One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

An Efficient Second-Order Convergent Scheme for One-Side Space Fractional Diffusion Equations with Variable Coefficients

In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.

The Best m-Term One-Sided Approximation of Besov Classes by the Trigonometric Polynomials

In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.

Variation Inequalities for the Commutators of One-Sided Calderón-Zygmund Singular Integrals with Lipschitz Functions

In this paper, we establish the weighted Lp (1 < p < ∞) boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.

New Approach to Observer-Based Finite-Time H_(∞)Control of Discrete-Time One-Sided Lipschitz Systems with Uncertainties

This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.

THE CONVERGENCE OF TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PIECEWISE CONTINUOUS ARGUMENTS UNDER GENERALIZED ONE-SIDED LIPSCHITZ CONDITION

In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.

RELATIONS BETWEEN TWO SETS OF FUNCTIONS DEFINEDBY THE TWO INTERRELATED ONE-SIDE LIPSCHITZCONDITIONS

InthetheoreticalstudyofnumericalsolutionofstiffODEs,authorsusuallyassumethattherighthandfunctionfofsatisfytheone-sideLipschitzco.dition[1'2'31however,insomecases(suchasstudyofexistenceanduniquenessofthesolution),thefunctionfisassumedtosatisfyanothero...

Misalignment Tolerance in One-side and Symmetric Loading Hopkinson Pressure Bar Experiments

The split-Hopkinson pressure bar(SHPB)is a widely used experimental technique for studying the mechanical properties of materials at high strain rates.There are two kinds of loading methods applied in the SHPB technique,namely one-side loading and symmetric loading.However,the experimental accuracy of the two loading methods is affected by the interface contact.The present study focused on the inadequate contact caused by the misalignment of the pressure bars.The commercial software ABAQUS was used for simulations.The result shows that the inadequate contact caused by the alignment of the bars has a non-negligible effect on the calculated results.Compared with the one-side loading Hopkinson pressure bar,the symmetric loading Hopkinson pressure bar has a more relaxed requirement for the alignment of the bars.The conclusion arrived at in this paper can help researchers to make a reasonable choice between one-side and symmetric loading Hopkinson pressure bars according to actual requirements.

Tail asymptotic for discounted aggregate claims with one-sided linear dependence and general investment return

In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with c`adl`ag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.

Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances.In case there is no perturbation,the exponential convergence of the observer was confirmed.When external disturbances appear in the system,a separation principle is established,and the authors show that the closed loop system is exponentially practical stable.By choosing a suitable Lyapunov-Krasovskii functional,the authors derive new sufficient conditions to guarantee the exponential stability of the systems.Finally,a physical model is performed to prove the efficiency and applicability of the suggested approach.

Further Result on the Observer Design for One-Sided Lipschitz Systems

This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)condition but not quadratic inner-boundedness(QIB).Moreover,the case where the OSL constant is negative is specially investigated.Firstly,a full-order observer is constructed for the original system.Then,a reduced-order observer is also designed by using the decomposition method.The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.

Distributional Chaos Occurring on the Set of Proper Positive Upper Banach Density Recurrent Points of One-sided Symbolic Systems

The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.

Reference tracking and transient response shaping of uncertain quasi one-sided Lipschitz nonlinear systems

This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.

Limit Cycle for the RC Circuit with Square-Wave-Type Voltage

The goal of this paper is to prove, by means of calculations the existence of the ω-limit cycle of a simple circuit where a resistor, a capacitor and a square-wave-type voltage source are in series.

双参数指数分布l个未来样本的顺序统计量单边联合预测系数表

对过去样本为Ⅱ型截尾样本,给出了双参数指数分布l个未来样本的顺序统计量单边联合预测下限的预测系数数表,并用数值例说明了数表的应用。

ON THE EXISTENCE AND UNIQUENESS OF SOLUTION OF IMPLICIT HYBRID METHODS

In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.

