Background:The masseter vestibular evoked myogenic potential(mVEMP) is a novel test that has been explored in various brainstem lesions. However, it has not yet been studied in individuals with definite Meniere's ...Background:The masseter vestibular evoked myogenic potential(mVEMP) is a novel test that has been explored in various brainstem lesions. However, it has not yet been studied in individuals with definite Meniere's disease. Therefore, the current study aimed to investigate m VEMP responses in individuals with definite Meniere's disease and compare them with those of a reference group.Method:The present study investigated narrowband Claus Elberling chirp-evoked m VEMP responses in 22 ears diagnosed with definite Meniere's disease and 22 ears with hearing sensitivity ≤ 15 dB HL across three stimulation frequencies.Results:m VEMP responses in participants with definite Meniere's disease varied from normal to reduced or absent across three octave frequencies. These individuals exhibited significantly reduced P11-N21 peak-to-peak amplitudes compared to those in the reference group. Although a frequency tuning shift toward 1000 Hz was observed, the inter-frequency amplitude ratio of m VEMP was not found to be a sensitive parameter for detecting individuals with definite Meniere's disease. Additionally, no association was found between the degree of hearing loss or the duration of the disease and m VEMP responses. Conclusion: Participants with definite Meniere's disease exhibited reduced P11-N21 amplitude and a tuning shift toward 1000 Hz. These findings suggest the involvement of the vestibulo-trigeminal reflex pathway in this condition.展开更多
The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used t...The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.展开更多
The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive de...The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.展开更多
Background and Objective The development of modern palliative care in China began in the 1980s and is currently in an accelerating phase.However,inconsistencies in terminology and concepts have hindered policy-making,...Background and Objective The development of modern palliative care in China began in the 1980s and is currently in an accelerating phase.However,inconsistencies in terminology and concepts have hindered policy-making,clinical practice,and academic research.The Terminology of Clinical Medicine(2023 edition)has determined huan-he-yi-liao(缓和医疗)and an-ning-liao-hu(安宁疗护)as the formal terms of"palliative care"and"hospice care",respectively.To align with these terms,this study aims to establish expert consensus definitions tailored to the Chinese context.Methods We systematically retrieved and collected domestic and international literature and policy documents related to the definition of palliative care,then deconstructed and analyzed the relevant conceptual elements of these definitions.Core expert panel built the initial recommended definition upon the conceptual elements and consensus definition of palliative care by the International Association for Hospice and Palliative Care(IAHPC)through two rounds of online discussions.After nomination and selection,61 professionals in the field of palliative care in China were invited to participate in the consensus expert group.Two rounds of Delphi consultation were conducted among the consensus experts,who were asked to score their agreement using Likert scale to the items in the initial recommended definition and the definition statements of palliative care and hospice care.Agreement rate of over 80%was considered as reaching consensus for each items.The core expert panel revised the items and the statements of recommended definitions based on the results from Delphi surveys.The final recommended definitions were formulated after feedback from patient and public involvement(PPI)group members.Results The response rates for the first and second round of Delphi surveys were 83.6%and 100.0%,respectively.The agreement rates of the items and statements of the recommended definitions exceeded 90%.Accordingly,the definitions based on Chinese expert consensus are recommended.Palliative care is an active holistic approach aimed at patients of all ages suffering from life-threatening illness and their families and caregivers.It seeks to improve their quality of life by preventing,assessing,and relieving physical,psychological,social,and spiritual suffering.Hospice care is an integral part of palliative care,focusing on holistic care for patients at the end of life and their families and caregivers.Its goal is to help patients to maintain dignity and achieve a good death by alleviating physical,psychological,social,and spiritual distress without intentionally hastening or postponing death,meanwhile improve the quality of life for families and caregivers.Conclusions This study has established the Chinese expert consensus definitions of palliative care and hospice care in China,as well as the relationship between the two.The definitions highlight the holistic nature of palliative care,providing a foundation for discipline development,clinical practice,and public communication.展开更多
Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric posit...Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.展开更多
To solve the symmetric positive definite linear system Ax = b on parallel and vector machines, multisplitting methods are considered. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a spe...To solve the symmetric positive definite linear system Ax = b on parallel and vector machines, multisplitting methods are considered. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a special form (e.g. the dissection form [11]). The main tool for deriving our methods is the diagonally compensated reduction (cf. [1]). The convergence of such methods is also discussed by using this tool. [WT5,5”HZ]展开更多
In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
In this note,we establish a new version of Schur-Horn type theorem for symplectic matrices.Meanwhile,we establish a necessary and sufficient condition for the equality to hold in the above result.
