关于a|multiply from i=1 to n(cosa_i)|+b|multiply from i=1 to n(sina_i)|的最值

命题 设a_i∈R(1≤i≤n),n∈N,记则 (Ⅰ)当ab【0时,min(a,b)≤y≤max(a,b);

A Result on Multiply Perfect Number

Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if σ(n)=kn(k≥3) then n is said to be a multiply perfect number. In this paper according to Euler theorem and Fermat theorem, we discuss the result of σ(n)=ω(n)n and prove that only n=2 3·3·5, 2 5·3·7, 2 5·3 3·5·7 satisfies σ(n)= ω(n) n(ω(n)≥3). ...

Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Multiply Type-ⅡCensoring

In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.

Multiply accumulate operations in memristor crossbar arrays for analog computing

Memristors are now becoming a prominent candidate to serve as the building blocks of non-von Neumann inmemory computing architectures.By mapping analog numerical matrices into memristor crossbar arrays,efficient multiply accumulate operations can be performed in a massively parallel fashion using the physics mechanisms of Ohm’s law and Kirchhoff’s law.In this brief review,we present the recent progress in two niche applications:neural network accelerators and numerical computing units,mainly focusing on the advances in hardware demonstrations.The former one is regarded as soft computing since it can tolerant some degree of the device and array imperfections.The acceleration of multiple layer perceptrons,convolutional neural networks,generative adversarial networks,and long short-term memory neural networks are described.The latter one is hard computing because the solving of numerical problems requires high-precision devices.Several breakthroughs in memristive equation solvers with improved computation accuracies are highlighted.Besides,other nonvolatile devices with the capability of analog computing are also briefly introduced.Finally,we conclude the review with discussions on the challenges and opportunities for future research toward realizing memristive analog computing machines.

Intercalation of multiply solvated hexafluorophospate anion into graphite electrode from mixtures of methyl acetate,ethyl methyl and ethylene carbonates

Graphite is a universal host material for ion intercalation. Li+-graphite intercalation compounds (GICs) have been successfully utilized as the anode material in commercial lithium-ion batteries.Similarly, anion-graphite intercalation compounds (AGICs) have been coming into their own in dual-ion batteries [1]. It is imperative to deepen an understanding of anion storage mechanisms in graphite electrode.

Implementing Delay Multiply and Sum Beamformer on a Hybrid CPU-GPU Platform for Medical Ultrasound Imaging Using Open MP and CUDA

Anovel beamforming algorithmnamed Delay Multiply and Sum(DMAS),which excels at enhancing the resolution and contrast of ultrasonic image,has recently been proposed.However,there are nested loops in this algorithm,so the calculation complexity is higher compared to the Delay and Sum(DAS)beamformer which is widely used in industry.Thus,we proposed a simple vector-based method to lower its complexity.The key point is to transform the nested loops into several vector operations,which can be efficiently implemented on many parallel platforms,such as Graphics Processing Units(GPUs),and multi-core Central Processing Units(CPUs).Consequently,we considered to implement this algorithm on such a platform.In order to maximize the use of computing power,we use the GPUs andmulti-core CPUs inmixture.The platform used in our test is a low cost Personal Computer(PC),where a GPU and a multi-core CPU are installed.The results show that the hybrid use of a CPU and a GPU can get a significant performance improvement in comparison with using a GPU or using amulti-core CPU alone.The performance of the hybrid system is increased by about 47%–63%compared to a single GPU.When 32 elements are used in receiving,the fame rate basically can reach 30 fps.In the best case,the frame rate can be increased to 40 fps.

Recovery of multiply injured ascending reticular activating systems in a stroke patient

Consciousness is controlled by ular activating system （ARAS）. lower and upper parts between activation of the ascending retic- The ARAS consists mainly of the the thalamus and cerebral cortex （Edlow et al., 2012; Yeo et al., 2013; Jang et al., 2014）. Because the ARAS is composed of several neuronal circuits connecting the brainstem to the cortex. These neuronal connections begin from the reticular formation （RF） of the brainstem and the intralaminar nucleus of thalamus to the cerebral cortex （Gosseroes et al., 2011）. In addition, the ARAS system also includes several brainstem nuclei （such as dorsal raphe, locus coeruleus, pedun-culopontine nucleus, median raphe and parabrachial nucleus）, non-specific thalamic nuclei, hypothalamus, and basal forebrain （Fuller et al., 2011）.

