This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue.
In this paper, we are devoted to consider the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of periodic mild solutions for the equations. In addition, with the aid of an integral inequality with impulsive and delay, we present essential conditions on the nonlinear and impulse functions to guarantee that the equations have an asymptotically stable ω-periodic mild solution.
The aim is to study the periodic solution problem for neutral evolution equa-in Banach space X, where A : D(A) ⊂ X → X is a closed linear operator, and −A generates a compact analytic operator semigroup T (t)(t ≥ 0). With the aid of the analytic operator semigroup theories and some fixed point theorems, we obtain the existence and uniqueness of periodic mild solution for neutral evolution equations. The regularity of periodic mild solution for evolution equation with delay is studied, and some the existence results of the classical and strong solutions are obtained. In the end, we give an example to illustrate the applicability of abstract results. Our works greatly improve and generalize the relevant results of existing literatures.
A Progressing Cavity Pump (PCP) works by forming a progressive seal cavity through the eccentric rotation of rotor. PCP parameters, such as eccentricity ratio [Formula: see text], can influence its performance and cavitation characteristics. The internal correlation among clearance fluid, cavitation characteristics, and pump performance should be explored to reveal the variation laws of internal flow and cavitation characteristics in PCP under different [Formula: see text]. In this study, a contrast analysis on external characteristics (e.g. volume efficiency) of pump with different eccentricity ratios was carried out by combining an RNG [Formula: see text] turbulence model based on Singhal full-cavitation model and the model pump test method. Moreover, gas volume distribution of PCP was analyzed and the optimal value range of eccentricity ratio was proposed. Results demonstrate that the axial force and axial power of PCP basically remain the same, volume efficiency increases, and cavitation performance decreases with the increase of [Formula: see text], and the optimal value for [Formula: see text] ranges from 0.17 to 0.24. In addition, a revised NPSHQ is proposed to quantify the cavitation characteristics of PCP.
In this paper, we deal with the existence and uniqueness of the solutions of two-point boundary value problem of fourth-order ordinary differential equation:The problem describes the static deformation of an elastic beam whose left end-point is fixed and right is freed, which is called slanted cantilever beam. Under some weaker assumptions, we establish a new maximum principle by the perturbation of positive operator and construct the monotone iterative sequence of the lower and upper solutions, and, based on this, we obtain the existence and uniqueness results for the slanted cantilever beam.
Our previous study indicated that multiprojection chest radiography could significantly improve radiologists' performance for lung nodule detection in clinical practice. In this study, the authors further verify that multiprojection chest radiography can greatly improve the performance of a computer-aided diagnostic (CAD) scheme. Methods: Our database consisted of 59 subjects, including 43 subjects with 45 nodules and 16 subjects without nodules. The 45 nodules included 7 real and 38 simulated ones. The authors developed a conventional CAD scheme and a new fusion CAD scheme to detect lung nodules. The conventional CAD scheme consisted of four steps for (1) identification of initial nodule candidates inside lungs, (2) nodule candidate segmentation based on dynamic programming, (3) extraction of 33 features from nodule candidates, and (4) false positive reduction using a piecewise linear classifier. The conventional CAD scheme processed each of the three projection images of a subject independently and discarded the correlation information between the three images. The fusion CAD scheme included the four steps in the conventional CAD scheme and two additional steps for (5) registration of all candidates in the three images of a subject, and (6) integration of correlation information between the registered candidates in the three images. The integration step retained all candidates detected at least twice in the three images of a subject and removed those detected only once in the three images as false positives. A leave-one-subject-out testing method was used for evaluation of the performance levels of the two CAD schemes. Results: At the sensitivities of 70%, 65%, and 60%, our conventional CAD scheme reported 14.7, 11.3, and 8.6 false positives per image, respectively, whereas our fusion CAD scheme reported 3.9, 1.9, and 1.2 false positives per image, and 5.5, 2.8, and 1.7 false positives per patient, respectively. The low performance of the conventional CAD scheme may be attributed to the high noise level in chest radiography, and the small size and low contrast of most nodules. Conclusions: This study indicated that the fusion of correlation information in multiprojection chest radiography can markedly improve the performance of CAD scheme for lung nodule detection. V
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