Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.

On Second-Order Duality in Nondifferentiable Continuous Programming

A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-invexity various duality theorems are established for this pair of dual continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and the proofs of its various duality results are briefly outlined. Further, it is shown that our results can be regarded as dynamic generalizations of corresponding (static) second-order duality theorems for a class of nondifferentiable nonlinear programming problems already studied in the literature.

Continuity of Care in Primary Health Care Affecting Control of Diabetes

Background: Continuity of care is a distinguishing feature of primary care. Better continuity of care program showed a significant effect in controlling diabetes and it is complications. This study explores the effect of continuity of care on control of diabetes mellites in primary health care centres. Objectives: 1) To assess the effect of Continuity of care on controlling haemoglobin (Hb A1C) and fasting blood Sugar (FBS);2) To compare the control of Diabetes by using (Hb A1C and FBS) indices on same patient before and after application of chronic illness clinic;3) To identify the relation between age and gender affecting continuity of care in diabetic patient. Methods: It is a Prospective cohort study design. Included both gender and diabetic patient age above 24 years old. The data extracted from health care specialty center (HCSC) clinics in National guard hospital at Riyadh, through HCSC data base on three phases: 1) Phase 1: the data extracted of diabetic patients from October to November 2022 including MRN, diabetic patient, age, Hb A1C, Fasting blood glucose. 2) Phase 2: the same MRN extracted from phase 1 was extracted again retrospectively for six months from April to September 2022, to compare the indices before implanting the chronic illness clinic including Hb A1C, Fasting blood glucose. 3) Phase 3: prospectively from December 2022 to September 2023. Results: Among diabetic patients aged 60 years old and above showed better control of HbA1C and FBS comparing to these patients below age of 60 years old, with significant improvement of HbA1C after implanting chronic illness clinic. Conclusion: The significant improvement in the control of diabetic patients followed in primary health care centers reinforce the evidence of the importance of continuity of care.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Continuity of truncated Hardy-Littlewood maximal function

This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

THE HOLDER CONTINUITY OF THE LYAPUNOV EXPONENT FOR A QUASI-PERIODIC SZEGO COCYCLE

In this paper,I consider the Hölder continuity of the Lyapunov exponent for a quasi-periodic Szegö cocycle with weak Liouville frequency.I extend the existing results about the regularity of the Lyapunov exponent from the Schrödinger cocycle in[24]to a Szegö cocycle.

Coordinated Control of Second-order Harmonic Voltage and Current Fluctuations in Cascaded H-bridge Inverter with Supercapacitor and DC-DC Stage at Variable Output Frequencies

In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.

Analysis of the Nursing Effect of Continuity of Care on Elderly Patients with Coronary Heart Disease Unstable Angina and its Impact on Quality of Life

Objective:To analyze the effect of using continuity of care for elderly patients with coronary heart disease(CHD)with unstable angina pectoris(UAP)and its impact on their quality of life.Methods:100 cases of elderly patients with CHD with UAP admitted to our hospital from March 2022 to March 2023 were selected and grouped into an observation group and a control group of 50 cases each according to the randomized number table method.The nursing effect and quality of life of the observation group(continuity nursing)and the control group(routine nursing)were compared.Results:The total effective rate of nursing care was 96.00%observation group and 80.00%for the control group,and the differences were significant(χ2=6.061,P<0.05).Patients in the observation group had fewer episodes(1.42±0.21)times/week and a shorter duration(5.46±0.39)min,which were better than the control group(t=3.465,2.973;P<0.05).The depression self-rating depression scale(SDS)score(42.16±6.64)and anxiety self-rating scale(SAS)score(32.26±7.35)in the observation group were lower and the quality of life was higher as compared to that of the control group(P<0.05).Conclusion:Continuous nursing care improved the nursing effect of elderly CHD with UAP patients,promoted the alleviation of UAP symptoms,improved patient mentality,and improved their quality of life.Hence,continuous nursing care possesses significant clinical application value.

Second-order interference of two independent and tunable single-mode continuous-wave lasers

The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.

