Nonholonomic Theory of Principal-direction Orthonormal Basis for a Layer of Surfaces

In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.

Effect of extended nursing based on self-efficacy theory on the anxiety of patients with intertrochanteric fracture

BACKGROUND Extended care based on self-efficacy theory to elderly patients with intertrochanteric fractures will provide data reference to optimize the care plan of these patients,reduce patients’concurrent mental diseases,and improve prognosis.AIM To analyze the value of extended nursing based on the self-efficacy theory in older patients with intertrochanteric fractures.METHODS Older patients with intertrochanteric fractures(n=88)admitted to our hospital between January 2021 and December 2024 were randomly divided into two groups-the control group(n=44,routine nursing)and the observation group(n=44,extended nursing)-via balloting and treated for 12 weeks.The mental state,pain severity,limb function,and self-nursing ability of all patients before and after nursing were analyzed.RESULTS After nursing,the Hamilton Anxiety Scale and General Self-Efficacy Scale scores of patients in the two groups improved.Notably,Hamilton Anxiety Scale and General Self-Efficacy Scale scores in the observation group were lower and higher,respectively,than those in the control group(P<0.05).The pain severity in the observation group(2.64±0.22)was lower than that in the control group(2.85±0.41)(P<0.05).The recovery rate of limb function was higher in the observation group than in the control group(P<0.05).In addition,the self-nursing ability scores of the patients in both groups increased,with a significantly higher score in the observation group(P<0.05).CONCLUSION Extended nursing based on the self-efficacy theory can significantly improve mental state,relieve pain,and promote the recovery of limb function and self-nursing ability in older patients with intertrochanteric fractures.

Nursing interventions based on Snyder’s hope theory for depression following percutaneous coronary interventions:A clinical study

BACKGROUND Patients with depression following coronary heart disease often exhibit insufficient psychological resilience and self-care abilities;therefore,emphasis must be placed on nursing interventions.AIM To analyze the application value of problem-oriented education combined with nursing interventions based on the Snyder hope theory model in depressed patients after percutaneous coronary intervention(PCI).METHODS This study included 150 patients diagnosed with PCI postoperative depression because of coronary heart disease between February 2022 and February 2024.Participants were divided into two groups:A control group(n=75)receiving problem-oriented education and an observation group(n=75)receiving combined nursing interventions based on the Snyder hope theory model.Depression status,psychological resilience,self-care ability,and quality of life were compared between the two groups.RESULTS Before nursing interventions,there were no significant differences between the two groups(P>0.05).After the interventions,depression scores decreased while psychological resilience,self-care ability,and quality of life scores increased significantly in the observation group compared to that in the control group,with statistically significant differences noted(P<0.05).This combined approach can enhance psychological resilience,improve self-care abilities,and elevate the overall quality of life,warranting further promotion in clinical practice.CONCLUSION Combination of problem-oriented education and nursing interventions based on the Snyder hope theory model effectively alleviates depression in patients following PCI for coronary heart disease.

A comparative investigation of an AB- and AA-stacked bilayer graphene sheet under an applied electric field:A density functional theory study

An AB-and AA-stacked bilayer graphene sheet （BLG） under an electric field is investigated by ab initio calculation. The interlayer distance between the two layers, band structures, and atomic charges of the system are investigated in the presence of different electric fields normal to the BLG. The AB-stacked BLG is able to tune the bandgap into 0.234 eV with the increase of the external electronic field to 1 V/nm, however, the AA-stacked BLG is not sensitive to the external electric field. In both the cases, the spacing between the BLG slightly change in terms of the electric field. The charges in the AB-stacked BLG are increased with the increase of the electric field, which is considered to be the reason that causes the bandgap opening in the AB-stacked BLG.

Development of mean-field electrical double layer theory

In order to understand the electric interfacial behavior, mean field based electric double layer （EDL） theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice- gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversi0n among them can be achieved by reducing the basic assumptions.

Transition‐metal‐atom‐pairs deposited on g‐CN monolayer for nitrogen reduction reaction:Density functional theory calculations

The development of highly active DFT catalysts for an electrocatalytic N_(2)reduction reaction(NRR)under mild conditions is a difficult challenge.In this study,a series of atom‐pair catalysts(APCs)for an NRR were fabricated using transition‐metal(TM)atoms(TM=Sc−Zn)doped into g‐CN monolayers.The electrochemical mechanism of APCs for an NRR has been reported by well‐defined density functional theory calculations.The calculated limiting potentials were−0.47 and−0.78 V for the Fe_(2)@CN and Co_(2)@CN catalysts,respectively.Owing to its high suppression of hydrogen evolution reactions,Co_(2)@CN is a superior electrocatalytic material for a N_(2)fixation.Stable Fe_(2)@CN may be a strongly attractive material for an NRR with a relatively low overpotential after an improvement in the selectivity.The two‐way charge transfer affirmed the donation‐acceptance procedure between N_(2)and Fe_(2)@CN or Co_(2)@CN,which play a crucial role in the activation of inert N≡N bonds.This study provides an in‐depth investigation into atom‐pair catalysts and will open up new avenues for highly efficient g‐CN‐based nanostructures for an NRR.

Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

Application of self-consistent field theory to self-assembled bilayer membranes

Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.

Timing theory integrated nursing combined behavior change integrated theory of nursing on primiparous influence

BACKGROUND The comprehension and utilization of timing theory and behavior change can offer a more extensive and individualized provision of support and treatment alternatives for primipara.This has the potential to enhance the psychological well-being and overall quality of life for primipara,while also furnishing healthcare providers with efficacious interventions to tackle the psychological and physiological obstacles encountered during the stages of pregnancy and postpartum.AIM To explore the effect of timing theory combined with behavior change on selfefficacy,negative emotions and quality of life in patients with primipara.METHODS A total of 80 primipara cases were selected and admitted to our hospital between August 2020 and May 2022.These cases were divided into two groups,namely the observation group and the control group,with 40 cases in each group.The nursing interventions differed between the two groups,with the control group receiving routine nursing and the observation group receiving integrated nursing based on the timing theory and behavior change.The study aimed to compare the pre-and post-nursing scores of Chinese Perceived Stress Scale(CPSS),Edinburgh Postpartum Depression Scale(EPDS),Self-rating Anxiety Scale(SAS),breast milk knowledge,self-efficacy,and SF-36 quality of life in both groups.RESULTS After nursing,the CPSS,EPDS,and SAS scores of the two groups was significantly lower than that before nursing,and the CPSS,EPDS,and SAS scores of the observation group was significantly lower than that of the control group(P=0.002,P=0.011,and P=0.001 respectively).After nursing,the breastfeeding knowledge mastery,selfefficacy,and SF-36 quality of life scores was significantly higher than that before nursing,and the breastfeeding knowledge mastery(P=0.013),self-efficacy(P=0.008),and SF-36 quality of life(P=0.011)scores of the observation group was significantly higher than that of the control group.CONCLUSION The integration of timing theory and behavior change integrated theory has been found to be an effective approach in alleviating negative mood and stress experienced by primipara individuals,while also enhancing their selfefficacy and overall quality of life.This study focuses on the key concepts of timing theory,behavior change,primipara individuals,negative mood,and quality of life.

Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory

This manuscript presents the comprehensive study of thickness stretching effects on the free vibration,static stability and bending of multilayer functionally graded(FG)carbon nanotubes reinforced composite(CNTRC)nanoplates.The nanoscale and microstructure influences are considered through a modified nonlocal strain gradient continuum model.Based on power-law functions,four different patterns of CNTs distribution are considered in this analysis,a uniform distribution UD,FG-V CNTRC,FG-X CNTRC,and FG-O CNTRC.A 3D kinematic shear deformation theory is proposed to include the stretching influence,which is neglected in classical theories.Hamilton's principle is applied to derive the governing equations of motion and associated boundary conditions.Analytical solutions are developed based on Galerkin method to solve the governing equilibrium equations based on the generalized higher-order shear deformation theory and the nonlocal strain gradient theory and get the static bending,buckling loads,and natural frequencies of nanoplates.Verification with previous works is presented.A detailed parametric analysis is carried out to highlight the impact of thickness stretching,length scale parameter(nonlocal),material scale parameter(gradient),CNTs distribution pattern,geometry of the plate,various boundary conditions and the total number of layers on the stresses,deformation,critical buckling loads and vibration frequencies.Many new results are also reported in the current study,which will serve as a benchmark for future research.

Novelties Filtration Theory of Liquid Chromatography-Mass Spectrometry in Volume Nanotube of Cotton Filament of Layers Woven Fabrics

Objectives of the research to present a modern theory of water purification for multiple purposes entitled “a novelties filtration theory of liquid chromatography-mass spectrometry” is an exceedingly sensitive and specific analytical technique in volume layers woven fabrics that can precisely determine the identities and quantities of compounds within volume Nanotube of cotton filament of layers woven fabrics. The problems are that the filters in the local and international markets have increased complications in configuration, installation and cost without reaching the efficiency that humanity hopes. Throw materials and methods the chromatography-mass spectrometry in layers woven fabrics, and throw the nanotube of cotton filament for purification of water dyes and smells. Industry, in which mass spectrometry is a convenient, versatile method for characterization and identification of process throw the Nanotube of cotton filament for purification of water dyes and smells. Results came up with a theme “innovations in textiles”, and also, for characterization of fibers and contaminants of the fabrics. Additive manufacturing in layers woven fabrics, are the processes used to synthesize a volume object under computer control with successive material layers that have been used and highlighted. The conclusions has included chromatography-mass spectrometry drop, physico-chemical, biological, combined physical-biological and chemical-biological treatment processes recently being developed to meet Jet-filtration, the strict discharging limits set by ASTM standards. Some important aspects of both qualitative and quantitative data analysis have been described and the power of using mass profiles to enhance selectivity and sensitivity has been demonstrated.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive （ferromagnetic interaction） and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative （ferromagnetic or antiferromagnetic interaction）. The temperature dependence of the layer magnetizations of the system is examined to characterize the nature （continuous or discontinuous） of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point （TP）, critical end point （E）, multicritical point （A）, isolated critical point （C） and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.

