Study on High Frequency Surface Discharge Characteristics of SiO2 Modified Polyimide Film

Polyimide (PI) can be used as a cladding insulation for high frequency power transformers, and along-side discharge can lead to insulation failure, so material modification techniques are used. In this paper, different doped nano-SiO2 are introduced into polyimide for nanocomposite modification. The results of testing the life time of high-frequency electrical stress along-side discharge show that the 10% SiO2 doping has the longest life time. The results show that: for composites prone to corona, their flashover causes more damage, and both positive half-cycle and polarity reversal discharges are more violent; compared to pure PI, the positive half-cycle and overall discharge amplitude and number of modified films are smaller, but the negative half-cycle is larger; at creeping development stages, the number of discharges is smaller, and the discharge amplitude of both films fluctuates in the mid-term, with the modified films having fewer discharges and the PI films discharging more violently in the later stages. The increase in the intensity of the discharge was greater in the later stages, and the amplitude and number of discharges were much higher than those of the modified film, which led to a rapid breakdown of the pure polyimide film. Further research found that resistivity plays an important role in the structural properties of the material in the middle and late stages, light energy absorption in the modified film plays an important role, the distribution of traps also affects the discharge process, and in the late stages of the discharge, the heating of the material itself has a greater impact on the breakdown, so the pure polyimide film as a whole discharges more severely and has the shortest life.

Existence of positive solutions for a class of BVPs in Banach spaces

In this work, we use index xed point theory for perturbation of expan- sive mappings by l-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear di erential equation on the positive half-line. The nonlin- earity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave di erently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given.

Nonuniform biorthogonal wavelets on positive half line via Walsh Fourier transform

In this article, we introduce the notion of nonuniform biorthogonal wavelets on positive half line. We first establish the characterizations for the translates of a single function to form the Riesz bases for their closed linear span. We provide the complete characterization for the biorthogonality of the translates of scaling functions of two nonuniform multiresolution analysis and the associated biorthogonal wavelet families in $$L^2({\mathbb {R}}^+)$$ L 2 ( R + ) . Furthermore, under the mild assumptions on the scaling functions and the corresponding wavelets associated with nonuniform multiresolution analysis, we show that the wavelets can generate Reisz bases.

On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs

The aim of this work is two fold: first we extend some results concerning the computation of the fixed point index for the sum of an expansive mapping and a $k$-set contraction obtained in \cite{DjebaMeb, Svet-Meb}, to the case of the sum $T+F$, where $T$ is a mapping such that $(I-T)$ is Lipschitz invertible and $F$ is a $k$-set contraction. Secondly, as illustration of some our theoretical results, we study the existence of positive solutions for two classes of differential equations, covering a class of first-order ordinary differential equations (ODEs for short) posed on the positive half-line as well as a class of partial differential equations (PDEs for short).

Frames associated with shift invariant spaces on positive half line

In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.

Solvability for nonlocal boundary value problems with generalized 𝑝-Laplacian on an unbounded domain

This paper is devoted to the existence of solutions for a class of nonlinear boundary value problems with integral boundary conditions and generalized 𝑝-Laplacian on the positive half-line. We establish sufficient conditions to guarantee the existence of solutions in a special function space by using Leray–Schauder-type arguments. Examples are also given to illustrate the main results.

26 COVID-19 Diagnosis in Patients with Acute Abdominal Pain Without Respiratory Symptoms: A UK Emergency General Surgical Unit Experience

Introduction Evidence has emerged reporting atypical symptoms of the coronavirus (COVID-19). There is a sparsity of existing studies examining COVID-19 related abdominal pain and the role of investigative imaging for the virus in these patients. Study aims were to determine COVID-19 incidence in those with acute abdominal pain in the absence of respiratory symptoms and to assess the performance of Computer Tomography (CT) thoracic imaging. Method Retrospective analysis of all patients admitted to our emergency general surgical unit between 1st March 2020 and 31st May 2020 was performed. All patients underwent nasal and oro-pharyngeal COVID-19 RT-PCR swabs as well as CT on admission. Results From 112 patients admitted with acute abdominal pain in the absence of respiratory symptoms, 16 (14.3%) tested positive for COVID-19 on RT-PCR swab testing. 50% (8/16) of these patients had no intra-abdominal pathology on CT. The sensitivity and specificity of CT thoracic imaging for COVID-19 was 43.8% and 91.7%. Conclusions One in seven patients with abdominal pain without any respiratory symptoms tested positive. Half these patients represented COVID-19 manifesting primarily as acute abdominal pain. Combined swab testing and CT imaging should be performed in all abdominal pain presentations due to the varying diagnostic performance of thoracic CT in diagnosing COVID-19.