The vibration analysis of Kirchhoff plates requires robust mass lumping schemes to guarantee numerical stability and accuracy.However,existing methods fail to generate symmetric and positive definite mass matrices whe...The vibration analysis of Kirchhoff plates requires robust mass lumping schemes to guarantee numerical stability and accuracy.However,existing methods fail to generate symmetric and positive definite mass matrices when handling rotational degrees of freedom,leading to compromised performance in both time and frequency domains analyses.This study proposes a manifold-based mass lumping scheme that systematically resolves the inertia matrix formulas for rotational/torsional degrees of freedom.By reinterpreting the finite element mesh as a mathematical cover composed of overlapping patches,Hermitian interpolations for plate deflection are derived using partition of unity principles.The manifold-based mass matrix is constructed by integrating the virtual work of inertia forces over these patches,ensuring symmetry and positive definiteness.Numerical benchmarks demonstrate that the manifold-based mass lumping scheme performance can be comparable or better than the consistent mass scheme and other existing mass lumping schemes.This work establishes a unified theory for mass lumping in fourth order plate dynamics,proving that the widely used row-sum method is a special case of the manifold-based framework.The scheme resolves long-standing limitations in rotational/torsional inertia conservation and provides a foundation for extending rigorous mass lumping to 3D shell and nonlinear dynamic analyses.展开更多
Sepsis,characterized as life-threatening organ dysfunction resulting from dysregulated host responses to infection,remains a significant challenge in clinical practice.Despite advancements in understanding host-bacter...Sepsis,characterized as life-threatening organ dysfunction resulting from dysregulated host responses to infection,remains a significant challenge in clinical practice.Despite advancements in understanding host-bacterial interactions,molecular responses,and therapeutic approaches,the mortality rate associated with sepsis has consistently ranged between 10%and 16%.This elevated mortality highlights critical gaps in our comprehension of sepsis etiology.Traditionally linked to bacterial and fungal pathogens,recent outbreaks of acute viral infections,including Middle East respiratory syndrome coronavirus(MERS-CoV),influenza virus,and severe acute respiratory syndrome coronavirus 2(SARS-CoV-2),among other regional epidemics,have underscored the role of viral pathogenesis in sepsis,particularly when critically ill patients exhibit classic symptoms indicative of sepsis.However,many cases of viral-induced sepsis are frequently underdiagnosed because standard evaluations typically exclude viral panels.Moreover,these viruses not only activate conventional pattern recognition receptors(PRRs)and retinoic acid-inducible gene-I(RIG-I)-like receptors(RLRs)but also initiate primary antiviral pathways such as cyclic guanosine monophosphate adenosine monophosphate(GMP-AMP)synthase(cGAS)-stimulator of interferon genes(STING)signaling and interferon response mechanisms.Such activations lead to cellular stress,metabolic disturbances,and extensive cell damage that exacerbate tissue injury while leading to a spectrum of clinical manifestations.This complexity poses substantial challenges for the clinical management of affected cases.In this review,we elucidate the definition and diagnosis criteria for viral sepsis while synthesizing current knowledge regarding its etiology,epidemiology,and pathophysiology,molecular mechanisms involved therein as well as their impact on immune-mediated organ damage.Additionally,we discuss clinical considerations related to both existing therapies and advanced treatment interventions,aiming to enhance the comprehensive understanding surrounding viral sepsis.展开更多
The time went by fairly fast.I have definitely changed a lot in the past three years.I used to be short,but now I am taller.The biggest change,though,is that I enjoy reading more than I used to.During my first vacatio...The time went by fairly fast.I have definitely changed a lot in the past three years.I used to be short,but now I am taller.The biggest change,though,is that I enjoy reading more than I used to.During my first vacation in junior high school,my teacher asked us to read more classics,so I read a variety of books like The Little Prince and Harry Potter,which taught me to be brave in the face of difficulties and never give up.After that,no matter how busy I was,I would read for an hour every day.展开更多
