Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions

Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.

All Admissible Linear Estimators under Quadratic Loss in Multivariate Model

For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimators of SXΘ are given under each of four definitions of admissibility.

Fixed point theorems for better admissible multimaps on Abstract convex spaces

In this paper, a better admissible class B＋ is introduced and a new fixed point theorem for better admissible multimap is proved on abstract convex spaces. As a consequence, we deduce a new fixed point theorem on abstract convex Ф-spaces. Our main results generalize some recent work due to Lassonde, Kakutani, Browder, and Park

L^p INEQUALITIES AND ADMISSIBLE OPERATOR FOR POLYNOMIALS

Let p（z） be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P（Z）[ls for every α, β∈ C with ｜a｜≤ 1, ｜β｜〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.

Admissible Periodic Bouncing Solutions for A Class of Semi-linear and Non-conservative Impact Oscillators

In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.

ADMISSIBLE WAVELETS ON THE PRODUCT HEISENBERG GROUP H_n

Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμl).

ALL ADMISSIBLE LINEAR ESTIMATORS UNDER MATRIX LOSS IN MULTIVARIATE MODEL

Under maids loss, tall paper dicusses the admissibility of homgeneous or nonhomgeneous linear estimators of regresaion coefficient of multivarate linear model in some common classes of estimators, the necessary and sufficient conditions are obtained.The results indicate that the admissibility of linear estimetors in multiate linear model is different from the admiedbility of linear estimators in Gauss-Markoff model.

Robust Admissible Analyse of Uncertain Singular Systems via Delta Operator Method

This paper investigates the problem of robust admissible analysis for uncertain singular delta operator systems(SDOSs).Firstly,we introduce the definition of generalized quadratic admissibility to ensure robust admissibility.Then,by means of LMI,a necessary and sufficient condition is given to prove a uncertain SDOS is generalized quadratic admissible.Finally,a numerical example is provided to demonstrate the effectiveness of the results in this paper.

Ultralight,ductile metal mechanical metamaterials with super elastic admissible strain(0.1)

Mechanical metamaterials are architectured cellular materials with unusual properties.Herein we report another type of metal mechanical metamaterials-their elastic admissible strain(EAS)is on the order of 0.1,compared to about 0.01 for common metallic materials.Four conditions are required for a metal mechanical metamaterial to achieve this super EAS:(i)bending-dominated deformation;(ii)low density;(iii)an appropriate lattice topology,and(iv)an intrinsically high EAS for the lattice strut constituent material.The findings of this work extend perspectives on metal mechanical metamaterials.

Superelastic metastable Ti-Mo-Sn alloys with high elastic admissible strain for potential bio-implant applications

The demand for titanium alloys simultaneously having high elastic admissible strain and large recovery strain for bio-implant applications is increasing.Ni-free Ti-based shape memory alloys are promising candidates for obtaining the required multifunctional properties.In this study,a wide content range of(0-15)wt%of low-cost,toxicity-free,and high-biocompatible Sn element was added to the Ti-8Mo(wt%)alloy to study its effect on the superelastic recovery and mechanical properties of biomedical Ti-Mo-Sn alloys.By tailoring Sn content,desired multifunctional properties of high elastic admissible strain and room temperature superelasticity were achieved in the studied Ti-Mo-Sn alloys.It was found that the increase in Sn content stabilized theβphase and a singleβphase was obtained at room temperature in Ti-8Mo-(13,15)Sn alloys.The addition of Sn modified the lattice parameters of theα″martensite andβphase and affected the lattice deformation stain ofβ→α″.The lattice deformation strain along the[011]βdirection was found to be decreased by-0.26%/wt%Sn.The room temperature superelasticity with a recovery strain of 3.1%and an elastic admissible strain of 1%was obtained in the Ti-8Mo-13Sn alloy.As Sn content increased to 15 wt%,a high elastic admissible strain of 1.56%and a recovery strain of 2.0%were obtained.These Ti-Mo-Sn alloys with excellent multifunctional properties are promising candidates for bio-implant applications.

Uniqueness of admissible meromorphic functions in the unit disc

The uniqueness of admissible meromorphic functions in the unit disc is

Singular formalism and admissible control of spacecraft with rotating flexible solar array

This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identi- ties about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a space- craft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov＇s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.

Stabilization of switched linear systems under asynchronous switching subject to admissible edge-dependent average dwell time

The problem of stabilizing switched linear systems under asynchronous switching is addressed.The admissible edge-dependent average dwell time method is applied to design a switching signal that comprises slow admissible edge-dependent average dwell time and fast admissible edge-dependent average dwell time.Under this switching signal,the restriction that the maximum delay of asynchronous switching is known in advance is removed.The constructed Lyapunov function is associated with both the system mode and controller mode.The stabilization criteria and the corresponding algorithm are presented to obtain the controller gains and to design the switching signal.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Weakly Admissible Meshes and Discrete Extremal Sets

We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points.These provide new computational tools for polynomial least squares and interpolationon multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.

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.

Maximal admissible mode decision delay in terminal guidance

Mode decision-maker is a critical component in the logic-based Integrated Estimation and Guidance(IEG) system. For the best possible estimation and guidance performance, the mode decision delay of the mode decision-maker should be limited to a range as small as possible. This paper presents a numerical method for computing the maximal admissible mode decision delay that varies with time-to-go. Particular attention has been paid to highly maneuvering target interception in terminal guidance. The results of this research offer useful guidelines for the design of the mode decision-maker in IEG systems.

A Tree-valued Markov Process Associated with an Admissible Family of Branching Mechanisms

Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].

A class of admissible estimators of multiple regression coefficient with an unknown variance

Suppose that we observe y|θ,τ∼N_(p)(Xθ,τ^(−1)I_(p)),where θ is an unknown vector with unknown precisionτ.Estimating the regression coefficient θ with known τ has been well studied.However,statistical properties such as admissibility in estimating θ with unknownτare not well studied.Han[(2009).Topics in shrinkage estimation and in causal inference(PhD thesis).Warton School,University of Pennsylvania]appears to be the first to consider the problem,developing sufficient conditions for the admissibility of estimating means of multivariate normal distributions with unknown variance.We generalise the sufficient conditions for admissibility and apply these results to the normal linear regression model.2-level and 3-level hierarchical models with unknown precisionτare investigated when a standard class of hierarchical priors leads to admissible estimators of θ under the normalised squared error loss.One reason to consider this problem is the importance of admissibility in the hierarchical prior selection,and we expect that our study could be helpful in providing some reference for choosing hierarchical priors.

A Study on Social Choice Making:the Number of Admissible Preference Orderings for SMV

In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.