P-kernel Normal Systems in Weakly P-inversive Semigroups

In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.

P-kernel Normal System of Strong P-congruences on P-inversive Semigroups

Let S（P） be a P-inversive semigroup. In this paper we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. We prove that any strong P-congruence on S（P） can present a P-kernel normal system; conversely any P-kernel normal system of S（P） can determine a strong P-congruence.

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.

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.

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\left(\int_{\mathbb{R}^N}\vert\nabla u\vert^2{\rm d}x\right)\Delta u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,u\in H^1(\mathbb{R}^N),N\geq 1,satisfying the normalization constraint\int_{\mathbb{R}^N}u^2{\rm d}x=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.

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.

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.

Depth-Guided Vision Transformer With Normalizing Flows for Monocular 3D Object Detection

Monocular 3D object detection is challenging due to the lack of accurate depth information.Some methods estimate the pixel-wise depth maps from off-the-shelf depth estimators and then use them as an additional input to augment the RGB images.Depth-based methods attempt to convert estimated depth maps to pseudo-LiDAR and then use LiDAR-based object detectors or focus on the perspective of image and depth fusion learning.However,they demonstrate limited performance and efficiency as a result of depth inaccuracy and complex fusion mode with convolutions.Different from these approaches,our proposed depth-guided vision transformer with a normalizing flows(NF-DVT)network uses normalizing flows to build priors in depth maps to achieve more accurate depth information.Then we develop a novel Swin-Transformer-based backbone with a fusion module to process RGB image patches and depth map patches with two separate branches and fuse them using cross-attention to exchange information with each other.Furthermore,with the help of pixel-wise relative depth values in depth maps,we develop new relative position embeddings in the cross-attention mechanism to capture more accurate sequence ordering of input tokens.Our method is the first Swin-Transformer-based backbone architecture for monocular 3D object detection.The experimental results on the KITTI and the challenging Waymo Open datasets show the effectiveness of our proposed method and superior performance over previous counterparts.

Neuroimaging in atypical normal tension glaucoma:debating routine implementation in the absence of classic neurological findings

●AIM:To assess the necessity of neuroimaging in patients with neurological or atypical findings of normal tension glaucoma(NTG)who do not exhibit typical glaucoma manifestations.●METHODS:A retrospective analysis was conducted on 90 atypical NTG patients who underwent cranial magnetic resonance imaging(MRI)due to atypical symptoms.The demographic characteristics,clinical parameters,and radiological findings were recorded.●RESULTS:Among the patients,66.7%had abnormal radiology results,with the most common findings being gliosis(34.4%),sequelae of cerebrovascular events and vascular malformations(14.4%),and benign intracranial mass lesions(11%).Non-glaucomatous visual field defects were more frequently observed in patients with abnormal neuroimaging results.However,there were no significant differences in intraocular pressure,optic disc parameters,retinal nerve fiber layer thickness,and visual field indices between patients with normal and abnormal radiological results.The mean age of the patients was 58.74y.Interestingly,there was a significant age difference,with the abnormal radiology group having a higher median age(P=0.021).●CONCLUSION:The study highlights the importance of cranial imaging in older NTG patients to detect underlying pathologies and prevent misdiagnosis.It suggests that neuroimaging may be warranted in NTG patients with atypical visual field defects incompatible with glaucoma.However,routine neuroimaging in all NTG patients without classic neurological signs may not be necessary.