BACKGROUND Sepsis is a critical medical condition,and poses a substantial global health burden,with significant morbidity,mortality,and economic costs,particularly pronounced in low-and middle-income countries.Effecti...BACKGROUND Sepsis is a critical medical condition,and poses a substantial global health burden,with significant morbidity,mortality,and economic costs,particularly pronounced in low-and middle-income countries.Effective management of sepsis relies on early recognition and appropriate intervention,underscoring the importance of accurate classification to guide treatment decisions.The correct diagnosis will lead to effective antimicrobial stewardship practices.AIM To assess the distribution of sepsis categories and the use of empirical antibiotics classified by the World Health Organization(WHO)Access,Watch,and Reserve(AWaRe)system in a tertiary care hospital in Northern India and to correlate antibiotic usage with sepsis classifications.METHODS This longitudinal observational study in the Department of General Medicine,in a tertiary care hospital in Northern India,from 2023 to 2024,aimed to assess the use of empirical antibiotics classified by the WHO AWaRe system.The study also aimed to correlate antibiotic usage.Patients were categorized into sepsis classes(Asepsis,Possible Sepsis,Probable Sepsis,Confirmed Sepsis)and followed until discharge or Day-28.Descriptive and inferential statistical analyses were employed to assess sepsis categories and empirical antibiotic usage classified by the WHO AWaRe system.RESULTS A total of 1867 patients admitted with suspected sepsis were screened,with 230 meeting the inclusion criteria.Among the study cohort(mean age 40.70±14.49 years,50.9% female),initial sepsis classification predominantly included probable sepsis(51.3%)and possible sepsis(35.7%),evolving to asepsis(57.8%)upon final classification,but all received antibiotics.Empirical antibiotic use showed a predominance of Watch group antibiotics(72.2%),with ceftriaxone and piperacillin-tazobactam being the most commonly prescribed;however,no statistical association could be established among the different classes of sepsis with the AWaRe groups.CONCLUSION Accurate sepsis classification is pivotal for clinical decision-making,optimizing antibiotic use,and combating antimicrobial resistance.The majority of the asepsis category was labelled as probable or possible sepsis and given antibiotics at initial hospitalization.The high reliance on Watch group antibiotics in empirical therapy signals a need for enhanced diagnostic strategies to refine treatment initiation,potentially reducing unnecessary antibiotic exposure.Future efforts should focus on establishing sepsis classification checklists as in this study and promoting adherence to antimicrobial stewardship principles to mitigate the global threat of antimicrobial resistance.展开更多
BACKGROUND Fever of unknown origin(FUO)remains a diagnostic challenge and was originally defined in 1961.Its classic criteria include fever≥38.3°C(≥101°F)on multiple occasions,fever lasting three weeks or ...BACKGROUND Fever of unknown origin(FUO)remains a diagnostic challenge and was originally defined in 1961.Its classic criteria include fever≥38.3°C(≥101°F)on multiple occasions,fever lasting three weeks or longer,and a diagnosis after one week of inpatient evaluation.However,these criteria may not fully encompass the varied clinical presentations seen in resource-limited settings such as India.The adaptation of FUO definitions to local healthcare contexts is crucial for enhancing diagnostic accuracy and optimizing patient outcomes.AIM To investigate the applicability of revised FUO criteria in a tertiary care setting in India.METHODS This longitudinal-exploratory study at All India Institute of Medical Sciences Rishikesh(January 2018–December 2022)analyzed 228 adult patients with fever≥99.1°F lasting over three days.Patients diagnosed within three days of admission were excluded.Data were collected retrospectively and prospectively using predefined FUO definitions based on durations of nondiagnosis(3-21 days,>21 days),temperature ranges(99.1°F-100.9°F,≥101°F),and hospitalization durations(3-7 days,>7 days).Descriptive statistics and comparative tests(Fisher's exact test,χ2 test)evaluated outcomes across definitions.RESULTS Among the proposed FUO definitions,Definition B(fever lasting 3-21 days,temperatures between 99.1°F-100.9°F,hospitalization>7 days)predominated(40.8%),while only 2.2%met the classical criteria.Notably,36.5%of Definition B patients remained undiagnosed after 7-10 days,despite 94%undergoing diagnostic workups within 21 days.Infection emerged as the leading etiology across definitions,without significant variation in outcomes or mortality during hospitalization(χ2=27.937,P=0.142).CONCLUSION Adapting FUO criteria to local contexts improves diagnostic accuracy and treatment.Definition B(40.8%prevalence)showed practical utility,with higher mortality in patients discharged on empirical'Anti-tuberculosis therapy'.展开更多
