FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.

An Efficient Method to Estimate Admittance of Black-boxed Inverter-based Resources for Varying Operating Points

Traditional analytical approaches for stability assessment of inverter-based resources(IBRs),often requiring detailed knowledge of IBR internals,become impractical due to IBRs’proprietary nature.Admittance measurements,relying on electromagnetic transient simulation or laboratory settings,are not only time-intensive but also operationally inflexible,since various non-linear control loops make IBRs’admittance models operating-point dependent.Therefore,such admittance measurements must be performed repeatedly when operating point changes.To avoid time-consuming and cumbersome measurements,admittance estimation for arbitrary operating points is highly desirable.However,existing admittance estimation algorithms usually face challenges in versatility,data demands,and accuracy.Addressing this challenge,this letter presents a simple and efficient admittance estimation method for blackboxed IBRs,by utilizing a minimal set of seven operating points to solve a homogeneous linear equation system.Case studies demonstrate this proposed method ensures high accuracy across various types of IBRs.Estimation accuracy is satisfying even when non-negligible measurement errors exist.

INFINITELY MANY SOLUTIONS OF DIRICHLET PROBLEM FOR p-MEAN CURVATURE OPERATOR

The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in R n(n>p>1) with smooth boundary Ω.Under some natural conditions together with some conditions weaker than (AR) condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)|u| p-2u→+∞ as u→∞.

Single SH guided wave mode generation method for PPM EMATs

Using periodic permanent magnet(PPM)electromagnetic acoustic transducers(EMATs),different shear horizontal(SH)guided wave modes can form simultaneously in some situations,which can interfere with the inspection.The main cause of this phenomenon(typically named multiple modes)is related to the frequency bandwidth of excitation signals and the transducer spatial bandwidth.Simply narrowing the frequency bandwidth cannot effectively limit the number of different SH modes.Previous researches showed that unnecessary SH wave modes can be eliminated by using dual EMATs.However,in practical applications,it is more convenient to change the excitation frequency than to use dual EMATs.In this paper,the stress boundary conditions of the PPM-EMAT are analyzed,the analytical expression of SH guided wave is established,and the magnitude of SH guided wave mode under continuous tone and tone-burst input is obtained.A method to generate a single SH mode by re-selecting an operating point is proposed.Furthermore,the influence of the frequency bandwidth of the tone-burst signal is analyzed.Finally,a single SH mode excitation is achieved with tone-burst input.

Dynamic Analysis for the Global Performance of An SPM-Feeder-Cage System Under Waves and Currents

In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodynamics coefficients of the vessel are calculated by using a 3D diffraction/radiation panel program. First- and second-order wave forces are included in the calculations. Morison equation is used to compute the drag force on line elements representing the net. Drag coefficients are determined at every time step in the simulation considering the relative normal velocity between the structural elements and the fluid flow. The dynamic response of the coupled system is analyzed for various environments and net materials. The results of the study show the effects of solidity ratio of the net and vertical positions of the cage on the overall dynamic response of the system, confirming the viability of this type of configuration for future development of offshore aquaculture in deep waters.

Simulation of detection and scattering of sound waves by the lateral line of a fish

A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressures on lateral lines on different fish flanks,as well as the cross section of sound scattering on both the lines,strongly depends on angles of incidence of incoming sound waves.The strong angular dependence of the pressure ratio seems to be sufficient for the fish to determine the directions from which the sound is coming.

PROPERTIES OF p-ω-HYPONORMAL OPERATORS

The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.

On Fatou Type Convergence of Convolution Type Double Singular Integral Operators

In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].

A Variational Principle and Best Proximity Points

We generalize Ekeland＇s Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different classes of cyclic maps.