Systems Theory-Driven Framework for AI Integration into the Holistic Material Basis Research of Traditional Chinese Medicine

This paper introduces a systems theory-driven framework to integration artificial intelligence(AI)into traditional Chinese medicine(TCM)research,enhancing the understanding of TCM’s holistic material basis while adhering to evidence-based principles.Utilizing the System Function Decoding Model(SFDM),the research progresses through define,quantify,infer,and validate phases to systematically explore TCM’s material basis.It employs a dual analytical approach that combines top-down,systems theory-guided perspectives with bottom-up,elements-structure-function methodologies,provides comprehensive insights into TCM’s holistic material basis.Moreover,the research examines AI’s role in quantitative assessment and predictive analysis of TCM’s material components,proposing two specific AIdriven technical applications.This interdisciplinary effort underscores AI’s potential to enhance our understanding of TCM’s holistic material basis and establishes a foundation for future research at the intersection of traditional wisdom and modern technology.

Transient response of doubly-curved bio-inspired composite shells resting on viscoelastic foundation subject to blast load using improved first-order shear theory and isogeometric approach

Investigating natural-inspired applications is a perennially appealing subject for scientists. The current increase in the speed of natural-origin structure growth may be linked to their superior mechanical properties and environmental resilience. Biological composite structures with helicoidal schemes and designs have remarkable capacities to absorb impact energy and withstand damage. However, there is a dearth of extensive study on the influence of fiber redirection and reorientation inside the matrix of a helicoid structure on its mechanical performance and reactivity. The present study aimed to explore the static and transient responses of a bio-inspired helicoid laminated composite(B-iHLC) shell under the influence of an explosive load using an isomorphic method. The structural integrity of the shell is maintained by a viscoelastic basis known as the Pasternak foundation, which encompasses two coefficients of stiffness and one coefficient of damping. The equilibrium equations governing shell dynamics are obtained by using Hamilton's principle and including the modified first-order shear theory,therefore obviating the need to employ a shear correction factor. The paper's model and approach are validated by doing numerical comparisons with respected publications. The findings of this study may be used in the construction of military and civilian infrastructure in situations when the structure is subjected to severe stresses that might potentially result in catastrophic collapse. The findings of this paper serve as the foundation for several other issues, including geometric optimization and the dynamic response of similar mechanical structures.

A Data Intrusion Tolerance Model Based on an Improved Evolutionary Game Theory for the Energy Internet

Malicious attacks against data are unavoidable in the interconnected,open and shared Energy Internet(EI),Intrusion tolerant techniques are critical to the data security of EI.Existing intrusion tolerant techniques suffered from problems such as low adaptability,policy lag,and difficulty in determining the degree of tolerance.To address these issues,we propose a novel adaptive intrusion tolerance model based on game theory that enjoys two-fold ideas:(1)it constructs an improved replica of the intrusion tolerance model of the dynamic equation evolution game to induce incentive weights;and (2)it combines a tournament competition model with incentive weights to obtain optimal strategies for each stage of the game process.Extensive experiments are conducted in the IEEE 39-bus system,whose results demonstrate the feasibility of the incentive weights,confirm the proposed strategy strengthens the system’s ability to tolerate aggression,and improves the dynamic adaptability and response efficiency of the aggression-tolerant system in the case of limited resources.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Anisotropy of Critical Fields in MgB_2: Two-Band Ginzburg-Landau Theory for Layered Superconductors

The temperature dependence of the anisotropy parameter of upper critical field γHe2 （T） = Hc2^‖ （T） /Hc2^⊥ （T） and London penetration depth γλ （T） = λ‖（T）/λ⊥ （T） are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 （T） is increased, while the London penetration depth anisotropy γλ（T） reveals an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations..Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.

Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory

Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data.

Enhancing the resolution of sparse rock property measurements using machine learning and random field theory

The travel time of rock compressional waves is an essential parameter used for estimating important rock properties,such as porosity,permeability,and lithology.Current methods,like wireline logging tests,provide broad measurements but lack finer resolution.Laboratory-based rock core measurements offer higher resolution but are resource-intensive.Conventionally,wireline logging and rock core measurements have been used independently.This study introduces a novel approach that integrates both data sources.The method leverages the detailed features from limited core data to enhance the resolution of wireline logging data.By combining machine learning with random field theory,the method allows for probabilistic predictions in regions with sparse data sampling.In this framework,12 parameters from wireline tests are used to predict trends in rock core data.The residuals are modeled using random field theory.The outcomes are high-resolution predictions that combine both the predicted trend and the probabilistic realizations of the residual.By utilizing unconditional and conditional random field theories,this method enables unconditional and conditional simulations of the underlying high-resolution rock compressional wave travel time profile and provides uncertainty estimates.This integrated approach optimizes the use of existing core and logging data.Its applicability is confirmed in an oil project in West China.