Accurate drought assessment demands thoughtful consideration of drought definition first of all.Drought is commonly defined as a prolonged period of below-average precipitation leading to water shortages that impact e...Accurate drought assessment demands thoughtful consideration of drought definition first of all.Drought is commonly defined as a prolonged period of below-average precipitation leading to water shortages that impact ecosystems,agriculture,and human societies.However,meteorologists,hydrologists,and agronomists often use different criteria to define drought,depending on their specific focus areas.For example,hydrologists define drought according to water deficits in some components of the hydrological cycle(such as precipitation,soil moisture,river flow,and groundwater)or its impacts on the level of services provided to public water supply,irrigation,or hydropower demands(Tate and Gustard,2000).Differences in drought definitions may result in great uncertainties in drought assessment(Satoh et al.,2021).We cannot expect the existence of any workable generalized objective definition of drought(Lloyd-Hughes,2014).展开更多
In this paper,a nonlinear control approach for an unstable networked plant in the presence of actuator and sensor limitations using robust right coprime factorization is proposed.The actuator is limited by upper and l...In this paper,a nonlinear control approach for an unstable networked plant in the presence of actuator and sensor limitations using robust right coprime factorization is proposed.The actuator is limited by upper and lower constraints and the sensor in the feedback loop is subjected to network-induced unknown time-varying delay and noise.With this nonlinear control method,we first employ right coprime factorization based on isomorphism and operator theory to factorize the plant,so that bounded input bounded output(BIBO)stability can be guaranteed.Next,continuous-time generalized predictive control(CGPC)is utilized for the unstable operator of the right coprime factorized plant to guarantee inner stability and enables the closed-loop dynamics of the system with predictive characteristics.Meanwhile,a second-Do F(degrees of freedom)switched controller that satisfies a perturbed Bezout identity and a robustness condition is designed.By using the CGPC controller that possesses predictive behavior and the second-Do F switched stabilizer,the overall stability of the plant subjected to actuator limitations is guaranteed.To address sensor limitations that exist in networked plants in the form of delay and noise which often cause system performance degradation,we implement an identity operator definition in the feedback loop to compensate for these adverse effects.Further,a pre-operator is designed to ensure that the plant output tracks the reference input.Finally,the effectiveness of the proposed design scheme is demonstrated by simulations.展开更多
In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
Let F be the strong p-division ring [4]. This paper is sequel to [1]. Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned mat...Let F be the strong p-division ring [4]. This paper is sequel to [1]. Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented. Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.展开更多
The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian ...The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.展开更多
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence ...In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.展开更多
文摘Background:The masseter vestibular evoked myogenic potential(mVEMP) is a novel test that has been explored in various brainstem lesions. However, it has not yet been studied in individuals with definite Meniere's disease. Therefore, the current study aimed to investigate m VEMP responses in individuals with definite Meniere's disease and compare them with those of a reference group.Method:The present study investigated narrowband Claus Elberling chirp-evoked m VEMP responses in 22 ears diagnosed with definite Meniere's disease and 22 ears with hearing sensitivity ≤ 15 dB HL across three stimulation frequencies.Results:m VEMP responses in participants with definite Meniere's disease varied from normal to reduced or absent across three octave frequencies. These individuals exhibited significantly reduced P11-N21 peak-to-peak amplitudes compared to those in the reference group. Although a frequency tuning shift toward 1000 Hz was observed, the inter-frequency amplitude ratio of m VEMP was not found to be a sensitive parameter for detecting individuals with definite Meniere's disease. Additionally, no association was found between the degree of hearing loss or the duration of the disease and m VEMP responses. Conclusion: Participants with definite Meniere's disease exhibited reduced P11-N21 amplitude and a tuning shift toward 1000 Hz. These findings suggest the involvement of the vestibulo-trigeminal reflex pathway in this condition.
基金Supported by the National Natural Science Foundation of China(60473035)~~
文摘The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.
文摘The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.
