ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

Microstructure and mechanical properties of stationary shoulder friction stir welding joint of 2A14-T62 aluminum alloy

2A14-T62 butt joint was successfully welded by stationary shoulder friction stir welding(SSFSW)method.The results showed that using a pin with small shoulder could broaden the process window,and under a rotation speed of 2000 r/min and welding speed of 30 mm/min,joint with smooth surface,small reduction in thickness and little inner defects was obtained.The weld nugget zone was approx-imately circular,which was a unique morphology for SSFSW.The heat-affected zone(HAZ)and thermo-mechanically affected zone(TMAZ)were both quite narrow due to the lower heat input and slight mechanical action of the stationary shoulder.The fraction of high angle grain boundaries(HAGBs)exhibited a“W”shape along horizontal direction(from advancing side to retreating side),and the minim-um value located at HAZ.The average ultimate tensile strength and elongation of the joint were 325 MPa and 4.5%,respectively,with the joint efficiency of 68.3%.The joint was ductile fractured and the fracture surface contained two types of dimples morphology in different re-gions of the joint.Microhardness distribution in the joint exhibited a“W”shape,and the difference along the thickness direction was negli-gible.The joint had strong stress corrosion cracking susceptibility,and the slow stain rate tensile strength was 139 MPa.Microcrack and Al2O3 particulates were observed at the fracture surface.

Modeling Rainfall Intensity-Duration-Frequency (IDF) and Establishing Climate Change Existence in Uyo-Nigeria Using Non-Stationary Approach

This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.

Recent applications and chiral separation development based on stationary phases in open tubular capillary electrochromatography(2019–2022)

Capillary electrochromatography(CEC)plays a significant role in chiral separation via the double separation principle,partition coefficient difference between the two phases,and electroosmotic flow-driven separation.Given the distinct properties of the inner wall stationary phase(SP),the separation ability of each SP differs from one another.Particularly,it provides large room for promising applications of open tubular capillary electrochromatography(OT-CEC).We divided the OT-CEC SPs developed over the past four years into six types:ionic liquids,nanoparticle materials,microporous materials,biomaterials,non-nanopolymers,and others,to mainly introduce their characteristics in chiral drug separation.There also added a few classic SPs that occurred within ten years as supplements to enrich the features of each SP.Additionally,we discuss their applications in metabolomics,food,cosmetics,environment,and biology as analytes in addition to chiral drugs.OT-CEC plays an increasingly significant role in chiral separation and may promote the development of capillary electrophoresis(CE)combined with other instruments in recent years,such as CE with mass spectrometry(CE/MS)and CE with ultraviolet light detector(CE/UV).

AN INFORMATIC APPROACH TO A LONG MEMORY STATIONARY PROCESS

Long memory is an important phenomenon that arises sometimes in the analysis of time series or spatial data.Most of the definitions concerning the long memory of a stationary process are based on the second-order properties of the process.The mutual information between the past and future I_(p−f) of a stationary process represents the information stored in the history of the process which can be used to predict the future.We suggest that a stationary process can be referred to as long memory if its I_(p−f) is infinite.For a stationary process with finite block entropy,I_(p−f) is equal to the excess entropy,which is the summation of redundancies that relate the convergence rate of the conditional(differential)entropy to the entropy rate.Since the definitions of the I_(p−f) and the excess entropy of a stationary process require a very weak moment condition on the distribution of the process,it can be applied to processes whose distributions are without a bounded second moment.A significant property of I_(p−f) is that it is invariant under one-to-one transformation;this enables us to know the I_(p−f) of a stationary process from other processes.For a stationary Gaussian process,the long memory in the sense of mutual information is more strict than that in the sense of covariance.We demonstrate that the I_(p−f) of fractional Gaussian noise is infinite if and only if the Hurst parameter is H∈(1/2,1).

On numerical stationary distribution of overdamped Langevin equation in harmonic system

Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.