Mechanism analysis of free formation of backing weld by the pulsed MAG-TIG double arc tandem welding

Because of the presence of lower-level automation and efficiency in the backing welding of medium–thick plates,pulse-metalactive-gas–metal-inert-gas(MAG–MIG)dual-arc welding was applied to backing welding of 24-mm-thick Q235-B plate and the process and mechanism of root welding with back formation were investigated.The heating position of the MAG-arc at the front of the molten pool could be adjusted by using the electromagnetic force between the MAG-arc and the MIG-arc,and part of the arc energy could work on the root face directly.By combining the arc-discharge behaviour and analysis of flow in the molten pool,the shear stress of a tungsten inert gas(TIG)arc to the molten pool could make the liquid metal flow backwards.Thus,the quality of the front and bottom liquid metal were reduced,which favored the balance and stability.Continuous and stable back formation with uniform penetration could be achieved by using the pulse MAG–TIG dual-arc welding technology.

Dielectric Permittivity of Rigid Rapeseed Oil Polyol Polyurethane Biofoams and Petrochemical Foams at Low Frequencies

Early investigations of dielectric permittivity of rigid polyurethane foams at low frequencies were made on petrochemical-origin foams,mainly by means of parallel plate capacitors.In the present investigation biopolyol was synthesized from Latvia-grown rapeseeds’oil by the transesterification method with triethanolamine,in an environmentally friendly process,without emission of harmful substances,at temperatures 175℃±5℃.Rigid,closed-cell rapeseed oil polyol polyurethane biofoams and petrochemical foams were made ensuring content of the renewable rapeseed oil polyol in ready foams 27 wt.%–29 wt.%.Dielectric permittivity of the polyurethane foams and the underlying monolithic petrochemical-origin polyurethane and biopolyurethane was measured with a non-destructive dielectric spectrometer equipped with a capacitive sensor of one-side access type at 16 discrete frequencies distributed geometrically over the band 10 Hz,…,330 kHz.Permittivity value of the gaseous phase in the closed-cells was estimated to beεg≈1.001 that corresponds to the values,characteristic for the most of gases.Dielectric permittivity of petrochemical polyurethane foams and the mentioned biofoams was compared with permittivity of polyurethane foams from industrial producers Sika JSC and General Plastics Manufacturing Co.Polyurethane foams of the developed formulation exhibit competitive,low dielectric permittivity,not exceeding that of the foams from industrial producers:petrochemical foams up to 550 kg/m^(3) and the mentioned biofoams,comprising the renewable rapeseed oil polyol,up to densities 230–250 kg/m^(3).Considering petrochemical-origin polyurethane foams as a heterogeneous media“Polymer—gaseous phase”,the applicability of the rule of mixture and Maxwell–Garnett equation to model mathematically the dependence of effective dielectric permittivity on the volume fraction of phases was showed.

Study of High-Tech Industry Integration Model of Base,Project,and Talent

The high-tech industry is highlighted for advanced techniques,substantial capital investment,and smart talents.But their effective combination can not be achieved in the development of high-tech industry,which impedes its industrialization.Meanwhile,an effective mechanism is needed to develop the high-tech industry healthily.The aim of this paper is to explore the integration model of base,project,and talent which is presented and served as a new road for high-tech industry development as well as prove this model rational.Some results of the model are appealing.Firstly,start-ups in the park have the higher success probabilities;secondly,higher expected return attracts talents to join into start-ups in park;thirdly,side payment is the inner incentive to initiate this high-tech industry integration model.

Analysis of Noise under Regime Switching

In this paper we consider a stochastic nonlinear system under regime switching. Given a system x(t)=f(x(t),r(t),t) in which f satisfies so-called one-side polynomial growth condition. We introduce two Brownian noise feedbacks and stochastically perturb this system into dx(t)=(x(t),r(t),t)dt+ σ (r(t))|x(t)|βx(t)dW1(t)+q(r(t))x(t)dW2(t) . It can be proved that appropriate noise intensity may suppress the potentially explode in a finite time and ensure that this system is almost surely exponentially stable although the corresponding system without Brownian noise perturbation may be unstable system.