文摘Background and Objective The development of modern palliative care in China began in the 1980s and is currently in an accelerating phase.However,inconsistencies in terminology and concepts have hindered policy-making,clinical practice,and academic research.The Terminology of Clinical Medicine(2023 edition)has determined huan-he-yi-liao(缓和医疗)and an-ning-liao-hu(安宁疗护)as the formal terms of"palliative care"and"hospice care",respectively.To align with these terms,this study aims to establish expert consensus definitions tailored to the Chinese context.Methods We systematically retrieved and collected domestic and international literature and policy documents related to the definition of palliative care,then deconstructed and analyzed the relevant conceptual elements of these definitions.Core expert panel built the initial recommended definition upon the conceptual elements and consensus definition of palliative care by the International Association for Hospice and Palliative Care(IAHPC)through two rounds of online discussions.After nomination and selection,61 professionals in the field of palliative care in China were invited to participate in the consensus expert group.Two rounds of Delphi consultation were conducted among the consensus experts,who were asked to score their agreement using Likert scale to the items in the initial recommended definition and the definition statements of palliative care and hospice care.Agreement rate of over 80%was considered as reaching consensus for each items.The core expert panel revised the items and the statements of recommended definitions based on the results from Delphi surveys.The final recommended definitions were formulated after feedback from patient and public involvement(PPI)group members.Results The response rates for the first and second round of Delphi surveys were 83.6%and 100.0%,respectively.The agreement rates of the items and statements of the recommended definitions exceeded 90%.Accordingly,the definitions based on Chinese expert consensus are recommended.Palliative care is an active holistic approach aimed at patients of all ages suffering from life-threatening illness and their families and caregivers.It seeks to improve their quality of life by preventing,assessing,and relieving physical,psychological,social,and spiritual suffering.Hospice care is an integral part of palliative care,focusing on holistic care for patients at the end of life and their families and caregivers.Its goal is to help patients to maintain dignity and achieve a good death by alleviating physical,psychological,social,and spiritual distress without intentionally hastening or postponing death,meanwhile improve the quality of life for families and caregivers.Conclusions This study has established the Chinese expert consensus definitions of palliative care and hospice care in China,as well as the relationship between the two.The definitions highlight the holistic nature of palliative care,providing a foundation for discipline development,clinical practice,and public communication.
文摘Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.
文摘To solve the symmetric positive definite linear system Ax = b on parallel and vector machines, multisplitting methods are considered. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a special form (e.g. the dissection form [11]). The main tool for deriving our methods is the diagonally compensated reduction (cf. [1]). The convergence of such methods is also discussed by using this tool. [WT5,5”HZ]
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
基金supported by the National Natural Science Foundation of China(Grant Nos.12201332,12271108)by the Fujian Provincial Natural Science Foundation of China(Grant No.2024J01874)by the Fujian Key Laboratory of Financial Information Processing(Putian University).
文摘In this note,we establish a new version of Schur-Horn type theorem for symplectic matrices.Meanwhile,we establish a necessary and sufficient condition for the equality to hold in the above result.
基金supported by National Natural Science Foundation of China(Grant Nos.42107214 and 52130905)the Natural Science Foundation of Chongqing(No.CSTB2024NSCQMSX0740)the Henan Province Science and Technology Research Projects(No.252102220050).
文摘The vibration analysis of Kirchhoff plates requires robust mass lumping schemes to guarantee numerical stability and accuracy.However,existing methods fail to generate symmetric and positive definite mass matrices when handling rotational degrees of freedom,leading to compromised performance in both time and frequency domains analyses.This study proposes a manifold-based mass lumping scheme that systematically resolves the inertia matrix formulas for rotational/torsional degrees of freedom.By reinterpreting the finite element mesh as a mathematical cover composed of overlapping patches,Hermitian interpolations for plate deflection are derived using partition of unity principles.The manifold-based mass matrix is constructed by integrating the virtual work of inertia forces over these patches,ensuring symmetry and positive definiteness.Numerical benchmarks demonstrate that the manifold-based mass lumping scheme performance can be comparable or better than the consistent mass scheme and other existing mass lumping schemes.This work establishes a unified theory for mass lumping in fourth order plate dynamics,proving that the widely used row-sum method is a special case of the manifold-based framework.The scheme resolves long-standing limitations in rotational/torsional inertia conservation and provides a foundation for extending rigorous mass lumping to 3D shell and nonlinear dynamic analyses.
基金supported by the National Natural Science Foundation of China(82372176,82272217,82002026,81971818)the Hubei Provincial Key Research and Development Program of China(2023BCB091)the National Key Research and Development Program of China(2021YFC2500802,2021YFC2300200).