Stationary Measures of Three-State Quantum Walks with Defect on the One-Dimension Lattice

In this paper, we focus on the space-inhomogeneous three-state on the one-dimension lattice, a one-phase model and a two-phase model include. By using the transfer matrices method by Endo et al., we calculate the stationary measure for initial state concrete eigenvalue. Finally we found the transfer matrices method is more effective for the three-state quantum walks than the method obtained by Kawai et al.

The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering

The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.

Robust edge detection based on stationary wavelet transform

By combining multiscale stationary wavelet analysis with fuzzy c-means, a robust edge detection algorithm is presented. Based on the translation invafiance built in multiscale stationary wavelet transform, components in different transformed sub-images corresponding to a pixel are employed to form a feature vector of the pixel. All the feature vectors are classified with unsupervised fuzzy c-means to segment the image, and then the edge pixels are checked out by the Canny detector. A series of images contaminated with different intensive Gaussian noises are used to test the novel algorithm. Experiments show that fairly precise edges can be checked out robustly from those images with fairly intensive noise by the proposed algorithm.

Separation Properties of a New Polysiloxane-Anchored β-Cyclodextrin Derivative as Gas Chromatography Stationary Phase

A new capillary gas chromatography stationary phase, monokis (2,6 di O benzyl 3 O propyl (3’)) hexakis(2,6 di O benzyl 3 O methyl) β CD bonded polysiloxane, was synthesized. It exhibited separation abilities to disubstituted benzene isomers and some chiral solutes. It was also found that the polarity of CD derivatives can be lowered both by chemically bonding it to polysiloxane and by diluting it in polysiloxane. The separation abilities of the polysiloxane anchored CDs (SP CD) are higher than that of the unbonded CDs (S CD) and the diluted S CD at lower column temperature. Hydrosilylation reaction is one of the best methods to lower the operating temperature of CDs.

The stationary phase analysis of the Kirchhoff-type d emigrated field

In the literature,stationary phase analysis of Kirchhoff-type demigrated fields is carried out mainly under the following two conditions：（1） The considered isochrone and the target reflector are tangential to each other;（2） The spatial duration of the wavelet of the depthmigrated image is short.For the isochrones that are not tangential to the target reflector and for the depth-migrated images that have a large spatial duration,the published stationary phase equation for the demigrated field will become invalid.For performing the stationary phase analysis of the Kirchhoff-type demigrated field under the conditions that the considered isochrone and the target reflector are not tangential to each other and that the spatial duration of the wavelet of the depth-migrated image is not short（the general conditions）,I derive the formulas for the factors appearing in the stationary phase formula in two dimensions,from which I find that for different isochrones the horizontal coordinates of the stationary point of the depth difference function are different.Also,the equation for the Kirchhoff-type demigrated field consists of two parts.One is the true-amplitude demigrated signal and the other is the amplitude distortion factor.From these facts the following two conclusions can be drawn：（1） A demigrated signal is composed of many depth-migrated images and one depth-migrated image trace provides only one sample to the demigrated signal;and（2） The amplitude distortion effect is an effect inherent in the Kirchhoff-type demigration and cannot be eliminated during demigration.If this effect should be eliminated,one should do an amplitude correction after demigration.

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.

CYCLOSTATIONARY MODEL IN DS SPREAD SPECTRUM COMMUNICATION SYSTEM

During the past research, Direct Sequence (DS) Spread Spectrum (SS) signal is modeled as stationary in most cases. Cyclostationary model for SS signal is introduced in this letter. Compared with stationary model, cyclostationary model can preserve more information,and its advantages are shown through example.

