Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems

This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.

Admissibility of Bayes estimate with inaccurate prior in surveying adjustment

Based on the concept of admissibility in statistics, a definition of generalized admissibility of Bayes estimates has been given at first, which was with inaccurate prior for the application in surveying adjustment. Then according to the definition, the generalized admissibility of the normal linear Bayes estimate with the inaccurate prior information that contains deviations or model errors, as well as how to eliminate the effect of the model error on the Bayes estimate in surveying adjustment were studied. The results show that if the prior information is not accurate, that is, it contains model error, the generalized admissibility can explain whether the Bayes estimate can be accepted or not. For the case of linear normal Bayes estimate, the Bayes estimate can be made generally admissible by giving a less prior weight if the prior information is inaccurate. Finally an example was given.

ADMISSIBILITY OF LINEAR ESTIMATORS IN A GROWTH CURVE MODEL SUBJECT TO AN INCOMPLETE ELLIPSOIDAL RESTRICTION

This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for linear estimators to be admissible in classes of the homogeneous and non-homogeneous linear estimators, respectively, are obtained under the quadratic loss function. They are generalizations of some existing results in literature.

ADMISSIBILITY IN THE GENERAL GROWTH CURVE MODEL WITH RESPECT TO RESTRICTED PARAMETER SETS UNDER MATRIX LOSS FUNCTION

In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear estimators of KBL are admissible in the class of homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to restricted parameter sets, respectively.

Admissibility Conditions for Symbolic Sequences in Dynamics of Digital Filter with Two's Complement Arithmetic

In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.

A necessary and sufficient condition for generalized admissibility of Bayes estimate

A definition of generalized admissibility of Bayes estimates has been given. This generalized admissibility is a rule to identify whether Bayes estimates is acceptable or not under the condition of incorrect prior information. In this paper, a sufficient and necessary condition for the generalized admissibility is derived under quadratic loss. From this we can conclude that, when deviation of prior mean and deviation of prior variance do not go beyond the bound, the Bayes estimation is acceptable and it is discussed that how the deviation of the prior information influences on generalized admissibility. Because the precise distribution of prior information is unknown, the example gives a way to select the prior distribution. The example shows that this method is efficient and feasible.

General Optimality and General Admissibility of Linear Estimates on the Mean Matrix

In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function Sk×p （S’ μ（X’）） of the mean matrix in multivariate linear model: Yn×m=Xn×p +ε E（ε）=0, Cov（ ）=σ2Un×n Vm×m, n≥m. In general, the general optimality of a parametric matrix follows analogously. The above X, S, U≥0 and V≥0 （but V≠0） are known matrix, and σ2】0 are unknown parameters, =（ε1’, ε2’, …, εn’）’, where εi is the ith row of ε, U V denotes the

NS Condition of Admissibility for the Linear Estimator of Normal Mean with Unknown Variance

Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given.

A New Admissibility Condition of Discrete-time Singular Systems with Time-varying Delays

This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS UNDER QUADRATIC LOSS

For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators under the loss function (d -- Sr)'D(d --Sr), whereD≥0 is known. For the general random effects linear model: Y = Xβ+ε,(βε)～N((Aα 0), (V_(11)V_(12)V_(21)V_(22))), ∧= XV_(11)X'+XV_(12)+ V_(21)X+V_(22)≥0, we also get the necessaryand sufficient conditions for LY+a to be admissible for a linear estimable function Sα+Qβin the class of all estimators under the loss function (d-Sα-Qβ)'D(d-Sα-Qβ).whereD≥0 is known.

Fever assessment in children under five: Are we following the guidelines?

BACKGROUND Fever is a common cause of medical consultation and hospital admission,particularly among children.Recently,the United Kingdom’s National Institute for Health and Care Excellence(NICE)updated its guidelines for assessing fever in children under five years of age.The efficient assessment and management of children with fever are crucial for improving patient outcomes.AIM To evaluate fever assessment in hospitalized children and to assess its adherence with the NICE Fever in under 5s guideline.METHODS We conducted a retrospective cohort review of the electronic medical records of children under five years of age at the Department of Pediatrics,Salmaniya Medical Complex,Bahrain,between June and July 2023.Demographic data,vital signs during the first 48 h of admission,route of temperature measurement,and indications for admission were gathered.Fever was defined according to the NICE guideline.The children were divided into five groups according to their age(0-3 months,>3-6 months,>6-12 months,>12-36 months,and>36-60 months).Patients with and without fever were compared in terms of demography,indication for admission,route of temperature measurement,and other vital signs.Compliance with the NICE Fever in the under 5s guideline was assessed.Full compliance was defined as>95%,partial compliance as 70%-95%,and minimal compliance as≤69%.Pearson’sχ^(2),Student’s t test,the Mann-Whitney U test,and Spearman’s correlation coefficient(rs)were used for comparison.RESULTS Of the 136 patients reviewed,80(58.8%)were boys.The median age at admission was 14.2[interquartile range(IQR):1.7-44.4]months,with the most common age group being 36-60 months.Thirty-six(26.4%)patients had fever,and 100(73.6%)were afebrile.The commonest age group for febrile patients(>12-36 months)was older than the commonest age group for afebrile patients(0-3 months)(P=0.027).The median weight was 8.3(IQR:4.0-13.3)kg.Patients with fever had higher weight than those without fever[10.2(IQR:7.3-13.0)vs 7.1(IQR:3.8-13.3)kg,respectively](P=0.034).Gastrointestinal disease was the leading indication for hospital admission(n=47,34.6%).Patients with central nervous system diseases and fever of unknown etiology were more likely to be febrile(P=0.030 and P=0.011,respectively).The mean heart rate was higher in the febrile group than the afebrile group(140±24 vs 126±20 beats per minute,respectively)[P=0.001(confidence interval:5.8-21.9)]with a positive correlation between body temperature and heart rate,r=0.242,n=136,P=0.004.A higher proportion of febrile patients received paracetamol(n=35,81.3%)compared to the afebrile patients(n=8,18.6%)(P<0.001).The axillary route was the most commonly used for temperature measurements(n=40/42,95.2%),followed by the rectal route(n=2/42,4.8%).The department demonstrated full compliance with the NICE guideline for five criteria:the type of thermometer used,route and frequency of temperature measurement,frequency of heart rate measurement,and use of antipyretics as needed.Partial compliance was noted for two criteria,the threshold of fever at 38°C or more,and the respiratory rate assessment in febrile patients.Minimal compliance or no record was observed for the remaining three criteria;routine assessment of capillary refill,temperature reassessment 1-2 h after each antipyretic intake,and refraining from the use of tepid sponging.CONCLUSION This study showed that fever assessment in hospitalized children under five years of age was appropriate,but certain areas of adherence to the NICE guideline still need to be improved.