Normalized glandular dose coefficients for digital breast tomosynthesis using detailed Chinese breast models

The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female population to replace the traditional standard that utilizes simplified breast models,for the accurate estimation of the mean glandular dose of a patient undergoing digital breast tomosynthesis(DBT).The first set of detailed Chinese female breast models and representative breast parameters was constructed.Considering backscatter radiation and computational efficiency,we improved the combination of these models and the Chinese reference adult female whole-body voxel phantom.Image acquisition for four commercial DBT systems that are widely employed in China was simulated using the Monte Carlo method to obtain the normalized glandular dose coefficients of DBT(D_(gN)^(DBT))and the glandular depth dose(D_(g)^(dep)(z))for different breast characteristics and X-ray spectra.We calculated a series of D_(gN)^(DBT) values for breasts with different percentage mass glandularities(5%,25%,50%,75%,and 100%)and compressed breast thicknesses(2,3,4,5,6,and 7 cm)at various tube potentials(25,28,30,32,35,and 49 kV)and target/filter combinations(W/Rh,W/Al,Mo/Mo,Rh/Rh,and Rh/Ag).The parameter dependence of the breast characteristics and beam conditions on D_(gN)^(DBT) in detailed breast models was investigated.The D_(gN)^(DBT) results were 14.6-51.0%lower than those of the traditional dosimetry standard in China.The difference in D_(gN)^(DBT) was mainly due to a decrease in the depth of the main energy deposition area caused by the glandular distribution along the depth direction.The results obtained in this study may be used to improve breast dosimetry in China and provide more detailed information on risk assessment during DBT.

Strategies for Cultivating Public Funded Targeted Normal Students Based on Goal Management Theory : A Case Study of East, West and North Guangdong

Public funded targeted normal students are an important component of China's teacher team construction.Since its implementation in 2007,a large number of outstanding rural teachers who have been striving on the front line of education have been trained.Based on the theory of goal management,this paper explores the problems and countermeasures in the training of public funded targeted normal students.It strives to solve the problems of low willingness to teach and high default rates among public funded normal students,and hopes that the suggestions proposed in this paper can further promote the effective implementation of policies for public funded normal students.

MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE FRACTIONAL SCHR?DINGER-POISSON SYSTEM WITH DOUBLY CRITICAL GROWTH

In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.

Geometry and 3D seismic characterisation of post-rift normal faults in the Pearl River Mouth Basin,northern South China Sea

Based on high-resolution 3D seismic data acquired in the Pearl(Zhujiang)River Mouth Basin of the northern South China Sea,this study investigated the geometry,spatial extension,and throw distribution of the post-rift normal fault through detailed seismic interpretation and fault modeling.A total of 289 post-rift normal faults were identified in the study area and can be classified into four types:(1)isolated normal faults above the carbonate platform;(2)isolated normal faults cutting through the carbonate platform;(3)conjugate normal faults,and(4)connecting normal faults.Throw distribution analysis on the fault planes show that the vertical throw profiles of most normal fault exhibit flat-topped profiles.Isolated normal faults above the carbonate platform exhibit roughly concentric ellipses with maximum throw zones in the central section whereas the normal faults cutting through the carbonate platform miss the lowermost section due to the chaotic seismic reflections in the interior of the carbonate platform.The vertical throws of conjugate normal faults anomalously decrease toward their intersection region on the fault plane whereas the connecting normal faults present two maximum throw zones in the central section of the fault plane.According to the symmetric elliptical distribution model of fault throw,an estimation was made indicating that normal faults cutting through the carbonate platform extended downward between-1308 s and-1780 s(two-way travel time)in depth and may not penetrate the entire Liuhua carbonate platform.Moreover,it is observed that the distribution of karst caves on the top of the carbonate platform disaccord with those of hydrocarbon reservoirs and the post-rift normal faults cutting through the carbonate platform in the study area.We propose that these karst caves formed most probably by corrosive fluids derived from magmatic activities during the Dongsha event,rather than pore waters or hydrocarbons.

