High-Order Radial Derivatives of Harmonic Function and Gravity Anomaly

The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.

A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo-Fabrizio Derivative

In this paper, we consider numerical solutions of fractional ordinary diferential equations with the Caputo-Fabrizio derivative, and construct and analyze a high-order time-stepping scheme for this equation. The proposed method makes use of quadratic interpolation function in sub-intervals, which allows to produce fourth-order convergence. A rigorous stability and convergence analysis of the proposed scheme is given. A series of numerical examples are presented to validate the theoretical claims. Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique. The advantage of our scheme is that the solution can be obtained step by step, which is cheaper than a block-by-block-based approach.

Time derivative of earthquake acceleration

Unlike acceleration, velocity, and displacement, the time derivative ofacceleration (TDoA) of ground motion has not been extensively studied. In this paper, the basiccharacteristics of TDoA are evaluated based on records from the 1999 Chi-Chi, earthquake (Mw 7.6)and one of its aftershocks (Mw 6.2). It is found that the maximum TDoA at a free-field station wasover 31,200 cm/s3 (31.8 g/s); and the duration of 'strong' TDoA, between the first and the last timepoints exceeding 2,000 cm/s3 (2 g/s), was almost one minute near the epicenter area. Since groundTDoA sensors are not commonly available, the time series are calculated by direct numericaldifferentiation of acceleration time series. Relative error analysis shows that the error isnon-transitive and total error is within 4%. The density function of TDoA amplitude, frequencycontent and spatial distribution of peak ground jerk (PGJ) are evaluated. The study also includesexamination of some TDoA responses from a seven-story building and comparison of ground TDoA withthe limit TDoA used in the transportation industry for ride comfort. Some potential impacts of TDoAon humans have also been reviewed.

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.

Retrieval of Electron Return Time from High-order Harmonics Generated in a Mixture of He and Ne Gases

In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwell＇s equation of harmonic field. And then we show the validity of mixture formulation by Wagner et al. [Phys. Rev. A 76 （2007） 061403（R）] in macroscopic response level. Finally, using/east squares fitting we retrieve the electron return time of short trajectory by formulation in Kanai et al. [Phys. Rev. Lett. 98 （2007） 153904] when the gas jet is put after the laser focus.

Multi-factor high-order intuitionistic fuzzy timeseries forecasting model

Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.

DIRECTIONAL DERIVATIVE OF VECTOR FIELD AND REGULAR CURVES ON TIME SCALES

The general idea in this paper is to study curves of the parametric equations where the parameter varies in a so-called time scale, which may be an arbitrary closed subset of the set of all real numbers. We introduce the directional derivative according to the vector fields.

On Conformable Delta Fractional Derivative on Time Scales

In this paper, we introduce and investigate the concept of conformable delta fractional derivative on time scales. By using the theory of time scales, we obtain some basic properties of the conformable delta fractional derivative. Our results extend and improve both the results in [9] and the usual delta derivative.

Micro-Sized Pinhole Inspection with Segmented Time Reversal and High-Order Modes Cluster Lamb Waves Based on EMATs

Pinhole corrosion is difficult to discover through conventional ultrasonic guided waves inspection,particularly for micro-sized pinholes less than 1 mm in diameter.This study proposes a new micro-sized pinhole inspection method based on segmented time reversal(STR)and high-order modes cluster(HOMC)Lamb waves.First,the principle of defect echo enhancement using STR is introduced.Conventional and STR inspection experiments were conducted on aluminum plates with a thickness of 3 mm and defects with different diameters and depths.The parameters of the segment window are discussed in detail.The results indicate that the proposed method had an amplitude four times larger than of conventional ultrasonic guided waves inspection method for pinhole defect detection and could detect micro-sized pinhole defects as small as 0.5 mm in diameter and 0.5 mm in depth.Moreover,the segment window location and width(5-10 times width of the conventional excitation signal)did not affect the detection sensitivity.The combination of low-power and STR is more conducive to detection in different environments,indicating the robustness of the proposed method.Compared with conventional ultrasonic guided wave inspection methods,the proposed method can detect much smaller defect echoes usually obscured by noise that are difficult to detect with a lower excitation power and thus this study would be a good reference for pinhole defect detection.

PRECISE MOMENT ASYMPTOTICS FOR THE STOCHASTIC HEAT EQUATION OF A TIME-DERIVATIVE GAUSSIAN NOISE

This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.

High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes

A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.

IMPULSIVE EXPONENTIAL SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX DYNAMICAL NETWORKS WITH DERIVATIVE COUPLINGS VIA FEEDBACK CONTROL BASED ON DISCRETE TIME STATE OBSERVATIONS

This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.