General Admissibility for Linear Estimators in a General Multivariate Linear Model under Balanced Loss Function

A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.

Entropy Production and Admissibility of Shocks

Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.

Admissibility of Linear Estimators with Respect to Inequality Constraints Under Some Loss Functions

In this paper, we study the issue of admissibility of linear estimated functions of parameters in the multivariate linear model with respect to inequality constraints under a matrix loss and a matrix balanced loss. Under the matrix loss, when the model is not constrained, the results in the class of non-homogeneous linear estimators [Xie, 1989, Chinese Sci. Bull., 1148-1149; Xie, 1993, J. Multivariate Anal., 1071-1074] showed that the admissibility under the matrix loss and the trace loss is equivalent. However, when the model is constrained by the inequality constraints, we find this equivalency is not tenable, our result shows that the admissibility of linear estimator does not depend on the constraints again under this matrix loss, but it is contrary under the trace loss [Wu, 2008, Linear Algebra Appl., 2040-2048], and it is also relative to the constraints under another matrix loss [He, 2009, Linear Algebra Appl., 241-250]. Under the matrix balanced loss, the necessary and sufficient conditions that the linear estimators are admissible in the class of homogeneous and non-homogeneous linear estimators are obtained, respectively. These results will support the theory of admissibility on the linear model with inequality constraints.

拟双曲度量空间中广义反演函数的性质

基于一般度量空间中flattening函数和admission反演函数的概念,在拟双曲度量空间中引入拟对偶的概念,并借助于拟双曲度量作为工具,结合flattening函数和admission反演函数的性质来刻画了拟双曲度量空间中广义反演函数的几何特征。

Journey of DNA Evidence in Legal Arena:An Insight on Its Legal Perspective Worldwide and Highlight on Admissibility in India

DNA profiling is one of the powerful breakthroughs in forensics.This specialized technique has made the identification of an individual possible even by a tiny shred of tissue or drop of blood thus,has strongly revolutionized various criminal investigations.Rape,paternity,and murder cases are the type of criminal cases commonly solved by the use of this technique.It has been recently introduced to forensic odontology and is also used frequently.Although this is a powerful and reliable scientific technique but its forensic use is a major contribution to the debate on law reform.The application of DNA profiling in the criminal justice system,i.e.,the admissibility of DNA evidence in court of law is an important issue which is being faced by the courts and forensic experts worldwide today.Thus,a proper legal outlook is required while dealing with this kind of scientific evidence.Therefore,this review intends to make forensic experts/odontologists aware about the admissibility of DNA evidence in court,with a highlight on the laws related to the admissibility of evidence worldwide,having a special focus on the laws related to admissibility of evidence in Indian judicial system.For this review,the literature was overviewed from articles on DNA evidence and admissibility retrieved by searches on electronic databases such as Google,PubMed,and EMBASE from 1975 through July 2015.

THE ADMISSIBILITY OF PRE-TRIAL TESTIMONIAL TRANSCRIPTS： A DISCUSSION OF PRACTICE IN CHINA AND IN THE INTERNATIONAL CRIMINAL TRIBUNALS

In Chinese criminal procedure, the issues of illegally obtained evidence and witnesses not appearing in courtroom are under fire, which is partly rooted in the fact that the Chinese courts do not limit the admissibility ofpre-trial testimonial transcripts in judicial practice, zealously pursue the ＂truth of fact＂ while disregard defendant＇s right to confront. Focusing on the admissibility ofpre-trial testimonial transcripts, the article will first analyze the current legislations and judicial practice in China, then from a comparative perspective introduce the corresponding written testimony rules of the International Criminal Tribunal （Court） which distinguishes the admissibility of different categories of written testimony, with an aim of both protecting the criminal defendant＇s right of confrontation and pursuing truth in fact-finding. The practice in International Criminal Tribunal （Court） provides a good starting point for China to rethink its own practice and learn from.

ADMISSIBILITY OF LINEAR ESTIMATES OF REGRESSION COEFFICIENT UNDER MATRIX LOSS FUNCTION

We consider the linear model (1) where V>0 and X are known, n≥p; β∈R^p, and 0<σ~2<∞ are unknown. Consider the problem of estimating Sβ which is linear estimable. Prof. C. R. Rao has given the necessary and sufficient condition that LY is admissible for Sβ within

ADMISSIBILITY FOR LINEAR ESTIMATES ON MULTIVARIATE REGRESSION COEFFICIENTS

Consider the multivariate linear