3-D CFD simulation of transients in multiple pump system with some pumps being stopped

The computational fluid dynamics(CFD)approach can be used to obtain both internal and external characteristics of centrifugal pumps,and the variations of the hydrodynamic force,the pressure and the torque on the blades acquired by the CFD are highly associated with the safety of the pumping system.Based on the CFD simulations,this paper investigates the stopping characteristics of multiple pumps with some pumps being stopped.The 3-D geometric model is built,including all 6 pumps,the valves,the pipes,the tanks and other components,and using the Realizable k-ε turbulence model.The CFD results for the operating points agree well with the results from the theoretical analysis.With some pumps being stopped,the key parameters of the operating pumps would not be stable,with a larger fluctuation;the direction of the hydrodynamic force might be opposite with more than 3 stopped pumps.For the stopped pumps,the maximum reverse values of the discharge and the rotational speed would be larger when fewer pumps are stopped,and could be more than 120%of the rated values,which is dangerous for the pumping system.The CFD results could help understanding the stopping process of multiple pump systems with some pumps being stopped.

Mechanism analysis and evaluation of thermal effects on the operating point drift of servo valves

Operating point drift over large temperature spans can significantly degrade the performance of servo valves.The direction and magnitude of the deviation of the operating point are uncertain.To analyze and evaluate the mechanism of this complex system with a multi-level structure and multi-variables,it is necessary to construct a theoretical model with a clear physical concept to describe it.However,since the physical processes contain complex variations of structural parameters and flow properties,there is a problem of simplifying approximations in deriving analytical mathematical relations.The advantages of multi-physics field numerical analysis can compensate for this shortcoming of analytical formulations.Based on this,we constructed a whole-valve transfer function model to realize the mechanism analysis and evaluate the operating point drift when a thermal effect acts on a servo valve.The results show that the asymmetric fit relationship between the armature-nozzle assemblies is an important reason for the drift of the operating point caused by the thermal effect.Differences in structural parameters and fluid medium characteristics at different temperatures lead to nonlinear changes in the operating point.When the deviation angle reaches±1°,an increase in temperature will cause the absolute value of the tangent slope of the displacement deviation of the spool to decrease from 1.44×10^(−5) m/℃to 1.25×10^(−6) m/℃.The influence of the deviation angle is reflected in the change in the absolute value of the tangent slope of the pressure deviation from 1.14×10^(3) Pa/℃to 110 Pa/℃.

An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration

In this paper,we propose a fast proximity point algorithm and apply it to total variation(TV)based image restoration.The novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation(TV)based image restoration have been proposed.Many current algorithms for TV-based image restoration,such as Chambolle’s projection algorithm,the split Bregman algorithm,the Berm´udez-Moreno algorithm,the Jia-Zhao denoising algorithm,and the fixed point algorithm,can be viewed as special cases of the new first-order schemes.Moreover,the convergence of the new algorithm has been analyzed at length.Finally,we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at present.Numerical experiments illustrate the efficiency of the proposed algorithms.

Schedule refinement for homogeneous multi-core processors in the presence of manufacturing-caused heterogeneity

Multi-core homogeneous processors have been widely used to deal with computation-intensive embedded applications. However, with the continuous down scaling of CMOS technology, within-die variations in the manufacturing process lead to a significant spread in the operating speeds of cores within homogeneous multi-core processors. Task scheduling approaches, which do not consider such heterogeneity caused by within-die variations,can lead to an overly pessimistic result in terms of performance. To realize an optimal performance according to the actual maximum clock frequencies at which cores can run, we present a heterogeneity-aware schedule refining(HASR) scheme by fully exploiting the heterogeneities of homogeneous multi-core processors in embedded domains.We analyze and show how the actual maximum frequencies of cores are used to guide the scheduling. In the scheme,representative chip operating points are selected and the corresponding optimal schedules are generated as candidate schedules. During the booting of each chip, according to the actual maximum clock frequencies of cores, one of the candidate schedules is bound to the chip to maximize the performance. A set of applications are designed to evaluate the proposed scheme. Experimental results show that the proposed scheme can improve the performance by an average value of 22.2%, compared with the baseline schedule based on the worst case timing analysis. Compared with the conventional task scheduling approach based on the actual maximum clock frequencies, the proposed scheme also improves the performance by up to 12%.

Asymptotically Isometric Copy of l~β(0<β<1) in Spacesof Bounded Linear Operators

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.