High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.

Second-Order Duality for Continuous Programming Containing Support Functions

A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Application Effect of WeChat Platform Continuity of Care Model Based on KAP Theory on Self-Management of Stroke Patients with Hypertension

Objective: To explore the impact of the WeChat platform continuity of care model based on the KAP (knowledge, attitudes, and practices) theory on the self-management of stroke patients with hypertension after discharge from the hospital. Methods: 62 stroke patients with hypertension discharged from the rehabilitation department of a tertiary A hospital in Nanning City, Guangxi Zhuang Autonomous Region, from October 2022 to April 2023 were sampled by convenience sampling method. Patients discharged from Rehabilitation I were included in the control group, and conventional nursing care was used;while patients discharged from Rehabilitation II were included in the observation group, and WeChat platform continuity of nursing care model based on the KAP theory was implemented. The intervention effect of the two groups was compared. Results: After 4 and 12 weeks of intervention, the diastolic and systolic blood pressure of the patients in the observation group were lower than those in the control group (P < 0.05);after 12 weeks of intervention, the rate of medication adherence and the score of adherence to hypertension treatment in the observation group were significantly higher than those in the control group (P < 0.05). Conclusion: The application of the WeChat platform continuity of care model based on KAP theory to stroke patients with hypertension can improve blood pressure, medication adherence rate, hypertension treatment adherence, and overall enhance the self-management level of these patients.

Study of Second-Order Continuities of a Composite Surface

There are two classes of continuities, parametric continuities and geometric continuities, which are used to illuminate the smoothness of a composite surface in surface construction and reconstruction in computer graphics (CG) and computer aided design (CAD). A parametric continuity is more stiff than its corresponding geometric continuity of the same order. This paper uncovers the geometric properties of parametric and geometric continuities less than and equal to second order and presents the proofs for the corresponding propositions. These propositions can be applied to the existent or promising schemes of surface construction or reconstruction, which can provide a convincing theory for researchers to establish their schemes in surface construction. Three examples are used in this paper to show the applications of these propositions.

The Impact of Continuity of Care on Negative Emotions and Self-Efficacy in Patients Undergoing Digestive Endoscopic Tumor Resection

Objective:To explore the impact of a continuity of care model on negative emotions and self-efficacy in patients undergoing digestive endoscopic tumor resection.Methods:A retrospective analysis was conducted on 80 patients who underwent digestive endoscopic tumor resection in the Gastroenterology Department of Baoying County People’s Hospital between October 2022 and October 2024.Patients were randomly divided into a control group(n=40)and an observation group(n=40)using a random number table.The control group received routine nursing care,while the observation group was additionally provided with continuity of care interventions.After two months of intervention,the negative emotions and self-efficacy of the two groups were compared and statistically analyzed.Results:There was no statistically significant difference in baseline data between the two groups(P>0.05).After two months of intervention,the observation group demonstrated significantly lower HAMD and HAMA scores compared to the control group(both P=0.000),and significantly higher GSES scores(P=0.000).Conclusion:Applying a continuity of care model to patients undergoing digestive endoscopic tumor resection can alleviate negative emotions,enhance self-efficacy,and improve self-care abilities.

Clinical Study on the Effect of Continuity of Care in CICU on Improving Cognitive Function and Psychological State in Patients with Heart Failure

Objective:To analyze the effect of continuity of care in the cardiac intensive care unit(CICU)on improving cognitive function and psychological state in patients with heart failure(HF).Methods:A total of 112 chronic HF patients admitted to the CICU of Xuzhou Traditional Chinese Medicine Hospital from July 2022 to August 2024 were selected and randomly divided into two groups using the red and blue ball method:a control group(n=56)and a study group(n=56).The control group received routine CICU nursing management,while the study group received routine CICU nursing combined with continuity of care management.Cognitive function(using the Montreal Cognitive Assessment,MoCA),psychological state(using the Self-Rating Depression Scale,SDS,and Self-Rating Anxiety Scale,SAS),and quality of life(using the Minnesota Living with Heart Failure Questionnaire,MLHFQ)were compared between the two groups.Results:After the intervention,the cognitive function scores of the study group were significantly higher than those of the control group(P<0.05).The SDS and SAS scores of the study group were significantly lower than those of the control group after the intervention(P<0.05).The quality of life in the study group was also significantly better than in the control group(P<0.05).Conclusion:CICU continuity of care can effectively improve cognitive function and psychological state in patients with HF,while also enhancing their quality of life.

Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems

Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems are proved under second-order pseudoinvexity and second-order quasi-invexity. A pair of Mond-Weir type dual variational problems with natural boundary values is formulated to derive various duality results. Finally, it is pointed out that our results can be considered as dynamic generalizations of their static counterparts existing in the literature.

Correlation between key indicators of continuous glucose monitoring and the risk of diabetic foot

BACKGROUND Continuous glucose monitoring(CGM)metrics,such as time in range(TIR)and glycemic risk index(GRI),have been linked to various diabetes-related complications,including diabetic foot(DF).AIM To investigate the association between CGM-derived indicators and the risk of DF in individuals with type 2 diabetes mellitus(T2DM).METHODS A total of 591 individuals with T2DM(297 with DF and 294 without DF)were enrolled.Relevant clinical data,complications,comorbidities,hematological parameters,and 72-hour CGM data were collected.Logistic regression analysis was employed to examine the relationship between these measurements and the risk of DF.RESULTS Individuals with DF exhibited higher mean blood glucose(MBG)levels and increased proportions of time above range(TAR),TAR level 1,and TAR level 2,but lower TIR(all P<0.001).Patients with DF had significantly lower rates of achieving target ranges for TIR,TAR,and TAR level 2 than those without DF(all P<0.05).Logistic regression analysis revealed that GRI,MBG,and TAR level 1 were positively associated with DF risk,while TIR was inversely correlated(all P<0.05).Achieving TIR and TAR was inversely correlated with white blood cell count and glycated hemoglobin A1c levels(P<0.05).Additionally,achieving TAR was influenced by fasting plasma glucose,body mass index,diabetes duration,and antidiabetic medication use.CONCLUSION CGM metrics,particularly TIR and GRI,are significantly associated with the risk of DF in T2DM,emphasizing the importance of improved glucose control.

Continuous-flow columns packed with zero-valent iron and iron sulfide as a feasible strategy to remediate the persistent contaminant nitroguanidine

The insensitive munitions compound nitroguanidine(NQ)is used by the U.S.Army to avoid unintended explosions.However,NQ also represents an emerging contaminant whose environmental emissions can cause toxicity toward aquatic organisms,indicating the need for effective remediation strategies.Thus,we investigated the feasibility of treating water contaminated with NQ in continuous-flow columns packed with zero-valent iron(ZVI)or iron sulfide(FeS).Initially,the impact of pH on NQ transformation by ZVI or FeS was evaluated in batch experiments.The pseudo first-order rate constant for NQ transformation(k_(1,NQ))by ZVI was 8-10 times higher at pH 3.0 compared to pH 5.5 and 7.0,whereas similar k_(1,NQ)values were obtained for FeS at pH 5.5-10.0.Based on these findings,the influent p H fed to the ZVIand Fe S-packed columns was adjusted to 3.0 and 5.5,respectively.Both reactors transformed NQ into nitrosoguanidine(Nso Q).Further transformation of Nso Q by ZVI produced aminoguanidine,guanidine,and cyanamide,whereas Nso Q transformation by Fe S produced guanidine,ammonium,and traces of urea.ZVI outperformed Fe S as a reactive material to remove NQ.The ZVI-packed column effectively removed NQ below detection even after 45 d of operation(490 pore volumes,PV).In contrast,NQ breakthrough(removal efficiency<85%)was observed after 18 d(180 PV)in the Fe S-packed column.The high NQ removal efficiency and long service life of the ZVI-packed column(>490 PV)suggest that the technology is a promising approach for NQ treatment in packed-bed reactors and in situ remediation.