非参数Monotonic回归及其应用

本文针对不满足经典回归条件的一对变量，讨论并介绍了非参数Ｍｏｎｏｔｏｎｉｃ回归的建模思想、条件与方法。通过实例说明，Ｍｏｎｏｔｏｎｉｃ回归比最小二乘回归拟合误差小，模型精度高，计算简单，有一定的实用价值。

The Monotonicity Problems for Generalized Inverses of Matrices in H (n, ≥)

On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.

MONOTONICITY IN ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM

In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.

Monotonicity-Preserving激波捕捉格式在湍流大尺度模拟中的评估

对高阶激波捕捉格式的性能进行了系统的测评,重点分析了Suresh和Huynh(1997)所提出的Monotonicity-Preserving格式的性能.结果表明Monotonicity-Preserving格式的性能显著优于原始WENO(Weighted Essentially Non-Oscillatory)格式,和改进型WENO格式相当.对格式的分析进一步表明,迎风型的激波捕捉格式在湍流模拟方面的性能都不及高阶中心格式,其原因归结为激波捕捉格式所包含的线性和非线性耗散.因此,改进高阶激波捕捉格式的关键在于同时降低格式的线性耗散和非线性耗散,以提高格式对湍流脉动能量的保持和对小尺度脉动结构的捕捉能力.

Monotonicity of the tail dependence for multivariate t-copula

This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.

Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions

In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(4)(50x+41)^(2),x>0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).

SOME PROPERTIES OF STRONGLY MONOTONICALLY T2 SPACES

This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.

Response of Skirted Suction Caissons to Monotonic Lateral Loading in Saturated Medium Sand

Monotonic lateral load model tests were carried out on steel skirted suction caissons embedded in the saturated medium sand to study the bearing capacity. A three-dimensional continuum finite element model was developed with Z_SOIL software. The numerical model was calibrated against experimental results. Soil deformation and earth pressures on skirted caissons were investigated by using the finite element model to extend the model tests. It shows that the ＂skirted＂ structure can significantly increase the lateral capacity and limit the deflection, especially suitable for offshore wind turbines, compared with regular suction caissons without the ＂skirted＂ at the same load level. In addition, appropriate determination of rotation centers plays a crucial role in calculating the lateral capacity by using the analytical method. It was also found that the rotation center is related to dimensions of skirted suction caissons and loading process, i.e. the rotation center moves upwards with the increase of the ＂skirted＂ width and length; moreover, the rotation center moves downwards with the increase of loading and keeps constant when all the sand along the caisson＇s wall yields. It is so complex that we cannot simply determine its position like the regular suction caisson commonly with a specified position to the length ratio of the caisson.

Constitutive model for monotonic and cyclic responses of loosely cemented sand formations

This paper presents a model to simulate the monotonic and cyclic behaviours of weakly cemented sands.An elastoplastic constitutive model within the framework of bounding surface plasticity theory is adopted to predict the mechanical behaviour of soft sandstone under monotonic and cyclic loadings. In this model, the loading surface always passes through the current stress state regardless of the type of loading. Destruction of the cementation bonds by plastic deformation in the model is considered as the primary mechanism responsible for the mechanical degradation of loosely cemented sands/weak rock.To model cyclic response, the unloading plastic and elastic moduli are formulated based on the loading/reloading plastic and elastic moduli. The proposed model was implemented in FLAC2D and evaluated against laboratory triaxial tests under monotonic and cyclic loadings, and the model results agreed well with the experimental observations. For cyclic tests, hysteresis loops are captured with reasonable accuracy.

Earth Pressure Distribution and Sand Deformation Around Modified Suction Caissons(MSCs) Under Monotonic Lateral Loading

The modified suction caisson(MSC) is a novel type of foundation for ocean engineering, consisting of a short external closed-top cylinder-shaped structure surrounding the upper part of the regular suction caisson(RSC). The MSC can provide larger lateral bearing capacity and limit the deflection compared with the RSC. Therefore, the MSC can be much more appropriate to use as an offshore wind turbine foundation. Model tests on the MSC in saturated sand subjected to monotonic lateral loading were carried out to investigate the effects of external structure sizes on the sand surface deformation and the earth pressure distribution along the embedded depth. Test results show that the deformation range of the sand surface increases with the increasing width and length of the external structure. The magnitude of sand upheaval around the MSC is smaller than that of the RSC and the sand upheaval value around the MSC in the loading direction decreases with the increasing external structure dimensions. The net earth pressure in the loading direction acting on the internal compartment of the MSC is smaller than that of the RSC at the same embedded depth. The maximum net earth pressure acting on the external structure outer wall in the loading direction is larger than that of the internal compartment, indicating that a considerable amount of the lateral load and moment is resisted by the external skirt structure.