文摘Sepsis,characterized as life-threatening organ dysfunction resulting from dysregulated host responses to infection,remains a significant challenge in clinical practice.Despite advancements in understanding host-bacterial interactions,molecular responses,and therapeutic approaches,the mortality rate associated with sepsis has consistently ranged between 10%and 16%.This elevated mortality highlights critical gaps in our comprehension of sepsis etiology.Traditionally linked to bacterial and fungal pathogens,recent outbreaks of acute viral infections,including Middle East respiratory syndrome coronavirus(MERS-CoV),influenza virus,and severe acute respiratory syndrome coronavirus 2(SARS-CoV-2),among other regional epidemics,have underscored the role of viral pathogenesis in sepsis,particularly when critically ill patients exhibit classic symptoms indicative of sepsis.However,many cases of viral-induced sepsis are frequently underdiagnosed because standard evaluations typically exclude viral panels.Moreover,these viruses not only activate conventional pattern recognition receptors(PRRs)and retinoic acid-inducible gene-I(RIG-I)-like receptors(RLRs)but also initiate primary antiviral pathways such as cyclic guanosine monophosphate adenosine monophosphate(GMP-AMP)synthase(cGAS)-stimulator of interferon genes(STING)signaling and interferon response mechanisms.Such activations lead to cellular stress,metabolic disturbances,and extensive cell damage that exacerbate tissue injury while leading to a spectrum of clinical manifestations.This complexity poses substantial challenges for the clinical management of affected cases.In this review,we elucidate the definition and diagnosis criteria for viral sepsis while synthesizing current knowledge regarding its etiology,epidemiology,and pathophysiology,molecular mechanisms involved therein as well as their impact on immune-mediated organ damage.Additionally,we discuss clinical considerations related to both existing therapies and advanced treatment interventions,aiming to enhance the comprehensive understanding surrounding viral sepsis.
文摘The time went by fairly fast.I have definitely changed a lot in the past three years.I used to be short,but now I am taller.The biggest change,though,is that I enjoy reading more than I used to.During my first vacation in junior high school,my teacher asked us to read more classics,so I read a variety of books like The Little Prince and Harry Potter,which taught me to be brave in the face of difficulties and never give up.After that,no matter how busy I was,I would read for an hour every day.
文摘BACKGROUND Sepsis is a critical medical condition,and poses a substantial global health burden,with significant morbidity,mortality,and economic costs,particularly pronounced in low-and middle-income countries.Effective management of sepsis relies on early recognition and appropriate intervention,underscoring the importance of accurate classification to guide treatment decisions.The correct diagnosis will lead to effective antimicrobial stewardship practices.AIM To assess the distribution of sepsis categories and the use of empirical antibiotics classified by the World Health Organization(WHO)Access,Watch,and Reserve(AWaRe)system in a tertiary care hospital in Northern India and to correlate antibiotic usage with sepsis classifications.METHODS This longitudinal observational study in the Department of General Medicine,in a tertiary care hospital in Northern India,from 2023 to 2024,aimed to assess the use of empirical antibiotics classified by the WHO AWaRe system.The study also aimed to correlate antibiotic usage.Patients were categorized into sepsis classes(Asepsis,Possible Sepsis,Probable Sepsis,Confirmed Sepsis)and followed until discharge or Day-28.Descriptive and inferential statistical analyses were employed to assess sepsis categories and empirical antibiotic usage classified by the WHO AWaRe system.RESULTS A total of 1867 patients admitted with suspected sepsis were screened,with 230 meeting the inclusion criteria.Among the study cohort(mean age 40.70±14.49 years,50.9% female),initial sepsis classification predominantly included probable sepsis(51.3%)and possible sepsis(35.7%),evolving to asepsis(57.8%)upon final classification,but all received antibiotics.Empirical antibiotic use showed a predominance of Watch group antibiotics(72.2%),with ceftriaxone and piperacillin-tazobactam being the most commonly prescribed;however,no statistical association could be established among the different classes of sepsis with the AWaRe groups.CONCLUSION Accurate sepsis classification is pivotal for clinical decision-making,optimizing antibiotic use,and combating antimicrobial resistance.The majority of the asepsis category was labelled as probable or possible sepsis and given antibiotics at initial hospitalization.The high reliance on Watch group antibiotics in empirical therapy signals a need for enhanced diagnostic strategies to refine treatment initiation,potentially reducing unnecessary antibiotic exposure.Future efforts should focus on establishing sepsis classification checklists as in this study and promoting adherence to antimicrobial stewardship principles to mitigate the global threat of antimicrobial resistance.
