Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.

A Survey Study on TPACK Framework for Normal Students of English Major in Ethnic Colleges and Universities:Empirical Analysis Based on Structural Equation Modeling

With the continuous advancement of education informatization,Technological Pedagogical Content Knowledge(TPACK),as a new theoretical framework,provides a novel method for measuring teachers’informatization teaching ability.This study takes normal students of English majors from three ethnic universities as the research object,collects relevant data through questionnaires,and uses structural equation modeling to conduct data analysis and empirical research to investigate the differences in the TPACK levels of these students at different grades and the structural relationships among the elements in the TPACK structure.The technological pedagogical knowledge element of the TPACK structure was not obtained by exploratory factors analysis but through path analysis and structural equation modeling,the results show that the one-dimensional core knowledge of technological knowledge(TK),content knowledge(CK),and pedagogical knowledge(PK)have a positive effect on the two-dimensional interaction knowledge of technological content knowledge(TCK)and pedagogical content knowledge(PCK);furthermore,TCK and PCK have a positive effect on TPACK;and TK,CK,and PK indirectly affect TPACK through TCK and PCK.On this basis,suggestions are provided to ethnic colleges and universities to develop the TPACK knowledge competence of normal students of English majors.

Basic mathematical model for the normal black smoker system and the hydrothermal megaplume formation

A tube model to simulate the normal black smoker system has been built, where the Darcy flow equation, the Ergun equation and the turbulent pipe flow equation are used respectively to describe the dynamic process of different key areas in the hydrothermal circulation system. At the same time, a convection - diffuse Equation for the temperature field is used for describe the exchange of thermal energy and the law of temperature variation. Combining the above facts and using efficient mathematical algorithms and programming with the MatLab programming language, the variation curves of temperature, pressure and mass flow rate are determined, while also the dynamic heat equilibrium and pressure equilibrium within the black smoker system are analyzed. On the basis of the model of the normal black smoker system, a megaplume formation model is further built. For instance, the hydrothermal venting plume on the Juan de Fuca Ridge has been simulated and the simulation results are fairly consistent with Baker＇ s imputed data in 1986. On the basis of the above productive simulation, a series of factors for megaplume formation and the effectiveness of the main parameters of the periodicity of the megaplume formation, temperature and the maximum mass flow rate are systematically discussed. Main conclusions are as follows： The normal black smoker system can evolve into a megaplum eruption. In fact, the passageway of the hydrothermal discharge is blocked by the hydrothermal sediments during the black smoker period, which leads to a hydrothermal fluid accumulation, rise of temperature and increase of buoyancy pressure under the seabed. After a period of 2 - 3 a, the megaplume hydrothermal eruption will occur when the increasing buoyancy pressure is high enough to crack the blockage （cap）. Meanwhile, the temperature of the heat source must exceed 500 ℃, while the highest temperature of the eruption fluid may be high up to 413 ℃, which is fairly consistent with the surveying data. If the temperature of the heat source were to be higher than 500 ℃, then the critical period for the megaplume formation could be obviously curtailed to be less than 1 a, while the critical temperature and the maximum mass flow rate are nearly invariable. As the permeability increases, the maximum mass flow rate increases gradually close to a steady value.

Construction and Implementation of Practice Teaching System of English Major in Local Normal Universities

English practice teaching has outstanding superiority over the extension and supplementation of English classroom teaching, and practice teaching is an indispensably important part of college English teaching. To students, cultivation of the ability of practice is vital, affecting students＇ employment and future. To universities, teaching quality has a direct impact on the development prospect of schools and decides the future of schools. Moreover, local normal universities also undertake a more important task to cultivate local high-quality talents teaching primary and junior high schools. These teaching talents undertake the great task of English teaching over primary and junior high school students, and thus the construction and implementation of practice teaching system of English major in normal universities are urgent.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

An Implementation of Multiscale Line Detection and Mathematical Morphology for Efficient and Precise Blood Vessel Segmentation in Fundus Images