A Normalizing Flow-Based Bidirectional Mapping Residual Network for Unsupervised Defect Detection

Unsupervised methods based on density representation have shown their abilities in anomaly detection,but detection performance still needs to be improved.Specifically,approaches using normalizing flows can accurately evaluate sample distributions,mapping normal features to the normal distribution and anomalous features outside it.Consequently,this paper proposes a Normalizing Flow-based Bidirectional Mapping Residual Network(NF-BMR).It utilizes pre-trained Convolutional Neural Networks(CNN)and normalizing flows to construct discriminative source and target domain feature spaces.Additionally,to better learn feature information in both domain spaces,we propose the Bidirectional Mapping Residual Network(BMR),which maps sample features to these two spaces for anomaly detection.The two detection spaces effectively complement each other’s deficiencies and provide a comprehensive feature evaluation from two perspectives,which leads to the improvement of detection performance.Comparative experimental results on the MVTec AD and DAGM datasets against the Bidirectional Pre-trained Feature Mapping Network(B-PFM)and other state-of-the-art methods demonstrate that the proposed approach achieves superior performance.On the MVTec AD dataset,NF-BMR achieves an average AUROC of 98.7%for all 15 categories.Especially,it achieves 100%optimal detection performance in five categories.On the DAGM dataset,the average AUROC across ten categories is 98.7%,which is very close to supervised methods.

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.

Stroke Patients’ Reintegration into Normal Living Post-Discharge from Inpatient Rehabilitation: An Integrative Review

Background: Stroke rehabilitation professionals have historically focused rehabilitation on physical functions and overlooked the concept of community reintegration after discharge from inpatient rehabilitation. The lack of focus on psychosocial functions post-stroke may lead to lower levels of satisfaction during community reintegration. Methods: This integrative review synthesized findings from research literature on stroke patients’ reintegration into the community after inpatient rehabilitation to address three research questions: a) What specific physical and psychosocial functions have been identified as predictors of successful reintegration into normal living after stroke?, b) How do physical and psychosocial functions promote successful reintegration into normal living after stroke?, and c) What factors have been identified that hinder stroke patients’ reintegration into normal living after stroke? Results: A systematic search of literature identified sixteen studies that provided significant context for the research questions. What physical and psychosocial functions of stroke patients included, for example, improved mobility, independence in daily activities, reduced disability, psychological well-being, self-efficacy, social support, and personal relationships. How physical and psychosocial functions promote reintegration included, for example, disability management, emotional well-being, self-care independence, sense of purpose, and employment influence. Factors that hinder stroke patients’ reintegration consisted of longer stride time, impaired balance/mobility, activities limitation, severe stroke, presence of comorbidity, depressive symptoms, speech and language challenges, inadequate self-efficacy, fear of falling, older age, low educational level, lack of social support, and social isolation. Conclusion: Successful community reintegration after stroke requires a shift of focus from rehabilitation interventions that target physical functions to include interventions that address psychosocial functions.

Effect of the mixing of s-wave and chiral p-wave pairings on electrical shot noise properties of normal metal/superconductor tunnel junctions

We study theoretically the electrical shot noise properties of tunnel junctions between a normal metal and a superconductor with the mixture of singlet s-wave and chiral triplet p-wave pairing due to broken inversion symmetry. We investigate how the shot noise properties vary as the relative amplitude between the two parity components in the pairing potential is changed. It is demonstrated that some characteristics of the electrical shot noise properties of such tunnel junctions may depend sensitively on the relative amplitude between the two parity components in the pairing potential, and some significant changes may occur in the electrical shot noise properties when the relative amplitude between the two parity components is varied from the singlet s-wave pairing dominated regime to the chiral triplet p-wave pairing dominated regime. In the chiral triplet p-wave pairing dominated regime, the ratio of noise power to electric current is close to 2e both in the in-gap and in the out-gap region. In the singlet s-wave pairing dominated regime, the value of this ratio is close to 4e in the inner gap region but may reduce to about 2e in the outer gap region as the relative amplitude of the chiral triplet pairing component is increased. The variations of the differential shot noise with the bias voltage also exhibit some significantly different features in different regimes. Such different features can serve as useful diagnostic tools for the determination of the relative magnitude of the two parity components in the pairing potential.

Fuzzy Multi-Criteria Decision Support System for the Best Anti-Aging Treatment Selection Process through Normal Wiggly Hesitant Fuzzy Sets

This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.