ANN-Time Varying GARCH Model: Simulations and Application in Modelling Temperature for Weather Derivatives

In economics and finance, minimising errors while building an abstract representation of financial assets plays a critical role due to its application in areas such as risk management, decision making and option pricing. Despite the many methods developed to handle this problem, modelling processes with fixed and random periodicity still remains a major challenge. Such methods include Artificial Neural networks (ANN), Fuzzy Inference system (FIS), GARCH models and their hybrids. This study seeks to extend literature of hybrid ANN-Time Varying GARCH model through simulations and application in modelling weather derivatives. The study models daily temperature of Kenya using ANN-Time Varying GARCH (1, 1), Time Lagged Feedforward neural network (TLNN) and periodic GARCH family models. Mean square error (MSE) and coefficient of determination R2 were used to determine performance of the models under study. Results obtained show that the ANN-Time Varying GARCH model gives the best results.

Derivation and application of time step model in solidification process simulation

The heat transfer during the casting solidification process includes the heat radiation of the high temperature casting and the mold,the heat convection between the casting and the mold,and the heat conduction inside the casting and from the casting to the mold. In this paper,a formula of time step in simulation of solidification is derived,considering the heat radiation,convection and conduction based on the conservation of energy. The different heat transfer conditions between the conventional sand casting and the permanent mold casting are taken into account in this formula. The characteristics of heat transfer in the interior and surface of the casting are also considered. The numerical experiments show that this formula can avoid computational dispersion,and improve the computational efficiency by about 20% in the simulation of solidification process.

A Paradoxical Consistency Between Dynamic and Conventional Derivatives on Hybrid Grids

It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.

TD-DFT Study on Pyrazoline Derivatives

The molecular structures of ground state and first single excited state for pyrazoline derivatives are optimized with DFT B3LYP method and ab initio “configuration interaction with single excitations”（CIS） method, respectively. The frontier molecular orbital characteristics have been analyzed systematically, and the electronic transition mechanism has been discussed. Electronic spectra are calculated by using TD-DFT method. These results are consistent with those from the experiment.

Stability Analysis for Stochastic Delayed High-order Neural Networks

In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.

Time, Length, and Mass Are Derived Quantities

Fundamental units of measurements are kilograms, meters, and seconds—in regards to mass length, and time. All other measurements in mechanical quantities including kinetic quantities and dynamic quantities are called derived units. These derived units can be expressed in terms of fundamental units, such as acceleration, area, energy, force, power, velocity and volume. Derived quantities will be referred to as time, length, and mass. In order to explain that fundamental units are not equivalent with fundamental quantities, we need to understand the contraction of time and length in Special Relativity. If we choose the velocity of light as fundamental quantity and length and time as derived quantities, then we are able to construct three-dimensional space-time frames. Three-dimensional space-time frames representing time with polar coordination, time contraction and length contraction can be shown graphically.

肉中猪源性成分Real-time PCR定量检测技术

【目的】建立一种快速、准确的肉中猪源性成分定量检测方法。【方法】首先从GenBank数据库中筛选猪特异性的微卫星DNA,根据微卫星DNA核酸序列设计引物,对常见10种动物基因组DNA进行PCR扩增,通过有无扩增产物判断筛选的微卫星DNA对猪源性成分的特异性。然后根据微卫星DNA核酸序列,设计特异性引物和探针,建立猪源性成分Real-time PCR检测方法,采用双标准曲线分别对猪源性成分和总动物源性成分进行定量,计算猪源性成分的百分含量。【结果】筛选到猪特异性微卫星DNA(Accession EF172428),根据其序列设计的引物SEQ-sus2-F/R只能从猪基因组DNA中扩增出目的条带,其他动物的基因组均无目的条带扩增。建立的Real-time PCR检测方法灵敏度为0.02 ng/25μL反应体系。该方法能够准确检测出混合DNA样品中猪源性成分和混合肉样品中猪源性成分,百分误差分别约为1.32%和1.06%-7.12%。【结论】本研究利用Real-time PCR技术建立的定量猪源性成分的检测方法可以用来检测猪源性成分在混合样品中的百分含量。

Real-time PCR和双向电泳联合鉴别婴幼儿配方羊乳粉的乳源成分

为实现对婴幼儿配方羊乳粉中乳源成分的准确判别,将基因检测作为初筛方法,以蛋白质双向电泳作为确证方法,研究该技术路线下对乳源成分检测的灵敏度、准确性等指标。优化建立的基于嗜热蛋白酶的一步式DNA提取法,仅需通过温控反应在17 min内完成DNA步骤,极大缩短了样品前处理时间;建立的快速实时聚合酶链式反应(real-time polymerase chain reaction,real-time PCR)程序仅需28 min 26 s即可完成检测。通过牛(家牛、水牛、牦牛)、羊(山羊和绵羊)、山羊、绵羊单一乳源成分,以及哺乳动物内参照检测体系,可以实现对低至10~100 pg/μL DNA的检测,对混合样品中牛源性成分检测的灵敏度可达1%(m/m)。然后结合双向电泳技术进一步确证产品的蛋白成分来源,可以判定牛基因检测阳性的样品是否含有来源于牛乳酪蛋白或乳清蛋白,进而对样品的真实性进行判定。real-time PCR法和双向电泳技术联合检测解决了以往婴幼儿配方乳粉检测中因配料复杂乳源判别困难的瓶颈问题。