Diagnosing various diseases such as glaucoma,age-related macular degeneration,cardiovascular conditions,and diabetic retinopathy involves segmenting retinal blood vessels.The task is particularly challenging when dealing with color fundus images due to issues like non-uniformillumination,low contrast,and variations in vessel appearance,especially in the presence of different pathologies.Furthermore,the speed of the retinal vessel segmentation system is of utmost importance.With the surge of now available big data,the speed of the algorithm becomes increasingly important,carrying almost equivalent weightage to the accuracy of the algorithm.To address these challenges,we present a novel approach for retinal vessel segmentation,leveraging efficient and robust techniques based on multiscale line detection and mathematical morphology.Our algorithm’s performance is evaluated on two publicly available datasets,namely the Digital Retinal Images for Vessel Extraction dataset(DRIVE)and the Structure Analysis of Retina(STARE)dataset.The experimental results demonstrate the effectiveness of our method,withmean accuracy values of 0.9467 forDRIVE and 0.9535 for STARE datasets,aswell as sensitivity values of 0.6952 forDRIVE and 0.6809 for STARE datasets.Notably,our algorithmexhibits competitive performance with state-of-the-art methods.Importantly,it operates at an average speed of 3.73 s per image for DRIVE and 3.75 s for STARE datasets.It is worth noting that these results were achieved using Matlab scripts containing multiple loops.This suggests that the processing time can be further reduced by replacing loops with vectorization.Thus the proposed algorithm can be deployed in real time applications.In summary,our proposed system strikes a fine balance between swift computation and accuracy that is on par with the best available methods in the field.

Unveiling the silent link:Normal-tension glaucoma's enigmatic bond with cardiac blood flow

This comprehensive review embarks on a captivating journey into the complex relationship between cardiology and normal-tension glaucoma(NTG),a condition that continues to baffle clinicians and researchers alike.NTG,characterized by optic nerve damage and visual field loss despite normal intraocular pressure,has long puzzled clinicians.One emerging perspective suggests that alterations in ocular blood flow,particularly within the optic nerve head,may play a pivotal role in its pathogenesis.While NTG shares commonalities with its high-tension counterpart,its unique pathogenesis and potential ties to cardiovascular health make it a fascinating subject of exploration.It navigates through the complex web of vascular dysregulation,blood pressure and perfusion pressure,neurovascular coupling,and oxidative stress,seeking to uncover the hidden threads that tie the heart and eyes together in NTG.This review explores into the intricate mechanisms connecting cardiovascular factors to NTG,shedding light on how cardiac dynamics can influence ocular health,particularly in cases where intraocular pressure remains within the normal range.NTG's enigmatic nature,often characterized by seemingly contradictory risk factors and clinical profiles,underscores the need for a holistic approach to patient care.Drawing parallels to cardiac health,we examine into the shared vascular terrain connecting the heart and the eyes.Cardiovascular factors,including systemic blood flow,endothelial dysfunction,and microcirculatory anomalies,may exert a profound influence on ocular perfusion,impacting the delicate balance within the optic nerve head.By elucidating the subtle clues and potential associations between cardiology and NTG,this review invites clinicians to consider a broader perspective in their evaluation and management of this elusive condition.As the understanding of these connections evolves,so too may the prospects for early diagnosis and tailored interventions,ultimately enhancing the quality of life for those living with NTG.

Reflections on Talents Training Mode of Music Education Major in Local Normal Universities

The local normal university is the cradle of training music teachers for rural primary and secondary schools. The talent training of the music education major in local normal universities has a direct influence on the basic music education reform in rural areas, and also decides the survival and development of the music education major in local normal universities. Based on the definition of the talent training mode of the music education major, this paper deeply majoring in music education in local normal universities. discusses the special quality and the training strategies of talents

Study on Current Situation and Countermeasures of English Language Culture Teaching for English Majors in Local Normal Universities

At present, English language teaching for English majors in local normal universities in China has been restricted by many aspects of factors, and the current situation is not optimistic. The main reason for this situation is that the teachers and students of English majors in some local normal universities have some deviation in understanding the English language. The teachers can not have the right attitude towards English language culture teaching,and they make one-sided emphasis on the skill learning of English language majors,but ignore the normal teaching of professional English language culture. To improve this situation and improve the overall level of English majors in normal univerities, it requires us teachers and students to work together, improving the overall level of this course from the two aspects of ＂teaching＂ and ＂learning＂ , in order to help students to truly grasp the English language culture and skillfully use English in daily life and work.