Three Cinnamyl β-Cyclodextrins Used as GC Stationary Phases

Aim To study the chromatographis beheviors of three new cinnamyl cyclodextrin derivative stationary phases. Mehtods Three new cinnamyl β-cyclodextrins, heptakis-(2, 6-di-O-cinnamyl-3-O-methyl)-β-CD, heptakis-(2, 6-di-O-cinnamyl-3-O-acetyl-)-β-CD and heptakis-2, 6-di-O-cirinamyl-3-O-trifluoroacetyl)-β-CD were synthesized and coatal on fused-silica capillary columns . Results The new stationary phases have better thermal stability, good column efficiency and excellent mpaxation power for some sutstituted benzene positional isomers. It was found that the introduction of cinnamyl groups has a significant effect on these stationary phases. Conclusion There new subetituted β-CD compounds are very suitable to be ed as gas chromatographic stationary phases.

Investigation on Two Novel Substituted β-Cyclodextrins Used as GC Stationary

Aim To study the chromatographic behaviors of two dipentyl cyclodextrin derivative stationary phases. Methods Two new β-cyclodextrin derivatives, heptakis-[2, 6-di-O-pentyl-3-O-(4-nitrobenzyl)] -β-CD and heptakis-[2, 6-di-O-pentyl-3 -O-(5 -hexenyl)]-β-CD, were synthesized and coatal on fed-silica capillary columns. The chromatographic behaviors of the columns were characterized . Results It was found that the she, polarity, and aromatic property of the substituted group at the 3-position of heptakis-(2, 6 - di - O - pentyl) - β - cyclodextrins greatly influenced their chromatographic properties and separation ability. The introduction of aromatic group or a group containing a double-bond may bring π-π interactions between the host and guest molecules, and therefore increases the separation ability of the β-CDs for substituted benzene isomers. Conclusion The new substituted β-CD compounds are very suitable for being used as gas chromatogaphic stationary phases.

Effect of Single-walled Carbon Nanotubes on Cellulose Phenylcarbamate Chiral Stationary Phases

Single-walled carbon nanotubes（SWNTs） have a high adsorption ability and nanoscale interactions. Cellulose trisphenylcarbamates possess high enantioseparation ability in high-performance liquid chromatography（HPLC）. Single-walled carbon nanotubes mixed with cellulose trisphenylcarbamate are coated on the silica gel as chiral stationary phases and higher enantioseparation factors are obtained. After a single-walled carbon nanotube is linked to the 6-pesition of cellulose 2,3-bisphenylcarbamate, its enantioseparation resolution increases compared to that of the cellulose trisphenylcarbamate. It is the first time that SWNTs have been applied to enantioseparation. The results indicate that the single-walled carbon nanotubes are good promoters of chiral recognition. This method can be used to improve the enantioseparation efficiency of the polysaccharide chiral stationary phases.

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.

Structural Scheme Optimization Design for the Stationary Platen of a Precision Plastic Injection Molding Machine

The current development of precision plastic injection molding machines mainly focuses on how to save material and improve precision, but the two aims contradict each other. For a clamp unit, clamping precision improving depends on the design quality of the stationary platen. Compared with the parametric design of stationary platen, structural scheme design could obtain the optimization model with double objectives and multi-constraints. In this paper, a SE-160 precision plastic injection molding machine with 1600 kN clamping force is selected as the subject in the case study. During the motion of mold closing and opening, the stationary platen of SE-160 is subjected to a cyclic loading, which would cause the fatigue rupture of the tie bars in periodically long term operations. In order to reduce the deflection of the stationary platen, the FEA method is introduced to optimize the structure of the stationary platen. Firstly, an optimal topology model is established by variable density method. Then, structural topology optimizations of the stationary platen are done with the removable material from 50%, 60% to 70%. Secondly, the other two recommended optimization schemes are given and compared with the original structure. The result of performances comparison shows that the scheme II of the platen is the best one. By choosing the best alternative, the volume and the local maximal stress of the platen could be decreased, corresponding to cost-saving material and better mechanical properties. This paper proposes a structural optimization design scheme, which can save the material as well as improve the clamping precision of the precision plastic injection molding machine.

MULTIPLE STATIONARY SOLUTIONS OF EULER-POISSON EQUATIONS FOR NON-ISENTROPIC GASEOUS STARS

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.