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.

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.

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.

Impact of an emergency department nursing intervention on continuity of care, self-care, and psychological symptoms

BACKGROUND The emergency department plays a crucial role in providing acute care to patients.Nursing interventions in this setting are essential for improving the continuity of care,enhancing patients’self-care abilities,and reducing psychological symp-toms.AIM To evaluate the effect of nursing interventions in the emergency department on these indicators in an emergency department.METHODS A retrospective analysis was conducted on 120 patients admitted to the emergency department between January 2022 and May 2023.The patients were divided into two groups:The control group(conventional nursing intervention)and the observation group(conventional nursing intervention+emergency department nursing intervention).The two groups were compared regarding continuity of care,self-care ability,psychological symptoms,and satisfaction with care.RESULTS The emergency department nursing interventions significantly improved the continuity of care,enhanced patients’self-care abilities,and reduced psycho-logical symptoms such as anxiety and depression.CONCLUSION Nursing interventions in the emergency department positively impact continuity of care,self-care,and psychological symptoms.However,it is important to acknowledge the limitations of this study,including the small number of studies,variable methodological quality,and the heterogeneity of the study population.Future research should address these limitations and further explore the effects of different types of nursing interventions in the emergency department.Additionally,efforts should be made to enhance the application and evaluation of these interventions in clinical practice.

Situational continuity-based air combat autonomous maneuvering decision-making

In order to improve the performance of UAV's autonomous maneuvering decision-making,this paper proposes a decision-making method based on situational continuity.The algorithm in this paper designs a situation evaluation function with strong guidance,then trains the Long Short-Term Memory(LSTM)under the framework of Deep Q Network(DQN)for air combat maneuvering decision-making.Considering the continuity between adjacent situations,the method takes multiple consecutive situations as one input of the neural network.To reflect the difference between adjacent situations,the method takes the difference of situation evaluation value as the reward of reinforcement learning.In different scenarios,the algorithm proposed in this paper is compared with the algorithm based on the Fully Neural Network(FNN)and the algorithm based on statistical principles respectively.The results show that,compared with the FNN algorithm,the algorithm proposed in this paper is more accurate and forwardlooking.Compared with the algorithm based on the statistical principles,the decision-making of the algorithm proposed in this paper is more efficient and its real-time performance is better.

Comparative Analysis of Continuous versus Intermittent Proton Pump Inhibitor Therapy in Patients with Upper Gastrointestinal Bleeding Due to Ulcers

Upper gastrointestinal bleeding (UGIB) presents as a prevalent clinical challenge, with annual incidence rates ranging from 80 to 150 cases per 100,000 individuals. Guidelines for managing patients with UGIB due to bleeding ulcers recommend a continuous infusion of proton pump inhibitors (PPI). However, studies comparing intermittent dosing of PPI therapy show that this regimen achieves similar clinical benefits. If the clinical efficacy remains equivalent, intermittent dosing will be more cost-effective for patients and the health care system. Our research study aims to analyze the comparative effectiveness of intermittent versus continuous PPI therapy after endoscopic treatment in patients with UGIB, focusing on such endpoints as rebleeding risk at 3-and 7-day mortality rates. Methods: Resources searched included MEDLINE, EMBASE, PUBMED, and the Cochrane Central Register of Controlled Trials databases from January 2010 through December 2023 with the inclusion of meta-analysis, systematic review, review, or ACG guideline recommendations. Results of the analysis show how recommendations regarding high vs. low PPI regimen changed over time: from no difference in regimen in 2010 to recommending continuous regimen in 2012 to declaring insufficient evidence between choosing one regimen over another in 2013 to determine that both regimens were comparable to each other in 2014-2018 and finally to recommending both regimens in 2021. To conclude, our review shows that in patients with bleeding ulcers and high-risk endoscopic findings, intermittent PPI therapy is non-inferior to continuous PPI infusion for three days, seven days bleeding risk or mortality rates;however, it remains challenging to determine the most optimal intermittent regimen due to heterogeneity of RCTs included in meta-analyses, and further trials will need to be performed.

Continuity of Commitment

As a popular saying goes,do not be afraid to celebrate a promise when kept.In doing so,you are embracing the potential for a better world.In keeping with its unshakable promise made over three decades ago and following the footsteps of his predecessors,China’s new Foreign Minister Qin Gang is beginning his term with a seven-day visit to five African nations-Ethiopia,Gabon,Angola,Benin,and Egypt-from 9 to 16 January.The visit also brought him to the African Union(AU)Headquarters and the League of Arab States Headquarters.