Reliability and sensitivity analyses of HPT blade-tip radial running clearance using multiply response surface model

To reasonably design the blade-tip radial running clearance(BTRRC) of high pressure turbine and improve the performance and reliability of gas turbine, the multi-object multi-discipline reliability sensitivity analysis of BTRRC was accomplished from a probabilistic prospective by considering nonlinear material attributes and dynamic loads. Firstly, multiply response surface model(MRSM) was proposed and the mathematical model of this method was established based on quadratic function. Secondly, the BTRRC was decomposed into three sub-components(turbine disk, blade and casing), and then the single response surface functions(SRSFs) of three structures were built in line with the basic idea of MRSM. Thirdly, the response surface function(MRSM) of BTRRC was reshaped by coordinating SRSFs. From the analysis, it is acquired to probabilistic distribution characteristics of input-output variables, failure probabilities of blade-tip clearance under different static blade-tip clearances δ and major factors impacting BTRRC. Considering the reliability and efficiency of gas turbine, δ=1.87 mm is an optimally acceptable option for rational BTRRC. Through the comparison of three analysis methods(Monte Carlo method, traditional response surface method and MRSM), the results show that MRSM has higher accuracy and higher efficiency in reliability sensitivity analysis of BTRRC. These strengths are likely to become more prominent with the increasing times of simulations. The present study offers an effective and promising approach for reliability sensitivity analysis and optimal design of complex dynamic assembly relationship.

INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

Reliability evaluation for Weibull distribution under multiply type-? censoring

The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Efficient 2D Analysis of Interfacial Thermoelastic Stresses in Multiply Bonded Anisotropic Composites with Thin Adhesives

In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.

High signal-to-noise ratio sensing with Shack–Hartmann wavefront sensor based on auto gain control of electron multiplying CCD

High signal-to-noise ratio can be achieved with the electron multiplying charge-coupled-device（EMCCD） applied in the Shack–Hartmann wavefront sensor（S–H WFS） in adaptive optics（AO）.However,when the brightness of the target changes in a large scale,the fixed electron multiplying（EM） gain will not be suited to the sensing limitation.Therefore an auto-gain-control method based on the brightness of light-spots array in S–H WFS is proposed in this paper.The control value is the average of the maximum signals of every light spot in an array,which has been demonstrated to be kept stable even under the influence of some noise and turbulence,and sensitive enough to the change of target brightness.A goal value is needed in the control process and it is predetermined based on the characters of EMCCD.Simulations and experiments have demonstrated that this auto-gain-control method is valid and robust,the sensing SNR reaches the maximum for the corresponding signal level,and especially is greatly improved for those dim targets from 6 to 4 magnitude in the visual band.

Multiply Charged Anions,Maximum Charge Acceptance,and Higher Electron Affinities of Molecules,Superatoms,and Clusters

The addition of electrons to form gas-phase multiply charged anions(MCAs)normally requires sophisticated experiments or calculations.In this work,the factors stabilizing the MCAs,the maximum electron uptake of gas-phase molecules,X,and the electronic stability of MCAs X^(Q-),are discussed.The drawbacks encountered when applying computational and/or conceptual density functional theory(DFT)to MCAs are highlighted.We develop and test a different model based on the valence-state concept.As in DFT,the electronic energy,E(N,v_(ex)),is a continuous function of the average electron number,N,and the external potential,v_(ex),of the nuclei.The valence-state-parabola is a second-order polynomial that allows extending E(N,v_(ex))to dianions and higher MCAs.The model expresses the maximum electron acceptance,Q_(max),and the higher electron affinities,A_Q,as simple functions of the firstelectron affinity,A_1,and the ionization energy,I,of the"ancestor"system.Thus,the maximum electron acceptance is Q_(max,calc)=1+12A_1/7(I-A_1).The ground-state parabola model of the conceptual DFT yields approximately half of this value,and it is termed Q_(max,GS)=?+A_1/(I-A_1).A large variety of molecules are evaluated including fullerenes,metal clusters,super-pnictogens,super-halogens(OF_3),super-alkali species(OLi_3),and neutral or charged transition-metal complexes,AB_(m )L_n^(0/+/-).The calculated second electron affinity A_(2,calc)=A_1-(7/12)(I-A_1)is linearly correlated to the literature references A_(2,lit) with a correlation coefficient R=0.998.A_2 or A_3 values are predicted for further 24 species.The appearance sizes,n_(ap)^(3-),of triply charged anionic clusters and fullerenes are calculated in agreement with the literature.

SHEAR STRESS ANALYSIS OF TIMOSHENKO'S BEAM WITH MULTIPLY CONNECTED CROSS SECTION

In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the neutral axis of the beam, an improved definitionof the shear coeffi- cient is presented. Based on this definition, aGalerkin-type finite element formulation is proposed to analyze theshear stresses and shear deflections. Numerical solutions of theexamples for some typical cross-sections are compared with thetheoretical results. The shear coefficient of tower sections of theTsing Ma Bridge is calculated by use of the proposed approach, sothat the finite element modeling of The bridge can be developed withthe accurate values of the sectional properties.

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.

On the growth of transcendental entire functions with multiply connected components

Let g and h be two transcendental entire functions. Suppose that the Fatou set F（goh） contains multiply connected components. In this article, we will consider the growth of the functions g and h.

The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains

In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain D.The above boundary value problem will be called Problem P.Under certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem（0.1） and（0.2）.

Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.