文摘BACKGROUND Fever of unknown origin(FUO)remains a diagnostic challenge and was originally defined in 1961.Its classic criteria include fever≥38.3°C(≥101°F)on multiple occasions,fever lasting three weeks or longer,and a diagnosis after one week of inpatient evaluation.However,these criteria may not fully encompass the varied clinical presentations seen in resource-limited settings such as India.The adaptation of FUO definitions to local healthcare contexts is crucial for enhancing diagnostic accuracy and optimizing patient outcomes.AIM To investigate the applicability of revised FUO criteria in a tertiary care setting in India.METHODS This longitudinal-exploratory study at All India Institute of Medical Sciences Rishikesh(January 2018–December 2022)analyzed 228 adult patients with fever≥99.1°F lasting over three days.Patients diagnosed within three days of admission were excluded.Data were collected retrospectively and prospectively using predefined FUO definitions based on durations of nondiagnosis(3-21 days,>21 days),temperature ranges(99.1°F-100.9°F,≥101°F),and hospitalization durations(3-7 days,>7 days).Descriptive statistics and comparative tests(Fisher's exact test,χ2 test)evaluated outcomes across definitions.RESULTS Among the proposed FUO definitions,Definition B(fever lasting 3-21 days,temperatures between 99.1°F-100.9°F,hospitalization>7 days)predominated(40.8%),while only 2.2%met the classical criteria.Notably,36.5%of Definition B patients remained undiagnosed after 7-10 days,despite 94%undergoing diagnostic workups within 21 days.Infection emerged as the leading etiology across definitions,without significant variation in outcomes or mortality during hospitalization(χ2=27.937,P=0.142).CONCLUSION Adapting FUO criteria to local contexts improves diagnostic accuracy and treatment.Definition B(40.8%prevalence)showed practical utility,with higher mortality in patients discharged on empirical'Anti-tuberculosis therapy'.
基金supported by the National Natural Science Foundation of China(Grant No.42471027).
文摘Accurate drought assessment demands thoughtful consideration of drought definition first of all.Drought is commonly defined as a prolonged period of below-average precipitation leading to water shortages that impact ecosystems,agriculture,and human societies.However,meteorologists,hydrologists,and agronomists often use different criteria to define drought,depending on their specific focus areas.For example,hydrologists define drought according to water deficits in some components of the hydrological cycle(such as precipitation,soil moisture,river flow,and groundwater)or its impacts on the level of services provided to public water supply,irrigation,or hydropower demands(Tate and Gustard,2000).Differences in drought definitions may result in great uncertainties in drought assessment(Satoh et al.,2021).We cannot expect the existence of any workable generalized objective definition of drought(Lloyd-Hughes,2014).
文摘In this paper,a nonlinear control approach for an unstable networked plant in the presence of actuator and sensor limitations using robust right coprime factorization is proposed.The actuator is limited by upper and lower constraints and the sensor in the feedback loop is subjected to network-induced unknown time-varying delay and noise.With this nonlinear control method,we first employ right coprime factorization based on isomorphism and operator theory to factorize the plant,so that bounded input bounded output(BIBO)stability can be guaranteed.Next,continuous-time generalized predictive control(CGPC)is utilized for the unstable operator of the right coprime factorized plant to guarantee inner stability and enables the closed-loop dynamics of the system with predictive characteristics.Meanwhile,a second-Do F(degrees of freedom)switched controller that satisfies a perturbed Bezout identity and a robustness condition is designed.By using the CGPC controller that possesses predictive behavior and the second-Do F switched stabilizer,the overall stability of the plant subjected to actuator limitations is guaranteed.To address sensor limitations that exist in networked plants in the form of delay and noise which often cause system performance degradation,we implement an identity operator definition in the feedback loop to compensate for these adverse effects.Further,a pre-operator is designed to ensure that the plant output tracks the reference input.Finally,the effectiveness of the proposed design scheme is demonstrated by simulations.
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
文摘Let F be the strong p-division ring [4]. This paper is sequel to [1]. Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented. Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.
基金The National Natural Science Foundation of China(No.11371089)the China Postdoctoral Science Foundation(No.2016M601688)
文摘The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.
基金Supported by the National Natural Science Foundation of China (Grant No.11071079)the Natural Science Foundation of Zhejiang Province (Grant No.Y6110043)
文摘In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.