Strengthening effect of prefabrication(10-12)tensile twinning on AZ80+0.4%Ce magnesium alloy and inhibition mechanism of discontinuous precipitation

This paper provided an effective method to further improve the mechanical properties of the AZ80+0.4%Ce magnesium alloy wheel spoke.The effect of high strength and ductility was obtained with a yield strength of 295.36 MPa,an elongation of 10%,by the combination of pre-deformation(7%deformation)and two-stage aging treatment(120℃/9 h+175℃/24 h).The evolution of the microstructure and properties of the alloy was explored under the coupling conditions of different pre-deformation degrees and multi-stage aging.The results show that,pre-deformation introduced a large number of(1012)tensile twinning and dislocations,which greatly promoted the probability of continuous precipitates(CPs)appearing.On the contrary,the discontinuous precipitates(DPs)were limited by the vertical and horizontal twin structure.As a result,the pre-nucleation method of two-stage aging increased the proportion of CPs by 34%-38%.Owing to the DPs was effectively suppressed,the alloy's yield strength has been greatly improved.Besides,under multi-stage aging,the twin boundaries induce protruding nucleation to form static recrystallization by hindering the migration of dislocations,and the matrix swallows the twins,then the texture gradually tilts from the two poles to the basal plane.As an important supplement,the grain refinement and oblique texture promoted the improvement of the yield strength of the component.

Enhanced measurement precision with continuous interrogation during dynamical decoupling

Dynamical decoupling(DD)is normally ineffective when applied to DC measurement.In its straightforward implementation,DD nulls out DC signal as well while suppressing noise.This work proposes a phase relay method that is capable of continuously interrogating the DC signal over many DD cycles.We illustrate its efficacy when applied to the measurement of a weak DC magnetic field with an atomic spinor Bose-Einstein condensate.Sensitivities approaching standard quantum limit or Heisenberg limit are potentially realizable for a coherent spin state or a squeezed spin state of 10000 atoms,respectively,while ambient laboratory level noise is suppressed by DD.Our work offers a practical approach to mitigate the limitations of DD to DC measurement and would find other applications for resorting coherence in quantum sensing and quantum information processing research.

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme

In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme(MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol.We conduct a comprehensive analysis of the improved protocol's performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.

Irregular initial solidification by mold thermal monitoring in the continuous casting of steels:A review

Occasional irregular initial solidification phenomena,including stickers,deep oscillation marks,depressions,and surface cracks of strand shells in continuous casting molds,are important limitations for developing the high-efficiency continuous casting of steels.The application of mold thermal monitoring(MTM) systems,which use thermocouples to detect and respond to temperature variations in molds,has become an effective method to address irregular initial solidification phenomena.Such systems are widely applied in numerous steel companies for sticker breakout prediction.However,monitoring the surface defects of strands remains immature.Hence,indepth research is necessary to utilize the potential advantages and comprehensive monitoring of MTM systems.This paper summarizes what is included in the irregular initial solidification phenomena and systematically reviews the current state of research on these phenomena by the MTM systems.Furthermore,the influences of mold slag behavior on monitoring these phenomena are analyzed.Finally,the remaining problems of the formation mechanisms and investigations of irregular initial solidification phenomena are discussed,and future research directions are proposed.

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

Effect of continuous nursing on rehabilitation of older patients with joint replacement after discharge

BACKGROUND Joint replacement is a common treatment for older patients with high incidences of hip joint diseases.However,postoperative recovery is slow and complications are common,which reduces surgical effectiveness.Therefore,patients require long-term,high-quality,and effective nursing interventions to promote rehabilitation.Continuity of care has been used successfully in other diseases;however,little research has been conducted on older patients who have undergone hip replacement.AIM To explore the clinical effect of continuous nursing on rehabilitation after discharge of older individuals who have undergone joint replacement.METHODS A retrospective analysis was performed on the clinical data of 113 elderly patients.Patients receiving routine nursing were included in the convention group(n=60),and those receiving continuous nursing,according to various methods,were included in the continuation group(n=53).Harris score,short form 36(SF-36)score,complication rate,and readmission rate were compared between the convention and continuation groups.RESULTS After discharge,Harris and SF-36 scores of the continuation group were higher than those of the convention group.The Harris and SF-36 scores of the two groups showed an increasing trend with time,and there was an interaction effect between group and time(Harris score:F_(intergroup effect)=376.500,F_(time effect)=20.090,Finteraction effect=4.824;SF-36 score:F_(intergroup effect)=236.200,Ftime effect=16.710,Finteraction effect=5.584;all P<0.05).Furthermore,the total complication and readmission rates in the continuation group were lower(P<0.05).CONCLUSION Continuous nursing could significantly improve hip function and quality of life in older patients after joint replacement and reduce the incidence of complications and readmission rates.

Development of high-power microwave mechanical integrated continuous mining device

This article introduces a high-power microwave mechanical integrated continuous mining device,which can achieve synchronous cutting of hard rocks by microwave and machinery.The device includes a cutting system,a rotary translation system,a loading system,a high-power microwave system,and a control and monitoring system.The technology of“master-slave follow-up”disc cutter alternating side cutting of rock was proposed,which could improve the effectiveness of rock breaking.The integrated structure of a microwave-cut system was then proposed,and synchronous motion of the microwave-cut system and adjustment of the loading system could be realized.The automatic adjustment technology of the microwave working distance was developed to dynamically control the optimal microwave working distance.The basic functions of the equipment were verified by tests.By comparing the two types of disk cutters,it is found that the master-slave follow-up disk cutter can improve significantly the dust removal effect and rock breaking efficiency in rock breaking process versus the conventional large disc cutter.Cutting tests of slate with or without microwave were conducted using a master-slave follow-up disk cutter.The results show that the cutting patterns of slates change from intermittent chunks(without microwave irradiation)to persistent debris(with microwave irradiation),and the cutting speed is significantly improved(170%).The development of the device provides a scientific basis for changing the conventional mining technology of metal mines and realizing the mechanical continuous mining in hard metal mines.