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Extraction of Acoustic Normal Mode Depth Functions Using Range-Difference Method with Vertical Linear Array Data

Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when two or more singular values obtained from the cross-spectral density matrix diagonalization are nearly equal,this results in unsatisfactory extraction outcomes for the normal mode depth functions.To address this issue,we introduced in this paper a range-difference singular value decomposition method for the extraction of normal mode depth functions.We performed the mode extraction by conducting singular value decomposition on the individual frequency components of the signal's cross-spectral density matrix.This was achieved by using pressure and its range-difference matrices constructed from vertical line array data.The proposed method was validated using simulated data.In addition,modes were successfully extracted from ambient noise.

Combining reinforcement learning with mathematical programming:An approach for optimal design of heat exchanger networks

Heat integration is important for energy-saving in the process industry.It is linked to the persistently challenging task of optimal design of heat exchanger networks(HEN).Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem,it is not easy to find solutions of high quality for large-scale problems.The reinforcement learning(RL)method,which learns strategies through ongoing exploration and exploitation,reveals advantages in such area.However,due to the complexity of the HEN design problem,the RL method for HEN should be dedicated and designed.A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods.An insightful state representation of the HEN structure as well as a customized reward function is introduced.A Q-learning algorithm is applied to update the HEN structure using theε-greedy strategy.Better results are obtained from three literature cases of different scales.

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.

NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

NORMALITY AND THE NUMBER OF ZEROS

In this paper,we study normal families of meromorphic functions.By using the idea in[11],we obtain some normality criteria for families of meromorphic functions that concern the number of zeros of the differential polynomial,which extends the related result of Li,and Chen et al..An example is given to show that the hypothesis on the zeros of a(z)is necessary.

Learning to represent 2D human face with mathematical model

How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.

Shear mechanical properties and frictional sliding responses of rough joint surfaces under dynamic normal displacement conditions

A comprehensive understanding of the dynamic frictional characteristics in rock joints under high normal load and strong confinement is essential for ensuring the safety of deep engineering construction and mitigating geological disasters.This study conducted shear experiments on rough rock joints under displacement-controlled dynamic normal loads,investigating the shear behaviors of joints across varying initial normal loads,normal loading frequencies,and normal loading amplitudes.Experimental results showed that the peak/valley shear force values increased with initial normal loads and normal loading frequencies but showed an initial increase followed by a decrease with normal loading amplitudes.Dynamic normal loading can either increase or decrease shear strength,while this study demonstrates that higher frequencies lead to enhanced friction.Increased initial normal loading and normal loading frequency result in a gradual decrease in joint roughness coefficient(JRC)values of joint surfaces after shearing.Positive correlations existed between frictional energy dissipation and peak shear forces,while post-shear joint surface roughness exhibited a negative correlation with peak shear forces through linear regression analysis.This study contributes to a better understanding of the sliding responses and shear mechanical characteristics of rock joints under dynamic disturbances.

A novel mitigation measure for normal fault-induced deformations on pile-raft systems

Evidence from recent earthquakes has shown destructive consequences of fault-induced permanent ground movement on structures.Such observations have increased the demand for improvements in the design of structures that are dramatically vulnerable to surface fault ruptures.In this study a novel connection between the raft and the piles is proposed to mitigate the hazards associated with a normal fault on pile-raft systems by means of 3D finite element(FE)modeling.Before embarking on the parametric study,the strain-softening constitutive law used for numerical modeling of the sand has been validated against centrifuge test results.The exact location of the fix-head and unconnected pile-raft systems relative to the outcropping fault rupture in the free-field is parametrically investigated,revealing different failure mechanisms.The performance of the proposed connection for protecting the pile-raft system against normal fault-induced deformations is assessed by comparing the geotechnical and structural responses of both types of foundation.The results indicate that the pocket connection can relatively reduce the cap rotation and horizontal and vertical displacements of the raft in most scenarios.The proposed connection decreases the bending moment response of the piles to their bending moment capacity,verging on a fault offset of 0.6 m at bedrock.