with numerical simulation to analyze graphically,which results in 1-and 2-soliton solutions and also periodic and cross-kink solutions profiles.That will be extensively used to report many attractive physical phenomena in the fields of acoustics,heat transfer,fluid dynamics,classical mechanics,and so on.We have shown that the assigned method is further general,efficient,straightforward,and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering.We have depicted the figures of the evaluated solutions in order to interpret the physical phenomena.

Periodic Solution for Neutral Type Neural Networks

The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.