Path-Dependent Progressive Failure Analysis for 3D-Printed Continuous Carbon Fibre Reinforced Composites

In order to predict the damage behaviours of 3D-printed continuous carbon fibre(CCF)reinforced composites,when additional short carbon fibre(SCF)composite components are employed for continuous printing or special functionality,a novel path-dependent progressive failure(PDPF)numerical approach is developed.First,a progressive failure model using Hashin failure criteria with continuum damage mechanics to account for the damage initiation and evaluation of 3D-printed CCF reinforced polyamide(PA)composites is developed,based on actual fibre placement trajectories with physical measurements of 3D-printed CCF/PA constituents.Meanwhile,an elastic-plastic model is employed to predict the plastic damage behaviours of SCF/PA parts.Then,the accuracy of the PDPF model was validated so as to study 3D-printed CCF/PA composites with either negative Poisson's ratio or high stiffness.The results demonstrate that the proposed PDPF model can achieve higher prediction accuracies in mechanical properties of these 3D-printed CCF/PA composites.Mechanism analyses show that the stress distribution is generally aggregated in the CCF areas along the fibre placement paths,and the shear damage and matrix tensile/compressive damage are the key damage modes.This study provides a new approach with valuable information for characterising complex 3D-printed continuous fibre-matrix composites with variable mechanical properties and multiple constituents.

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]3 is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v3 wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v3 is spatially finite on the Riemann Sphere and the forcing is oscillatory in y3 component if the velocity v3 is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3 is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.

Microstructure and mechanical properties of continuous drive friction welded Ti_(2)AlNb alloy under different rotational rates

Ti_(2)AlNb-based alloy was joined in a continuous drive friction welding machine under different rotational rates(500,1000 and 1500 r/min).The microstructure and mechanical properties of the joints were investigated.It is shown that the weld zone(WZ) is fully composed of recrystallized B2 phase,and the grain size decreases with increasing rotational rate.The thermo-mechanically affected zone(TMAZ) suffers severe deformation during welding,due to which most of original precipitation phase is dissolved and streamlines are present.In the heat affected zone(HAZ),only the fine O phase is dissolved.The as-welded joint produced using 1000 r/min has the best mechanical properties,whose strength and elongation are both close to those of the base metal,while the as-welded joint obtained using 500 r/min exhibits the worst mechanical properties.Post-weld annealing treatment annihilates the deformation microstructure and fine O phase precipitates in the joints,consequently improving the mechanical properties significantly.Decomposed α_(2) phase is a weakness for the mechanical performance of the joint since microcracks are apt to form in it in the tensile test.

Large-scale particle trapping by acoustic vortices with a continuously variable topological charge

Strengthened directivity with higher-order side lobes can be generated by the transducer with a larger radius at a higher frequency. The multi-annular pressure distributions are displayed in the cross-section of the acoustic vortices(AVs)which are formed by side lobes. In the near field, particles can be trapped in the valley region between the two annuli of the pressure peak, and cannot be moved to the vortex center. In this paper, a trapping method based on a sector transducer array is proposed, which is characterized by the continuously variable topological charge(CVTC). This acoustic field can not only enlarge the range of particle trapping but also improve the aggregation degree of the trapped particles. In the experiments, polyethylene particles with a diameter of 0.2 mm are trapped into the multi-annular valleys by the AV with a fixed topological charge. Nevertheless, by applying the CVTC, particles outside the radius of the AV can cross the pressure peak successfully and move to the vortex center. Theoretical studies are also verified by the experimental particles trapping using the AV with the continuous variation of three topological charges, and suggest the potential application of large-scale particle trapping in biomedical engineering.

Application and Evaluation of Continuous Care Model Based on the Omaha System in Stroke Patients after Discharge

[Objectives]To explore the effect of continuous nursing model based on the Omaha system on stroke patients.[Methods]A total of 40 stroke patients in the inpatient department of the Rehabilitation Department of Affiliated Hospital of Jinggangshan University were selected and divided into two groups by the random number table method.Patients in the control group were given routine nursing,and those of the observation group were given continuous nursing based on the Omaha system theory.The score of neurological impairment,daily living ability scale and the quality of life,as well as patients satisfaction rate before and after treatment were compared between the two groups.[Results]The score of neurological impairment,daily living activity ability and the quality of life,as well as patients nursing satisfaction rate in the observation group were significantly better than those of the control group,with statistical significance(P<0.05).[Conclusions]The continuous nursing model based on the Omaha system can significantly improve the neurological function of stroke patients,improve their quality of life and life ability,and promote their rehabilitation.