Undrained monotonic and cyclic behavior of sand-ground rubber mixtures

In this study the stress–strain characteristics of sand-ground rubber mixtures are investigated in the sandlike zone,at different confining pressures,using hollow cylinder specimens subjected to torsional monotonic and cyclic loading.Under monotonic loading a mixture of sand-ground rubber with 10% and 25% rubber content show more contraction behaviour than that observed in a pure sand specimen.Phase transformation point in these mixtures are located on a larger shear strain.As expected,the shear strength of specimens decreases with increase of ground rubber content.However,with increasing of effective confining pressure,the loss in shear strength of the mixture is decreased.In addition,a mixture with 25% ground rubber shows a smaller loss in shear strength compared to a mixture with 10% ground rubber mixture.Under cyclic loading mixtures with 10% and 25% ground rubber have similar liquefaction resistance,especially at confining pressures of 110 k Pa and 260 k Pa.Therefore,by using of the mixture with 25% ground rubber,a larger volume of scrap tires could be recycled.The addition of ground rubber to sand would affect the shear strain variation and excess pore water pressure trends,and this effect was further intensified with increasing ground rubber percentage.

THE MONOTONICITY OF CONVERGENCE RATE FOR MGS METHODS

In this paper we prove that the convergence rate of the modified Gauss-Seidel method is a monotonic function for some precondition parameters.

SOME COMPLETELY MONOTONIC FUNCTIONS ASSOCIATED WITH THE q-GAMMA AND THE q-POLYGAMMA FUNCTIONS

In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].

An analysis of single-index model with monotonic link function

The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.

Some Generalizations of Monotonicity Condition and Applications

0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc..

Finding Symbolic and All Numerical Solutions for Design Optimization Based on Monotonicity Analysis and Solving Polynomial Systems

A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.

Monotonic Digit Filter for Limited-Area Model

Numerical diffusion or filter are used in most numerical models in order to eliminate small-scale (near two-grid intervals in wavelength) waves, However, conventional diffusion or filter schemes introduce the noise, and indeed few people realized, by filters themselves. For instance, most filters are troubled when they are put to use on meteorological fields with sharp gradient or with steep slope and consequently, the recurrence of undesirable numerical high-frequent oscillations (overshooting and undershooting) seems to be inevitable, Particularly when diffusion or filter is implemented in limited-area models, serious side effects on the limited-area boundaries often contaminate the modeling results. The merits and demerits are surveyed for commonly used diffusion or filter operations. A new type of monotonic digit filter is suggested to prevent overshooting and undershooting (due to the computational shock and Gibbs oscillation) nearby the discontinuous or nearly discontinuous locations when the filtering process was carried out, meanwhile the high selective property of damping is retained. Moreover, the new filter is designed on the implicit framework so that it can easily handle the problem of boundary diminishing in limited-area modeling.

Criteria for Response Monotonicity Preserving in Approximation of Fractional Order Systems

In approximation of fractional order systems,a significant objective is to preserve the important properties of the original system.The monotonicity of time/frequency responses is one of these properties whose preservation is of great importance in approximation process.Considering this importance,the issues of monotonicity preservation of the step response and monotonicity preservation of the magnitude-frequency response are independently investigated in this paper.In these investigations,some conditions on approximating filters of fractional operators are found to guarantee the preservation of step/magnitude-frequency response monotonicity in approximation process.These conditions are also simplified in some special cases.In addition,numerical simulation results are presented to show the usefulness of the obtained conditions.

Monotonic Property in Field Algebra of G-Spin Model

Let F be the field algebra of G -spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G . The paper builds a correspondence between D(H) and the D(H) -invariant sub- C * -algebra A H in F, and proves that the correspondence is strictly monotonic.

Direction monotonicity for a rational Bézier curve

The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized mono- tonicity, called direction monotonicity, is introduced for rational Bezier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine co- ordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bezier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.